Space-time Invariance and Quantum Gravity Space-time Invariance and Quantum Gravity Madness By Dr. Harold WilliamsDr. Harold Williams of Montgomery College.

Space-time Invariance and Quantum Gravity

Madness By Dr. Harold Williams

of Montgomery College Planetarium

Space-time Invariance and Gravity: only c and GGeneral Relativity 1915, continuous Real Numbers

Dr. Harold Alden Williams, Montgomery College Planetarium at the Takoma Park/Silver Spring Campus

Space-time Invariance and Quantum Gravity: or How c, G, and h create the fabric of time-space (reality)!Dr. Harold Alden Williams, Montgomery College Planetarium at the Takoma Park/Silver Spring Campus

World Lines• t for time• x for distance• dx/dt speed

Space-time• At least one

space dimension not shown

Special Relativity

• http://en.wikipedia.org/wiki/Special_relativity • http://en.wikipedia.org/wiki/Special_relativity_for_beginners • “Nothing but Relativity” by Palash B. Pal shows that only Galilean

and Einstein Relativity are even possible with the “Principle of Relativity”

• “Principle of Relativity” ≡ “Physical laws appear the same to any inertial observer.”

Speed of light, fastest speed

• c=by definition=299795458 (exact) metes/second

• There is a fastest speed because we leave in a causal universe.

• (if the principle of sufficient cause” is valid)

There is a Fastest Speed• What ever that fastest speed is nothing can move

faster than fastest. c is the fastest speed. Experimentally this, c, is the speed of light, electromagnetic radiation, in a vacuum.

1 21 2 2

1 21

v vv v

v v c

v is the speed, this formula actually is only correct when v1 and v2 are in the same direction collinear, velocity addition formulae.

A Paradox of Non-Relativistic Thinking

• If speed of light were not absolute, you would see the car coming toward you reach the collision point before the car it struck

• No paradox if light speed is same for everyone

Michelson–Morley experiment

• Same geometry as the previous diagram.

• History of special relativity

Luminiferous aether

• Quantum Foam

Test Relativity for Yourself

• If speed of light were not absolute, binary stars would not look like two distinct points of light

• You can verify relativity by simply looking through a telescope at a binary star system

Correct velocity addition formulae for non-colinear velocities

http://en.wikipedia.org/wiki/Addition_of_Velocities_Formula

Newton’s Universal Law of Gravity

F12 is the force on object 2 due to object 1.

G is the gravitational constant. m1 and m2 are respectively the masses of objects 1 and 2. r21 = |r2 − r1| is the distance between objects 2 and 1.

is the unit vector from object 1 to 2.

G, Newtonian constant of gravitation

G=6.673(10) × 10-11 m3 kg-1 s-2 measured in SI units.G=4π2 AU3/(yr2 M)

Max Planck the man

Max Planck 1918

Max Planck latter

History of Planck length, time, and mass

In 1899 a year before he formulated blackbody radiation in December of 1900 in Prussian Academy of Sciences, Max Planck: 'Über irreversible Strahlungsvorgänge'. Sitzungsberichte der Preußischen Akademie der Wissenschaften, vol. 5, p. 440-479-480 (1899). Just used dimensional analysis.

(Gh/(2πc5))1/2 =√Għ/c5=tP =5.3905x10-

44seconds the Planck time, a chronon, smallest time, quanta of time, when!

Time is quantitized at this level, so called “third quantitization.”

(Gh/(2πc3))1/2=√Għ/c3=lP =1.6160x10-

35meters the Planck length, an extention, smallest length, quanta of distance, where!

Space is quantitized at this level, so called “third quantitization.”

(ch/(2πG))1/2 =√cħ/G=MP =2.1761x10-

8kilograms=21µ grams the Planck mass, the minimum mass of a clock capable of

measuring time. The value of this mass is comparable to the mass of a flea egg. Pages

62-81 in Eugene P. Wigner’s book Symmetries and Reflections Scientific Essays Chapter 5,

Relativistic Invariance and Quantum Phenomena in the section titled “Quantum

Limitations of the Concepts of General Relativity.”

Einstein’s General Theory of Relativity, a

theory of Gravity

Spherically Symmetric Vacuum Solution to General Relativity

• Invariant ds2 in spherical coordinates

Black Hole Radius, Schwartzshield Radius

2

2s

GMR

c

Rs Schwartzshield Radius

G Newtonian Gravitational Constant

M Mass causing curvature

c speed of light

Einstein’s Energy Mass relationship

2 2/E Mc M E c

E is the energy, M is the mass, and c the speed of light

Speed = frequency wavelength tautology

or /c f f c c f

λ is the wavelength

f is the frequency

c is the wave speed, speed of light in a vacuum here.

Planck’s Law

E hf E hc h is Planck’s constant, energy time

Quantum Mechanics

h, Planck constant

• h=6.62606876(52)×10-34 J s (measured)• J=Joules = kg m2 s-2 (Energy SI unit)• ħ=h/(2π)=1.054571596(82)×10-34 J s some

times called the Dirac’s Constant or the reduce Planck’s Constant

Substituting things and solving for the wavelength

2 2

2 2

2 / 2 /s s

GE c G hc cR R

c c

1/ 22

3 3

2 2Gh Gh

c c

Substituting things and solving for the frequency

2 2

2 2

2 / 2 // s

GE c Ghf cc f R

c c

1/ 25 52

2 2

c cf f

Gh Gh

1/ 2

5

21/ 1/

Ghf T T f

c

T is the period of oscillation

Now we can actually derive the Planck time, length, and mass

The Universe we live in

• Had a beginning!• Is expanding,

getting larger with time.

• Is accelerating now, the rate of expansion is increasing, too.

46x109 light-years radius of the universe, so an estimate of the current information content, pixels, of the universe, since creation could be made. So here it is the current estimate of the information content of the universe, which is an always increasing number, because time is advancing; we get older and not younger; it’s a one way trip; no time travel allowed (you can not kill your mother before you were conceived); and the observable universe is expanding and accelerating since the creation event: 13.7x109 years/tP*4π/3*(46x109 light-years/lP)3 =6.6x10245.

Some modest Conclusions• No infinity in ticks or tocks yet or ever!• No infinitesimals!• Expansion drives order in our cosmos!• Just because we can imagine it does not

make it real or realizable!• Enjoy uncertainty and the increasing

container that you are in!• We no longer have to fear the irrational

numbers like the Pythagoreans, since they are not part of physics!

Wikipedia Resources

• Cosmic Background Radiation • Quantum Gravity• General Relativity• Planck Time • Planck Units

Wikipedia Cosmological Resources

• Cosmic Inflation• Cosmological Constant

(hc5/(2πG))1/2=eP=MP c2=1.95x109 joules the Planck Energy

eP=1.28x(1028 eV or 1019GeV or 1016TeVe0=0.467 tons of TNT

Possible Madness

• http://www.digitalphilosophy.org/ • Edward Fredkin

End

Sort of

Hubble Parameter

• H0 ≈ 70 km/sec 1/Mpc =2.3x10-18 sec-1

• H0 ≈1/4.4x1017sec=1/13.9x109years

• 1/ H0 is the age of the universe (somewhat model dependent)

• H0 ≈10-33eV

Cosmological Relativitythe Special and General Theories for the Structure of the Universe

by Moshe Carmeli (the man)• ds2=dx2+dy2+dz2-c2dt2-τ2dυ2

• x, y, z usual meaning lengths in space• c, maximum speed in the universe, speed of

light in a vacuum• t, time, what good clocks keep• τ, age of the universe=1/ H0

• υ, recessional velocity (of the galaxy)

Relativity: Modern Large-Scale Spacetime Structure of the Cosmos• Moshe Carmeli editor• Probably his last book• Finished by John Hartnett• Preface finished by Moshe Carmeli• Also in this text Gianluca Gemelli• 5-dimensional special relativistic hydrodyna

mics and cosmology by Gianluca Gemelli

Planck Mass, MP,

relative to some other masses

• MP=2.1761x10-8kilograms=21µ grams

• me = 9.10938188(72) × 10-31 kg electron mass

• Σ i=1 to 3 Δmνi = 0.7eV= 1.2 × 10-36 kg neutrino masses reference

World lines, sheets, and volumesof particles, strings, and branes

• We know we live in a universe with at least 3 space dimensions that we have some freedom in.

• Maybe more elaborate structures exist, but we do not as yet perceive them.

End for now!