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

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

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

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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.

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Special Relativity “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

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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

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Correct velocity addition formulae for non-colinear velocities Velocities_Formula

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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

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

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

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

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

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

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

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Substituting things and solving for the wavelength

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

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(Gh/(2 c 5 )) 1/2 =5.3905x 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 =1.6160x 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

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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 =6.6x

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

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WikipediaWikipedia Cosmological ResourcesCosmological Cosmic Inflation Cosmological Constant

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(h c 5 /(2 G )) 1/2 =1.95x10 9 joules=e P the Planck Energy e P =1.28x(10 28 eV or GeV or 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

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End Sort of

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Hubble Parameter H 0 ≈ 70 km/sec 1/Mpc =2.3x 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 ≈ eV

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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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