Space-time Invariance and Quantum Gravity

1. Space-time Invariance and Quantum Gravity By Dr. Harold Williams of MontgomeryCollegePlanetarium

2. 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

3. . 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 time • x for distance • dx/dtspeed

5. Space-time • At least one spacedimension not shown

6. 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.

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.”

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

12. G, Newtonian constant of gravitation G=6.673(10) × 10-11 m3 kg-1 s-2 measured

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

14. Spherically Symmetric Vacuum Solution to General Relativity • Invariant ds2 in spherical coordinates

15. Black Hole Radius, Schwartzshield Radius RsSchwartzshield Radius GNewtonian Gravitational Constant MMass causing curvature cspeed 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 cis the wave speed, speed of light in a vacuum here. λis the wavelength fis the frequency

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

19. 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 Constant

20. Substituting things and solving for the wavelength

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

22. (Gh/(2c5))1/2=5.3905x10-44stP the Planck time, a chronon, smallest time, quanta of time, when! Time is quantitized at this level, so called “third quantitization.” (Gh/(2c3))1/2=1.6160x10-35mlP the Planck length, an extention, smallest length, quanta of distance, where! Space is quantitized at this level, so called “third quantitization.”

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).

24. 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*4/3*(46x109 light-years/lP)3 =6.6x10245.

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

26. WikipediaCosmological Resources • Cosmic Inflation • Cosmological Constant

27. (hc5/(2G))1/2=1.95x109 joules=eP the Planck Energy eP=1.28x(1028 eV or 1019GeV or 1016TeV e0=0.467 tons of TNT Planck mass eP/c2=mP=2.17x10-8 kg

28. Meaning of the Planck Mass, mP • me = 9.10938188(72) × 10-31 kg • Σ i=1 to 3 Δmνi = 0.7eV= 1.2 × 10-36 kg reference

29. End Sort of

30. 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

31. Cosmological Relativitythe Special and General Theories for the Structure of the Universeby 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)

32. 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 hydrodynamics and cosmology by Gianluca Gemelli

33. End for now!