1. Space-time Invariance and Quantum Gravity
By Dr. Harold Williams
of Montgomery College Planetarium
Title slide

2. World Lines
t for time
x for distance
dx/dt speed

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

4. World lines, sheets, and volumes of 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.

5. Special Relativity
“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.”

6. 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.

7. Correct velocity addition formulae for non-colinear velocities

8. 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.

9. Einstein’s General Theory of Relativity, a theory of gravity

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

11. Black Hole Radius, Schwartzshield Radius
Rs Schwartzshield Radius
G Newtonian Gravitational Constant
M Mass causing curvature
c speed of light

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

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

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

15. Substituting things and solving for the wavelength
Wavelength of the smallest wavelength photon

16. Substituting things and solving for the frequency
Frequency of the largest photon
Smallest time interval
T is the period of oscillation

17. (Gh/(2c5))1/2=5.3905x10-44st0 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l0 the Planck length, an extention, smallest length, quanta of distance, where! Space is quantitized at this level, so called “third quantitization.”

18. 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/t0*4/3*(46x109 light-years/l0)3 =6.6x10245.

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

20. Wikipedia Cosmological Resources
Cosmic Inflation
Cosmological Constant