Top Banner
Question: Would a pinewood derby racer go faster if it had more weight? Replies: Actually, as far as I know, there is no reason why a racer would go faster if it weighed more. Well, it might go a little faster, because the force pulling on it (gravity) would be stronger relative to the air resistance, but I think the strongest source of resistance for pine- wood derby cars is friction in the wheels, and that should get bigger just as the weight gets bigger. What I would recommend is an experiment - if you can get a slightly sloped surface to race your car down, and time it carefully. You might find that it went faster with some extra weight. You might also figure out other ways to improve your car. Here are some suggestions that might help you out: 1) Make sure the wheels are round and smooth 2) If your track starts on an incline, (most do) put as much weight as you can near the rear of the car. You do not want to make it unstable, but you do want as much potential energy as possible. It will only help at the bottom of the track. 3) Try to make sure that the axles are straight. Eric Peterson Question: If friction is surface area independent, then why do dragsters have wide tires?
142
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Page 1: Newton Ask

Question:

Would a pinewood derby racer go faster if it had more weight? 

Replies:

Actually, as far as I know, there is no reason why a racer would go faster if it weighed more. Well, it might go a little faster, because the force pulling on it (gravity) would be stronger relative to the air resistance, but I think the strongest source of resistance for pine- wood derby cars is friction in the wheels, and that should get bigger just as the weight gets bigger. What I would recommend is an experiment - if you can get a slightly sloped surface to race your car down, and time it carefully. You might find that it went faster with some extra weight. You might also figure out other ways to improve your car. 

Here are some suggestions that might help you out:

1) Make sure the wheels are round and smooth 

2) If your track starts on an incline, (most do) put as much weight as you can near the rear of the car. You do not want to make it unstable, but you do want as much potential energy as possible. It will only help at the bottom of the track. 

3) Try to make sure that the axles are straight. 

Eric Peterson

Question:

If friction is surface area independent, then why do dragsters have wide tires? 

Replies:

The force of friction that the tires experience is independent of the tire size, certainly. However, what a dragster does not want is for the tires to slip - so the tires are spinning and the car is going nowhere. What determines when the tires will start to slip is the point at which static friction gives way to sliding friction. That force must of course increase with the area of the tires, and so the bigger the tires, the bigger the force you can use before you start slipping, and so the faster your dragster can accelerate. 

Page 2: Newton Ask

A. Smith 

Wide tires for drag racing tires also come in a variety of hardnesses or durometer ratings. The softer the tire, the more initial traction is provided. If you will notice, too, one of the biggest reasons for these wide tires has nothing to do with traction: When the car is sitting at the line, the diameter of the tire is relatively small. When the tires are spinning, the tires are constructed in such a way to allow the centripetal force to expand the diameter of the tire. This has the same desirable effect of changing the final drive gear ratio to allow for higher speeds. Racers very carefully size tires to allow for the optimum change in diameter over a given rotational speed of the wheel. This allows the racer to take advantage of the very narrow torque curve of their engines without changing gears too many times. This reason is more so taken into consideration than the width/friction reason. 

Eric Peterson 

The respondents do not answer the question properly. The reply by Smith claims that bigger areas make bigger forces without giving any reason. The reply by Peterson ignores the width question and instead focuses on diameter growth. 

There are several issues that must be considered when choosing a dragster tire. Friction is surface-area independent in only a few ideal examples. The real world is more complicated. Especially for tires that are made of rubber. You want to choose a width, height, and tire compound that gives the best friction for the duration of the race. Top fuel dragsters have one-speed transmissions and slip the clutch during the run. In engineering it is commonly thought that the friction force is proportional to the force pushing the two surfaces together. This is only correct over a certain range of conditions and materials. The constant of proportionality is called the "coefficient of friction." The coefficient of friction depends on the material and condition of BOTH of the surfaces being rubbed together. It is small for DuPont's Teflon (TM) rubbing on DuPont's Teflon (TM), larger for DuPont's Teflon (TM) rubbing on wood, much larger for wood rubbing on smooth concrete and very high for wood rubbing on rough concrete. 

However, if the surface becomes actually sticky, then conventional 'friction' theory simply does not work. It is possible to have large friction forces in the absence of a force pushing the two surfaces together. In fact, because the surfaces stick together when you try to pull them apart, a negative static friction coefficient is possible. I made a phone call to a company that makes dragster tires and their racing expert (Les Garbicz) provided me with some information. For most dragsters, certainly top fuel, the tires and track are sticky like scotch tape or flypaper. The tires may be inflated to only 7 psi and

Page 3: Newton Ask

are fairly large. Thus, the contact area between tire and track can be a couple of square feet. (Each tire is 17 inches wide and the contact length is as much as 10 inches front-to-back). This enables acceleration to be up to five times that of gravity. The contact area decreases as the speed goes up. 

The flypaper analogy is a useful image to illustrate the stickiness mechanism. However, the tire is not a flat surface sticking to a flat track surface. It is a rotating ellipsoid-shaped surface being compressed onto a flat unmovable surface. These ‘flypaper’ boundaries are localized on the surface and are made and broken as the tire rotates through the footprint. The rubber compounds that are used have the property that friction is low when cool. (Not really low, just lower than when hot). The friction increases with increasing temperature, even including the temperature when the rubber starts to melt. During a burnout, there is some melting of the surface, but the tires do not actually get runny and slippery. Prior to the race, the driver does a “burnout.” This short burnout liquifies a thin layer on the surface of the tire. This only makes the tire tacky and cleans the surface. This clean tacky surface grips the track very well. 

A wing is attached to top fuel dragsters that produces a downward force. The downward force can be as much as 8000 pounds on a 2000 pound machine when traveling 300 mph. Thus tire slip is not a problem at high speeds. Centripetal force at high speeds keeps the tire from being squashed by the downward force of the wing. Increasing tire diameter and tire width increases the contact area. But there is a limit - a very large tire would not be well matched to the engine or axle the torque becomes impracticable. 

When slip occurs between tire and track, the slip is not like a normal automobile tire where the tire slides on the road. Race tracks that are a quarter of a mile long are built of concrete and asphalt. The first 330 feet or so is concrete. The rest is asphalt. A new fresh track has a liquid rubber primer sprayed onto it which then dries. It is then mechanically abraded by a tractor pulling old tires across it. A second coat of primer is sprayed on. The result is sticky. During the races, more sticky rubber is transferred to the track. This, as well as the sticky nature of the rubber, accounts for the tremendous friction. 

Rubber is made into a useful tire by the process of curing at the factory. At a temperature much above 400F the rubber reverts to its uncured state, and becomes almost liquid. Obviously, the tire will fall apart if the body of the tire becomes that hot. If a dragster tire is abused or under inflated, the internal temperature can get very hot during the race, and racers make sure not to do that. The internal temperature is different from the surface temperature. When the racer does a 'burnout' prior to the beginning of the race, this liquifies a thin layer on the surface of the tire for good traction. The inside stays cool, and the clean, tacky surface is ready to race. 

Page 4: Newton Ask

Aside from the friction issue is the “abrasion” factor. If the load is too high, the tire surface starts to form shavings instead of smoothly getting tacky. The shavings act like little bearings. Thus friction plummets. The rate of this friction drop seems to be related to the “recipe” of the compound, also is related to its hardness (modulus). A a softer compound may become “greasy” on the track, leaving thick black lines on the surface while slightly harder compound may abrade into shavings with tearing. Fracture lines across the tread surface is called “graining” by engineers. These effects describe and explain the sliding coefficient of friction zone identified with high tire slip. 

To make sticky surfaces adhere, you need to push them together. That is why you push down on sticky tape. Thus, there is a controversy about what happens when the leading edge of the dragster tire slams down onto the strip as the tire rotates. It has been argued that this 'push' downwards causes the tire to grip much better than if it were gently rolling along. Overall this is why tires need to be wide: a tire that is too narrow will abrade (which is bad) instead of getting tacky (which is good). 

Bob Erck  

Question:

If you are on a motorcycle going down the highway, and you press on the inside of the left handle grip, why do the wheels turn to the right, but you turn to the left? 

Replies:

1991: This only happens, by the way, above a certain speed. If you are going slow enough, the bike will turn in the direction you would expect. The reason the motorcycle behaves as you describe at speed is due to a phenomena called precession. For a thorough explanation of precession, I recommend you look it up - it is a fairly complex subject. You can observe precession with a gyroscope. I will give you a quick explanation, though. When you try to turn a rotating object, you produce a force at 90 degrees to the direction of rotation. When you push on the left handlebar and turn the front wheel of the bike to the right, you produce a force which makes the whole motorcycle lean to the left. It is the leaning to the left that turns the bike. 

Unknown 

Update: 12/14/2004

Gyroscopic precession is one of two factors that cause the cycle to turn opposite the direction the handlebars are moved. A great explanation of precession is given in a

Page 5: Newton Ask

book called "Thinking Physics" by Lewis Epstein. However, the precessional force acting to tilt the wheel left when you move the handlebars right, is diminished by the fact that the front forks are not vertical, but angled forward. To exaggerate this, imagine that the front forks were completely horizontal. Turning the handlebars right would simply cause the wheel to tilt right, but precession would cause the wheel to try to angle right as viewed from above. Here now, would be a tendency for the front wheel to track to the right, as wanted. This fact is apparent in choppers which have long front forks. A second major force occurs when the wheel is deflected. When a cycle leans left or right, it tilts about a pivot point where the tires contact the road. If the wheel is forcefully deflected to the right, the wheel will immediately begin tracking to the right (slightly) even though precession makes the wheel lean left. As the cycle begins this slight change in direction (to the right), centrifugal force immediately throws the bike and rider to the outside of the turn, making it tilt about its pivot point, and lean to the left. Once you lean left, you're going left. 

T. Esposito 

Winter 2009-2010 Up-date

The respondent does not answer the question correctly. The question asks why the motorcycle turns to the left when the front wheel is turned to the right. 

A little background: first, motorcycles travel at speeds from low (gyroscopic forces are small) to high (gyroscopic forces are large). Most riding is conducted somewhere in the middle where gyroscopic forces influence steering, but not hugely so. 

At low speed, roughly speaking, there are three motorcycle motions that can be understood easily: a motorcycle can move along upright and straight, it can turn in a smooth arc or circle while maintaining a constant lean angle, or it can fall over. 

1) If a motorcycle is to continue in a straight line upright, it is necessary for the center of mass to remain directly above where the tires meet the road. 

2) If a motorcycle is leaning and moving along a smooth circular path, it is necessary for the "sideways" forces to balance: the tilt of the motorcycle creates a centripetal force, which provides the inward (toward the center of the circle) acceleration to keep the motorcycle moving in a smooth circle. Bicycles must do this too, as must people sprinting around a circular running track, they must lean into the turn. For a constant curve to the left, the motorcycle must lean to the l eft so that gravity acting through the center of mass exerts a force toward the center of the curve. 

3) If forces are not balanced then the tilt or lean of the motorcycle is unstable and the motorcycle will fall over. If a tire loses traction, a motorcycle or bicycle can fall over in a

Page 6: Newton Ask

fraction of a second. 

At low speeds, if the left handlebar is pushed, the front wheel does indeed turn to the right a small amount, and the contact where the tires meet the road move to the right. But the center of mass of the motorcycle continues along pretty much the same line and thus the motorcycle starts to lean to the left. This is good: a left lean allows it to travel in a curve. If the handlebar is continued to be pushed hard, the lean of the motorcycle will get larger and larger and the motorcycle will slam to the ground on the left side. Otherwise the motorcycle will be leaning to the left and continue a smooth turn to the left. 

(At this point, a push of the right handlebar turns the front wheel to the left, the tire contact patch moves from the right toward the center of mass of the motorcycle, and the motorcycle "straightens up.") 

In addition to these simple balancing forces, there are gyroscopic forces present due to the rotation of the wheels and engine parts. These gyroscopic forces influence the effort required to turn the handlebars, and also influence how the motorcycle tilts or leans or falls over when it is unbalanced. The gyroscopic forces become large at high highway speeds, where it is necessary to push the handlebars very hard to execute fast left and right turns by leaning the motorcycle fast left an fast right. 

The principle is the same though, but exaggerated: at high speeds, due to gyroscopic forces and the geometry of the fork suspension, a motorcycle will tend to be stable on two wheels. The motorcycle must still lean in the direction that it is curving. Considerable effort on the handlebars is required to lean (or un-lean) the motorcycle moving at high speed to make it go in the desired direction. 

Robert Erck 

Question:

How can Bees Fly?Can you please explain exactly how bees are able to fly? 

Replies:

Well, the first question is what the "theory" referred to is. I would guess this is based on standard airplane construction, that if you built an airplane with wings like a bees that was as heavy as a bee and was run by some engine (propeller or jet) that was as powerful as a bee, it would not get off the ground. The solution is that a bee does not

Page 7: Newton Ask

run like an airplane - its wings are not fixed, for one, and like all flying animals, it does not power itself with a jet or propeller, but by the actual flapping of its wings.

The result is probably some very complex air currents - I assume they can be modeled these days, and maybe somebody has done it, but in any case the flight of a bee cannot be described by any simple theory. 

A. Smith 

They fly because they flap their wings. The flapping motion imparts downward momentum to the air, and as a result, the bee stays aloft. 

The wings do not just move up and down. The tip of the wing also moves forward and backward and the end of the wing moves in an oval shape. In addition the wings tilt during each flap. 

All of this complicated "paddling" allows it to fly. It is not really known "exactly" how the bee flies. 

The direction the wings move was not known until high speed photography was invented. Even then, to get a GOOD understanding of air flow requires that some tracer be put in the air (like smoke) so that the researchers can find out how the wings are pushing the air around. 

If a bee hovers over your hand, you can feel a gentle breeze from the little wings. 

Bob Erck 

Question:

Does Centrifugal force really exist? If not, then why do so many people use it to explain everyday occurrences? For example, when you swing a bucket of water around, what keeps the water in? Most people would say centrifugal force. 

Replies:

Yes, this idea does have a sound meaning and valid existence. It does not represent a "real" force in the sense that Newton uses, which is: something that gives rise to accelerations in a reference frame which is not rotating or being accelerated (a frame in which objects at rest tend to stay at rest unless acted on by a force) (these frames are

Page 8: Newton Ask

called inertial frames). However, in a rotating reference frame (or coordinate system) such as a merry go round, objects that are at rest tend to slide and objects with no "real" force do not move in straight lines. Have you ever tipped over a glass full of liquid in a turning car? From the point of view of the rotating coordinate system what tipped the glass over is the "centrifugal force". From the point of view of the inertial frame of reference outside the car, the glass was still trying to go forward in a straight line when the car turned and the force acting on the bottom of the cup flipped it over. Both perspectives are valid and you can calculate the results from both perspectives as dictated by convenience, but there is no "real" force of this type. It is however very useful to think this way. 

Sam Bowen 

Question:

When you measure drag coefficient, you must obtain dynamic pressure (cm of Hg or water)or g/cm^2. Will the dynamic pressure change if you change the speed. What is the rate of change of dynamic pressure with respects to air velocity (dp/dv)? 

Replies:

Well, I am not sure I know exactly what you are asking. The frictional force (which gives a pressure if it is divided by area) caused by air on a moving body has several sources, and its dependenceon speed varies with the geometry of the body, due to turbulence. I think it is usually assumed, for simplicity maybe, that the friction goes as the square of the speed, but that may not generally be valid. Somebody who knows more fluid mechanics or aerodynamics should answer this. 

Arthur Smith 

Question:

Do you know of any good books to help me learn about Bernoulli's principles of flight? 

Replies:

May be helpful: 

http://www.allstar.fiu.edu/aero/airflylvl3.htm 

Page 9: Newton Ask

http://www.jal.cc.il.us/~mikolajsawicki/bad_physics.htm 

Unknown 

Question:

Why does the shower curtain bell inward (toward you) when you are taking a shower? Is that Bernoulli's principle at work? 

Replies:

Up-date April, 2001

A shower curtain will billow into the shower regardless of water temperature. A person taking a cold shower is no safer from a shower curtain attack than the person taking a hot shower. It is the movement of the water (and thereby the surrounding air) that creates the pressure difference, not the temperature of the air. Besides, if it was a thermal difference that caused the curtain to move, then by all rights it should billow outwards, since the tendency is to move from hot to cold. 

Elizabeth Wilson 

Question:

Rolling Cans, why do they roll different? I was rolling cans of soup with my students the other day and we noted that they rolled down a ramp in very different ways. Some rolled slowly and gained speed while others seemed to leap away after a slow start. Some stopped quickly once they were off the ramp and others continued on for a considerable distance. Could someone please help me with the physics of this phenomenon? 

Replies:

Sounds like a really fun experiment! Of course, it all depends on what is in the can. If the can contains very viscous material, or essentially solid material, like a can of molasses, it will roll as a solid body, with the inside having exactly the same angular speed as the outside. If the can contains a liquid, then the inside can behave quite differently, and if there are several different materials inside, you could have quite complex interactions, with heavy solid materials trying to stay on the bottom of the can all the time, and therefore preventing its rotation to some extent, for example. The basic physics is that of rotational angular momentum coupling to the gravitational force pulling the can down the plane, and the rotation caused by the fact that the surface of the can rolls, rather than sliding. There should be some treatments of slightly less complex

Page 10: Newton Ask

systems (wheels rolling down inclined planes, for example) in a mechanics text that discusses moments of inertia. Then, on the inside of your can, you have a fluid mechanics problem, which should be treated in books that discuss viscosity, since fluid motion in a rotating cylinder is a standard measure of viscosity. And finally you have possible solid objects that are sliding against the can on the inside, causing a frictional force. Hopefully, with all these elements, you can at least model most of the different behaviors you saw! 

Arthur Smith 

How about doing some experiments in which you control some of the variables Arthur Smith mentioned? Roll a can containing pure water, another containing molasses, another containing water and sand...do some experiments at constant volume (full cans) and others at constant weight. Vary the size of the can, keeping the contents fixed, and do this for several different contents. See if you can justify the results against the physical principles Arthur Smith described. 

Topper 

Question:

I am not a physicist, please forgive a "left field" question. I recently heard that if you took a simple child gyroscope and spun it in one direction that it would way different than if you spun it in the opposite direction. How can this be? Has anyone ever tried it? 

Replies:

There was an article published in Physical Review Letters a few years back in which an extremely careful experiment was performed to determine whether or not the weight of a gyroscope depends on the direction of its spin. The result of that experiment was that the weight does depend on the spin direction, and immediately everybody and their grandmother tried to reproduce 

mooney 

This stunning and completely unexpected result. Nobody could reproduce it, and I do not think anybody believes the original experiment was correct. The weight difference was extremely small, and I presume the result was came from systematic errors that were not adequately accounted for. 

Unknown 

Page 11: Newton Ask

Question:

If a football is kicked with velocity vector:v = (16m/s)x + (12m/s)y then how can I calculate: 1) the speed with which it hits the ground, 2) the angle it makes hitting the ground, 3) its "hang time" 4) it range and 5) its maximum height? Basically, what equations are needed here, concepts, etc. 

Replies:

For convenience, let us assume that the ball's location prior to being kicked is x=0, y=0, and that it is kicked at time t=0. Also let us ignore air friction. Then there is no horizontal force acting on the ball, and gravity is the only vertical force. The velocity-component equations are: v_x(t) = 16, v_y(t) = 12 - 9.8*t [both come from v(t) = v0 + a*t]; note that the acceleration due to gravity, 9.8 m/s^2, is negative in the v_y equation because gravity acts in the negative-y direction (we have implicitly chosen "up" as the positive-y direction because of the +12 y-component of the initial velocity). The position equations are: x(t) = 16*t, y(t) = 12*t - 4.9*t^2 [both come from s(t) = s0 + v0*t + (a*t^2)/2 ]. The ball hits the ground when y=0; setting y(t)=0 and solving, we get t=0 or t=12/4.9 ~ 2.449 s. The later time is the answer to (3). To answer (1), evaluate the v_x(t) and v_y(t) equations at t=12/4.9, then use the formula speed = sqrt[(v_x)^2 + (v_y)^2] = sqrt[16^2 + (-12)^2]= 20 m/s. Draw a picture of the x and y components of velocity and their vector sum at impact, with all three vector tails at a common point, and use trig to find the answer to (2) (its arctan(-12/16), or ~ -36.87 degrees). To get the range, use the x(t) equation evaluated at the time of impact: range = 16*12/4.9 ~ 39.18 m. Finally, to get the maximum height, recognize that this occurs at the time when the ball momentarily has zero velocity in the y-direction; set v_y(t)=0 and solve for t. This gives t=12/9.8 ~ 1.224 s. Evaluate y(t) at t=12/9.8 to get the answer to (5): max height = 72/9.8 ~ 7.347 m. 

R.C. Winther 

Question:

How do physicists determine the direction of probability amplitude for all types of light? I know that red light has a rotation of about 36,000 times per inch traveled. Does this have any relation to the frequency of this light? 

Page 12: Newton Ask

Replies:

Yes, your number 36,630 is the number of wavelengths of red light in an inch. The wavelength times the frequency is equal to the speed of light, so there is an indirect relationship to the frequency. For my number I assumed that the wavelength of red light is 7000 angstroms. The frequency would be 4.2 times 10 to the 14th power. Probability amplitudes are something different. 

Sam Bowen 

The relation between the wavelength of light and its frequency is given by: wavelength * frequency = speed of light (=300,000 km/second). So, for visible light, which covers wavelengths from 400 to 700 nanometers (4 to 7 X 10^-7 meters, or 1.5 to 2.7 X 10^-5 inches) the frequencies go from 7.5 to 4.2 x 10^14 Hertz (1 Hertz = 1 cycle per second). More on the human scale are radio stations - for example, an FM station at 100 Megahertz (a frequency which can be generated by ordinary electronics has a wavelength of: 3 x 10^8 meters/second/1 x 10^8 Hz = 3 meters. The ideal antenna for picking up radio signals is about one half of a wavelength, or about 1.5 meters (= 5 feet) for this frequency which, if you think about it (think of a car antenna), is about the size people actually use! For our radio station, the radio waves, like light, are known as "electro-magnetic" waves, and have electric and magnetic fields associated with them (That is why you can generate them with an electrical circuit). An electric field is something that causes an electrical charge to move in the direction the field is pointing, and similarly a magnetic field causes a magnet to orient itself along the direction it is pointing. So, at any instant, the radio waves have a certain collection of these electric and magnetic fields spread out all over the place. Imagine freezing this collection of fields, and testing the directions while moving towards and away from the station transmitter. What you will find is that first of all the fields are always pointing perpendicular to the line-of-sight from the transmitter (they never point along the direction they are going) and that the electric field is always perpendicular to the magnetic field. You will also find that every 1.5 meters (1/2 of a wavelength) both the electric and magnetic fields flip direction, so that after a full 3 meters, they are back where they started again. That is why they are called waves! Now unfreeze it. 1 of over the frequency is 10^-8 seconds, which is called the period. You will find that every 1/2 period (5 x 10^-9 seconds) in time, the electric and magnetic fields everywhere flip directions, so that after a full 10^-8 seconds, they are again back where the started. So the frequency (100 million inverse seconds) is the number of times a second the fields do one full cycle. The same (much faster and smaller) is true of light. 

Arthur Smith 

Page 13: Newton Ask

Question:

I have wondered for some time why the symbol "s" is commonly used to represent the quantity "displacement." 

Replies:

I have looked around and cannot find out where this started. It might be so simple as the fact that s is close to v and t which both appear in distance formulas. Lots of expressions have letters from similar parts of the alphabet as a way of recognizing copying errors. It may also be German. I will be look into this a little bit later. I note that in the math literature when the length of a line is mentioned it is often called s. Again I do not know of any reason. Many of these conventions are very old and often limited to a particular audience. 

Sam Bowen 

Question:

Is the unit of measure of weight a gram? It appears to be trivial but it is used in this context on the `IGAP' test. What gives? 

Replies:

Strictly speaking a gram is a unit of mass. However, it can be used as a unit of weight in the sense "however much a gram of matter weighs", which is about the same everywhere on the surface of the earth. If you think about it, there are almost no circumstances when a person would use the word "weight" and really mean weight. They do not care if the object being referred to as weighing 100 pounds (or grams) is on the earth or on the moon - what they are really doing is using "weight" to mean mass. Which is fine with everybody, since everybody understands it the same way. 

A. Smith 

If "weight" means "the force due to gravity" then I suppose one would measure it in terms of units of force, which would be Newtons in MKS and dynes in CGS units. 

Robert Topper 

Question:

Page 14: Newton Ask

What is the difference between weight and mass? How can I demonstrate this in my fourth grade classroom? 

Replies:

Here is a simple start. Masses are attracted to each other by the force of gravity. The amount of attraction on an object like you and me at the surface of a planet is what we call weight. It depends on what planet we are on and or it can depend on whether we are sitting still at the surface of the planet or are accelerating toward or away from it. If we are accelerating toward it we will weigh less (this means the force we feel on our butts against our chair will be less, and even could be zero. we will still be our old fat selves. We will not have lost mass, we will have simple lost the feeling of the chair seat pushing up against us. In one sense weight is about feeling the force of gravity pushing us against the surface of our chairs and floors. Mass is just the number of particles that make us up. Demonstrating this is another thing. One idea is to have kids feel their backs against the chair of the car seat when the car is speeding up or turning (it has to be accelerating) 

Sam Bowen 

A good thought experiment is this: An astronaut is taking a space walk and an asteroid the size of a car is floating next to him. The asteroid has no weight because no gravity is acting on it. But it has plenty of mass (stuff or molecules). If the astronaut gently pushes on the asteroid he can lift or move it because it has no weight, something he could not do on Earth. But if he tries to quickly punch it, he would break his hand (if it was not protected) because the asteroid still has mass. Or if he somehow got caught between the asteroid and his spaceship he would be crushed, for the same reason. (This all ignores friction, of course) This may not be exactly correct, someone else might want to edit it, but the mere fact that the asteroid is floating means it is weightless. 

Mark Fernau 

Question:

Is it possible to measure mass in a weightless environment? Also, why does mass exert gravitational forces? Does it go down to the atomic level where different particles have different charges, therefore attracting each other? 

Replies:

Page 15: Newton Ask

Yes, mass can be measured in a weightless environment. Basically, "inertial" mass is defined by Newton's law: F = m a. So, if you can measure a force and acceleration on an object, you can measure its mass. The standard method on earth uses force-balance, with one of the forces being the gravitational one, which is itself proportional to the "gravitational" mass, which has been experimentally shown to be exactly the same as "inertial" mass up to quite high precision. In weightlessness you could not use the gravitational force to measure mass and so you would have to measure it by the inertial approach, using an unbalanced force. For example, measuring the frequency of oscillation of a spring with the mass to be measured attached would give the mass pretty accurately. Gravity is not associated with the charges on things - otherwise it would not depend just on mass, but on what kind of microscopic relation there was between charge and mass. It is a very weak force, at least on a human scale, but it is indeed completely independent from the electrical forces. It was a good suggestion though - practically all the interactions of matter we run into in our lives are through electromagnetism - gravity is the one exception. There are two other forces at very short distances in the nucleus. One of the goals of physics is to try and unify all four forces to treat them as one, but there is no working theory of this yet! 

A. Smith 

I add that gravitational mass equals inertial mass by definition. That is the way the gravitation constant (big "G") is defined, in the equation F=GmM/r^2 in the equation for the force between masses m and M separated by a distance r (r^2 means "r-squared). What is important is that G is the same for ALL pairs of masses, no matter what they are made of. This fact, which is what has been verified to high precision by experiment, is sometimes referred to as "the principle of equivalence". 

jlu 

Question:

In nuclear physics, I have read that under some circumstances in a particle accelerator matter will change to energy and then back to matter in a matter of a few feet. Could you tell me how and why this happens? 

Replies:

Actually, modern physics theories have matter appearing and disappearing all the time, and if it is fast enough they do not even have to conserve energy (according to Heisenberg's uncertainty principle). Matter is always created as particle- antiparticle pairs, however, due to other conservation laws - for example electrons and positrons

Page 16: Newton Ask

get created together. In particle accelerators the idea is to bring protons or electrons to very high energies. Then these high energy particles are smashed into one another or into fixed targets, and all sorts of stuff can happen. The interesting thing is when new particles are created - in particular if the energies are right, the heavy quarks can be created (together with their anti quark pairs). Since they are unstable, they decay within a very short time (and most likely, having high energies themselves, after having traveled some distance, perhaps measured in feet). And the decay releases more particles with high energy. Actually I should probably clarify. "Energy" does not exist except as a property of matter (if you include all particles, including the photons that carry light, as matter). Since some particles are unstable, they can decay and release energy, but that energy is then owned by the decay products. 

A. Smith 

Question:

I have completely discharged a lead/acid battery. I have used the appropriate charger to bring it up to full capacity. It weighs more, right? How much of the weight difference is energy converted to matter, if any? How much weight would I have to pay for a balance to measure that difference in mass? 

Replies:

Yes, it weighs more. It is all energy converted from electrical to chemical form, manifesting itself in the binding energy of the matter. It is not really correct to speak of energy being converted to matter here; it s just changing form from electricity to chemical. 

A. Smith 

Yes, it weighs more. Energy does not have to be converted to mass to be affected by gravity. Energy has weight. Such a balance would be priceless, because it is far beyond our technological capability. However, if fingerprints were left on the battery, it would weigh many times more than the energy that was added to the battery. 

Mooney Question:

In an interesting book by Paul Davies and John Gribbin, called "THE MATTER MYTH". It explains that the concept of energy was originally introduced as a purely theoretical

Page 17: Newton Ask

quantity that could be changed and exchanged among its various forms. We cannot see or touch energy, yet "we accept that it really exists because we are so used to discussing it." I am one who accepts the existence of energy. In fact, I think it is a clearer concept than Matter itself. So is it then, that ENERGY is a property of MATTER, or the other way around? 

Replies:

Energy does exist. But, the concept of matter disappearing and energy appearing in its place is really not quite correct. So, what is energy? It is a quantity that describes the current state of a system, just as charge, mass, velocity, position, etc., also would describe the current state of a system. Moreover, like charge and mass and momentum (but not velocity), energy is additive - the energy of two objects is the sum of their individual energies (before they start interacting and interfering). And, energy is always conserved, just as momentum and charge are. Einstein's great discovery/idea was that mass is not conserved, and that the true energy of an object was not just the sum of the various parts that people had always assumed (kinetic energy from motion, chemical energy from interaction atoms) but also contained a huge piece that was associated with the mass of the object. So, does mass turn into energy? No! But, the energy that always was there, contained in the mass of the particle, can be released if the mass is reduced. Does energy ever leave a physical object and go off on its own? 

No!

It always is just one property of a particle (or collection of particles) that always has some other properties, such as spin, mass, charge, etc. but, there is some difference between the 3 types of neutrinos, and there is also a distinct difference between neutrinos and anti neutrinos (they spin the opposite way). The photon which carries light is even less "pure energy", because it carries along with it electric and magnetic fields, in some sense, and has a polarization as well. 

A. Smith 

I think it can also be argued that energy does NOT really xist. One can approach it from a viewpoint that energy, like momentum, is a human concept that is useful in understanding nature. 

Nature does whatever it wants to do, and it does it in ways which are mysterious and amazing. Whether the phenomenon is superfluidity, neutron decay, or photon scattering, nature just DOES it. 

Humans make measurements of these events and have come up with terms like

Page 18: Newton Ask

"mass," "energy," "momentum," "charge" and so on to help them quantify what they measure. Humans also come up with equations (Schroedinger equation, Einstein equation, Newton's laws, Maxwell's equations, etc.) which relate things like energy, mass, and so on. 

Fortunately, nature behaves in ways that are in agreement with the mathematics that people understand (so far). Newton's laws are able to describe "mechanics" using simple algebra. Schroedinger's equation requires differential equations and probability functions to describe "quantum mechanics." Einstein's equations involve tensors. Nobody knows how to properly describe quantum gravity, but some people think that "string theory" might do it. 

Humans can calculate the "energy" of systems and things and make useful predictions. So far, science has been spectacularly successful at using these terms to understand the operation of nature to astounding precision. "Energy" is one quantity that is universal in all branches of science, and is most useful. Other quantities, like momentum, are also universal, but are not as useful for answering questions. 

As to whether energy is a property of matter, I think it depends what kind of science you are doing. If you are doing simple mechanics, then no, your masses have no energy of themselves. If you are colliding electrons and positrons, then yes, all of your equations involve total energy and rest energy of the matter. I do not know enough of relativity or string theory to know how these fields relate energy or matter. 

Bob Erck 

Question:

To any scientist it may concern: I am in desperate need of physics help. I am having serious problems with my Physics 103: Mechanics class. I have a problem with vectors in particular. For example: A particle leaves an origin with an initial velocity of v=3.0i (i being the x- component of velocity vector v). It experiences a constant acceleration a=(-1.0i-o.5j), in m/s^2, (a) What is the velocity of the particle when it reaches its maximum x coordinate? (b) Where is the particle at this time? A detailed explanation of how to solve this problem and reasons for respective solution steps would be greatly appreciated. 

Replies:

Okay, the important thing is to write down the equation of motion for each component, the x and the y, separately. The definition of acceleration in the x direction is a_x = d2x /

Page 19: Newton Ask

dt2 , or the second derivative of x with respect to time. Since the acceleration is constant, if we integrate this equation, we get dx/dt = a_x * t + (v_x)_0, where dx/dt is the velocity of the x coordinate and (v_x)_0 is the initial velocity in the x direction. If we integrate again, we get x(t) = 0.5* a_x * t^2 + (v_x)_0 * t + x_0, where x(t) is the x coordinate as a function of time and x_0 is the initial position. Similarly, y(t) = 0.5* a_y * t^2 + (v_y)_0 * t + y_0. Now we plug in the initial conditions. In the problem, we start at the origin, so x_0 = y_0 = 0. The acceleration is (-1.0i,-0.5j) [the particle will be pulled down and to the left] and the initial velocity is (3.0i, 0.0j). Substituting these numbers into the two equations, we get x(t) = -0.5 * t^2 + 3.0 * t [ a_x = -1.0,(v_x)_0 = -0.5, x_0 = 0] y(t) = -0.25* t^2 [ a_y = -0.5,(v_y)_0 = 0.0, y_0 = 0] Now we can answer the questions. 

(a) What is the velocity of the particle when it reaches its maximum x coordinate? Well, it should be apparent that the velocity in the x coordinate will be zero when the particle reaches its maximum value of x. But what is the y component of the velocity at this time? Well, first we need to know at what TIME the particle is at its maximum x value. To find this time, we differentiate x(t) and set the result equal to zero; dx/dt = - t + 3.0 = 0 ; therefore, t=3.0 is the time at which x(t) takes on it maximum value (this can be checked by plugging it into d2x/dt2 and checking that the answer is negative, i.e., x(t) is "concave down" at this critical point). Next, we differentiate y(t), which results in dy/dt = -0.5* t. Plugging in t=3, we get dy/dt = -1.5, and so the velocity of the particle when it reaches its maximum x coordinate is ... (0.0i, -1.5j) m/sec. 

b) Where is the particle at this time? Just plug this value of t into the two equation above, and get x(3) = -0.5 * 9 + 3.0 * 3 = 4.5 y(3) = -0.25 * 9 = - 2.25 and the position is (4.5i, -2.25j) meters. 

Robert Topper 

Question:

If a block of wood floats in a pail of water with weight sitting on top of it, the waterline say is at the halfway point of the wood block. If we hand the weight from below the block -- into the water, will the water level on the block stay the same, increase, or go down. 

Replies:

You are correct that the water displaced should remain the same, and therefore the water level on the block should go down. (since the weight is displacing a little bit of water itself). This should be easy to test though - how about doing the experiment to check it? 

Page 20: Newton Ask

A. Smith 

If you hang the weight below the block, the water level will no longer reach exactly halfway up the block, but will reach slightly less than halfway up depending on the density of the weight. It is correct to say that the weight supported by the buoyant force is the same whether the weight is on top, or below, the block. Also, the water displaced is the same in both cases. The difference is that the weight displaces water when it is hung under the block, but not when it is placed on top. 

Mooney Question:

If you were in a boat in a small swimming pool (so that you could measure the water level) and there were rocks in the boat, What would happen to the water level if you threw the rocks into the water? Would it rise, lower, or remain the same level as when the rocks were in the boat? 

Replies:

Let us note in passing that since each rock sinks, each rock's overall density must be greater than that of water. When a rock is in the boat, Archimedes' principle tells us that the weight of the volume of water displaced due to that rock is equal to the weight of the rock. Since the rock is denser than water, this displaced volume of water is larger than the volume of the rock (weight = mass density times volume times g, the acceleration due to gravity). But when the rock is on the bottom of the pool, it merely displaces a volume of water equal to the rock's volume. Hence, more water is displaced when the rock is in the boat than when the rock is on the pool bottom. Therefore, the water level will drop each time a rock is thrown out of the boat into the water. 

R.C. Winther 

Question:

Suppose you had a plane with a 2000 lb payload (it could not fly if carrying over 2000 lbs) and you stuffed 2000 pounds of birds into the plane. If the birds began flying in the plane, could the plane now take off? 

Page 21: Newton Ask

Replies:

The question really is, is the total weight of the plane changed by the activities of those birds flying around inside it? The answer is that it cannot be. The birds are supporting their weight in the air by flapping their wings, certainly, and this increases the air pressure on the ground, but the total force on the floor of the plane is the same whether the birds are sitting on the floor or flying steadily around in it. Now, if the birds were not actually flying, but were jumping up and down then the force on the floor might fluctuate - if the birds were all coordinated the force could be quite large for a short while, and then very small until they hit the floor again. Over time the weight would still average out to the same 2000 pounds, though, and the plane should be able to take off (maybe with a few bumps and jumps). 

A. Smith 

I completely agree with the first response, but would like to add the following twist. Imagine this is not a pressurized plane. In fact all the windows are open and the atmosphere in the plane mixes freely with the outside. Now the birds flying does indeed decrease the weight of the plane. 

Unknown 

Question:

What is the average height that raindrops form? Do they fall at terminal velocity? If they do not fall at a terminal velocity, why not? The raindrop forms a shape that has the least resistance as it falls, does not it? Or, does it fall fast but have little momentum? 

Replies:

Raindrops do fall at terminal velocity or even faster if they are pushed by a downdraft. But terminal velocity for even a large drop is not very high because the drop flattens out into sort of a pancake shape, so it actually has more air resistance than a sphere. 

John Hawley 

Question:

Navier-Stokes equations I need to know what these equations are and some references so that my student team can understand them. We are going to the Cornell Super computing Contest and the FIDAP software package uses these equations. An understanding will help us better pose and solve our problem on wing design for paper

Page 22: Newton Ask

airplanes. 

Replies:

The Navier-Stokes equation is a standard equation that describes the flow of continuum matter in fluid form - that can be a liquid like water, or a gas like the air. The equation describes the change with time of the density and velocity of the fluid. From the density, (assuming constant temperature) you should be able to get pressure, which is needed for wing design. The equation involves derivatives with respect to space and time of this velocity and density, and the important thing that you need to take account of is the boundary between the air and the wing - these boundary conditions (and the plane's speed relative to the overall air speed) are what determine the solution. I do not know the name of any specific text, but an advanced aeronautical engineering text should give you more than you need. Look in the library under aeronautics, fluid dynamics, and maybe airplane design, or wing design. 

A. Smith 

Any good fluid dynamics or meteorology text will have an explanation of the NS equations. The exact form changes with coordinate systems and mathematical are vector notation, but I think the general idea is that the total rate of change of the system = the local rate of change with time + the rate at which the substance is transported by your location. So the temperature change at your location has two components, the local derivative as say the sun heats your air, and the advection term as hotter or cooler air is moved past your location by the wind. 

Mark Fernau 

Question:

If an astronaut is in a space station at zero g's, and he strikes a match, how will the flame burn (in what direction) assuming an atmosphere similar to that on earth? 

Replies:

The flame would be mostly spherical since there is no gravity. But that means there would be no convection either, so the flame extinguishes itself fairly quickly. I think this has been demonstrated on one of the space shuttle flights. 

John Hawley 

Page 23: Newton Ask

Question:

Why is it easier to maintain your balance while gliding on one ice-skate then while standing still on one ice-skate? 

Replies:

This is essentially the same as the reason why it is a lot easier to keep your balance on a moving bicycle than on a stationary one. The point of contact with the ground in both cases is well below the center of mass. That means that, when moving, there is a net angular momentum about that "pivot" point. If you are slightly off balance, your center of mass is not directly over the pivot point, but to one side of it. Then the force of gravity starts pulling you down, but because of the angular momentum (just like with a gyroscope) this gets changed into a turning motion - you change direction a little by leaning to one side or the other, and if you keep leaning in the same direction you will go around in circles. Of course there is some point (you lean too far, or slow down too much) where gravity wins out and you just fall over. But the faster you are going, the more stable you will be. 

A. Smith 

Question:

It takes an input of energy to convert liquid to vapor, thus increasing entropy. If an increase in entropy is natural, why does this not happen naturally with less effort on its own? 

Replies:

Actually, if you put a bowl of water in a room that was completely empty (no air either - although really the main condition is that there be no water vapor in the room to start with) then the water actually does naturally evaporate until there is a balance between the amount of water vapor and the temperature of the water (basically, it has a natural "vapor pressure" that it tries to achieve, for any given temperature). If the room is big enough, all the water will evaporate with no additional energy input. Depending on the circumstances, the average temperature of the water will also go down in this process, although that is a somewhat separate issue. The higher the water temperature, the higher the vapor pressure. There is actually a concept called "free" energy, which takes into account the entropy, so that any system tries to minimize its free energy - there is a balance between maximizing entropy and going into a higher energy state (the vapor as

Page 24: Newton Ask

opposed to the liquid) - the whole field of thermodynamics is based on understanding these rather complex relationships. 

A. Smith 

Question:

The quantum energy levels for the kinetic energy of a particle in a box are obtained as the eigenvalues for the wave equation. Is there any theoretical basis for E=hf in the harmonic oscillator? 

Replies:

If you plug in the potential for the 1-D harmonic oscillator into the time-independent Schroedinger equation and solve the resulting eigenvalue problem, you get that the allowed energy values are given by E_n = (n + 1/2)hf for n = 0,1,2,... This is in contrast to Planck's postulated quantification of E_n = n*hf; the "zero-point" energy is not zero! This is a consequence of the uncertainty principle. 

R.C. Winther 

True, but if you look at the formula for the difference in energy between state n and state n+1, you get delta E = hf(n+1+1/2) - hf(n+1/2) = hf! So the harmonic oscillator's energy can change only in units of hf. And, if the selection rules were right, one would observe that light would only be absorbed/emitted by such an oscillator with frequency f. 

Robert Topper 

Question:

Why is it that dark colors absorb more solar energy than light colors? That means that dark areas of the earth are warmer in sunny weather. Is this because less light is reflected? Would dark blue be a cooler color than dark purple or red? 

Replies:

Basically, darker colors are dark because they absorb more of the light that hits them. In general, light striking a non-shiny object is either scattered diffusely, transmitted through the material, or absorbed. When we look at the object we are seeing the diffusely

Page 25: Newton Ask

scattered light, and (assuming the object is opaque enough so that not much gets transmitted) the colors we see are all those in the original light source that did not get absorbed. A dark object absorbs most of the light that hits it, so almost no light is scattered back to give it color. 

A. Smith 

Question:

I teach physical science and am interested in color. Is there any way for me to tell if something yellow is reflecting yellow wavelengths of light or green and red, without analyzing the reflection spectrograph? Can you come up with a way that I can show them true yellow and an object that is really reflecting red and green? 

Replies:

I do not know much about color. However, Physics Today had a whole series of articles on color - from computer generation to our perceptions of it, about 3 or 4 months ago. Hopefully you can find it in your library, or get it from a University physicist somewhere nearby. (1993) I think you probably can do what you want by using simple colored filters on your light source. Filters usually will say what wavelengths they let pass through. Look at the object in white light, then in red, green and yellow. I am not sure what you should use as an object though - most things do not reflect just a single color, but a wide range, with some shown much better than others. 

A. Smith 

You could just illuminate a white screen with two light sources, one with a red filter and one with a green filter, and overlap the spots of light; the overlap region should look yellowish, even though there is no yellow light there (show this by viewing the overlap through a yellow filter; it should look as dark as the red and green regions.) 

R.C. Winther 

Neither respondent really answers the question. The answer is yes, you can tell whether the yellow that you are looking at is a true "yellow" (around 590 nm in wavelength), or whether the yellow is composed of red and green. 

To do so without a spectrometer would require you to get a special yellow filter. This filter would have to transmits narrowly in the yellow, and block both red and green. If your yellow object is really "yellow", it should still look yellow through the filter. If your

Page 26: Newton Ask

yellow object is really emitting red and green wavelengths, it will look dark when viewed through the yellow filter. 

Conventional photographers gels do not do this. They transmit broadly above 500 nm and are not selective. It might be difficult to find such a filter. 

It should be noted that light-emitting diodes are fairly monochromatic. For example, LEDs that make yellow light do it fairly narrowly around 590 nm. On the other hand, the yellow on a computer monitor must be a mixture of red and green because those are the colors of the pixels. 

Bob Erck 

Question:

Why does the color Black absorb heat and White reflect heat? What are the physical properties behind this fact? I have seen some Arabs where Black robes in the desert -- this seems to defeat the purpose. Do they wear them because black protects more against harmful UV rays? 

Replies:

First of all I have no idea why some Arabs wear black robes in the desert. It seems counter-productive...but oh well, different strokes for different folks. Anyway, the color that we observe (i.e. the color of a particular object) is really only the light that is reflected from that object. For example, a red ball appears red because when white light strikes it, all of the light is absorbed except for the red frequencies/wavelengths which are reflected into our eyes. A white light is made up of all visible (and invisible) wavelengths all mixed together. So an object that appears white, is reflecting all of the incident wavelengths and absorbing nothing (or very little). A black object, on the other hand is absorbing all of the incident wavelengths (along with all of their energies) which causes it to heat up. That is why snow does not melt in cold weather even when the sun is falling directly on it. All of the incident light energy is reflected away and none (or very little) is absorbed. 

Unknown 

Up-date July 2001

The explanation I heard for this is that the clothes themselves are very loose (rather like Roman togas). The extra heat caused by the black colour causes increased upward convection of the air between the cloth and their body. This additional air circulation

Page 27: Newton Ask

actually aids in evaporation of persiration and thus results in better cooling. 

Robert Wilson 

Question:

You are in a room, windows open but no sunlight coming in the windows. The air temperature out and inside is say 103F, you are concerned about feeling too warm. Using some physics, you decide that the color of you t-shirt will help you "cool" off which is the correct answer? A) White because it will reflect IR from your warm surroundingskeeping you cooler or B) Black because you would then be a black body radiator able to lose heat at the fastest rate I opt for B, but another physics teacher in my county says A? Which is right? 

Replies:

Why do Arabs were black robes in the desert? A white-colored object reaches a higher equilibrium temperature than a black one. On the other hand, why are all astronomical observatory domes painted flat white? I assume because flat white is almost as good as flat black for being a good black-body radiator AND it absorbs heat much more slowly. So, if you are going to be in the Sahara all day, do you wear black robes or white ones? 

John Hawley 

With no sun coming in the windows, your ability to reflect radiant heat is immaterial. Black body radiation does not have anything to do with the color of the object. The answer is that the color of your shirt will not have any affect on your temperature. Take the shirt off and fan yourself with it, because evaporation of your sweat is the only way your 98 degree body is going to cool down in a 103 degree room. 

Unknown 

First of all, heat is generally transferred by 3 mechanisms: convection, conduction, and radiation. Convection is the actual motion of hot things (air etc.) into cooler places, conduction is a microscopic transfer of heat from particle to particle so it gradually diffuses to cold areas (not so gradually for solid materials) and finally radiation, which seems to be the main topic of this question, is the generation of electromagnetic waves by a hot body, to be absorbed by cooler bodies. Now, there is an additional complication when you talk about a living person - the person is actually generating heat (otherwise the person is dead). To put the question in its simplest form then, imagine a corpse in a

Page 28: Newton Ask

vacuum-filled container (to prevent conduction and convection effects) with a window to the outside world. The container and world are at 103 degrees, the corpse at something cooler, initially (the vacuum does not have any meaningful temperature in this example). We know, thermodynamically, that eventually the corpse will reach the surrounding 103 degrees (two objects in equilibrium are at the same temperature). The only meaningful question to pose is, what color T-shirt should the corpse be wearing, to stay cool for as long as possible? Now, the spectrum of radiation from a body is always peaked at an energy that is roughly the same as the temperature multiplied by Boltzmann's constant. The sun, at 5000 degrees, has a peak around 0.5 eV, or slightly below the visible region. That is why the color of a shirt makes a difference when you are absorbing light from the sun - a black shirt does absorb in this region, a white shirt presumably does not absorb as much. But when we talk about radiation from bodies at 103 degrees Fahrenheit, or about 300 absolute degrees (Kelvin), the peak in the spectrum of radiation is down by a factor of 10-20. 

You cannot tell by looking at an object just how well it will absorb radiation in that region - it is way outside the visible. Shiny metallic things generally do not absorb anything very much at long wavelengths though, so you can at least count on those being good reflectors. So the answer to the question as rephrased in the preceding response is that neither the black T- shirt nor the white T-shirt can be counted on to keep the corpse cool for long, but a shiny metal T- shirt would probably do the job as well as it could be done. 

A. Smith 

Question:

I have some special 'coated' glasses. This coating is supposed glare from computer screens etc. When white, or sunlight shines on them, they reflect a greenish color (to the light). I think that the coating must absorb several colors of white light, but why cannot I notice a difference? What does the absorption spectrum look like for these coatings? 

Replies:

Usually glasses that reduce glare do so with polarizing filters. Glare from terminal screens may be different, though. There are glare reducing covers for most screens, but I am not sure how they work. 

John Hawley

Page 29: Newton Ask

Question:

How does gravity get out of a black hole? If gravity is mediated by a particle, say graviton, and the particle is subject to the usual limitation that nothing can travel faster than light, how do gravitons get across the event horizon? The part of the gravity of a black hole that is due to stress of space time outside the event horizon can certainly be mediated by gravitons without them needing to exceed the speed of light, but that just postpones the question: Why is space time stressed outside the event horizon, if gravitons cannot escape from it? Do they perhaps escape by Hawking-Penrose radiation? That does not seem right, because the intensity of Hawking-Penrose radiation decreases with increasing mass of the black hole. 

Replies:

Like I have said before, gravity and quantum mechanics have yet to be reconciled, and I think your question points out one possible place where reconciliation maybe difficult. I am sure there are resolutions for this though - for example, if you are actually outside the event horizon, then there is no way for you to distinguish a real black hole from something that is just barely about to become a black hole but has not quite made it yet because the last bit of matter between you and the black hole-to be is a little too far from the center. So, gravitons can, perhaps, escape just before the black hole forms, and that historical event of the black holes formation may provide enough information to keep up the gravitational field on the outside. I do not actually does gravitation could answer? 

A. Smith 

Question:

What would be effect be of a object generating its own gravitational field that can be manipulated in whatever way it wants (within limits)? 

Replies:

There is no basis for any kind of manipulation of gravity, at least, not that I am aware of. 

John Hawley 

Question:

Page 30: Newton Ask

Every particle that has mass generates (or at least is associated with) its own gravitational field. Matter, can be converted into energy. When that happens, what becomes of the gravitational field that was associated with that quantity of matter that has become energy? 

Replies:

It turns out that gravitation does not depend directly on mass - it depends only through the energy (and momentum) of the matter involved. If the matter changes in some way to reduce its rest mass, this has no effect on the total energy (or momentum) of the system, although it would certainly change the energies and momenta of the individual particles making up the matter in question. This would have a short range effect on the gravitational field, but only in the way one would expect an explosion to have an effect. There would be no long-range effect because there is no net change in energy of the gravitating matter. 

A. Smith Question:

What causes gravity? I know about Universal Gravitation, but what, other than a formula, really makes two things attract each other? 

Replies:

Your question is very profound. We simply do not know the cause. What we know is that the Gravitational constant G that appears in the gravitational force equation is fundamental. We have no theory that gives us its value. Aside from the actual size of the gravitational forces, the fact that a mass distorts the space around itself by producing a field at points distant from it is one of most profound assumptions of modern science. The electric and magnetic fields are the other familiar fields. With these we have detected the quanta of radiation and have measured their propagation in space. We have not yet detected the graviton for gravity, so we do not yet know how it is propagated in detail. We know in some detail how gravity works, but we do not have a clue about what causes it. For that we would need some theory that would predict at least the value of G. 

Sam Bowen 

Question:

Page 31: Newton Ask

When gravity acts to bend light, is it because a photon does have mass when it has velocity, or does gravity act on the energy of the photon, which I understand has no rest mass? 

Replies:

Well, gravity acts on everything since it really acts on space itself! Yes, a photon has no rest mass, and that means that it is always traveling at the speed of light. The energy of a photon is actually proportional to its frequency, y, which does not really have much to do with the way gravity acts on it. However, since bending involves a change of momentum, the force that gravity exerts on the photon is proportional to its momentum (which is in turn proportional to its energy). And in fact, it is generally the total energy (rest energy plus kinetic energy etc.) that is important for gravity, whether the particle in question has a rest mass or not. 

Arthur Smith 

Question:

What would the gravity be like on a donut shaped planet and could such a planet exist? 

Replies:

That is an interesting question. The problem can be done the hard way, by integrating the gravitational potential for such a system... but a rough answer can be obtained just by looking at the way gravity works. If you were standing on the planet, then each little piece of the planet is putting a little bit of force on you, attracting you towards it. If you were standing on the outside, with the center of the donut hole exactly beneath your feet, then you would feel a strong gravitational force straight down, because all the parts of the donut are on the same side of you, and the average direction is straight down. If you were standing on the inside, with your head pointing to the donut hole center, then you would feel a somewhat weaker gravitational force keeping your feet on the donut. The near parts of the donut are exerting the stronger force, and so keeping you attached, but the other side of the donut is above your head, and is exerting a weak force in that direction so that the force keeping your feet down is partially counteracted. If you stand at any other point on the rim, then the force on you is not quite vertical - the net force does not point through your feet, but there will be a small amount due to the other side of the donut pulling you towards it. Such a planet certainly could exist.

Page 32: Newton Ask

However, if it were the size of the earth it would quickly collapse into something like a sphere, due to the gravitational action of one side of the donut on the other -for a really big mass (like the earth) the force is so strong that no material would be strong enough to oppose it. 

A. Smith 

Question:

How do theories of six-dimensional geometry apply to time? Is there any validity to the transporters they created for "Star Trek: the Next Generation"? 

Replies:

There are theories of the universe that involve dimensions higher than 3 or 4, but they usually do not have any effect on time. These higher dimensions just increase the spatial dimensions, and only in a very minor way. Science fiction, of course, does not have to rely on the silly restrictions of modern physics theories. In principle, one could build some kind of "transporter". However, the only kind I can think of would be more like "duplicators", which would produce a second copy of the object being transported, rather than actually do the transporting. This of course creates all sorts of philosophical problems which Star Trek has chosen not to worry about. 

A. Smith 

A recent discovery in quantum mechanics has shown that there may be a sense in which "transporting" is different from just copying, so I guess my previous answer needs to be changed. However, this does not have anything to do with the fourth dimension (or higher). The technique is to prepare a pair of coupled quantum systems, then one person takes one of those quantum systems somewhere far away. Next, it is then possible to make a measurement on the local system, transmit the result of that local measurement and reconstitute a new quantum system on the other side. So, if the quantum mechanical properties of a person are important for keeping them alive, then people really cannot be duplicated; but they can (by this means) in principle be transported by sending enough classical information to the other side. Of course, most biologists do not think quantum coherence is at all important for life, and therefore be possible to duplicate living things with enough classical information. 

A Smith 

Question:

Page 33: Newton Ask

Is the concept of traveling at or beyond the speed of light related to travel through time? If so, how? 

Replies:

Theoretically, if you could travel at the speed of light, you would experience no passage of time! This is because of the time-dilation effect of Einstein`s Special Theory of Relativity that states that at velocities approaching the speed of light, c, your perception of time is proportional to the square root of ( 1 - v^2 / c^2 ) which goes to zero. 

John Hawley 

uestion:

With regard fourth dimension, I wonder what an imaginary dimension of time in the equations of relativity has to do with reality? Does this dimension actually manifest itself in observable ways, if it is imaginary? If so, why call it imaginary? 

Replies:

Stephen Hawking uses the term "imaginary time" in his book "A Brief History of Time". First of all, this is NOT a reference to some physical quantity different from "real" time, but another way of handling "real" time mathematically. As Hawking says on page 135, "...we may regard our use of imaginary time and Euclidean space-time as merely a mathematical device (or trick) to calculate answers about real space-time." There is an important quantity given by ds^2 = dx^2 + dy^2 + dz^2 - (c^2)*dt^2 where "^2" means "squared"; c is the speed of light; dx, dy, and dz are tiny changes in the three spatial directions; and ds is the resultant change in a sort of 4- dimensional "length". Suppose we define a new variable w by w=i*c*t where i is the square root of -1 (i is an example of an "imaginary" number. Then we get ds^2 = dx^2 + dy^2 + dz^2 + dw^2. Now, all four terms have the same form, and w (like x,y, and z) has units of length. One may think of w as "imaginary time", but the only thing that has changed is the mathematical form, not the underlying physics. 

R.C. Winther Question:

Page 34: Newton Ask

I was wondering if electron orbitals are really 4 dimensional (or higher) spheres because d and p orbitals look similar to pictures I have seen of 3-D projections of 4-D spheres. Any comments? 

Replies:

Well, there might be something to your observation, but I have never heard of this before. The equations describing p-orbitals, though, are really pretty simple - basically the wave function amplitude is proportional to x *f(r) (or y, or z) where r = sqrt(x^2 + y^2 + z^2) and f(r) is something like an exponential e^(-a*r), although it has oscillations or higher n values. The pictures normally shown are surfaces of constant amplitude; so solutions of an equation of the form x * f(r) = constant. Since f(r) has spherical symmetry, (it depends only on distance r from the nucleus) the angular dependence of the surface is due to the factor x - the surface pokes out along the x-axis, and comes in to the origin when it meets the x=0 plane.! Also, d- orbitals are kind of similar, but instead of x have a factor x^2 - y^2, or z^2, or xy, etc, so their extensions tend to be narrower (due to the higher power) and more complicated. 

A. Smith 

Question:

How do we know that time exists? I know that clocks tell what time it currently is, and that we age as this so called "time" passes. But what factual reason is there that explains HOW time exists, and if it truly does? But what scientific reasons are there for its actual existence? 

Replies:

Well, how do we know that anything exists? We look around ourselves, observe the world, and come to some conclusions about it. Time seems to be a very useful concept in making the world make sense. Human observations of the world about us are perfectly acceptable scientific reasons for stating that time exists. Science is incapable of proving anything, and although some people seem to think that some scientific theories are infallible, and therefore can be relied on to prove things about the world, such notions are really not compatible with true science - science rests on observation, NOT on theory. Theory simply helps make sense of the observations. The first thing in a scientific approach to anything is measurement. Can we measure time? Yes! To fractions of a picosecond, these days. But, if you want to hold out and claim that time

Page 35: Newton Ask

does not exist, that it is all a figment of our imaginations, that in fact there is only one time ever, which is the present, and all the past never existed, well, that is up to you. 

A. Smith 

Question:

What is the physical significance of the constant known as the permittivity of free space? 

Replies:

It is basically the scale factor between the unit of force and the unit of charge. There are actual electric and magnetic unit systems in which there is no such factor (since it would be 1). For most of our experiences we insist on measuring charge in coulombs and measuring forces (or electric fields) in Newtons (Newtons per coulomb). The coefficient that we need to make it come out right is related to the permittivity of free space. The words probably go back to the days when we thought there was an ether in space. You can also think about it as the way space effects the forces between two charges. In this way it become s a property of space. 

Sam Bowen 

Question:

I hear that some people claim that they can imagine 4-dimensional objects. I wonder how this can be since our universe only has three physical dimensions - is it really possible to imagine these things and do these people have any proof? I myself find it impossible to imagine anything but projections of these objects onto 3-dimensions. 

Replies:

With some practice in mathematics it is not, in principle, difficult to imagine objects in any dimension. It is a little harder to think about what they would look like. The reason that four dimensions seems to be important is that space (3) and time (1 dimension) are clearly linked by relativity. The large number of experiments in relativistic speeds verify this quite well. So, if our world is fundamentally four dimensional, it means that time and space can be mixed when we make measurements of quickly moving objects. For most of our everyday experience it simply means that we should consider time as our fourth dimension. This means that we are moving through a four dimensional space, but does not mean that there are four dimensional objects in the usual sense. Objects are still

Page 36: Newton Ask

only three dimensional at a given time. Their path through four dimensional space time can be represented by a four dimensional volume. 

Sam Bowen 

Four-dimensional objects do not exist in our universe because it has three dimensions. I do not know how people can imagine a Four-dimensional object. We live in three dimensions, and it is difficult to imagine another "direction" that is perpendicular to our existing dimensions. Perhaps people with special imaginations can do it. There are some speculations about more dimensions in string theory, but these are only speculations and in any case the size of the other dimension is microscopic. 

This difficulty would be analogous to color vision. Humans usually see three primary colors, and the brain is able to "see" the full spectrum of colors from these primaries. Some creatures, like insects, have a fourth primary color receptor. They might "see" colors that humans cannot imagine, or at least I cannot imagine. 

In terms of mathematics, there is no problem with four dimensions or any number dimensions. 

On the other hand, physics equations describe our reality in three dimensions and usually do not work when extended to four and higher dimensions. That is because physics equations describe physical reality and our reality is three dimensional. 

One can think about four-dimensional moons orbiting four-dimensional earths, but the equations do not work properly. And if you have a four-dimensional sun, do the nuclear reactions still operate that keep the sun generating heat? 

Or one can think about four-dimensional atoms and molecules forming a four-dimensional piece of salt, metal, or wood, but what structure and bonding would they have? In four-dimensions, would atoms even exist? At the center of an atom, protons and neutrons that are bound together into the nucleus. In four-dimensions, does this binding still take place? Nobody knows. 

Bob Erck 

Question:

Why does one twin age more slowly in the famous "twins paradox"? 

Page 37: Newton Ask

Replies:

Well, That is the whole point of the paradox! From the point of view of the twin who is in the space ship, that is exactly what happens. However, everything breaks down if the twin in the space ship decides to slow down, turn around, and come back and visit his twin back on earth. During that deceleration and turning phase, he suddenly sees his twin on earth get older and older and older, while he does not age much at all. Actually, motion in our universe really is not all that relative. Position is relative, and different positions in our universe have different average velocities of all the matter in that area (the velocity of the Hubble expansion), so if you think about the physical universe, relativity seems a little less than obvious. 

Arthur Smith 

Question:

Is time travel possible? 

Replies:

I assume that you mean time travel at a different rate than the rate that we are all now traveling forward in time. All of us and all the matter around us is currently traveling forward in time at the same rate ( at least locally) and there does not seem to be a way in which we can alter that. Relativistically time is dilated when we observe it in quickly moving reference frames and a twin that has been traveling and returns will be slightly younger than the twin that stayed behind in a stationary reference system. This experimental fact indicates that to move into frames where time is dilated effects all the manifestations of elapsed time for objects or beings. I think that this means the time traveler would be effected by the time travel as well. The mystery in the time travel stories is how the travelers have escaped being effected by the change in frames. There is no known way that someone can travel ahead or back in time. It would appear that there are several contradictions that would occur if it were possible. One of these would be the effect on what are called world lines and their restriction to be in what is called the forward light cone.

Sam Bowen

Actually, some physicists a few years back did work out a way in which time travel would be possible. One of the instigators was Kip Thorne, and I actually saw him give a talk on this. It seems that if civilization could advance sufficiently far to handle black holes with ease, so we could put black holes in a box of some sort, for example, then

Page 38: Newton Ask

they found a way in which one could start with two black holes close together, and then pull them apart, and instantaneous travel would be possible between the two black holes. Because of the theory of relativity, instantaneous travel and travel backwards (or forwards) in time are essentially equivalent (you actually have to take two instantaneous trips to get back to the same point in space at an earlier, or later, time). However, even with this scheme it was impossible to travel back to a time before the "time machine" was created. Which is good, since we really do not want people going around killing their grandmothers before their mothers were born. I think I may have read that there was something wrong with this scheme. So, in the end, it could be nobody really knows how to travel backwards in time. It is fun to speculate though! 

Arthur Smith

Question:

In the response to the original article, Sam Bowen stated that it is not difficult to imagine 4-dimensional objects but it is difficult to think about what they look like. My question is what is the difference between imagining them and thinking about what they look like? Sure its easy to write equations for 4- dimensional objects that are representable by functions but take for example a hyper-cube. How would one go about finding what the projections of this would be onto a 2-dimensional surface? I have seen the projection of a hyper-cube onto 2-dimensions but cant imagine what the actual hyper-cube would 'look like.' On the note of 4 dimensional space-time, I do realize that we live in a 4 dimensional universe, but I am talking about objects that are in 'mathematical' four space. It seems that since we experience time instantaneously and that it seems to be uni-directional that it is different from the other 3 dimensions. I still think that it is impossible to 'see' anything that exists in four 'physical' dimensions since we exist in only 3 'physical' dimensions, the temporal dimension would not seem to help in realizing what these four dimensional objects really are. 

Replies:

I guess we have a semantic problem. I was considering problems in spaces larger than 3 where the dimensions might be different products or activities and we might be trying to minimize or maximize some function over these spaces. Developing some imagination about what the volume in that space can aid in the seeking of a solution. If you are insisting on four physical dimensions I would have to agree with your original statement that these cannot be seen. In relativity there are often needs to calculate integrals over time and space and that leads to four dimensional integrals and their evaluation. While this is only mathematics it is very "real". 

Sam Bowen

Page 39: Newton Ask

Question:

I do not understand why space is not considered a tangible substance, if it has elastic properties. 

Replies:

Indeed, several people have looked for the manifestation of this which would be gravitons, the excitations of the gravitational field. So far there is no good evidence that we have seen any after almost 30 years of looking. Either they do not exist, or nothing is happening to produce them near by. The effects you are taking about are very small and would be very difficult to detect near a regular planet. Near a black hole they can be large, we think. 

Sam Bowen 

A new experiment that is designed to detect even extremely weak gravitational waves has been recently proposed, and may soon be built - this is called LIGO, or laser interferometric gravitational wave observatory (I think). If they exist, this experiment should see them within the next few years.

Arthur Smith 

Actually, gravity has not been shown to be an inertial effect. What is usually said is that the effect of gravity cannot be distinguished from the effect of an acceleration from any other source: a force is a force. It is a pretty strong statement, but I do not think it implies all that you are saying it implies. 

mooney 

Question:

Is it not a basic assumption in relativity theory an object is motionless relative to itself? If this is so, should this not also include spin? It seems to me that with only itself as a reference, an object cannot be spinning, but if this were so, then I would not understand how central force could work, or even exist. 

Replies:

Page 40: Newton Ask

Well, relativity and quantum mechanics have not been reconciled ...yet... Actually, though, your statement is not really true. A point object ought to be motionless with respect to itself, yes, but an extended object can be rotating, and there is a real meaning to rotation in our universe. Relativity eliminates the idea of a special frame of reference for translational motion, but there is still a special rotational frame of reference in our universe, and an object that is rotating relative to this frame really does experience the centripetal acceleration and corresponding apparent centrifugal force that tends to pull rotating objects apart. And, I guess, an elementary particle with spin really has some angular momentum. 

Arthur Smith

Question:

I wonder if someone has a new and fresh (and pretty easily understood) explanation for his theory of relativity? 

Replies:

Have a look at the book "Einstein for Beginners" by Joe Schwartz, illustrated by Michael McGuinness, put out by Pantheon Books. The format is certainly unlike any other book on relativity; I thought it was very entertaining. I do not know if the illustrations would make the book less formidable to someone afraid of science, or if today's 7th grader would find it unentertaining. You may well find the book at your local library. 

R.C. Winther  

Question:

Once, when I studied math, I read about the diverse versions of the GUT. One thing that puzzled me was, that the theories seemed to talk about space-time being some kind of 'quantum foam', that as a consequence time would be 'broken up'; a state that should presumably have existed at a very early time, when the energy density was high enough. But how can one talk about time, when time is not well defined. Or did I just not understand it? 

Replies:

Well, I do not think anybody understands it yet - That is why there really is no theory right now. The problem basically is how to quantize gravity. Gravity is associated with

Page 41: Newton Ask

the shape and actual fabric of space- time. From experience with the quantum versions of other forces, it is expected that at low energies, for long times and large distances (the realm of our normal experience) the laws of quantum gravity will reduce to the ordinary laws we know describe the universe pretty well - the "classical" version of gravity due to Einstein. It is also known from previous experience roughly where energies become "low", times become "long" and distances "large" for quantum gravity - these are the so-called Planck scales arrived at by combing Planck's constant h with the gravitational constant G and the speed of light. The energies at which the quantum nature of gravity become important are something like 10^16 times what particle accelerators can achieve, and the length scales and time scales are correspondingly shorter than anything we have investigated up to now. This puts it fairly well beyond experimental investigation for the foreseeable future. But theoretical speculation persists ence the quantum foam and other ideas. Basically we do not have a clue what space-time looks like at extremely short times and lengths, but we are pretty sure it is very strange. However, because regular laws are obeyed for longer times and lengths, the regular definition of time works fine for this. 

A. Smith

Question:

I am going to do a superquest project on least time paths given certain restraints such as the path a race car would take to minimize its time with its acceleration limited so that it does not skid. (or a robotic arm moving some fragile object). 

Replies:

The standard approach to "least time" problems like you mentioned is known as known as "constrained optimization". I do not know a whole lot of good references, but there are a lot of computational books on optimization. This is also known as the "nonlinear programming" problem - sort of a silly convention, but comes from the economics field, I think, where "linear programming" has been dominant for a long time. There are actually a number of packages already out there for doing these problems. You can find reviews of some of them in the literature... I have used the IMSL "nconf" and "n0onf" routines (the first just requires the function and constraints, the second requires derivatives also). See if the machine you are running on has IMSL - or look for other packages out there. I may have something you could use, if you cannot find anything that works. 

Arthur Smith

Question:

Page 42: Newton Ask

If string theories require us to have more than 4D space time, and these other dimensions are "folded" over each other somehow, how can they meet the criterion of being literally perpendicular to all previous dimensions and still be topographically curved? And how does the number of dimensions affect the number of proposed electron types (muon taon etc)? 

Replies:

Imagining strange higher-dimensional objects is one of the big joys and frustrations of many mathematicians and physicists who do this sort of thing. But it is usually a little difficult to put what they have imagined into ordinary language, since these objects usually just cannot exist in our space - and nothing like them really can, at least at the level of our normal perceptions. One of the simplest analogies that does not really work is simply the circle. What mathematicians and physicists discovered is that you can separate out the "closed-in-on-itself" property of the circle from the "curved" property - you kind of imagine a straight line segment with ends labeled A and B, and then declare that "A = B"! Such a circle of course cannot exist in the ordinary space we know, but as a mathematical object there is nothing wrong with it. Anyway, those extra dimensions you talked about all look sort of like this circle - they are straight line segments closed in on themselves without curving at all. You can also imagine a cylinder as an example - the axis of the cylinder is one dimension that extends to infinity both ways, while the circumference of the cylinder is a circle that is perpendicular to this axis. However, That is embedding the 2-dimensional cylinder into 3- dimensional space, and it turns out you do not actually need to even imagine embedding these higher dimensional spaces to work with them, although usually it is possible. 

Arthur Smith

Question:

I have heard of Absolute zero where all motion ceases. Is there a maximum temperature that objects can attain so that molecules reach a velocity approaching the speed of light? 

Replies:

Temperature scales are organized to be proportional to the energy of the matter involved. Since, as particles approach the speed of light, their energy increases without bound, the maximum temperature you are interested in, is in fact infinity. Actually, for an

Page 43: Newton Ask

isolated system of spins, it turns out there are some temperatures higher than infinity. Since what is really important there is particle over the temperature, called beta, that means beta values lower than zero, and therefore negative temperatures. I am not sure that anybody has ever succeeded in preparing a system in a negative-temperature state, but it would not last long.

A. Smith

I would like to expand a little. At absolute zero, all motion does not cease, at least not in a finite system. This is a quantum mechanical effect; closed systems have a zero-point motion, and are always in motion. This is easy to understand; if the system were motionless, you would be able to predict all the atomic positions and momenta simultaneously, which violates the Heisenberg Uncertainty Principle. Thus, the "perfect, motionless crystal" in the Nernst postulate (the "third law" of thermodynamics") does not actually exist; it is a mathematical abstraction used as a reference for entropy. Finally, lasers are an example of a system at infinite temperature; you have a population inversion in a finite-level system. The spin system defined by the spins of Li in LiF(s) will undergo population inversion if you just put the crystal in a magnetic field, then suddenly reverse it. So systems with (infinite temperature" are all around! In fact, I think that NMR spectroscopy works by population inversion, which is the basis of MRI imaging in medicine and chemistry. 

Robert Topper

Question:

Why is it easier to dry dishes washed in warm water then cold water? 

Replies:

I believe it is due to the strong temperature dependence of the evaporation rate. The warmer water molecules are more likely to leave the hotter object for the cooler air. 

Sam Bowen

Well, I guess I usually just let dishes dry in the dish drainer... What happens when you dry them with a cloth is that you soak up almost all the water onto the cloth, but the cloth has trouble picking up that last little bit because you just got the cloth wet drying the dish. So, whether the dish was washed in hot or cold water, if you wipe it once with a cloth, you will have a semi-wet cloth and a still-moist dish. Now, if the water was quite

Page 44: Newton Ask

hot, what you have just done is spread that hot water over quite a large surface area (the cloth, and the small amount remaining on the dish) and it can evaporate pretty fast. Several wipes, and you are done, and the cloth still is not that wet. But cold water is not going to evaporate just like that, and it may not even want to get into the air at all. The other possible explanation, of course, is that cold water sticks to dishes better than hot water. 

Arthur Smith

Question:

I have been wondering why heating elements (in an electric stove, in a toaster, etc.) hum when turned on. I asked our physics teacher here at my school and he was unable to come up with a theory. Do you have any thoughts? 

Replies:

I use a slight variation of this question for our application for employment test for our Engineers! Our question is more like "Why does a Soldering GUN heat up the tip. While the reason for the heat is different, the cause of the sound in a heating element and the source for heat in a U shaped soldering tip is the same. I would assume that the heating elements that the questioner is talking about is of the zig-zag type. The vibration that causes the sound (or buzz) comes from the pulsating eddy currents that "fight" the adjoining wire. Those eddy currents collapse at the rate of 60 hz in single phase applications. If the coil was DC, the reaction of this element would be different and probably silent. In a soldering gun, those eddy currents actually produce enough heat at the 180 turn that the tip heats enough to melt solder. Remember that the tip of a gun is actually a single turn of the secondary of a transformer in the gun. I am quite surprised at how few engineers get this answer on my test. In fact, most say that it is resistive! 

sysop

Question:

How come when I put a pizza in the oven, the aluminum foil does not get hot?

Replies:

It (aluminum foil) DOES get hot. In fact it gets hot much more quickly than the nearby pizza. It also cools off much more quickly, which is why we tend to think of it as not

Page 45: Newton Ask

getting hot. Here is the deal: At any given temperature, aluminum holds much less energy than an equivalent mass of pizza (or an equivalent mass of human flesh--and now we are getting to the point). When you touch the aluminum foil, your hand and the foil share the thermal energy in the foil. Your hand says "big deal! It takes MUCH more energy to raise my temperature because I am made mainly of water" (and water is phenomenal in its ability to hold energy without increasing temperature much). However, it is also true that the aluminum foil is much less massive than your hand, and so part of the answer is that there is just not much foil there. And its also true that the air cools thefoil more quickly than the pizza since the foil has more surface area in addition to holding less energy per degree of temperature. 

mooney

Question:

We were doing a science project on superconductivity and we were wondering what is the highest possible temperature superconductivity has worked at. 

Replies:

Only 6 years ago, the highest known superconductivity temperature was very cold - around 30 degrees above absolute zero (That is Kelvin degrees, and is also around -400 degrees Fahrenheit). Recently discovered materials have brought that temperature up to about 125 degrees above absolute zero, or around -230 degrees Fahrenheit. That is a big improvement, but obviously is still quite cold. It is warm enough, though, that liquid nitrogen can be used to maintain the superconducting state, and liquid nitrogen is pretty cheap, so these materials are definitely a great discovery. 

Arthur Smith

Question:

According the theory of relativity, nothing can surpass the speed of light, even the flow of information. But what of events that necessarily take place instantaneously? Ex: An object moves, and the gravitational force instantly changes proportionately a light-year away. I believe that Einstein resolved this difficulty in terms of gravity's warping space - time, but I still do not understand his explanation. And on a more basic level, if I were to shake a move a one light- year long pole, would not the tip move instantaneously, beating light by roughly 12 months? Or would some sort of spring action occur just to thwart my attempt of disproving relativity? 

Page 46: Newton Ask

Replies:

Actually, it turns out that all forces, including gravity, the electromagnetic and other forces, are what is called "retarded". That means that although they look like they act at a distance, they do not act instantaneously at a distance. In your example, the gravitational field one light-year away would not start changing until exactly one year later. Time- dependent forces are tricky. Concerning a pole that was extremely long - how do you suppose forces move from one end to the other? They actually cannot move any (or at least not much) faster than the speed of sound in the pole. Very rigid poles have very high speeds of sound but far less than the speed of light. 

A. Smith

Question:

What happens during the last 10 seconds before a light bulb burns out? 

Replies:

From my experience, light bulbs generally seem to go out right after you turn the light on - actually within a second, so there is not question of waiting 10 seconds there. Light bulbs contain a narrow wire (the filament) and as this wire heats up, it becomes more resistive. Since current is the ratio of voltage to resistance, more current than normal flows in the light bulb during the first fraction of a second, until the filament has completely heated up. This is the time of greatest stress on the wire, and the power (which is proportional to the square of the current) can be considerably higher than what the bulb uses under normal conditions. Over time (even if the bulb is never turned off) the metal atoms on the filament evaporate and eventually weaken the wire sufficiently that it will break if subjected to stress. If left on long enough, the wire can break even without any stress, but then it does not do anything spectacular, I do not think. Basically what happens is the metal gradually evaporates and at some point the wire breaks, and the bulb is burnt out. If you look inside a burnt out unfrosted bulb you can usually see bits of the filament dangling from the two supports in there.

A. Smith

Generally, I would agree with the previous response, but there is another factor which is significant. As the metal evaporates at a point, or as a flaw develops (we all know bulbs often fail after shocks, especially when the shock happens while the bulb is lit) the resistance at that point will go up. This is because the resistance of a wire is inversely related to its thickness. As the resistance increases, the temperature at that point also

Page 47: Newton Ask

increases due to I^2R heating. As the temperature goes up, the resistance at that point goes up even more (resistance is inversely proportional to temperature). This is a run-away situation. The increasing resistance drives temperature up, the increasing temperature drives resistance up, and so on. Eventually, the filament melts, and the bulb burns out. This whole process, once initiated, takes place very fast - it is very difficult to predict in advance when a bulb will burn out. 

Obiwan

Question:

What energy range are cosmic rays in are cosmic rays in when they hit the earth? Does the rate of cosmic rays hitting the earth change over time , if so how? 

Replies:

As far as I know, cosmic rays come in just about any energy range, up to extremely high energies (higher than anything that can be produced in an accelerator on earth). That is before they hit the atmosphere though. By the time they reach the ground I think most of the high energy ones have scattered to produce secondary "showers". The rate of cosmic ray influx does change with time - specifically with the solar cycle. When the sun is active, cosmic rays are not, and vice versa. 

A. Smith

Actually, when the sun is active, it sends out streams of high energy protons. These cause the Aurora borealis in the northern hemisphere and present a serious radiation hazard to astronauts. 

John Hawley

Question:

Why does sound travel faster in warm air than in cool air? 

Replies:

of 2 The warmer the air is the greater the average mean speed of the molecules of air. Since sound is transferred by collisions of molecules, the quicker they move the sooner the collisions transfer the sound energy down the path. 

Page 48: Newton Ask

gfb 

The traveling of sound depends on the forces between the atoms or molecules of the medium, and in a gas those force only act during the short period when they collide. But in liquids and solids the fundamental question is how fast the atoms jiggle around in their local positions (sound waves are actually coordinated long-wavelength "jiggles") which gets faster the higher the strength of the local forces keeping the atoms roughly in place. So, sound travels fastest in the most strongly bonded materials. 

A. Smith Question:

I just read an American Scientist article by Shapiro & Teukolsky about naked singularities forming from matter shaped as a prolate spheroid. How can a singularity not be cloaked in a black hole? What would a naked singularity look like in space? 

Replies:

Well, a singularity is a very unpleasant thing in physics - basically it means you have a place where things "blow up" - that is, diverge to infinity, and it usually means there is something wrong with the theory. People up till now have not been too upset about singularities in Einstein's theories because they thought they were always cloaked in black holes. Now it turns out they are not. Basically, a black hole is defined by the paths that light takes. Light cannot escape from inside a black hole. Since part of this singularity is outside a black hole, presumably light can escape from it. But, since something in the gravitational fields is diverging at this point, it would definitely be a very unpleasant place to even be near to. Probably would be fascinating to drop stuff into though - you could actually see matter being crushed and torn apart by arbitrarily large forces. 

A. Smith

Question:

I was wondering perhaps if a person was traveling in a starship at the speed of light, and a laser was fired in the direction the ship was traveling, would the laser travel at two times the speed of light? 

Page 49: Newton Ask

Replies:

I think some questions similar to this have already been asked, but first of all, "time distortion theories" are rather important, if you are interested in starships that travel at the speed of light. Unless they obey some laws of physics that humans have not yet discovered, nothing that has any mass can actually travel at the speed of light (it requires infinite energy). The laser would head off ahead of the ship, at the speed of light, exactly. Actually, light can effectively be traveling a little slower than the speed of light, if the medium it is traveling in is not a pure vacuum, and so interesting shock wave effects might happen (just like a supersonic plane's sonic boom) if the spaceship happened to be traveling faster than the speed of light in the medium there. But light cannot travel faster than the speed of light. 

A. Smith

Question:

When looking at a TI graphing calculator with an LCD display while wearing 3D or Polaroid sunglasses, quite interesting colors result depending on the orientation of the filters in the glasses. Why does this occur? 

Replies:

The colors result from a correlation between the wavelength of light that makes it through the LCD and the polarization of that light. I do not know the details of an LCD, but I can describe a similar, and simpler, effect that you might be interested in. Take two Polaroid filters (Polaroid sunglasses are fine) and place a crinkled up piece of cellophane between them. You will see beautiful colors that vary with the orientation of the filters and with the thickness (number of layers) of cellophane between them. This effect is easier to discuss because we are in complete control of the polarization of incoming light. We start with a definite polarization of the light that makes it through the first Polaroid--the polarization is independent of wavelength. Then, the cellophane *rotates* the plane of polarization of light passing through it; the amount by which the polarization is rotated depends on the wavelength. These two things happen because the index of refraction of cellophane depends both on the wavelength and on the polarization of the light passing through it. The second Polaroid accepts only light with a particular polarization, so, if "yellow" got its polarization rotated by the right amount to make it through both Polaroids, "blue" will probably not have. If you want to know more, you might look for information on the term "birefringence". Although I know little about LCD's, I strongly suspect a very similar thing is going on there. 

Page 50: Newton Ask

Mooney

Question:

Mirrors reflect light. Do they also reflect sound? 

Replies:

Any acoustically smooth hard surface will reflect sound, so a glass mirror is a pretty good sound reflector but aluminized mylar is not. What constitutes an acoustically smooth and hard surface changes with the frequency of the sound. 

John Hawley

Question:

Visible light is more energetic than electromagnetic radiation in the radio part of the spectrum (say, 1 MgH). Therefore, visible light should be able to penetrate to where radio waves cannot. And yet, the reverse seems to be the case - I can keep out light with plastic or wood, even though less energetic radio waves have not problem penetrating these materials. Why is that? 

Replies:

The interaction of EM radiation with matter is really a complex process. There is an oscillating electric field associated with an EM wave; the electrons (and to some extent the protons) in the material on which the radiation falls move in response to that electric field. An electron bound to an atom, or atoms bound together in a molecule, act a bit like a mass attached to a spring. If you wiggle the "free" end of the spring periodically, the mass will oscillate. If the wiggle rate is near the "natural" frequency of the spring, the mass will strongly respond (this is called resonance); however, if the wiggle rate is much less or much more than the "natural" frequency, the mass will not respond much. Depending on the nature of the electronic or interatomic bonds, a given frequency of radiation may be transmitted, absorbed, or reflected. So radio waves penetrate most substances because their frequency is too low to excite the electrons or atoms. Metals reflect them because their outer electrons are

Page 51: Newton Ask

virtually free to move around, so they respond almost instantly and reflect the wave. There is a limit to this; for high enough frequency, these "free" electrons cannot keep up with the electric field: most metals transmit ultraviolet light. And in general, for high enough frequency, the electrons and atoms of most materials respond weakly. Since a photon's energy is proportional to its frequency, it is true that high-energy stuff penetrates matter more readily, but it is because of its being high-frequency, not because of the energy. 

R.C. Winther

Question:

At what wavelength does visible light start? 

Replies:

I looked in some of my physics texts, and there are disagreements on exactly what is meant by "visible light". One book speaks of a "standard observer"; another intentionally avoids description in terms of response of the human eye. Both agree pretty much on the frequencies, however: from about 3.84 x 10^14 Hertz to 7.69 x 10^14 Hertz. This corresponds to a wavelength range from about 3900 Angstroms to about 7800 Angstroms. The lower frequency (and larger wavelength) corresponds to the lower limit of red light, and the higher frequency (and smaller wavelength) corresponds to the upper limit of violet light. I would not be surprised if there is an "official" international scientific definition of the various regions (microwave, infrared, visible, etc.) of the electromagnetic spectrum, though I have not as yet found mention of such; however, the divisions are, in any case, somewhat arbitrary.

R.C. Winthe

Question:

Has the speed of light slowed down over the centuries? 

Page 52: Newton Ask

Replies:

Earthbound measurements of the speed of light show no tendency of this quantity to change over time. But reliable measurements have been made for less than two centuries; perhaps this is too short a time span over which to detect a change. However, looking out at various objects in the universe, we can observe light from many past times, even billions of years ago. This has in fact been done. According to the theory, light from remote objects such as quasars, some of which recede from Earth at a speed nearly equal to the speed of light, will travel at the same speed as light from other sources. The "nearly constant" is a bit of hedging. It is risky to make absolute statements based on measurement; there is always some uncertainty in a measurement. 

R.C. Winthe

Question:

How is it that light from a laser can travel in a small glass fiber for many miles without regeneration of the original signal? 

Replies:

Light may be conveyed down a length of a glass fiber via a process called total internal reflection. Suppose a beam of light is traveling in material A and strikes an interface between this material and another material B, where these two materials have different indices of refraction. Imagine a line at right angles to the interface passing through the point where the beam hits. The angle between this line and the beam is called the angle of incidence.If this angle is 0 degrees, all of the beam is transmitted & none is reflected. Now suppose the light source is moved so that the beam strikes more and more obliquely, then the amount of beam transmitted decreases, and more and more of it is reflected. If B's index of refraction is smaller than A's, we will eventually reach an angle of incidence called the critical angle at which all of the beam is reflected and none transmitted. This is total internal reflection. If the angle of incidence is further increased, the total reflection persists. This is what happens inside the glass fiber. The beam enters traveling approximately

Page 53: Newton Ask

straight down the fiber. If there is a not-too-abrupt bend in the fiber, the beam will hit the fiber's inside wall (a glass-air interface) at a large angle of incidence and be totally reflected. This may occur thousands of times per meter of fiber. And this can be done with ordinary light as well as with laser light. Laser light works better because all parts of its beam start out traveling in essentially the same direction. Even if it is collimated, a "beam" of ordinary light will enter the fiber with some range of directions; some of the beam will not totally reflect, so some light is transmitted through the walls and is lost. 

R.C. Winther

Question:

The message sending device that Voyager 2 used to send pictures of Uranus was using 2 watts of power. Why was the power delivered to the Earth less than a trillionth of this? Was not the transmitter directed toward the Earth? Does not the signal dissipation follow the inverse square law? Why do so many science articles use watts as units of energy instead of power? Why do not they use joules? For example, Uranus receives 1/400th the solar light and heat that the Earth gets. Uranus is 20 A.U. from the sun while Earth is 1 A.U. 1/400 = 1/20(squared): So the above makes sense according to the inverse square law. Then why does not the same reasoning apply to energy coming from Uranus to Earth? Why is not the radiation decreased by (1/19)squared? Why is it really decreased by a trillionth instead? 

Replies:

Your understanding of the physics is excellent. Most writers do not understand the difference between energy and power. Much of what is written is thus not accurate. The inverse square law is accurate and correctly applied here. Your arguments are OK for comparing the amount of energy from the sun as a relative ratio. Here we want to know the power we would see over a certain area at a distance of R from the source. So our formula would be that the intensity over one square meter would be 4 * pi * (2 watts)/(R*R) where R is the distance in meters. The distance by my rough estimate should be 2.8 x 10^12. If the antenna has been isotropic the power should have been down by a factor of 10 to the negative 24 , 10 ^(-24) instead of only a trillion. If they are accurate in the report, it means that the directionality of the antenna was pretty great. Your understanding of the principles is great. I am now surprised

Page 54: Newton Ask

that the signal is so large when it gets back.

Sam Bowen

The first thing to realize about physics is that it does not just consist of mathematical formulas, but every formula has (or should have) an understandable meaning or implication. You were quite right to think of the inverse square law here, but because you apparently did not really understand what that law means, you applied it incorrectly. I hope the following discussion will make things clearer! First off, what could an inverse square law mean? Let us try and think of something that grows as the second power of distance. The first thing that should come to mind is area, since an area is always given by a product of two distances. So, does the inverse square law have anything to do with inverse areas? Imagine a point source of light. After the light is turned on, it spreads out in all directions at the speed of light and we can imagine traveling with the light as it goes on its way. At greater and greater distances from the light source, the same amount of light is spread out over a bigger and bigger area. Ah-Hah! So, how does that area change with distance? As the square of the distance of course! (The area of a sphere of radius r is 4 pi r^2.) So, if we detect light with our eyes, or with our fixed antenna, or whatever, the area of detection is the same for every distance from the source, and therefore we see a smaller and smaller portion of the light as we go further and further away. What is that small fraction? It is the ratio of the area of our detector (some fixed number) to the total area that the light is spread over, i.e. the fraction is some constant divided by the area of the big sphere the light is now spread over, so that it decreases as 1/r^2 as the distance r gets bigger and bigger. That the meaning of the inverse square law. Now actually, it does not matter that the source is radiating equally in all directions, because from far enough away, light from any kind of source (even a laser) has to spread apart over some possibly tiny portion of the sphere of radius r. A laser will have light spread over a very tiny portion of the sphere, but nevertheless, it will (from far enough away) also obey this inverse square law. So, to go back to your specific question - with the light from the sun, the earth is at 1/20 the distance of Uranus from the source (the sun), and therefore the area of the sphere the light from the sun is spread over is 400 times as big when you are out as far as Uranus, and therefore the light

Page 55: Newton Ask

intensity is only 1/400 as great. Fine. Now let us turn to the Voyager space craft, sending 2 Watts of radio waves to the earth. You asked, why does not the earth receive 1/400 of 2 Watts? Well, where would this 1/400 come from? Remember, the 1/400 for the light from the sun came from the ratio of two areas - the sphere at the earth's distance from the sun, and the sphere at Uranus' distance from the sun. What are the two areas we are taking a ratio of for Voyager? Well, we a not interested in the light intensity (power per unit area) this time, but in the total received power. So, let us say we have some specific radio detector in mind on the earth - say the Arecibo one, which is about 1 mile across. The area of our detector is thus about 1 square mile. What is the other area we need to divide into this 1 square mile? It is the total area that Voyager's 2 Watts must be spread over by the time it reaches the earth. The distance to Voyager is about 20 Astronomical units or about 2 Billion miles. (1 AU is 93 million miles, if I recall correctly.) So the area of a sphere at that distance is somewhere around 10 Billion square miles. Now, Voyager's antenna does have some directionality, so the radio waves spread out over only a small fraction of that total sphere. Even if that fraction was only 1 millionth, however, the area we are talking about is still 10 thousand billion, or ten trillion square miles, so the power being received by our mile-wide receiver is going to be perhaps 2 tenths of a trillionth of a Watt. 

Arthur Smith

Question:

According to Steven Hawking from "A Brief History...," when two black holes merge, they form one black hole greater than or equal to the sum of the original masses, or simply the equation: M(f) = M(1) + M(2). The generally accepted theory is that nothing can escape from a black hole, not even light. Yet recently I read somewhere that when matter and anti-matter collide in a black hole near the event horizon, the result would be a burst of energy, which may propel something out of the black hole. I theorize this: If you have two black holes, and one has anti-matter of the other, and the two merge, there would be two things: 1) It would result in annihilation of both matter and anti-matter particles, and this would result in the masses being LESS THAN the sum of the two original masses. 2) It may possibly propel something out of the black hole. I conferred with my Physics teacher and he came up with this. If the two black holes merged, one was the anti-matter of the other, the energy

Page 56: Newton Ask

would probably not be enough to propel anything out, BUT might break down the local gravitational field, allowing something to escape beyond the event horizon. Does anyone have anything that they might add to this theory that might help backup or disprove it? 

Replies:

Great question! If one was anti-matter and the other was matter, then when they collided they would create annihilation radiation which would convert mass into photons. My understanding is that mass is the source of the distortion of space-time that we call gravity. I do not think that EM radiation can be the source of gravitation which would mean that as the matter and anti-matter annihilated the mass of the black hole would decrease. This would make the event horizon of the object decrease. At some point matter or light might be able to "break down " the black hole. This would be interesting. I would guess that if the amount of matter decreased so much (complete annihilation) the black holes would disappear and then the light could escape.

Sam Bowen

Actually, matter and antimatter really have no meaning inside a black hole. I think, as far as is known, that the conservation laws that prevent matter from being converted into antimatter break down inside of a black hole. I could be wrong on this. Anyway, it does not matter what form the matter is in, it still has the same gravitational effect (even as light), and therefore should remain trapped. Remember that mass and energy are really the same thing, as far as gravity is concerned, and so even when an explosion occurs, there is no change in the total amount of energy (or mass) that is there -a matter-antimatter explosion converts some mass into a whole lot of energy, but the black hole really does not care. By the way, the Hawking radiation that has been discussed involves a very subtle effect - the creation of virtual pairs of particles - one matter, and the other antimatter, just outside the black hole. Virtual pairs normally cannot exist for very long before they must annihilate, since they violate the law of energy conservation. However, if the two particles were energetic enough that one fell into the black hole while the other flew away, the only way energy could end up being conserved is if the black hole

Page 57: Newton Ask

itself lost some energy (or mass) in the process. Actually, a very similar thing has been observed to happen with super heavy nuclei - the nucleus is so highly charged that it must always have at least one electron nearby. If this heavy nucleus is created without such an electron, it spontaneously creates an electron-positron pair, with the positron flying off and the electron staying behind, trapped. 

Arthur Smith

Question:

I read somewhere that the photon has three spin states, but since it travels at the speed of light the t, the transverse state does not exist. Why is this? 

Replies:

A partial response...The photon only has the transverse polarization of the electric and magnetic fields. If these are what are called circularly polarized (the electric vector spins either clockwise or counter-clockwise around the direction of travel) then the "spin" is along the direction of travel. In this sense the transverse spin state of the photon does not exist. 

Sam Bowen

Question:

What happens to light (photons) when it enters a black hole? Is light (photons) consumed? 

Replies:

Nobody really knows what happens to it, but it never comes back out, and the black hole's mass increases by E/(c^2), where E is the energy of the photon. 

mooney

Question:

Page 58: Newton Ask

What keeps light from going any faster? 

Replies:

Well, as best as I can explain it, the speed of light is a fundamental physical limitation, which no particle can exceed. It is kind of built into the structure of space and time in our universe. Any particle with no mass, by the way, will always move at the speed of light, so it is not just light that does it. Actually, in physical materials, light actually moves a little slower than the "speed of light". This is measured by the index of refraction of the material, and the reason is because light interacts with the electrons and other charged particles in the materials, which has the overall effect of slowing it down (as well as reflecting, and sometimes absorbing, the light). 

Arthur Smith

Question:

Why does violet refract more through a prism than red when its frequency is higher and hence it may have more penetrating ability (i.e. UV vs. X-ray?). 

Replies:

If I recall correctly, light refraction and absorption are connected, in that if you have a frequency of light that is strongly absorbed, then the amount of refraction is strongest on either side of that absorption frequency, and gets weaker as you go further away. I think that in a prism, for example, the absorption frequencies are at quite high energies (where the electrons start to get excited), maybe in the high UV. The glass is transparent because it has a "band gap" of maybe 1 electron- volt, and so that would be where the first absorption occurs. Anyway, that means that, at frequencies well below this absorption frequency, such as at visible light frequencies, the refraction increases with increasing frequency. At very high frequencies (such as X-rays) the refraction decreases again, because you are on the other side of the absorption peak. Right in the absorption region, of course, light is not refracted, but is absorbed by the material, and it becomes opaque. 

Page 59: Newton Ask

Arthur Smith

That does sound reasonable. Perhaps we can sum it up by saying that the refractive index of the prism has a strong wavelength dependence, which just happens to be in the visible part of the spectrum (for the reasons you have stated)? Snell's law says that light will bend as it enters the prism and as it exits on the opposite face, and that the angle of each "bend" is given by n1 sin(theta1) = n2 sin(theta2). Here n_1,n_2 are (respectively) the index of the air and the glass when considering the first reflection, and the index of the glass and the air on the second reflection. BUT..this equation is only valid for a single wavelength of light. If the refractive index of the glass has a strong wavelength dependence, then the exit angles will be different for each wavelength. (Assuming that the refractive index of air does not depend much on the wavelength). Now, the student could actually figure out what the wavelength dependence was by measuring the entrance and exit angles of the various wavelengths and using Snell's law...a fun experiment. Just a little expansion on Arthur Smith's (correct) answer. 

Robert Topper

Question:

What is resonant frequency? Does every material have a resonant frequency? What are the implications of a resonant frequency? 

Replies:

Resonant frequency is observed in a wide variety of systems, from simple mechanical systems to complex electronics circuits. But the resonant frequency is a property of the SYSTEM, not any material in it. Take a simple resonant mechanical system: a pendulum. Its resonant frequency does not depend on the materials it is made of, or even on the mass of the pendulum weight. It depends only on the length of the pendulum, and on the local acceleration of gravity. Another simple system, a mass hanging from a spring, also has a resonant frequency. Here the frequency depends on the mass and

Page 60: Newton Ask

the spring, but not on the materials involved. As these examples show, a resonant system generally involves a mass that can be displaced and a restoring force that is proportional to the displacement. In electrical or acoustical systems, there are similar concepts involving some sort of mass or inertia and some sort of restoring force. Every musical instrument, including your voice, depends on resonant frequencies. 

proach

Question:

This question has to do with the speed of light. If you are traveling at the speed of light and then turn on a light will you see that light? 

Replies:

Einstein's special relativity asserts that the laws of physics do not change no matter how fast you are going relative to somebody else - you will see the same things in objects you manipulate at your speed as the other person sees at their speed. So, turning on a light in a speeding spaceship looks just like turning on a light in your living room. Actually, no object with non zero rest mass can travel at exactly the speed of light - only the special massless particles can do it, such as the photon, the particle of light itself. So your experiment is not actually possible. 

A. Smith

Question:

Please send any information about neon and other lighting systems. 

Replies:

Light is emitted either by atoms emitting energy as the atom changes energy states or by random thermal motions. Neon or light emitted from chambers of gas that are excited by currents (fluorescent lights also) give off light at

Page 61: Newton Ask

specific frequencies, while incandescent lamps give off a broad spectrum of light that is determined by the temperature of the material itself. More details can be found in various encyclopedias, especially the Encyclopedia of Chemical Technology. 

Sam Bowen

Question:

Why is an echo weaker than the original sound? 

Replies:

An echo is a signal that has been propagated through the air from some object whose surface created a reflection of the signal. Whenever a signal propagates in space, it spreads out with some of the signal going off in different directions away from the original direction. The signal left on the original beam is less than the whole beam that started so the energy in the received beam is always less. For a point source the energy per unit area drops off as the inverse square of the distance. 

Sam Bowen

Question:

Could you explain how information -- like my "hello" when I answer the phone -- is carried over a phone line? 

Replies:

There are two distinct ways at present. Both of them rely on the ability of an electrical signal to be generated at your phoneand be sent over the wires to the receiving set. The actual signal is a series of time varying pulses or oscillations of voltage over the wires. The two ways your signal is coded represent the two ways that signals are sent over the lines. The old and still used way if for the strength of the signal in response to your words to be

Page 62: Newton Ask

directly sent over the line. This is called analog and is essentially the same thing that happens with AM radio. The second method is for a computer to convert your message into digital signals, essentially short pulses at different frequencies , to code your message so that it is converted at the other end by another computer. Some of this is done for long distance calls. 

Sam Bowen

Question:

How does a voice travel over a wire? How can a picture or picture with sound do the same? How does ISDN allow multiple independent transmissions to occur at high speed over normal copper wires? 

Replies:

Basically, a phone is analog (from your house to the local switching station). Analog means that the air patterns (pulses of air) from your mouth are transformed to analog signal. The analog signal is a electric 'wave' that represent the sound in electric form. Actually, this electric form is a varying voltage that can duplicate your voice by moving a diaphragm connected to magnet in the receiver on the other end. It can be thought of as when you talk you move a magnet in a coil which produces a signal. This signal cause a similar action on a coil in the receiver on the other end. Now let us cover ISDN next: I said your current phone is analog to the local switching station (in many cases anyway). From the switching station, to other switching stations, is digital. This means that analog (wave pattern) is translated to digital and transmitted. Well, the digital signal is much more efficient. WHY? Well, the digital signal is translated and packaged in a "Packet". This packet has a header that has an address. This address is then pushed out on a high speed network (like an expressway). The expressway is full of many signals. All actually going lets say single file, but since each signal is en capsuled in its own packet or envelope, special devices can grab the packets and route them to the correct destination (like exit ramps). So, in essence, you call can share the same road as many other calls. When you talk, your words are packaged and sent out on this busy network. ISDN means that the whole process is

Page 63: Newton Ask

digital. Your "voice" never gets transmitted in analog. So, to send a video or voice signal, all that is needed is to convert them to digital. Then package them and send them along. On the other end they are unpackaged, converted back (in some cases like CD or other digital technology this is not needed), and displayed or played. 

The key to the process is bandwidth. In other words, how much data can flow at one time. You need very high speed data paths to allow the rate of video to travel across this network. Fiber optics have a much greater potential of carrying large amounts of data than do copper cables. Soon (some are experimenting with it today) it will be possible to transmit voice, data (computer stuff), and video all over a single connection at your house. That is when ISDN comes to the house. 

sysop

Question:

When walking across wet sand it will sometimes squeak. Why? 

Replies:

This case might be similar to chalk squeaking on a blackboard. In that case, the chalk is vibrating against the blackboard. In any case, something must be vibrating in order to create sound. Since there are only the sand and your feet involved here, the sand would have to be the object vibrating.

John Hawley

I did not have access to some wet sand to walk on, so instead I got a bowl of sand from the parking lot to experiment with. And the sound of "walking" one's fingers on dry sand is qualitatively very different from that using wet sand. The dry sand produces a kind of a dull, crunchy sound; the wet sand makes a crisper, louder) sound. One is tempted to guess that the spectrum of the wet sand sound has more high frequency component than that of the dry sand sound. The behavior of the sand in the two cases is also distinctly different:

Page 64: Newton Ask

dry sand moves laterally "out of the way" much more readily than the wet. Water and sand have a great affinity for each other; it is amazing how well wet sand "sticks together". I speculate that the water holds the sand grains so tightly together that, under shear (from being stepped on) they rub hard enough against each other to produce more high frequency sound, resulting in the squeak. Or perhaps dry sand also squeaks, but the air in between the grains dampens the sound, whereas water transmits it. It is also clear that the effect depends on the fineness of the sand; this will not happen with, say, wet gravel, and I doubt it would happen with wet powdered sand. 

R.C. Winther

Question:

What vibrates to cause sound in a flute? Is there a solid portion that vibrates or is it just the air? 

Replies:

There is no solid vibrating material in a flute. Thesound from a flute comes from compressive waves (as opposed to transverse waves) in the flute, the wavelength of which corresponds to the positions of the holes. Basically, at the holes, the wave must have a node. The simplest case of no holes is the classic bottle sound, when one blows over the opening of a bottle. In that case, the wavelength depends on the size of the chamber alone. 

obiwan

Question:

They call it a stereoscope. What is it? How does itwork? 

Replies:

Yeah, I just discovered one of those the other day. At least, I think it is the same thing you are talking about. Normally, to see a 3-D image, your two

Page 65: Newton Ask

eyes have to see slightly different versions of the same thing, and then your brain does some complicated mathematics to convert the two images into a 3-D representation. Stereo images have been around for quite a while, but up until very recently always came in pairs - one for the left eye, the other for the right - that are best viewed through a special stereo viewer that presents each image to the eye it was intended for. Recently, somebody seems to have figured out that by printing an image (of a dinosaur or space shuttle) using special patterns, you could combine those two images into one. The result looks like a big mess of these little patterns, until your left eye notices the dark/light contours that it was intended to see, and the right eye notices the contours it was supposed to see, and suddenly the brain transforms that mess of little patterns into a 3-D image of a big structure. It is really pretty neat. 

Arthur Smith

Question:

Can someone explain to me the concept of light cones? What are these cones actually "used for? 

Replies:

Nothing very practical! The light cone is just one of many tools used by physicists as a way of seeing how certain things have to be true, or how certain things might work. First of all, a light cone is 4-dimensional, so visualizing the cone itself is a little tricky. Think of a 3-dimensional cone first though. If you place the mouth of the cone down on the floor, with the point of the cone on top some of the properties of the cone should be clear. For example, the cone touches the floor in a circle, and any horizontal slice through the cone makes a circle, up to the top where there is just a single point. Similarly, a light cone starts at a point (say a place in space and time where a flash of light was emitted) and then at any later time the surface of the cone forms a sphere (the sphere in space where the light has reached by that particular time). If we take a vertical slice through our cone on the floor - say by just looking at its profile from some horizontal distance away, then we notice that the sides are straight lines coming from the point. Similarly, the

Page 66: Newton Ask

edges of the light cone are formed by individual rays of light leaving the central flash - each ray moves out at a constant speed (the speed of light) and that means that the relation between position and time is linear - the edges are "straight" in space-time. Also, the slope of our 3-dimensional cone can be anything - it can be wide and short, or tall and slender. However, the slope of the light-cone is fixed - it is simply the speed of light! (Remember speed is a ratio of distance over time, and slope is a ratio of one axis over the other). Ok, so it really is like a cone, except in four dimensions, and the slope can only have one value. What does it mean? Well, if nothing can travel faster than the speed of light, that means that somebody watching at a particular point in space can not know anything about this light flash actually having occurred until that time when the sphere of light has expanded to include where the observer is waiting. At earlier times, those points in space-time were OUTSIDE the light cone, and could have had no communication from the light flash. At later times, the corresponding sequence of points in space-time is INSIDE the light cone, and there has been communication from the light flash. In essence, the light-cone is a surface that divides space-- time into two pieces - one piece that can never have yet known about the flash, and a second piece that can know. If the light flash is supposed to set in motion some other events elsewhere in space (to "cause" things to happen) then those other events can only be INSIDE the light cone. The light flash cannot cause anything to happen OUTSIDE. This is pretty fundamental stuff. The light cone is also often extended back in time, because there is an exact reversal there - going backwards the things OUTSIDE cannot have caused the light flash, whereas the things INSIDE could have. Of course, this does not have anything to do with a spherical shell of light expanding backwards in time! It is just another way of dividing space-time into 2 fundamentally distinct regions, from the point of view of the light-flash. In fact, allowing things to be moving at any speed relative to one another (as is usually supposed in discussions of relativity) we cannot say whether the light flash happened first, or one of the OUTSIDE events happened first - in some frames of references any event in the OUTSIDE happens at exactly the same moment as the light flash. But all the events in the INSIDE of the original light cone (going forward in time) must happen after the light flash, and all the events in the INSIDE of the backwards light cone must have happened before the light flash, so there IS a meaning to sequence in time for those events. 

Page 67: Newton Ask

Arthur Smith

Question:

How do holograms work? 

Replies:

Most of the time we can ignore the wave nature of light, since it basically travels in straight lines and obeys simple laws when passing through lenses or with mirrors. However, when light is specially prepared (as in a laser) the wave nature can be readily seen - for example, laser light passed through a pair of slits will produce an "interference" pattern of alternating dark and light areas as long as the slits are close enough together, and this is very different from the straight line images you might expect. A hologram is made by "interfering" in this sort of fashion, laser light that has been reflected from a 3-dimensional object with light directly from the laser, or reflected from a flat mirror. Because of the different distances traveled by the light striking different parts of the object, the light waves arrive at different parts of their cycle and combine or cancel out. This produces a very complicated image, which can be recorded on film as a hologram, and played back to produce something resembling the original 3-dimensional image (played back by shining laser light through it in the other direction). The details are pretty complicated, and I have always been amazed that it actually works. People can now produce these interference patterns on the computer, and generate a hologram that can be used to produce three-- dimensional images that were designed on the computer. 

Arthur Smith

Question:

My friend stated that the first and second laws of thermodynamics contradict the theory of evolution. Also what are stated in the first and second laws of thermodynamics? 

Page 68: Newton Ask

Replies:

Your friend is wrong, but he /she is in good company. A lot of people misunderstand thermodynamics and think that they contradict the theory of evolution. Here are some basic definitions: The First Law: Heat put into a system + work done on a system = increase in internal energy of the system, or dQ + dW = dU. This is just conservation of energy; if you take a system and heat it, and do work on it, you will increase its internal energy. The Second Law: If a system is changed by doing work on it or by heating/cooling it, the entropy will either increase or stay the same. Notice that in the above definitions, I have not yet said what a "system" is. The main thing to remember is that although the total entropy of a system must increase or stay the same, local fluctuations can be positive or negative. For example, by cooling water, we can make ice. Water, a liquid, has a higher entropy than ice, a solid. So by freezing water we DECREASE the water's entropy. Therefore, it is possible to raise or lower the entropy of a system, as long as it is an OPEN system (one that can exchange energy with its surroundings). The earth is an open system, and so is a biological system (like a frog or an ape). So evolution does NOT violate thermodynamics. 

Robert Toppe

Question:

Why is the sky blue? Why is glacial ice blue? What common properties cause them both to appear blue? 

Replies:

In this case the reflected color is a measure of the size of the centers that are scattering the light. The fact that a sunset is red and the sky is blue indicates that the scattering centers for light are not big enough to scatter red light, but are big enough to scatter blue light or shorter wavelength light. Usually dust is regarded as a contributor, but molecular sizes are also involved. I believe.

Page 69: Newton Ask

Sam Bowen

Air molecules scatter (reflect) the shorter wavelengths (violet, blue, and green) more effectively than the other colors. As you look at the sky the violet, blue, and green strike your eyes from all directions, combining to make blue. Pure ice crystals also scatter light so as to give a blue color, the purer the ice the bluer the color. Glacier ice is purer than other ices. A sunset is red because the light is going through so much air that the short wavelengths are scattered away and only the longer wavelengths are bent into your eyes. Dust particles scatter all wavelengths about the same so a really dusty sky looks white. 

Mark Fernau 

The reasons for why the sky is blue and why glacial ice is blue are different. The sky is blue because the air molecules scatter the short (violet/blue) wavelength part of the visible spectrum more strongly that the long wavelength (red) part. For an excellent discussion, see "Colors of the Sky," C. F. Bohren and A. B. Fraser, The Physics Teacher, May 1985, pp. 267-272.

Question:

Is it meaningful to claim that physical constants can vary and that their values are remarkably coincidental? It seems that since they have never been shown to vary, that one can not claim that their current values are unusual. 

Replies:

The changes considered in the constants are over long time scales. I am not sure that these considerations have yielded explanations of effects in a compelling way. 

Sam Bowen

Question:

Page 70: Newton Ask

Does humidity affect the distance a baseball can travel ? 

Replies:

I quote from a recent letter in Science News from Michael K. McBeath at Kent State: "...The magnitude of trajectory curvaturecaused by Bernoulli's principle, the Magnus effect, and drag crisis is a function of ball size, mass, roughness, spin rate, and velocity as well as air temperature and density..." He did not mention humidity specifically, but I am sure That is a factor, too. 

John Hawley

Question:

Is it true that water in the southern hemisphere swirls the other way? Why? 

Replies:

Martin Gardner, in "The Ambidextrous Universe," a book I recommend to anybody, mentions some enterprising people in Kenya, which lies right on the equator. There was a line in the village where the equator was, and a few of these guys had some frying pans with a little hole in the middle. They would put water in and a twig on the water to make it easier to see, and, sure enough, on the north side of the line the water swirled out of the pan one way, and on the south side it went the other way! They apparently were quite good at this, and made quite a bit of money... Basically, nobody has ever (properly) demonstrated this effect with water in ANY size bathtub. The Coriolis effect is simply too weak to have any effect on an ordinary quantity of water. It does have a strong effect on the circulation of air in the atmosphere, however, and hurricanes in the southern hemisphere do indeed swirl in the other direction. An easy way to imagine the Coriolis effect is to think of the effect it has on missiles launched on a North-South trajectory. If the missile is launched north from the equator, it has a certain East-West speed as well due to the rotation of the earth. At higher latitudes, the rotational speed is lower because the distance to the rotational axis is lower (at the poles the rotational speed is

Page 71: Newton Ask

zero), but the missile retains its initial speed in that direction, and thus appears to be bending out of its initial north-south direction relative to the ground. If launched south, the "handedness" of the bending is reversed. There has been concern expressed that the waste heat from large- scale fusion reactors could be significant. If current concerns about global warming are valid, we should give careful consideration to the potential effects of additional heating of the atmosphere. 

A. Smith

Question:

A 9-year old boy would like to know whether earthquakes can be predicted. 

Replies:

We are working on it: there are several approaches: big earthquakes are usually preceded by precursors, small earthquakes that occur in the same place right before the big one. The Japanese who are VERY concerned about earthquakes think they can predict earthquakes by measuring electricity in the ground. There have been reports that some animals can sense when an earthquake is about to happen. 

John Hawley

Question:

Why is it that some objects are easier to charge with static electricity than others? 

Replies:

Basically, friction is caused by electrical forces, and so when ever you have friction between two different materials there is some chance of charge being transferred. The materials that are easier to get a charge from (or to charge), I think, are those which have very long needle-like shapes on their surfaces.

Page 72: Newton Ask

Whenever you have electric fields around, they get extremely concentrated near needle-like shapes, and so more charge is going to get transferred. What I mean by needle-like shapes is things like fur, or carpets, or blankets (usually older ones work better), where little hairs poke out of the surface. 

A. Smith

Question:

What is the physics of static electricity buildup on clothes in a dryer? How does a liquid fabric softener in the rinse cycle prevent subsequent static in the dryer? 

Replies:

The static develops in the last part of the cycle, when the clothes are dry; the presence of water or water vapor inhibits its buildup Some materials are charge donors (they fairly readily give up electrons) and others are charge acceptors. Many synthetic materials are one or the other. 

Sweaters and socks often seem to make a dandy donor-receptor pair. Fabric softeners are waxy materials distantly related to soap. Fabric softeners work by coating your laundry with lubricant and humectant chemicals. The lubricants let the fibers slide past each other, reducing wrinkling. The humectants help the fabric retain moisture to dissipate the static charges. 

R.C. Winther

Question:

How do you explain picking up a penny with Aluminum Foil? 

I was shown a demonstration the other day that mystified me. A man could pick up small pieces of aluminum foil with a penny by just touching the two together. There was no adhesive on either surface. What was the force that was lifting the foil? I cannot find any reference to similar experiments anywhere. Any ideas? 

Page 73: Newton Ask

Replies:

This is an educated guess: Aluminum and copper have different numbers of electrons and have the highest filled energy level at different energies. This means that if you put the two metals together the electrons will move from one to the other because electrons can lower their energy by filling lower energy levels. This does not continue forever since the electrons leave positive charges on the metal they have left. When the metal is charged up enough the electrons stop moving and then we have two materials with opposite charges and these charges will attract, hence the force of attraction. 

Sam Bowen 

Question:

Can a spark travel across a vacuum? What happens to the air between two charged objects to allow a spark to jump between them? 

Replies:

In the air between two highly charged objects there is a large electric field. If there happens to be a free electron in that space it will be accelerated to high speeds by the electric field. While it is being accelerated it will collide with the gas atoms and be slowed down. When the field gets so strong that it gains enough energy between collisions so that it can ionize (excite another electron from the colliding atom) the atom it hits, the number of electrons in the air can increase very quickly (called an electron avalanche) This large number of electrons increases quickly as each electron frees a new electron and the whole group makes up the spark. The spark can move in a vacuum, but the creation of the spark requires the gas atoms to be present as source of new electrons and the avalanche. The breakdown field depends on the density and how tightly held are the atomic electrons. 

Sam Bowen

Up-date 1/25/2005

Page 74: Newton Ask

The previous answer describes a spark that occurs in air or another medium, and describes it well. 

The question is actually fairly tricky because the word "spark" is not well defined. Usually by "spark" we mean a momentary flow of electricity through a medium that does not usually conduct electricity. We have sparks through air, but not through metal. When we think of the word "spark" we think of a bright flash. The word "arc" usually connotes a continuous flow of electricity. Like an arc welder. 

A good vacuum is a very good insulator. Much better than air because there are no molecules to ionize and participate in an avalanche. However, researchers who work with high-vacuum, high-voltage equipment know that little "sparks" occur in vacuum with a few thousand volts or more. We do not know why it happens, but we think it has something to do with dirt or dust on charged surfaces. The strange thing is that these sparks are little points of light that do not apparently jump between anything, like a normal spark. 

It is possible to have a stream of electrons travel in a vacuum. To do this the emitter must be sharply pointed and the applied voltage must be large. Electrons come off the sharply pointed emitter. This is the basis of the field-emission electron microscope. But these electrons do not make light, so they are not a "spark" or "arc" as commonly used. So, no, it does not seem possible to have a 'spark' in the conventional sense in a good vacuum. 

There is something called a "triggered vacuum spark-gap switch." It at first seems like a switch based on a spark through a vacuum, but the current is really conducted by a tiny burst of evaporated metal atoms, which carry the current like air ions do. 

Bob Erck 

Question:

Page 75: Newton Ask

Why can a moving charge produce a magnetic field? 

Replies:

This is a really great question! It is hard to answer. The question is really what kind of field area is created in the space around a charged particle. When a charged particle is not moving the electric field lines emanate from the charge outward in all directions and until we move the charge we might think this is the only kind of field that the charge can create. When the charge moves, we find that there is the possibility for a new kind of field that can have lines which do not start or end on charges, but which can form closed loops. These are the magnetic field lines. As soon as there is movement of the charges, there is time changes of the electric fields, and that can produce magnetic fields. There is really no profound answer other than the fact that the electromagnetic field has 6 different degrees of freedom and that it requires the electric and magnetic field to represent these. Also when objects are moving relative to each other, the two fields can mix together. I do not think I have done a good job. Your question is very profound. Maybe we do not yet know the answer. 

Sam Bowen 

Maybe it would help you to know that we humans actually know of only two ways of creating a magnetic field. One is based on moving charges around, and is how an electromagnet works, for example. The other uses the fact that all elementary particles have a tiny magnetic "moment" (like a little bar magnet) associated with a fundamental property called "spin" (again making it sound like the motion of charges, although this time that does not seem to be the explanation), and under certain circumstances you can get those moments to all line up on their own - this would form a permanent magnet. However, if you know anything about electrons in atoms, you will realize that they whiz around the atomic nucleus, and since electrons are of course charged, they must produce another magnetic field, giving them an "orbital" moment, which adds in complicated ways to their "spin" moment. In real permanent magnets, such as those based on iron, it is these combined moments that all line up, and so even in most permanent magnets the magnetism comes at least in part (and perhaps mostly) from the motion of charges - this time electrons moving around the atomic nuclei. Actually, the "spin" property of elementary particles seems to me even more mysterious

Page 76: Newton Ask

than the factthat moving charges create magnetic fields. Maybe some particle theorists out there can explain it a little better than I can. No particle theories have risen to the challenge? Well, I actually looked up "spin" in the Encyclopedia of physics, and was reminded that it is not all that mysterious, or at least that, since we know all the interactions between the electron (as a point particle) and the electromagnetic field. In terms of the theory of quantum electrodynamics, we can actually predict the ratio of the electron's true magnetic moment to what would be expected for an electron with an angular momentum of 1/2 hbar in a semiclassical treatment. This ratio, called the g-factor, turns out to be pretty close to 2, and can be calculated to 11 digits which all agree with experiment. This is one of the big achievements of QED, in fact. Unfortunately, the electron is the only particle we know how to do this with yet. The magnetic moments of the proton and neutron are really known only from experiment, since the theory of the structure of the neutron and proton (quantum chromo dynamics) is not yet (with current computers) able to calculate it. 

Arthur Smith 

I just wanted to add that Dirac's famous equation, in which he presented a "relativistic" equation of motion for a charged particle, predicted that: (1) electron's had an intrinsic property called "spin," and (2) that a particle existed with equal mass and spin but with opposite charge, which was dubbed the "positron" when it was eventually observed experimentally. So, "spin" falls out of a relativistic treatment of quantum mechanics - or at least this is what they told me in school. I also would like to hear from a particle theorist on this question! 

Topper 

Question:

I am interested in information about MHD for a science fair project. I need to know how I can build a magnet for a desk-top size experiment. How much magnetic energy is required? How many volts will I need for the electrical energy? 

Page 77: Newton Ask

Replies:

There are many books that will give a good description. You could buy some insulated wire from a hardware store, the type they use for doorbells, wrap it around a steel bolt, and run the current from a dry cell battery and it will be a magnet. The magnet will be strong enough to pick up light paper clips, but not much more. It does take lots of current to make magnetic fields. 

You can make a demo MHD from a magnet and magnetic marbles. The marbles can be purchased at places like Toys-R-Us. Make sure that the magnets inside are spherical not the cheap Asian stuff which is cylindrical. 

Sam Bowen 

Question:

How does rotating charge create a magnet? 

I know that a moving charge creates a magnetic field encircling its direction of motion, but why does a rotating charge produce a magnetic field when it is not changing its position? 

Replies:

If you can have the charge rotating, it must have some extent, is the charge is at some radius, so the charge density is moving as the shell of the charge moves, this is the moving charge. 

Sam Bowen 

You may have in mind the idea of a particle with spin having a magnetic moment, which is not quite the same thing as a rotating charge. As far as I know, the reason is not terribly clear this is just a fundamental property of the particle. 

Arthur Smith

Page 78: Newton Ask

Question:

Two copper wires have the same mass and, necessarily, the same volume. The first wire is twice as long as the second. What is the ratio of their resistances? 

Replies:

Resistance is proportional to length and inversely proportional to cross-sectional area. Another way to work the problem is to imagine two identical wires of resistance R laid (1) side by side. The total resistance is R/2 (2) end to end. The total resistance is 2R. 

mooney

Question:

Can you give me examples of simple physical phenomena that are not functions? I can understand about discontinuous phenomena. But what phenomena have more than one y for any one x possibility fory at any one x? 

Replies:

Well, the simplest thing I can think if is a circle. A circle has two y for every x, except where it does not have any at all (except at two special points). If a circle does not sound like a physical phenomenon, you might want to explain how light works. I light wave is a sinusoidal variation of electric and magnetic fields. If x is the electric field value and y is the magnetic field value, they trace out a circle as time goes on. In fact, many "orbits" are circular - for example, a plot of a harmonic oscillator (like a spring bouncing up and down) with x = displacement and y = velocity also will give you a circle. 

Arthur Smith 

There must be thousands! How about Lissajous figures from simple circuits? You hook an oscilloscope up to two components of a circuit which are

Page 79: Newton Ask

oscillatory in time and plot one voltage as x, the other as y. All sorts of interesting closed curves result, depending on the phase difference and the frequency ratio between the two oscillators. Also, there is the phase diagram of water...but there is no simple equation associated with that, I know. I guess that I vote for the velocity (or momentum ) of a harmonic spring plotted against its position. 

Topper 

Question:

What would happen if I use superconductive wire, to connect the two terminals of a cell, or a generator? 

Replies:

Actually, superconductors have a maximum current (called a critical current) which they can hold. If you put to much current in, the wire loses its superconductivity and suddenly heats up very fast, which could cause an explosion. But it would not be a very good idea. 

Arthur Smith 

Question:

Why does the current density have a unit of J sub c? 

Replies:

I think you are misusing the word "unit" here. The units of current density (i.e. current per unit area) are amps per square meter. The reason for this is simply that current is a flow of charge per unit time, and it has a direction (the direction the charge is moving in) and so if you consider a plane perpendicular to the direction of flow, the current is exactly the charge going through that plane per unit time. If you have a uniform material that extends out over an area A in this plane, through which the current is flowing, then the "intensive"

Page 80: Newton Ask

quantity (like density, charge density, etc) associated with the current in this material is just the current divided by the area A. I assume the J sub c you are referring to is a symbol used for current density. The most common symbol is simply a J. I guess to differentiate from total current usually denoted I. The "sub c" is probably to distinguish one kind of current from another. The flow of heat can also be measured by a heat current density, and usually has quite a different symbol (something involving Q, for example). But symbols really do not matter that much, although there are conventions in physics that help people communicate more quickly, you can usually be understood even if you use nonstandard symbols. 

A. Smith 

Question:

What are the materials most often used to achieve superconductivity? 

Replies:

Well, the most important material for many years was liquid helium; just about any metal turns superconducting when it is cold enough. It is actually easier to list the exceptions - none of the noble metals (copper, silver, gold) do it, for example, at least to temperatures as low as can be measured. The materials "most often" used change with time. Basically, people try to use the best materials available, which depends on a whole lot of different properties, the most important of which being a high enough superconducting transition temperature. Of the old low-Tc superconductors, probably the most common were the Niobium compounds, particularly Niobium-Tin, because they can remain superconducting up to about 30 absolute degrees. Just 6 or 7 years, ago, that old 30 degree barrier was dramatically broken by experiments discovering that certain ceramic materials (nonmetallic or very poorly metallic, containing Oxygen, which was a surprise) could super conduct at up to 100 degrees and more. The record is now around 130 degrees. This means that liquid helium is not necessary to cool these new superconductors - you can get superconductivity with ordinary liquid nitrogen. The first good materials, still widely studied, consisted of a compound of Yttrium, Barium, Copper, and

Page 81: Newton Ask

Oxygen. Lots of other combinations have been tried in the last few years, and it looks like the Copper-Oxygen layers in these systems are the essential element. But these new materials are not widely used yet. Just wait a few years! 

A. Smith 

Question:

Einstein's photo electric equation K=hv-eV gives the maximum kinetic energy of electrons emitted from a metal if incident em radiation of frequency v exceeds the potential barrier eV. For a given frequency above the emission threshold, the number of electrons emitted increases with the intensity of the light source. Since electric current is the rate of electron flow in a conductor, and power = current times voltage drop, then would not more intense light increase the power of photo-voltaic cells? Would the use of concentrators such as Fresnell lenses and parabolic mirrors be a cost- effective method of increasing the power of photo-cells? 

Replies:

You are quite right. Concentrators will certainly increase the power from the photo-cells. But cost effectiveness is rather more complicated. How does the cost of the concentrator compare to the cost of additional photo-cells? Does the concentrator need to track the source (sun)? This would be an additional cost. Some concentrators are unfocused and do not require close tracking. Another concern is whether the increased intensity at the photo- cell might overheat the device. All of these concerns affect the cost-effectiveness. 

Unknown 

Question:

How fast do electrons move (under typical circumstances in a typical atom)? 

Replies:

Page 82: Newton Ask

We tend to think of atoms in electrons in an atom as like planets rotating around the sun. While this view is attractive, the basis of semiweeklies of the first theories of atom structure by Bohr, is a simplification. Really, the electron should be considered as smeared out over a large volume surrounding the atom. In this sense, the electron does not move inside the atom. 

Unknown 

Well, that is all strictly true, but still it is possible to ascribe approximate velocities to electrons in bound states. This is done all the time to ascribe whether relativistic effects are important in calculating these bound states; for example, relativistic contraction of the inner core of electrons is the explanation typically used to explain the unique properties of transition metals, and relativistic corrections to calculations are currently a frontier area in theoretical atomic and chemical physics. A sort of gross model for "speeds" of electrons in bound states can be obtained from the Bohr model. This model predicts that the electron associated with a hydrogen nucleus would be moving at 2.42 x 10^8 cm /sec, which you may wish to compare with the speed of light: c = 3.00 x 10^10 cm/sec. So the velocity of an electron in the first Bohr orbit (ground state) is a tiny fraction of the speed of light, which is why non relativistic forms of quantum theory work quite well for hydrogen. However, start increasing Z (the charge on the nucleus) and the Bohr velocity for the inner electrons starts to get huge...and experimentally, there is a considerable contraction of the spatial extent of these electrons relative to H. So, although velocities are not strictly defined for electrons whipping around a nucleus, an approximate model (the Bohr model) does give one a sense of when one might need to start formulating relativistic corrections to quantum mechanics. 

Topper 

Question:

From reading Richard Feynman's book QED I have gotten a sprinkling of the mathematics of the probabilities involved in subatomic particle physics. At the same time I am beginning to learn about fractal geometry. Is there anything interesting to be done with mixing these two? Perhaps a way to use fractal

Page 83: Newton Ask

geometry as a graphical tool for working with the probabilities of subatomic events? 

Replies:

Actually, the concept of "renormalization" and critical phenomena in condensed matter may be somewhat related to your question. This is somewhat removed from the Feynman diagrams of particle physics, but similar diagrams associated with statistical mechanics appear in understanding the behavior of systems with many particles. The "renormalization" effect basically is associated with the fact that the system of many particles can be treated almost as if it were a system of a fewer number (maybe half as many, say), with all lengths rescaled by an appropriate factor, and other quantities in the description of the system (usually by a Hamiltonian) "renormalized" appropriately. It is hard to give a short example that really captures what this means, though. At a critical point, the renormalization becomes very simple, in some way, so that basically all length scales look essentially the same, which is one of the definitions of a fractal. In fact, the result of the calculations is that you find non-integer exponents relating various quantities in the system at the critical point (or near to it), somewhat similar to the non-integer dimensions of fractals. 

A. Smith

Question:

What exactly is a quark? Is it a particle like a neutron? A bunch of smaller particles that make up a neutron? 

Replies:

A quark is a particle with a charge of 1/3 or 2/3 the charge on an electron, and several quarks go together to make a proton or neutron (3 quarks each) or various mesons (a quark and an anti quark in each). The theory describing them has recently received a big confirmation in that they have actually

Page 84: Newton Ask

predicted the binding energy, and therefore the mass, for a large number of particles, based on this fundamental theory (quantum chromodynamics). It turns out that you cannot take a single quark out of a neutron or any other particle; they always must be close to other quarks that add up to a net integer multiple of the electron's charge. 

A. Smith 

Question:

I would appreciate someone updating the situation with the quark theory. I ran across an article, I think it was in People magazine, maybe Time, about how researchers were close to finding the last of the quarks that make up the atomic nucleus. Does this mean that the quark model will soon be complete? What about the make-up of the various other sub-atomic particles, have all those quarks been found? As an aside to this, I would also greatly appreciate an explanation of the method that is used to detect quarks, I had heard that they could not exists outside the particles they made up. Also, I know what a 'bubble chamber' is used for but what physically is it and how exactly does it work? One additional thought, what are your opinions on some of the other quantum theories esp. the 'bootstrap' theory? And do you absolutely believe the quark model? 

Replies:

Essentially, if you assume that quarks make up the baryons (3) and mesons (2) and that the quarks are conserved, i.e., they can only be made in quark and anti-quark pairs, you can make sense of the kind of products that come about from high energy particle reactions. If you look at the energy that goes into a collision and comes out, along with the momentum you can often, for certain reactions, determine the missing mass of particles that would have participated in the collision, but could not escape the interior of the particles except for short times and distances. These indirect calculations based on the observations of the particles that came out are the way in which we measure and "observe" quarks. Fermilab is rumored to have enough data to give the mass of the last heaviest quark in the standard model. This will give us a final piece of data. However, we do not really know how to calculate the masses of the particles themselves. Our best theory uses a large number of parameters. You will have to read to get a more complete picture. 

Page 85: Newton Ask

Sam Bowen 

Well, first of all, this last quark (the top quark) really does not appear in the atomic nucleus, except maybe very rarely in the "virtual" sense. The quarks that are supposed to make up the proton and the neutron are the "up" and "down" quarks, which have been known for a long time (the existence of the proton and neutron would be considered evidence for their existence, for example). There is considerable evidence that quarks do exist, or at least that the neutron and proton have internal structure consistent with the quark model. A Nobel prize was awarded two or three years ago for studies of electrons bombarding protons at quite high energies to try to discern this internal structure - there is a Scientific American article by the people who won this prize, published sometime within the last two years. 

Arthur Smith

Question:

Please explain how beta particles can be positive. 

Replies:

Technically, beta particles are electrons produced by radioactive decay, when a neutron changes into a proton, an electron which is ejected from the nucleus, and a neutrino (also ejected, but very hard to detect), are negatively charged. However, some radioactive processes result in the emission of a positron, a particle of the same mass as an electron but positively charged. Both processes are referred to as "beta decay". Beta particles were discovered by Madame Curie and Becquerel in the late 1890's. Positrons were not detected until 1933 (and this was in cosmic rays, not radioactive decay); in fact, their existence was predicted on theoretical grounds by Dirac, three years before they were detected! A positron has only a fleeting existence, at least in our part of the universe, since when it meets up with an electron the two annihilate, producing gamma rays. (This process is called

Page 86: Newton Ask

pair annihilation.) That is probably why positrons were not detected in radioactive decay until much later; they annihilate long before they can show themselves in the sort of detector used by Curie & Becquerel. 

R.C. Winther 

Question:

Two electrons with the same spin are not allowed to occupy the same orbital. How does one electron "know" what the other's spin is? 

Replies:

This is another of those mysteries involving spin in quantum mechanics. A single electron can have a spin that points in any direction, unless there is some external effect (like a magnetic field) that forces an energy difference between two opposite spin directions (either in the direction of the field, or opposite to it). When you bring two electrons together, they have an effect on each other similar to the effect of the magnetic field - the energy eigenstates either have both electrons spins pointing in the same direction (a so-called "triplet" state) or they have them always opposite (a "singlet" state) although the actual direction that both point (either parallel or opposite to) is again arbitrary. So, there is actually a direct interaction between electrons that depends on their spins - this is called the "exchange" interaction -resulting in different energy states depending on their relative spin orientations. 

A. Smith 

Question:

Has anyone seen an atom? 

Replies:

We have seen atoms in many ways. Some of them are very indirect. Large microscopes that use electrons instead of light have been able to see single

Page 87: Newton Ask

atoms as fuzzy pictures on film. The atoms we have seen this way are the larger atoms that contain a lot of protons and neutrons in their nuclei. This was a good question. I hope you have as much fun with science as we do. 

Sam Bowen 

A very good question. The answer is Yes. And No. The reason for No is that it is actually impossible for anybody to "see" an individual atom, since all atoms are thousands of times smaller than the smallest light waves we can see using our eyes. The reason for Yes is that, even though they cannot be seen directly with our eyes there is so much evidence for atoms, and we know so much about them, that it is impossible to say they do not exist. One of the greatest achievements of the last few years (which won a Nobel prize) was a new kind of microscope called the "scanning tunneling microscope", which allows an extremely sensitive "probe" (basically a rod with a very fine tip) to wander around on the outside of some solid materials, and actually feel the bumps that are caused by the atoms there, and then a computer can convert those bumps into a picture of the surface, showing the individual atoms lying there, and the patterns they form, the steps as one layer of atoms gives way to another, and all sorts of details that could never be seen before. So, in the expanded sense of the word "see", using these new instruments and computers, people have now actually "seen" atoms. Let me just list a few of the other bits of evidence for atoms. The very first real evidence came in the 1800's when people were first able to measure the details, such as pressure, volume, and weight, for gases. They discovered that gases obeyed certain laws such that at a standard temperature and pressure, a certain volume of Oxygen, for example, weighed almost exactly 16 times as much as the same volume of Hydrogen gas, and that when you combined two volumes of Hydrogen gas with one volume of Oxygen, you got pure water out of it with nothing left over. Similarly, a lot of other elements seemed to have a ratio of mass to Hydrogen that was almost exactly a whole number, and that when these elements were combined to form compounds, they always did it in whole number ratios (such as 2 H's and 1 O forming water, which is H_2 O). All of this led to the idea that the molecular compounds actually were composed of a collection of atoms bonded together, and that these atoms had specific weights, which were often whole number multiples of the weight of

Page 88: Newton Ask

Hydrogen. This led to the periodic table of the elements, first devised by Mendeleev, at the end of the 1800's, and since improved and copied into every Chemistry classroom in the world. Other evidence for atoms comes from radioactivity. With the Geiger counter, every time you hear a "tick" you know an atom just decayed. Modern particle detectors allow people to see the tracks left by high-energy particles that are even much smaller than atoms, even though it is impossible for them to see these particles directly. These techniques are possible because the high energy particles can lose a little bit of their energy to the atoms around them, and this energy can be magnified by making those surrounding atoms a little unstable to start with. Therefore a little energy goes a long way to making a noise, or visible tracks. The discovery of X-rays at the end of the 1800's, and the realization that X-rays are just a very short-wavelength version of light, meant that X-rays could in principle be used just like light, to look at things much smaller than could ever be seen with visible light. Unfortunately, nobody has been able to make an X-ray microscope that works like a regular light microscope. However, it was soon discovered that a beam of X-rays shot into a solid would notice layers of atoms in that solid and the resulting "diffraction pattern" can be used to figure out exactly where the atoms were located, at least for special types of solids known as crystals. Many common solids can then be understood as just regular arrangements of atoms, and the exact distances between the layers of atoms can be determined from the X-rays, telling us how big the individual atoms must be. The layering of the atoms also show up on the outside sometimes, when the crystals form "facets", or very nice flat faces, with sharp edges and fixed angles between neighboring faces. People really like gems with facets, especially diamond, but a lot of other materials can form facets also (ordinary table salt for example). Another kind of microscope is the electron microscope. This works by sending a beam of electrons, instead of light, onto the material you want to look at, and since we can easily make electrons with very short wavelengths, these electron microscopes are almost strong enough to see atoms. They can see large molecules relatively easily, and are also used to look at the tiny features on the latest computer chips, since those are now also too small to see with regular light. I think the Guinness Book of World Records lists the most powerful microscope, and at least until a few years ago it was some kind of electron microscope. Another way in which individual atoms or electrons can be "seen" is in special traps

Page 89: Newton Ask

which trap only one, or a few, at a time. It is then possible to shine light or other types of radiation at these trapped atoms or electrons, and to notice the effects of the individual particles on the radiation. For example, I believe one recent experiment was able to make the atoms fluoresce (that is, send out their own radiation) so that their positions could be seen using a sensitive camera. There are also special semiconductor devices (on a chip) that can trap and look at individual electrons. From all these experiments come details of how much atoms weigh, and how big they are, and in the 1920's and 30's, a theory was finally developed that actually explained all these things. This theory is called quantum mechanics, and is extremely precise in its predictions, especially for the interactions of atoms with light (both visible and invisible). The many agreements on numbers, often with 10 or more digits, between the theory of quantum mechanics and experiments involving spectroscopy (the study of different frequencies of light) is perhaps the most convincing evidence that atoms exist, and that we do know an awful lot about them. 

Arthur Smith 

Question:

I have before me a Radio Shack Archer (cat no. 276-099) INFRARED SENSOR. The sensor is used to identify and locate near-infrared radiation emanating from either LED or laser sources. When a source, such as a remote control device, is shined onto the card, it has a visible light emission. How can a lower energy IR source activate a higher energy visible light emission? Is not this a violation of conservation of energy? It says that the sensor must be charged by short exposure to daylight or fluorescent light prior to use. Why? What is the material, and can it be made for less than $7/cm^2? 

Question #2. -- On the recent Space Shuttle mission, they shot a stream of electrons into the atmosphere below them to stimulate an aurora. Where did the protons go (it would be difficult to attach a long wire to ground)? 

Replies:

Page 90: Newton Ask

The simplest answer is that the energy of the emitted visible light comes from the power supply of the circuit and the infrared light simply supplies charge carriers to the circuit. I do not know the details of this device or why it is so cheap, but I will give a brief explanation. This is a semiconductor device. A semiconductor has an energy gap within which no electron can move or exist with that energy. If there are impurity atoms put into the material there can be localized energy levels in the gap that will hold electrons until something can exit them into the conduction band at the top of the gap. Once the electrons are in the conduction band at the top, they will flow to a boundary where they can be made to cascade to the bottom of the band and create visible light. The charging of the device is essentially exciting enough electrons in to the impurity band where they remain trapped until an infrared photon can excite them into the conduction band. 

Question 2. -- The protons stay on the ship and its electrostatic energy becomes larger, making it harder to shoot more electrons off and ultimately causing other electrons in the plasma of space to be attracted to the ship. 

Sam Bowen 

Question:

s it true that the exact nature of electrons inside the atom is not yet known? If this is true, why are students in physics and chemistry continually shown the model of the atom that depicts electrons as discrete particles orbiting at various distances from a nucleus without even being told that this model is completely incorrect? 

Replies:

A lot about electrons in atoms is known very well. We know that electrons are point particles that have a charge, a mass, and an intrinsic spin. We know the equations that specify the probability of our finding the electrons if we were to look for them. We know the energies that the electrons will have in those states. We cannot find the electrons position exactly because they are so light that any probe we would use would disrupt them and destroy our knowledge

Page 91: Newton Ask

about where they were. That means that we must use quantum mechanics which only allows us to find out where it is likely to find the electrons. Measurements of these probabilities (wave functions) and energies have been confirmed to great accuracy for simple systems where we can do the calculations can be done exactly. For more complex systems, we cannot carry out the calculations quite as accurately, but the results we get are very accurate and let us make many predictions. We know a lot. The pictures students see often make it look like we can determine where the particles are when we cannot, but we can determine the energy and wave function so well that we really know about all that we can know about such small particles. 

Sam Bowen

Question:

What is a shape memory alloy and how does it work? 

Replies:

These are materials that can be deformed somewhat, (for example, folded, bent, twisted, etc,) and then when they are heated up a little, they return to almost their original shape. I believe that the principle is that there are impurities, called dislocations, that are locations where atoms are out of place. Some of these are extended through out large regions of the material. When you bend the material these are deformed but not destroyed. When you heat the material up these dislocations tend to move to their original shape and carry the surrounding material with them. This restores the shape. If the material is melted or heated to much the dislocations are changed or completely destroyed and this property is gone. 

Sam Bowen 

Question:

In the book/movie "A Brief History of Time," Steven Hawking mentions that black holes can be detected by looking at virtual particle creation and annihilation events near a black hole event horizon. What are virtual particles?

Page 92: Newton Ask

How is it speculated they are created? What are the products of the annihilation? 

Replies:

This is difficult, but here goes. Particles and anti-particles if they come too close, combine and disappear in the creation of two photons (light quanta) of generally high energy. This is called annihilation. Energy and momentum are conserved, but mass disappears and light energy appears. Virtual particles is an idea that represents pairs of particles and anti- particles that appear for very short times. If these particles appear for very short times it appears that they can violate energy conservation a little. Since we expect real particles to obey energy conservation we call such things virtual. They have real effects. Their presence effects the energy levels of atoms by a very small amount which was calculated accurately and that is why physicists believe these things exist and are important. 

Sam Bowen 

Question:

How fast do force carrying particles travel? Are they photons? Do they have an electromagnetic frequency as do all photons, even if they are not carrying electromagnetic force? 

Replies:

Some force carrying particles have mass, and therefore they do not travel at the speed of light. You can tell whether a force carrying particle has mass or not by how long-ranged the force is. Gravity and electromagnetism have mass-less force carriers (the graviton - not yet observed - and the photon) while the strong and weak forces are very short- ranged, and have very massive force carriers. The force carriers for the weak force are the W and Z particles (intermediate vector bosons) which were observed first about 10 years ago. It was originally thought that pions were one of the fundamental

Page 93: Newton Ask

force carriers for the strong force, but the theory of Quantum Chromo dynamics has force carriers called gluons. These particles all have energy (analogous to the frequency of photons), and in addition they can have charge, and color charge for the gluons. One thing they all have in common is that they are all bosons (that is, they have an integer spin value, and do not have to obey the Pauli exclusion principle). 

Arthur Smith

Question:

I have two questions. First, I have seen reference to "cosmic strings", and was wondering exactly what these are. Second, is there a way to construct some kind of detector for particles? I have heard of a homemade cloud chamber, but this uses dry ice, of which I do not know any readily available sources of. Is there any kind of rudimentary detector that could be built at home using fairly common and easily obtainable items? 

Replies:

Cosmic strings are hypothetical entities based on some ideas from particle physics that there is some kind of background "field" of some sort that permeates the universe, and that can have slightly different values in different places, such that singularities in the field value can occur along lines called strings. When you go around the string, this field value looks like it is traveling around a circle, and so as you approach the string from different directions, the field has different values, and those different values must all be made to agree somehow at the center of the string. This creates a very high energy defect in the structure of the universe. If such a string closed in on itself, it would release a whole lot of energy by ontracting and disappearing. 

Arthur Smith 

Question:

I recently watched a video on particle accelerators. The video stated that a "special alloy" was involved with the high-vacuum storage ring. Can you give me information on the special alloy? 

Page 94: Newton Ask

Replies:

I think the reason they need a special alloy for high vacuum is that ordinary iron or steel is very porous to some molecules - particularly hydrogen. Since particle accelerators usually produce small nuclei, like protons,the problem could be that a steel liner would absorb all this hydrogen, and let some of it out gradually, and they could never get it all out without pumping for ages. 

A. Smith

Question:

Could somebody out there please explain to me how an RF cavity is used to accelerate a particle in a cyclotron? Specifically, I do not understand how a klystron tube is used, and what the frequency has to do with anything. Finally, how or what do the particles absorb, RF energy , a wave, or electricity? 

Replies:

You might want to check past issues of Scientific American for details on how particle accelerators work - I am sure I have read something in there. Either there or an issue of "Physics Today" in the past few years might have something. Anyway, here is a very rough answer. The electrons are moving very fast once they get to the RF acceleration section (you have to start them off with quite a bit of energy some other way). When they pass by one of these "klystrons," they do it in a rather short time. The klystron is arranged so that it produces an electric field along the direction the electrons (or other particles) are going, and this electric field oscillates (switches from one direction to the other) with the frequency in question. As long as the electric field is pointed in the forward direction, so that the particles accelerate in it, during the short period of time that the electrons are actually in that vicinity, you will get a net acceleration of the electrons. Basically, accelerating charged particles with a constant field requires enormous voltages (a trillion volts for the new SSC) which cannot be achieved. But oscillating electric fields can do

Page 95: Newton Ask

the trick without needing more than a few hundred thousand volts at a time. It does require careful timing of the "bunches" of particles that get accelerated together. The energy comes from the electric field - it is kind of a normal absorption process. 

A. Smith 

Question:

What is a half-spin? 

Replies:

In elementary-particle physics there is a term called "fermion". This refers to any particle that has a spin of (1/2)*[h/(2 Pi)] where "h" is Planck's constant. (The term in brackets,[h/(2 Pi)], is often written as an "h" with a line through it, and is referred to as "h-bar"). Electrons, protons, and neutrons are examples of fermions, and one often speaks of them as "spin-1/2 particles". 

R.C. Winther

Question:

What are the limits to the size of a fusion reactor? I have read Sci-Fi stories that include the hero carrying a portable generator and heard rumors about a (discontinued) experimental fusion aircraft. I would guess that you must have a certain mass to keep the reaction going, but what is the minimum? 

Replies:

The basic process of a fusion reactor has no real minimum mass. But the complex equipment required to keep it going and make itefficient is enormous. (With present technology) The basic process just needs a few atoms of tritium or deuterium. It is the equipment that brings the atoms together at high velocity or heats them to high temperature that is complicated and bulky. This is quite different from a fission reaction, where a minimum mass, called the critical mass, is needed. I think the experimental nuclear airplane used a

Page 96: Newton Ask

fission reactor. A typical critical mass for a fission reaction would be several kilograms. This would be very portable, if it was not for the shielding needed to keep from frying everybody in the vicinity. Plus, you need cooling and heat exchangers to use the heat that is produced. Both fusion and fission reactors put out heat as their primary method of energy production. 

Unknown 

Actually, so far no fusion experiment has produced any more power than went into heating the stuff up in the first place. That means that not only do we not have portable generators, we do not have ANY fusion reactors that actually produce power. There is actually a proverbial "20 year" effect involved - reactors planned for 20 years in the future should finally be producing power, maybe even commercially. Unfortunately, it hss sort of been that way for the past 30 years or so. 

A. Smith 

Question:

I was wondering if anybody has come up with some proposed models for the electron that are renormalized and compatible with Quantum Electrodynamics. In QED, the electron can not be thought of as a spheroid with an evenly distributed charge because it should then repel and explode. According to the inverse square law, the formula for charge rests on the phrase 1/r. As it turns out when all is said and done, the QED electron model has no radius to boast, and an infinite energy. Also, is it possible that in same fashion a photon (being a boson) has no rest mass, an electron (being a fermion), has no , shall we say, "rest radius"? Note the difference in angular momentum in each family. Might this relate to the"hidden" information in each case (volume for the fermions and mass for the bosons)? 

Replies:

Basically the standard model regards all the elementary particles as point particles (i.e. with infinite energy in principle, if the electric field energy is really included). This is clearly unsatisfactory. Note that it does not have much to do

Page 97: Newton Ask

with spin, though - for example a proton has spin 1/2, but it is a composite particle containing 3 quarks, and so the protons really does have a certain radius. But, electrons really do behave as point particles down to the length scales they have been tested on (fractions of the size of a proton, anyway, and orders of magnitude less than the "classical" radius of an electron in which its mass arises from its electrostatic energy). The string theories are intended as a way to depart from the pointparticle model, not that they do not have problems of their own. But some of them actually do end up getting rid of the infinities in QED - at least in principle. No one has actually gotten as far as deriving QED from string theory (at least that I am aware of) - but in principle the electron would then be modeled by these strings, with certain kinds of vibrations on the string. Of course, all sorts of other theories can be imagined - it is really an open question, but unfortunately one that no experiments are likely to address for many years. 

A. Smith 

Question:

I have read that bosons are particles that convey force (gravtons, photons, etc.) and fermions (protons, neutrons, the heavy stuff) are the particles themselves that are acted upon by these messenger particles. How do messenger particles convey force, ("pursuadine)? Example: How is a graviton going to convince a hydrogen molecule to change direction and head towards the gravitating mass? 

Replies:

The question really is, how to get an attractive interaction. Getting a repulsive interaction looks easy - particle 1 fires off an exchange particle in the direction of particle 2, which receives it, and the momentum of the exchange particle causes the 2 interacting particles to head away from each other. Imagine 2 kids on skateboards, exchanging a basketball. This repulsive interaction is just what happens when they throw the basketball straight at each other back and forth. So, how can we get an attractive interaction? If the kids are close enough, they can just hand the ball to one another, and this can be done in such a way that the net momentum transferred is in the other direction - so

Page 98: Newton Ask

they really are pulled towards one another. But this does not seem to be directly related to the physical system - particles do not have long arms! Or do they? Remember Heisenberg's uncertainty principle? If you have specified momentum completely, position is completely uncertain. I think this is most of the explanation. 

A. Smith