My (Discovered) Unified Field Theory

George Gamow in his book “Thirty Years That Shook Physics” states the following. “It was once suggested by Dirac that Newton’s “constant of gravity” is not really a constant but a variable which decreased in inverse proportion to the age of the Universe. And he may very well be right!”

Dirac never discovered a viable model that worked. I have.

I can confidently state the following.

All the fundamental laws or principles of physics are based upon a geometric expansion of Spacetime.

The following properties of nature are predicted.

1. The inverse square law as a property of spacetime
2. The principles of Conservation of momentum and conservation of Energy are geometrically determined.
3. The speed of light is geometrically determined by an extra dimensional expansion which also produces the E = mcc relationship.
4. The relationships of Quantum Physics are the result of the probabilistic expansion of space-time a “grain” at a time.
5. Since the model predicts physical properties of quantum physics and the inverse square law, the long sought for theory that unites quantum physics with gravitational physics is realized. What Einstein and so many others tried to do is now done. (I am being a bit brash, but I think it is the only way I can get some attention. The mainstream will just ignore me otherwise.)
6. The model is consistent with the observations and relationships associated with Special and General Relativity but the geometry is significantly different.
7. It resolves many of the astrophysical problems associated with the big bang.
8. No dark energy and no dark matter are needed.

The basic geometry can be described in two parts, but both parts are based upon the same set of field equations.

The basic geometry; Part 1

First a few definitions.

There are two dimensions of time.

Relative time - This is the time interval between points as expressed by the speed of light. It is also the local measure of intervals of time.

Absolute time - Also called Cosmic time or more meaningfully, Historical time. This dimension of time demarcates a point’s location historically. The movement of creation (The big bang if you wish) marks the beginning of time and from that moment on every location in spacetime has a unique moment in history. We each occupy a unique place in time that no one else can ever have. This is truly a unique independent measure of time.

The basic geometry

A volume of spacetime varies to the square of the absolute time elapsed. If you double the age of the universe the volume enclosed increased 4 times. Simple isn’t it.

This is a uniform expansion, which means that everything is expanding at this rate, even rulers. Traditionally such an expansion has been argued as being trivial, if everything remains proportionally the same, nothing has changed. However, objects in the past would be denser and thus the effect of gravity would be more powerful in the past. If the Earth were 1/2 it’s present diameter, the effect of gravity on the surface would be increased 4 times. The effect of gravity diminishes with the passage of time, just as Dirac and Gamow believed.

S = Volume of Spacetime
S == T^2

The volume of any object is a distance measure cubed times some constant,
D^3 x k = S = A Volume of spacetime. Combining the relationships results in the following

D^3 = k T^2

[size=3]Note; this is the exact form of Kepler’s Law.
Actually, the theoretical model truly produces Kepler’s law. It will be shown that this is indeed the relationship predicting the inverse square law required for celestial stability. Kepler’s law, which was experimentally established, is now theoretically predicted from a geometric model. Epistemologically, this is as important a relationship as E= mcc, or e = hv

Rewriting the above equation we get

D = k T^(2/3)

Taking the first derivative with respect to absolute time we get how the absolute velocity will vary for two points in spacetime

V = k (2/3) / T^1/3

Similarly for Acceleration we get

A = (-k 2/9)/T^(4/3)

We do not know the value for k but since this is a geometrically described rate of expansion it is possible to state that at a particular time, T1, points in spacetime are a particular distance D1. Similarly at another later time, T2, the objects are at location D2. Dividing the two relationships by each other eliminates the constants resulting in

D1/D2 = (T1/T2)^(2/3)

Similarly for Velocity and Acceleration we get

V2/V1 =(T1/T2)^(1/3)
A2/A1 = (T1/T2)^(4/3)

These formulas are actually field formulas in that they describe, in absolute measures, the properties of an object when associated with a point in free space. (Free space means that no other unaccounted force is acting.)

The Ratios of Time
(Capitol letters indicate “absolute measures”, 1 and 2 are earlier and later measures respectively)
D1/D2 == (T1/T2)^(2/3)
V2/V1 == (T1/T2)^(1/3)
A2/A1 == (T1/T2)^(4/3)
E2/E1 == (T1/T2)^(1/3)

E = energy, which for now can be considered just the square of the velocity term but this relationship is valid for all forms of energy.

There are two important checks that need to be made; will celestial stability be preserved and will relative measures of time be preserved.

Celestial Stability and the Laws of Physics.
Two objects proportionally expanding maintain their relative distances so it is only from an “eye of God” perspective that such an expansion can be visualized. The laws of physics should be consistent, irregardless of the observer’s perspective. The question is, will such an expansion preserve celestial stability for both an “absolute” observer and a “relative” observer? If the Earth were expanded away from the Sun, the Gravitational Force would be reduced more than the Centrifugal force, resulting in the destruction of the solar system. Any theoretical expansion must preserve celestial stability for both the “eye of mankind” and the “eye of God”.

Centrifugal force must equal Gravitational force; The laws of physics are consistent.

Assuming two orbiting systems start with a stable orbit, will the stability be preserved by absolute measures?

Centrifugal force varies as

CF = = V^ 2/R
Gravitational Force varies as
GF = = 1/ R^2
== means proportional to, for the masses involved

Centrifugal force must equal Gravitational Force for stability

CF = GF
V^ 2/R = 1/ R^2
According to the Ratio of times formulas, the absolute velocity and absolute distance varies over the passage of absolute time. If one plugs in how the proposed measures of absolute velocity and absolute distance vary over time, it is found that the necessary celestial balance is preserved no matter what two measures of T1 and T2 are considered.

Example
Centrifugal Force1/Centrifugal Force2 =
Gravitational Force1/Gravitational Force2, which =
(V1/V2)^2/(D1/D2) = (D2/D1)^2

Substituting the ratios of time field temporal relationship for the velocity ratios, and for the Distance ratios, transforms
(V1/V2)^2/(D1/D2) = (D2/D1)^2 , to
((T2/T1)^(1/3))^2 / (T1/T2)^(2/3) = ((T2/T1)^(2/3))^2
(T2/T1)^(4/3) = (T2/T1)^(4/3)
(I used a slight “trick” here, I wonder if anyone catches it. Hint, it is not in the algebra, it is in the application of the relationships).

Theoretical model produces inverse square law structure of spacetime

Newton’s Law of Gravitation establishing the inverse square law for gravity is experimentally derived. Similarly the inverse square law observed for electromagnetic and electrostatic relationships are experimentally established. It is not based upon a theoretical model. For example, Einstein’s Energy equation, E = mcc, was theoretically derived, it was not initially determined by experimental observations. The proposed geometric model does predict inverse square relationships for spacetime.

The proof, deriving the inverse square law
According to the uniform expansion model
A1/A2 = (T2/T1)^4/3 and R2/R1 = (T2/T1)^2/3

From the above equation it can be seen that by squaring the relationship that predicts how the radius between two objects changes with the expansion of spacetime will produce the same relationship that predicts the acceleration associated with the same points. Acceleration varies according to the square of the distance measures.

(R2/R1)^2 =( (T2/T1)^2/3 )^2 = A1/A2 = (T2/T1)^4/3

This theoretical model produces a field structure that is consistent with producing the inverse square relationships of space-time.
Actually the inverse square law is being predicted. A geometric model is producing the inverse square laws as a property of spacetime.

Preserving Relative measures of time.
It is easy to see that a uniform expansion maintains relative distance measures; proportionally everything remains the same. Our relative measure of time is another matter, for this model to be correct, all relative measure of time must also keep their relative measures. From an Absolute perspective outside the expansion, relative time is slowing down, but since all relative measures of time are all slowing down at the same rate, relative measures of time are perceived as constant.

In order to preserve a constant measure of relative time, all clocks or physical processes, according to Absolute measures, must also slow down at the same exact rate.

Lets see if this is true

First a light clock
Imagine a light clock, which is simply a tube with mirrors on each end, with some kind of source and a detector. The time it takes for light to travel a cycle in the tube describes and interval of time. According to the proposed relationships, in absolute measures, the velocity of light slows over the passage of cosmic time as well as the length of the tube increases. This means that a relative interval of time is slowing down in absolute measures.

If one looks at the relationships in a light clock, the relative intervals of time vary as

delta t2/delta t1 = T2/T1 ,
(The reader can derive this relationship. Use the Ratio of Times formulas for V for the speed of light and the length of the light clock).

If the age of the universe were to double, the absolute measure of time associated with a cycle in the light clock would also double. (The speed of light “slows” and the length of the clock increased.).

If one applies the Ratio of Times formulas to an orbiting system, the same change in relative intervals would be found, double the age of the universe and it the absolute orbital interval takes twice as long, based on absolute measures, to complete the orbit.

If one applies the Ratio of Times formulas to a pendulum, even though the form of the equations are drastically different, the same exact slowing exists, double the age of the universe and it takes twice as long for a pendulum to swing a cycle.

If one considers a spinning planet, the same time relationships are predicted. Double the age of the universe and it takes twice as long to describe a revolution.

No matter what system is considered, even ones that require relativistic considerations, the relative measure always remain locally the same.

Using a geometric model that is based upon an “eye of God” perspective, some very fundamental relationships are being established. Relative clocks are keeping their relative measures. This corresponds to establishing the principles of conservation of momentum and conservation of energy. All relative measures of distance and time are established and conform to a geometric expansion of spacetime using an “Eye of God” perspective.

“Before God we are equally wise – and equally foolish”
Albert Einstein

Snowflake

Cool!! Has it been accepted for publication???

Just a little question: how is an "eye of God" perspective possible in a universe where relativity applies?

Oh I talked to 'em... and got confirmation... 8)

Hi Lurker

Thank you for the positive response. It means a lot to me.

My experience has been that “mainstream” theorists are so entrenched in General Relativity that if any model alters gravity with out using tensors, they simply ignore you. However once it looks like others are listening to your ideas (Thank God for Grad students), they begin to pay attention. You have helped me more than you know. Thank you.

Regarding publishing, I have made several presentations of various aspects of the theory (The 8th Gravitational conference at Wake Forest in NC, a poster board and oral presentation at MIT, and 2 presentations at the American Physical Society’s Convention in Florida.) All that will come out of these presentations is a publication that lists the abstracts. I have recently been to the Natural Philosophical Society convention and they expressed interest in publishing at least one of the papers in it’s entirety. (A few years ago I tried to have the work published in a mainstream journal but it was rejected. The reason was “It was too simple to be true”. )

Again, thanks.

John AKA snowflake

Hi Gullible Jones

You asked

Just a little question: how is an "eye of God" perspective possible in a universe where relativity applies?

Relativity still applies. I have done nothing to alter any of the mathematical relationships of relativity.

Snowflake

Gullible Jones

I looked at my response and it did not quite answer your question.

Lets say we draw dots on a rubber membrane. All these dots represent points in the metric of relativity. Each point is separated by a relative measure of distance and each point is separated by a relative measure of time.

Now lets expand the membrane. Since this is a uniform expansion, all rulers are proportionally expanded, so all relative measures of distance have stayed the same. As I showed in the paper posted here, all relative measures of time also stay the same. So based upon relative measures, everything stays the same. All the relationships of relativity still work. I have not changed them one bit.

Now if one has a little imagination, it is not too hard to assign your perspective of the membrane expanding to that of an “eye of God” perspective watching spacetime expanding.

“Imagination is more important than knowledge”
Albert Einstein

Snowflake

Superb logic and deduction, Snowflake. I had always suspected that the speed of light was slowing down and, if it was an intrinsic part of the nature of the universe, derivable from first principles. Unfortunately, I never had the mathematical wizardry, or gusto, to work it out.
Are you saying, as I believe, that the speed of light is extra-dimensional and therefore the only non-expanding ruler, ie, as we expand it remains the same consequently appearing to shrink.
For your next trick, can you determine a formula for the speed of light, and it's diminishing variability, to extrapolate an age of the universe. Good confirmation if it correlates with accepted values.
Keep up the good work, this is very exciting stuff.

I suppose that the hyperspacial "eye of God" perspective would work, in this case... But what about establishing that same perspective for the higher dimension? Wouldn't that require an infinite number of dimensions?

People have been making more or less accurate measurements of the strength of gravity for a a couple of centuries now. If you want to be taken seriously you should used these published resources to place an upper bound on the rate of space-time expansion and show that it is compatible with your theory. Bonus points for using Kepler's observations of Mars.
True for spheres and cubes. Not true for cylinders (V = k z r^2) or ellipsoids (V = k a b c), or are you just doing dimensional analysis? If so even the dimensional analysis wouldn't be correct for objects with fractal surfaces. You did say any object didn't you?
That should be:

V = k (2/3) / T^-1/3
A = (-k 2/9)/T^(-4/3)

This may just be a typo, since you give an apparently correct expression for V2/V1 and A2/A1 latter on.
Do you have any justification for why you take the ratio D1/D2 for distances but then take the inverse ratio for the velocities and accelerations: V2/V1 A2/A1? It looks entirely arbitrary and the danger is that given enough arbitrary manipulations to can turn almost any equation into almost any other equation. You really need to provide some physical reasoning for the flip.

Snowflake is right is his derivations. V = dD/dT = k (2/3) * T^(-1/3) = k (2/3) / T^(1/3) and A = dV/dT = (-k 2/9)*T^(-4/3) = (-k 2/9)/T^(4/3). 2/3 - 1 = -1/3, and that's on top. Same thing for the next derivative. (I'm being detailed here for my own benefit as well as anybody else's since it's currently 3am.)

I was going to correct these, but I didn't read the LHS well at first. It might make for a better presentation if you used the same ratios in all four of these equations, snowflake (i.e. D2/D1 = (T1/T2)^(-2/3) ).

Also, you wrote, "E2/E1 == (T1/T2)^(1/3)," but said that energy was the square of the velocity. Wouldn't it be "E2/E1 == (T1/T2)^(2/3)" instead?

My mistake. I didn't see the quotient symbol (even while I was cutting and pasting).

What cause in this theory an expansion. Does the time T has an energy to overcome gravity ?.

How do you explain that the expansion acceleration begins 6 billions years ago and the expansion as it is since 14 billions years ago ?

OK, you've got a real problem here. A velocity has two properies: magnitude and direction. Since you have previously defined V = dR/dt, all you have is the radial component of a velocity. However, the velocity that should get plugged into CF is the component of the velocity perpendicular to the radial component. See for example this definition of angular velocity. Plugging in the radial component of velocity is simply incorrect, and none of your previous equations provide any value for the component of velocity perpendicular to the radial component.

Ok i'm a layperson, and eve i have some problems with your theroy here.

It's with the algebra, your formulas are only accountin for 1 of your two time dimensions. It either the Local time, or the absoute time, but not both.

When you ploting in a 5 dimensional contruct, all the dimensions should be acounted for, if if there is no change in motion in one of them.

IE for a three dimensions but only with motion along two, i come up with a formula of lV = (X^2 + Y^2 + (Z^2 = 0))^1/2

For a 4D Space time, I come up with a formula of lV = (X^3 + Y^3 + Z^3 + T^3)^1/3

In a five dimensional costruct, I come up with something like.
lV = (X^4 + Y^4 + Z^4 + LT^4 + AT^4)^1/4

__________________
"There is no problem that cannot be solved by a suitable application of high explosives" - US Army Demolitions School

http://worldsofothersuns.home.comcast.net/

I've been lurking here for about a year. Made a point to register tonight just to say that I think this thread is very interesting and, AFAIK, credible. Good job!

When I was 11, I used to take long walks pondering the mystery of the 1837:1 ratio of the mass of the proton to the electron. I degenerated and became a lawyer. But I still love thinking about this stuff. I have always intuited that gravity changed over time, and it's interesting to read a theory about that here.

__________________
"Imagination is more important than knowledge." -Albert Einstein

To all the kind people who reviewed this work and are waiting for a response, I would like to assure you that I shall be responding soon. I have most of Monday free and I will respond then. I have to work this weekend.

Thankfully yours,
Snowflake

Hi Senor Molinero

Thank you for your kind words.

You stated

"Are you saying, as I believe, that the speed of light is extra-dimensional and therefore the only non-expanding ruler, ie, as we expand it remains the same consequently appearing to shrink. "
I did not think of explaining it that way, but I guess you could. The speed of light slows down, based upon absolute measures. The speed of light always appears to be constant locally and it gives an accurate historical “absolute” measure of “look back time”.

You also stated, “can you determine a formula for the speed of light, and it's diminishing variability, to extrapolate an age of the universe. Good confirmation if it correlates with accepted values. “

First, I must admit that the proposed model is not complete. Why are the distance measures for the force of gravity so much larger than the distance measures associated with electromagnetic forces? Why does the proton have so much more mass than an electron even though they carry the same magnitude of charge? There has to be some geometry here that I am missing. (But I believe all these constant relationships are based upon a geometric process).

However, the rate of the expansion of spacetime is geometrically tied to the speed of light and results in establishing Hubble’s varying rate of expansion. The expansion is Flat, (Minkowski or Friedman cosmology). The age of the univese is 2/3 1/Ho but the details of this requires a bit more than a simple post. I am rechecking my work and I am fairly certain that no dark energy is necessary and no dark matter is necessary.


John