Williams Research Gravity Pharis E. Williams 19 th Natural Philosophy Alliance Albuquerque, NM 25-28 July, 2012.

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Gravity

Pharis E. Williams

19th Natural Philosophy Alliance

Albuquerque, NM

25-28 July, 2012

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For Newton Gravity was independent of his fundamental laws of dynamics.

For Einstein gravity and dynamics were tied together in the geodesics of a curved

space.

Thermodynamic laws provide the equations for dynamics caused by a force

AND the gravitational force law.

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The Dynamic Theory Premise

The fundamental laws are sufficiently general to determine both the force of

interactions and the dynamics that force causes.

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Fundamental Laws

1st Law Conservation of Energy

2nd Law Denial of Perpetual Motion

đ , where 1,2,3,4iiE dU F dx i

Neighboring any state point there exist points that the system may not go to reversibly.

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Integrating Denominator Defines Entropy

Entropy determines:1. How the dynamics flows (i.e. Time)2. Very stable states and the Entropy Principle3. Characteristic properties of fundamental particles.

.dU Fdx dU

dS = - - fdx

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Stability Conditions

2 2 220 0

2 00

0

2 0

, and , 1,2,3,4o

U U Udx dx dx dx dx

x x x xx

S x f

Parameterize by choosing

2 20 000 02 0h dx h dx dx h dx dx cdt

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Maximum Entropy Principle

or

where the Entropy space is integrable while the sigma space is not integrable. And the

gauge function behaves as a geometric integrating factor.

2 20 20

00

12dx c dt h Adtdx h dx dx

h

2 20 1 1i jijdx g dx dx d

f f

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Weyl Scale Factor in the sigma manifold

Isentropic states require that

then the Weyl Scale Factor is unity, or

A Unity Scale Factor requires

iidx

f ol l e

f ol l

1

iidx

e

2 iiiN dx

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London showed that, given the Gauge potentials, a unity scale factor requires the

isentropic paths that satisfy

must follow the paths given by Schrodinger’s Wave Equation.

Isentropic paths with unity scale factor follow quantum mechanics!

2 iiiN dx

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What are the gauge potentials that a fundamental particle may possess that

satisfy the requirements of a unity scale factor and remain unchanged as the

particle moves around in space and time?

2 iiiN dx

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1 2 3 0

1 3 2 1

2 3 1 2

3 2 1 3

0 1 2 3

0

0

0

0

0

ij

E E E V

E B B V

F E B B V

E B B V

V V V V

.

40 0

40 0

44 0 4

1 BB = 0 + E = 0

c t

1 E V 4 J VB - + = E + = 4a a

c t c

BJ + J + = 0 V + = 0a a

t

1 V E 1 4V + = V + = -V a J

c t c t c

The Gauge fields

must satisfy the unity scale factor and the field equations

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The gauge function that satisfies the unity scale factor and all of the field equations is

Hubble’s constant is the coefficient of time in the exponential while it combines with the maximum mass conversion rate in the

coefficient of the mass density.

1

2ln , with N

o KH tro o

o

r Hf e e e K

r a c

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The gauge fields allowed for a fundamental particle are

2

0 0 0 0

0 0 0

0 0 0 0 011

0 0 0 0 04

0 0 0 0

N

o

o o

o o oo

ij o

H trN

o

oo

o

r HZ

c

r H a cZ Ze r K

F c H

ee e

r ra c

Ze r KH

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The ratio of the electric force to the gravitational force for these fundamental

particles is given by

No other theoretical prediction of this value is known.

2

2

2 2 2 2

4o oratio

o

eH

Fa c K Gm

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Comparison between theoretical predictions and existing experimental data:

1. Perihelion Advance – Proportional to Lambda

2. Red Shifts – exponential w.r.t. time and mass

3. No Big Bang – non-singular potential

4. Dark Matter – time dependence

5. Dark Energy – changing Chandrasekhar limit

6. Fifth Force – non-singular changes gravity below surface

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Inductive Coupling Experiments

1. Radiation Pressure & Energy– Nichols & Hull: P<E

2. Cosmic Background Radiation – Radiation at P=0

3. Electromagnetogravitic waves – Trans & non-transverse

4. Alternate communications – energy conversion T to NT and back

5. Neutrinos –Non-transverse

6. Earth’s magnetic moment – Charge-to-mass ratio

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Inductive Coupling Experiments

1. Direct Measurement of Coupling – Dennis Suhre

2. Earth Flyby Anomalies – Effective charge of satellite interacting

with Earth’s magnetic field

4 oG

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Einstein’s Field Equations

1. Start with the Gauge Function with variables space-time-mass

2. Conserve mass3. Results: the curvature of the hyper-surface embedded by

conservation of mass into the space-time-mass manifold is given by Einstein’s field equations, where κ is the gravitational constant.

4. Two ways to get dynamics: force driven in chosen geometry or geodesics on curved hyper-surface.

2

1 8

2G R g R T

c

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Conclusions

Thermodynamic Laws Provide:1. Stability condition geometry with a gauge function2. Scale Factor based upon the Gauge function3. Isentropic paths given by quantum mechanics4. Fundamental particles gauge properties

a. Long range 1/r2 characterb. Non-singular short range characterc. Time dependent gravity

5. Inductive coupling between electromagnetism and gravity6. Gravitational component in transverse waves7. Non-transverse waves of electric and gravitational

components8. Einstein’s field equations for conservation of mass.

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Perihelion Advance

2

2 2

32 with

GMm GM

L c

Red Shifts

2exp 1

er

er

rRR

re or

r e e

e

M

RM e H LM eGz

c R R c M

R

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No Big Bang

2

2 2

41

3

RroGd R e

dt Rr R

Dark Matter

22

10

1 12

1 where (MOND)1.2 10

oN o o N o o

N cc

H ra a t H t a H

r c

r GMa r

r x

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Dark Energy

22 22

12 6 2 3 with

3 2 8o

o RO cc

z z HaH

a z G

But the Chandrasekhar mass limit changes in time as

9

41L Ch oM M H t

z is given by the Red Shift formula

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Radiation Pressure & Energy– Nichols & Hull: P<E

2 2 2

2 2 2

1

81

8

E B V

p E B V

Cosmic Background Radiation

2 2 2

2 20 0

0

0

4p p

p

p E B V

E B

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Electromagnetogravitic waves – Transverse

4

yz y

oy y

k cB E

a ckV E

Non-Transverse

24

4

4 4

4 and

ln lnx

x x x

o o

i k cV E V E

a c k i a c k i