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

2. Space-time Invariance and Gravity: only c and G General Relativity 1915, continuous Real Numbers Dr. Harold Alden Williams, Montgomery College Planetarium at the Takoma Park/Silver Spring Campus

3. . Space-time Invariance and Quantum Gravity: or how c, G, and h create the fabric of time-space (reality)!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

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

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

6. World lines, sheets, and volumes of particles, strings, and branesbranes 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.

7. 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.”inertial

8. 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

9. Speed of light, fastest speed c=by definition=299795458 (exact) m/s

10. Correct velocity addition formulae for non-colinear velocities http://en.wikipedia.org/wiki/Addition_of_ Velocities_Formula

11. 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

12. G, Newtonian constant of gravitation G=6.673(10) × 10 -11 m 3 kg -1 s -2 measured

13. Einstein’s General Theory of Relativity, a theory of GravityGeneral Theory of Relativityravity

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

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

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

17. Speed = frequency wavelength tautology λ is the wavelength f is the frequency c is the wave speed, speed of light in a vacuum here.

18. Planck’s Law h is Planck’s constant, energy time Quantum Mechanics

19. h, Planck constant h=6.62606876(52)×10 -34 J s (measured) J=Joules = kg m 2 s -2 (Energy SI unit) ħ=h/(2π)=1.054571596(82)×10 -34 J s some times called the Dirac Constant

20. Substituting things and solving for the wavelength

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

22. (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

23. 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).440479480

24. 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.

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

26. WikipediaWikipedia Cosmological ResourcesCosmological Cosmic Inflation Cosmological Constant

27. (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 Planck mass e P /c 2 =m P =2.17x10 -8 kg

28. Meaning of the Planck Mass, m P m e = 9.10938188(72) × 10 -31 kg Σ i=1 to 3 Δm ν i = 0.7eV= 1.2 × 10 -36 kg reference reference

29. End Sort of

30. 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

31. Cosmological Relativity Cosmological Relativity the Special and General Theories for the Structure of the Universe by Moshe Carmeli (the man)Special and General Theories for the Structure of the UniverseMoshe Carmelithe man 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)

32. Relativity: Modern Large-Scale Spacetime Structure of the Cosmos Moshe Carmeli editor Probably his last book Finished by John HartnettJohn Hartnett Preface finished by Moshe Carmeli Also in this text Gianluca Gemelli 5-dimensional special relativistic hydrodynamics and cosmology by Gianluca Gemelli5-dimensional special relativistic hydrodynamics and cosmology

33. End for now!