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

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

World Lines t for timetime x for distancedistance dx/dt speeddx/dtspeed

Space-time At least one space dimension not shown space dimension

World lines, sheets, and volumes of particles, strings, and branesstringsbranes We know we live in a universe with at least 3 space dimensions that we have some freedom in. universe Maybe more elaborate structures exist, but we do not as yet perceive them.

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”Nothing but Relativity “Principle of Relativity” ≡ “Physical laws appear the same to any inertial observer.”inertial

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.speed of light v is the speed, this formula actually is only correct when v 1 and v 2 are in the same direction, velocity addition formulae.velocity addition formulae

Newton’s Universal Law of Gravity F 12 is the force on object 2 due to object 1. G is the gravitational constant.gravitational constant m 1 and m 2 are respectively the masses of objects 1 and 2. r 21 = |r 2 − r 1 | is the distance between objects 2 and 1. is the unit vector from object 1 to 2.unit vector

Einstein’s General Theory of Relativity, a theory of gravityGeneral Theory of Relativitygravity

Spherically Symmetric Vacuum Solution to General Relativity Invariant ds 2 in spherical coordinates

BlackBlack Hole Radius, Schwartzshield Radius Schwartzshield Radius R s Schwartzshield Radius G Newtonian Gravitational Constant M Mass causing curvature c speed of light

Einstein’s Energy Mass relationship E is the energy, M is the mass, and c the speed of light

Speed = frequency wavelength tautology λ is the wavelength f is the frequency

Planck’s Law h is Planck’s constant, energy time

Substituting things and solving for the wavelength

Substituting things and solving for the frequency T is the period of oscillation

(Gh/(2  c 5 )) 1/2 =5.3905x10 -44 s  t P the Planck time, a chronon, smallest time, quanta of time, when! Time is quantitized at this level, so called “third quantitization.” Planck time (Gh/(2  c 3 )) 1/2 =1.6160x10 -35 m  l P the Planck length, an extention, smallest length, quanta of distance, where! Space is quantitized at this level, so called “third quantitization.” Planck length

46x10 9 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:universeobservable universe 13.7x10 9 years/t P *4  /3*(46x10 9 light-years/l P ) 3 =6.6x10 245.

WikipediaWikipedia Resources Cosmic Background Radiation Quantum Gravity General Relativity Planck Time Planck Units

WikipediaWikipedia Cosmological ResourcesCosmological Cosmic Inflation Cosmological Constant

(h c 5 /(2  G )) 1/2 =1.95x10 9 joules=e P the Planck Energy e P =1.28x(10 28 eV or 10 19 GeV or 10 16 TeV e 0 =0.467 tons of TNT e P /c 2 =m 0 =2.17x10 -8 kg=2.17x10 -5 gm the Planck mass

End Sort of

Hubble Parameter H 0 ≈ 70 km/sec 1/Mpc =2.3x10 -18 sec -1 H 0 ≈1/4.4x10 17 sec=1/13.9x10 9 years 1/ H 0 is the age of the universe (somewhat model dependent) H 0 ≈10 -33 eV

Cosmological Relativity the Special and General Theories for the Structure of the Universe by Moshe Carmeli ds 2 =dx 2 +dy 2 +dz 2 -c 2 dt 2 -τ 2 dυ 2 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/ H 0 υ, recessional velocity (of the galaxy)

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