Space-time Invariance and Quantum Gravity Madness

1. Space-time Invariance and Quantum GravityMadness 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. 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.”

7. 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)

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 collinear, velocity addition formulae.

9. 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

10. Michelson–Morley experiment • Same geometry as the previous diagram. • History of special relativity

11. Luminiferousaether • Quantum Foam

12. 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

13. Correct velocity addition formulae for non-colinear velocities http://en.wikipedia.org/wiki/Addition_of_Velocities_Formula

14. 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.

15. G, Newtonian constant of gravitation G=6.673(10) × 10-11 m3 kg-1 s-2measured in SI units. G=4π2 AU3/(yr2 M)

16. Max Planck the man

17. Max Planck 1918

18. Max Planck latter

19. 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'. SitzungsberichtederPreußischenAkademiederWissenschaften, vol. 5, p. 440-479-480 (1899). Just used dimensional analysis.

20. (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.”

21. (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.”

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

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

24. Black Hole Radius, Schwartzshield Radius RsSchwartzshield Radius GNewtonian Gravitational Constant MMass causing curvature cspeed of light

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

26. Speed = frequency wavelength tautology cis the wave speed, speed of light in a vacuum here. λis the wavelength fis the frequency

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

28. 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

29. Substituting things and solving for the wavelength

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

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

32. The Universe we live in • Had a beginning! • Is expanding, getting larger with time. • Is accelerating now, the rate of expansion is increasing, too.

33. 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.

34. 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!

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

36. WikipediaCosmological Resources • Cosmic Inflation • Cosmological Constant

37. (hc5/(2πG))1/2=eP=MP c2=1.95x109 joules the Planck Energy eP=1.28x(1028eV or 1019GeV or 1016TeV e0=0.467 tons of TNT

38. Possible Madness • http://www.digitalphilosophy.org/ • Edward Fredkin

39. End Sort of

40. 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

41. 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)

42. 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

43. 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

44. 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.

45. End for now!