GR Part 1: The Equivalence Principle is in Unit B: Dynamics “distinguish between reference systems (inertial and non-inertial) with respect to real and.

GR Part 1: The Equivalence Principle is in Unit B: Dynamics

“distinguish between reference systems (inertial and non-inertial) with respect to real and apparent

forces acting within such systems.”

GR Part 2: Curved Spacetime is in Unit D: Gravitational, Electric, and Magnetic Fields

“identify and compare the properties of fundamental forces that are associated with

different theories and models of physics (e.g. the theory of general relativity)”

GR Part 1: The Equivalence Principle

12U Dynamics:“Distinguish between inertial and accelerating

(non-inertial) frames of reference.”

1. A plastic water bottle has a small hole in the bottom. It is dropped, and the hole is uncovered. What happens while the bottle falls?

a)Water pours out normally.b)Water stays in the bottle.c)Water pours out more slowly.d)Water pours out faster.

2. A plastic water bottle has a small hole in the bottom. It is thrown straight up, and the hole is uncovered. What happens while the bottle is in the air?

a) Water pours out normally.b) Water stays in the bottle.c) Water pours out only on the way up.d) Water pours out only on the way down.

A frame of reference in freefall is like one where there is no gravity. This is true for falling down, projectile motion and orbits.

3. A cup of water is on a tray. The tray is swung rapidly in a horizontal circle. The water stays in the cup and the cup stays on the tray because there is a large acceleration…a) inwards which is equivalent to a large gravitational field outwards.b) outwards which is equivalent to a large gravitational field outwards.c) inwards which is equivalent to a large gravitational field inwards.d) outwards which is equivalent to a large gravitational field inwards.

A frame undergoing constant acceleration is equivalent to one in a constant gravitational field. There are no tests that you can do within the frame to tell the difference.

Bob and Alice are in a rocket far from any significant gravitational field. Bob is at the rear of the rocket and sends pulses of light towards Alice in the nose of a rocket every 100 ns. How often does Alice receive the pulses if the rocket is moving with4. constant velocity?5. constant acceleration?

Q 5: A rocket moving with constant acceleration.Q 4: A rocket moving with constant velocity.

2

2

6

a) every 100 nsb) more frequently than every 100 nsc) less frequently than every 100 ns

6. The rocket is parked on Earth. How often will Alice receive the pulses?

a) every 100 ns b) more frequently than every 100 ns c) less frequently than every 100 ns

The equivalence principle predicts that gravity will slow time. Experiments show that it does. The GPS must correct for this or else will be off by over 10 km each day! A free teaching resource - The GPS and Relativity - is now available from PI.

Three one-minute animations from the Perimeter Institute can help reinforce the concepts of the equivalence principle and gravitational time dilation.

http://q2cfestival.com/play.php?lecture_id=8247&talk=alice

7. The rocket is parked on Earth. Alice sends pulses every 100 ns to Bob. He receives them

a) every 100 nsb) more frequently than every 100 nsc) less frequently than every 100 ns

8. Alice carefully measures the wavelength of light that Bob sends to her and compares it to what Bob said he sent. She finds that its wavelength is

a) the sameb) slightly shorterc) slightly longer

This is called the gravitational redshift and it was first measured on Earth in 1960.

9. The rocket is still parked on Earth. Alice points a laser to her right. She does careful measurements and finds that the beam

a) travels horizontally b) curves slightly to the rear c) curves slightly to the front

The equivalence principle predicts that a beam of light will bend in a gravitational field - even though light has no mass. In 1908 Einstein calculated the defection that starlight passing near the sun would undergo.

He proposed that they measure this during an eclipse. If they had measured it then - he would have been wrong!

Fortunately, he had eleven more years to rethink his theory.

GR Part 2: Curved Spacetime

12U Gravitational, Electric and Magnetic Fields:“Identify and compare the properties of

fundamental forces that are associated with different theories and models of physics

(e.g. the theory of general relativity)”

Mass curves spacetime and light will travel as straight as it can in this space. This can be modelled with a long piece of masking tape

and a bowl placed upside down on the table.

The tape represents a beam of light and the bowl represents the curved space near the sun. Run the tape along the table toward one edge of the bowl. Stick it as smoothly as possibly up onto the bowl, along the bowl’s surface and back onto the table.

1.On the whiteboard sketch the path that light takes passing near the sun.

2.Sketch the path that ‘light’ takes if the bowl is upside down. Explain your results.

This highlights a limitation of our model. Rather than looking at a 2-D table surface that is curved up or down, we should really be looking at 3-D space curving into a fourth dimension.

The light bends toward the ‘mass’ in both cases.

In 1915 Einstein calculated the deflection again using the curved spacetime of general relativity. The new value was twice as big.

In 1919 the second deflection was measured during an eclipse and he became famous.

The light can go around either side and form a double image. Model this with a 2nd piece of tape.

The first double image ever found. (1979)

The light can go around the top and bottom as well and form a cross. Try to model this with two more pieces of tape.

If the mass is directly between the object and Earth it will form many images and it may form a ring .

Gravitational lenses are used by astronomers to detect extra solar planets and dark matter.

Black holes may also be seen within the next ten years and should look something like this.

5) A black hole will look like this from all directions. How is that possible?

The curved space of general relativity also explains something that bothered Newton.

6) How can gravity act without touching?

Mass warps spacetime and spacetime tells masses how to move.

7)What should you do to get a ‘planet’ to orbit as many times as possible?

Notice how Earth causes a dimple that will move around with it. General relativity predicts that this will cause gravitational waves.

Gravitational waves have been indirectly detected using two pulsars that are orbiting each other.

The waves radiate energy and cause the pulsars to slow down. This is the most precisely confirmed calculation in all of physics. Taylor and Hulse received the Nobel prize for it in 1993.

Not only can spacetime be warped - it can also expand. The galaxies are moving away from us!

Why? Do we have galactic body odour?

The expansion of the universe can be modelled with paper clips (galaxies) and elastics (space).

Stretch the chain.8) Why are all the galaxies moving away from Earth?9) Why are the more distant galaxies moving faster?10) How can we tell when the universe started?

The geometry of curved spaces is quite different from flat space and is easy to explore on a balloon.

11. Draw a triangle with three right angles.

12. Does the circumference of a circle = 2r?

13. What else is different?

Imagining the four dimensions of relativity is very difficult. “Dr. Quantum in Flatland” is a 5-minute video that helps. It looks at a 3-D person trying to explain things to a 2-D person.

http://www.youtube.com/watch?v=BWyTxCsIXE4

“There are two sides to gravity:

In part, gravity is an observer artefact: it can be made to vanish by going into free fall. Most of the gravity that we experience here on earth when we see objects falling to the ground is of this type, which we might call "relative gravity".

The remainder of gravity, "intrinsic gravity", if you will, manifests itself in tidal forces, and is associated with a specific property of geometry: The curvature of spacetime.”

From Einstein Online http://www.einstein-online.info/elementary/generalRT

The PowerPoint slides and digital versions of the handouts can be found at http://roberta.tevlin, where you will also find lots of other stuff about how to teach modern physics to high school students.

If you have any questions or suggestions please email me at [email protected]