What is the origin of mass and the progress in physics?

[SpaceGuy]

An experiment by Italian scientists using data from NASA's Cassini spacecraft , currently en route to Saturn, confirms Einstein's theory of general relativity with a precision that is 50 times greater than previous measurements.

Link.

 

[Chi Meson]

"like I always said: that guy is on to something."
paraphrased from A. Michelson

 

[Albrecht]

... confirms Einstein's theory of general relativity with a precision that is 50 times greater than previous measurements

This experiment shows that the velocity of light is in fact reduced in a gravitational field. This was originally proven by Shapiro in the 1970ies.

Why does the reduction of the velocity of light in a gravitational field prove that the spacetime is curved?? This is just a formal way used by Einstein to describe this phenomenon.

When a light-like particle (like e.g. a photon) passes a massive body it is subject to a lot of interactions with the exchange particles of the fields within the body (e.g. the strong and the electric interaction). These interactions disturb the path of the particle, so that the particle will need more time to pass a specific distance.

To my knowledge this was not quantitatively evaluated yet as a theory. But as soon as it is done it will us tell what really goes on, in terms of physics.

What Einstein has done is, from the point of science theory, a so called "geometrized" theory. This method is nomally a mathematically elegant way, but causes us to forget the physics behind.

 

[Hurkyl]

To my knowledge this was not quantitatively evaluated yet as a theory. But as soon as it is done it will us tell what really goes on, in terms of physics.

So if nobody has been able to quantitatively evaluate this theory in the affirmative, what justification do you have to claim it is what really occurs?

This method is nomally a mathematically elegant way, but causes us to forget the physics behind.

Well I guess I forgot the physics behind it, because to the best of my knowledge, the only physics that adequately explains gravity is General Relativity.

 

[Brad_Ad23]

What's the deal with needing to invoke all those extra fields. If spacetime around an object is curved, and light always follows a 'straight-line' path, we know from simple geometry that a curved trajectory is longer than a perfectly straight trajectory. The velocity of light remains c, it just has more distance to traverse. Asides from the mathematics to describe the actual curvature, that is about as simple as physical concepts gets right there.

 

[Coughlan]

light does follow a strait path ok, but if lights path must be strait how can it traverse the curved space time?[?]

 

[neutroncount]

Originally posted by Coughlan
light does follow a strait path ok, but if lights path must be strait how can it traverse the curved space time?[?]

Because light is following a straight path in curved space. The "path of least resistance" so to speak. Remember, the shortest distance in curved space doesn't always look straight.

 

[Coughlan]

Ok so if you were to be riding on the photon then its path would apear to be strait, but if you looked at space and how the light traveled then it would be curved...sort of like walking only at slower speeds...

 

[neutroncount]

Originally posted by Coughlan
Ok so if you were to be riding on the photon then its path would apear to be strait, but if you looked at space and how the light traveled then it would be curved...sort of like walking only at slower speeds...

The important thing here is light never slows down. It's always at c. In curved geometry, a curved path can be the shortest. Light takes the "shortest" path thinking it to be a straight shot to where ever it's traveling.

 

[Albrecht]

... the only physics that adequately explains gravity is General Relativity

General Relativity of Einstein does in fact not explain gravity.

Gravity is one of the big open problems in present physics. Gravity is in conflict with the standard model, it is in conflict with quantum mechanics.

But a solution is possible. If we take the fact that the velocity of light is reduced in a gravitational field and apply this to the internal oscillations of an elementary particle (as it is stated by the Dirac equation for the electron) then gravity is quantitatively explained and the conflicts to the rest of physics disappear.

So, the origin of gravity is the reduction of the velocity of light near a massive body. - Why is the velocity of light reduced? This is the open question and to explain gravity means to explain the reduction of the velocity of light.

Did Einstein explain, why it is? No, he did not! He just stated that the velocity of light is always constant, but the space is contracted/curved in the vicinity of a massive body. This is by his statement the reason why a photon needs more time to pass a specific distance. Why should the space contract?? I found no answer.

If you sit in your car and push the throttle control, the car will accelerate. That is a normal physical statement. Equivalently you can state that the speed of your car is always constant, but when you push the throttle control, the space in front of the car will contract. This is in fact a possible description of this process, and it can mathematically yield the correct results. But would you do it in this way? And will this explain why this contraction of space happens?

Einstein has not explained gravity, he only described the facts in a formal ("geometrized") mathematical way. The only quantitative parameter in gravity, the gravitational constant G, was not given by Einstein by a theoretical deduction, but was measured in experiments. And the measurements are, as we know, inconsistent to each other. Why are they? Most probably he theory is wrong!

If you are interested in the way how gravity follows from the reduction of the velocity of light, I have prepared a site in the web to explain this:
http://www.ag-physics.org/gravity

 

[Brad_Ad23]

Yeah I guess Einstein was wrong. I mean even with an agreement of 20 parts per million, its still so blatently wrong! The problem with G is that the very limits of our technology will not allow it to be determined precisely. Though one could take a given amount of mass/energy, and how much spacetime curves (again both measured) and derive G, an actual theoretical calculation is not present, I agree. But this cannot come about until we better understand just exactly what spacetime itself is. That does not mean Einstein is wrong. It just means he has a model. But that doesn't mean he is absolutely right either. It just means he's more right than you. But regardless, light does NOT slow down in a gravity well, it merely has to traverse more curved space.

 

[Albrecht]

But this cannot come about until we better understand just exactly what spacetime itself is.

I think it is a different point.

"Space" as well as "time" are human abstractions. We cannot measure them, we cannot notice them.

We can compare the sizes of objects, but we cannot measure "space".
We can compare the frequencies of periodic processes, but we cannot measure "time".

So we are very much free to define what "space" or "time" should mean. Our definition of space or time cannot be "right" or "wrong", it can only be practical or less practical.

By my example of an accelerated car I wanted to show a definition of space, which is not wrong, but which is not very practical.

In this meaning it is not practical to use space and time in the way as Einstein did it. He is/was not wrong, but he was not very practical.

I guess that we will find out soon which physical effect delays the motion of e.g. a photon. (I.e. the interaction with the exchange particles of the other forces). After this is made sure, (and I am very confident about it), what will then happen to the model of Einstein of a curved space/time??

Regarding the measurement of G: The differences of the results are greatly outside the measurement uncertainties (many standard deviations). I guess for the reason: Gravity does not depend on the mass of the gravitational source but on something different, which is however quite strongly related to the mass (e.g. the number of charges of all kinds in the source object).

 

[Hurkyl]

In this meaning it is not practical to use space and time in the way as Einstein did it. He is/was not wrong, but he was not very practical.

How do you figure? Einstein's use of space and time revolutionized physical thinking, correctly predicted many effects that were previously thought absurd, enabled the precise operation of the GPS system, and yields quantitative calculations that agree with reality better than any other known theory of gravitation.


And one point lost on most people is that modelling space-time with differential geometry (aka "curved space") is less of an assumption than that space-time looks globally Minowski or Newtonian.

The very definition of a differentiable manifold is that it looks like Rⁿ locally... which is the only thing our experiments have confirmed anyways. It is, pardon the expression, downright silly to insist that space-time must look like Rⁿ globally, and especially because this assumption appears to be inconsistent with the behavior of gravitation.

Einstein has not explained gravity, he only described the facts in a formal ("geometrized") mathematical way. The only quantitative parameter in gravity, the gravitational constant G, was not given by Einstein by a theoretical deduction, but was measured in experiments.

You do realize there are twenty-odd parameters in the Standard Model that are not given by theoretical deduction? (not to mention I can't imagine how one can presume that the existence of a ton of fields is any more of an explanation than curved space)

 

[Albrecht]

How do you figure? Einstein's use of space and time revolutionized physical thinking, correctly predicted many effects that were previously thought absurd, enabled the precise operation of the GPS system, and yields quantitative calculations that agree with reality better than any other known theory of gravitation.

Let's start from a simple point.

Some postings ago we had the following discussion which we can relate to the Shapiro experiment:

We find experimentally that a photon moving from Earth to Venus and back needs more time when the sun has to be passed closely, than at the other time when the sun is far.

Two explanations:

1. The velocity of light is reduced in the gravitational field of the sun ... or
2. The velocity of light is always the same, but the space is curved in the gravitational field.

The second statement follows Einstein.

What is the advantage to use the second way (Einstein)? We give up our traditional understanding of space (and of time in the general application). What do we get as a return?

When we look to the bending of light at the sun, which was observed at the sun eclipse experiment of 1922 (which made Einstein famous), this can be quantitatively explained by a normal refraction process. We know that the velocity of light is reduced in the gravitational field in the following way:

c(r) = c0*(1-(G*M)/(c0*r^2))

In every situation where c is dependent on r, we get - very classically - a refraction. This refraction explains quantitatively correct what happened during this sun eclipse. Without any space curvature.

The same refraction happens within an elementary particle to the internal oscillation going on there. This causes the normal gravitational acceleration.

I have asked at several occasions whether there are effects of General Relativity which cannot be explained in an analog way. Nobody told me such cases. If you can, please do, I would be really thankful.

For the details of the cases above I again refer to the website I made about it:

http://www.ag-physics.org/gravity

 

[Hurkyl]

What is the advantage to use the second way (Einstein)? We give up our traditional understanding of space (and of time in the general application). What do we get as a return?

A more accurate understanding of space-time, gravitational bending of light, gravitational redshift, black holes, gravitational waves, cosmic expansion (hubble redshift), GPS...

Anyways, before I know how to respond, I must know if you accept special relativity.

 

[Albrecht]

Originally posted by Hurkyl
A more accurate understanding of space-time, gravitational bending of light, gravitational redshift, black holes, gravitational
waves, cosmic expansion (hubble redshift), GPS...

That works also with the approach I gave you. But much easier to understand.

Anyways, before I know how to respond, I must know if you accept special relativity.

Sure, I accept special relativity. That means I accept the phenomena of contraction (of objects), dilation (of periodic processes), and the increase of mass at motion.

However, I do not use as a theory the (geometrized) version of Einstein, but the (physical) version of Lorentz / Poincare which delivers the same results. Special relativity is the consequence of the limited velocity of light by which all fields propagate, and of the inner structure of elementary particles.

I have described also this in a web site:
http://www.ag-physics.org/relat

Originally posted by Ambitwistor
Gravitational light bending cannot be explained by refraction. In refraction, the angle of deflection must be dependent strongly on the wavelength of light. But experiments have shown that gravitational light bending is independent of wavelength.

That is definitely wrong.
If the velocity of light depends on the wavelength (like in a glass lens), then also the refraction angle depends on the wavelength. The velocity of light in a gravitational field does not depend on the wavelength, so the angle is also independent from the wavelength. That is basic classical physics.

Anyway, a "variable speed of light" theory of gravity such as you propose cannot account for the multitude of other experiments concerning gravity that do not involve the deflection of light (Hafele-Keating, Taylor-Hulse, Lense-Thirring, Friedmann cosmology, etc. etc.).

Hafele-Keating is partially special relativity and is of course in agreement with the model I gave.
Lense-Thirring can also be explained by the refraction process, similar to the perihelion shift.
I do not know Taylor-Hulse and Friedmann cosmology, I shall check those two.

For the perihelion drift you are right, I should give the result in detail. I am going to add it to my web site.

Formally what I am doing is just a mathematical transformation of the theory of Einstein into something different, which gives us the possibility to understand it as physical phenomena. So the results will not be different.

It is up to you to prove that your theory accounts for all known effects, not for other people to check your theory against all known effects. Get Cliff Will's book and calculate what your theory predicts for all of the standard tests of GR. (Some of these tests are summarized in http://www.livingreviews.org/Articl...me4/2001-4will/)

You are right that I have to prove my theory myself. But it helps me if you provide me material. So thank you for the reference given. I shall read it and then respond. I have already read something in livingreviews, but did not find conflicts yet.

 

[russ_watters]

Originally posted by Albrecht
That works also with the approach I gave you. But much easier to understand.

No. What you are proposing does NOT fit with observations.

That is definitely wrong.
If the velocity of light depends on the wavelength (like in a glass lens), then also the refraction angle depends on the wavelength. The velocity of light in a gravitational field does not depend on the wavelength, so the angle is also independent from the wavelength. That is basic classical physics.

Thats basic classical physics except the part about gravity bending light. In any case, you said before that bending of light from the sun could be explained by the "normal refraction process." So which is it? Gravitational lensing (according to relativity) or atmosphereic refraction (according to classical physics)? Hint: only one can make predictions that fit with observations.

 

[Integral]

This is an execellent conversation for the Theory Development forum.

 

[Albrecht]

Originally posted by Ambitwistor
All right, prove it: where is your calculation of the magnitude of these effects?

Hafele-Keating:
The time dilation due to the motion of the air planes was special relativity, that is easy enough.
The time advance at altitude in comparison to the ground level results with the same calculation like in standard physics. Normally in GR the dependency of time from the gravitational potential is taken as a fundamental fact. The change in c is deduced from it. Here it is the other way around: I take the change of c as the fundamental fact and the change of time progress is a consequence. The same calculation as normal but the other direction.

Lense-Thirring:
I did not do calculations, but from the refraction it is clear that an effect of this kind must happen. Maybe I do it later quantitatively. It is very much related to the perihelion shift.

Your field theory has only one independent component of the gravitational field: the speed of light at an event. GR has 10 independent components.

This theory also has several components:
- the gravitational potential is 1
- the gradient of the grav. pot. are another 3
- the internal components of an elementary particle which is subject to refraction are ca. 5 more

The theory is easier to do because some of the particle parameters are constant (like the spin and the velocity of the internal oscillation which is essential for this theory).

In particular, the gravitational field you obtain for the Sun is mathematically equivalent to the metric,
ds^2 = -c(r)^2 dt^2 + dx^2 + dy^2 + dz^2

This is Minkowski metric which I do not use. I use the classical (Euklidian) metric also for special relativity as Lorentz and Poincare did. It works!

Originally posted by russ_watters
In any case, you said before that bending of light from the sun could be explained by the "normal refraction process." So which is it? Gravitational lensing (according to relativity) or atmosphereic refraction

If the velocity of light depends on the position, then there is always a refraction by simple geometrical reasons (length of the light path dependent on the position; you can also use Fermat's principle). Independent on what the reason of this dependency is. This causes in this context the gravitational lensing. Of course, nothing by atmosphere.
And this calculation fits perfectly to the observation as you may read in my web site:
http://www.ag-physics.org/gravity

 

[spacetravel101]

Originally posted by Albrecht
Regarding the measurement of G: The differences of the results are greatly outside the measurement uncertainties (many standard deviations). I guess for the reason: Gravity does not depend on the mass of the gravitational source but on something different, which is however quite strongly related to the mass (e.g. the number of charges of all kinds in the source object).

I new, and not a physicist. I believe this is so, that gravity does not depend on mass but on interactions of charged particles within matter. I'm at concept stage, and have very little mathematical formulations, but what I have documented (including experiments) can be found at http://www.QuantumRisk.com/www/BookStore/iSETI_DownLoad.htm

I would appreciate feedabck.

Ben

 

[Albrecht]

Originally posted by Ambitwistor
There isn't any change in c in GR.

We had this discussion before. With reference to the Shapiro experiment. I you observe that a photon takes more time for the way from Earth to Venus and back if the path is close to the sun than you have the choice to assume that either:
1. the velocity of light is reduced in the gravitational field (which is normal physical understanding) or
2. the velocity of light is always constant but the space is contracted close to the sun (Einstein)

Both assumptions yield the same results, it is just a formal transformation. But 1. can be related to physical causes, 2. cannot.

In any case, where is your calculation? You claim you have one, but where is it?

It is a problem of time. But look: the model I have given yields the deflection by the sun precisely (like the model of Einstein) and it yields the gravitational acceleration of an object at rest also precisely (which I do not find at Einstein). These are the fundamentals, all the rest are consequences. I do not see any reason why the rest should not work.
However, I will add the perihelion shift as soon as time permits.

So the coupling to gravity depends on internal components of the particle? What internal components? How is this consistent with tests of the Einstein equivalence principle?

The internal oscillations within an elementary particle are the cause or the gravitational acceleration for a particle at rest. For details please refer to the site:
http://www.ag-physics.org/gravity

There is no point about the equivalence principle. It is in fact not necessary. Gravity is from it's cause not a force but an acceleration. That is the secret. So it is unavoidable that all object have the same acceleration in free fall without a need of an equivalence principle. Please refer again to the website given above.

The Lorentz aether theory is mathematically equivalent to Minkowski spacetime: that's the whole point.

I agree! But I did not expect this statement from you. But it shall be mentioned that the Lorentz aether theory is much easier to understand, and it conforms to quantum mechanics in contrast to Einstein.

Originally posted by spacetravel101
... what I have documented (including experiments) can be found at www...[/URL]
I would appreciate feedabck[/QUOTE]
I shall respond to it. But please be patient for some days, I am presently on travel.

 

[Albrecht]

No, you simply do not accept Einstein's explanation as a "physical cause".

That is correct. I do not take that as a physical cause.

What Einstein did, is in science theory called "geometrization".

It is a known fact since ca. 200 years that every physical process and most technical processes can be completely transferred into purely geometrical processes. This is often a mathematically very elegant way but looses the connection to the physical facts and causes.

Einstein seems not to have known this, he has inadvertantly re_invented it. (As he did with many of his physical considerations.) After he was so successful formalizing the relativistic phenomena in this way, serveral physicists and mathematicians, mainly from Japan and from Russia, have given a lot of examples of it during the 20th century by tranferring physical and technical phenomena into a geometrical presentation.

To apply this to the Shapiro experiment: the statement that c is always constant but the space is curved is a prototype example of geometrization.

My opinion (which is shared by prominent physicists) is: we should go back to physics!

As far as I can tell, you only have small deflections. What about large deflections? The GR prediction has been verified out to 90 degrees and more.

I have used classical refraction. That works also for large angles.

Einstein's theory predicts the acceleration of an object at rest.

How can a curve spacetime make an object at rest moving? Please explain this by physical arguments.

The equivalence principle is an experimental fact

If you accept gravitation as a process of refraction then all corresponding experiments (Eötvös etc.) are completely explained.

Special relativity is much easier to understand, for it gives the same results with fewer entities. It also explains why all effects should propagate at light speed, not just electromagnetic effects; Lorentz's aether supports electromagnetic waves, but there is no intrinsic reason why it should support other waves in the same way;

I do not follow the Lorentzian aether. The only difference to Einstein is that there is an absolute system at rest (which is required by quantum mechanics to my knowledge) and to assume that the phenomena: contraction, dilation, mass increase have true physical causes, not only a geometrized description. And if we use this understanding, we can understand a lot more in physics as main stream does now; and by the way: it is much easier.

 

[spacetravel101]

iSETI Report

I've moved the link to http://www.QuantumRisk.com/iSETI_DownLoad.htm/ . (From the feedback, the previous link had "permission" errors.) This link works.

iSETI = Interstellar Space Exploration Technology Initiative

 

[Albrecht]

Originally posted by Ambitwistor
You're welcome to your opinion, but the fact is that the geometry of spacetime is physically measurable and determines the dynamics of physical processes.

This seems to me as the fundamental logical error.

You can measure the extension of objects, not of space.
You can measure the speed of clocks, not of time.

Space and time are entities of human abstraction. So we are free to define them at it seems practical to us. And I do not state that Einstein was not right, but I state that he was not practical for use in physics with his way of geometrization (what it in fact is).

Please do not pretend that prominent physicists reject Einstein's theory of gravity or its geometric interpretation.

To my knowledge the Austian physicist Roman Sexl was not happy with Einstein's relativity. But he alway stated it very cautiously ("between the lines"). He gave me the idea to explain gravity by refraction. I guess he has tried it but was not successful. My model of an elementary particle ("basic particle model") made it working. This model, by the way, explains a lot of other things like e.g. the origin of (inertial) mass, quantitatively correct.

I'm sorry, I only accept actual derivations and proofs, not your repeated assertions.

(That means the equivalence principle)

From the refraction approach of gravity the equivalence principle follows immeditately. I do not know any other theory which explaines this. For Newton and for Einstein it was just a believe, not taken from a theory. Perhaps my wording was not very clever when I stated that this principle is no longer necessary. I meant that it is no longer necessary as a believe (what a principle always is).

I shall give you another example of the ability of this model: the determination of the Schwarzschild radius.
Question: which is the radius at which a photon is just captured by the gravitational field of an object into it's orbit?

The orbital acceleration of the photon in the orbit is
a = c^2/r

This has to be compensated by the gravitational acceleration
a = 2GM/r^2 (the grav. accel. of a light-like object)

Result by equating a:
r= 2GM/c^2

Now, as an exercise, you may do the same using Einstein's field equations.

 

[russ_watters]

Originally posted by Albrecht
This seems to me as the fundamental logical error...

Space and time are entities of human abstraction. So we are free to define them at it seems practical to us. And I do not state that Einstein was not right, but I state that he was not practical for use in physics with his way of geometrization (what it in fact is).

Actually, that's YOUR fundamental logical error. Or rather your misunderstanding of what "science" is on a most basic level.

As discussed in another thread, words like "momentum" and "energy", may be arbitrary (you could call them "Bob" and "Fred") but their physical manifestations are unambiguous and very real. If you start calling them "Bob" and "Fred" you will confuse a lot of people and accomlish nothing of scientific use, though at least the existing equations will still work. If you change the definitions, then you will likely end up with nothing - useless words for things that don't exist.

Similarly, physical constants may be based on arbitrary units, but they are still very real manifestations of properties of the universe.

Time, space, mass, heat, etc are words invented by humans which are used to describe very real and measurable things.

Your (and most others who post pet theories in here) fundamental misunderstanding here is that science reflects reality, not the other way around. You cannot change definitions and write theories that reflect how you WISH the universe looks/operates and assume that the universe will conform to your theory. So you can call "up" "down" all you want, but that will not make you fall toward the sky.

 

[Albrecht]

Originally posted by Ambitwistor
If you, for instance, measure the ratio of the circumference of a circle to its diameter, and it doesn't come out to π, space is not flat, by definition.

Which type of circle do you mean? A circle of space? What would that mean?
No, you can only measure an object. There is a gedanken experiment, the Ehrenfest disk. If it is rotated with high speed it should break because the periphery contracts. This has to do with the fact that fields contract in motion. And this again was known in classical physics before Einstein started to develop relativity.

Lots of people weren't happy with the theory when it first came out. That's because it was new and different, and didn't have much experimental support.

Roman Sexl was to my knowledge one of the best known specialists for relativity worldwide. He died middle of the 1980ies. No one should guess that he did not understand relativity.

An amusing claim, considering that (a) you don't have a theory of gravity, and (b) you don't know if the theory you do have works.

I do not have and I do not need a specific theory of gravity. I refer mostly to classical physics. Refraction is not my invention but really classical physics, and it does happen in the context we discuss here. Refraction is not at all an option but an inevitable fact. The only special point is that I use particle physics as well. I use the internal oscillation of a particle as it follows from the Dirac equation for the electron, and I assume the same oscillation for a quark. Nothing more is necessary!

As I said, I do not accept repeated assertions, only derivations and proofs. You can claim all you want that thus-and-such follows from your theory, but you have not demonstrated it.

Of course I have. Please look to page 2 of my gravity website. I deduce from refraction:
a = 2*GM/r^2 (for a light like object; for an object at rest it is half of it).

This equation does not contain any parameters of the test-mass under acceleration. So it is a direct proof of equivalence.

What do you mean by "explains this"? You can derive the equivalence principle from the axioms of either Newton's or Einstein's theory.

The equivalence principle was not derived from axioms of either Newton's or Einstein's theory, but it is an axiom in both theories. In the refraction calculation on the other hand it is a deduced consequence.

Light cannot escape GR black holes at all.

Can you please refer to an experiment which proves this?

General relativity's prediction is r = 3GM/c2 for a circular photon orbit. It is r = 2GM/c2 for the Schwarzschild radius.

Thank you for this information. This is a good point to decide which way is correct. Can you please also for this case tell us an experiment (or direct observation) which can be used to make a decision?

Originally posted by russ_watters
Time, space, mass, heat, etc are words invented by humans which are used to describe very real and measurable things.

True, the words are all human inventions. But the word "size" (of an object) means something different than "space". And the size of something is measurable, space is not measurable.

An example from special relativity: It was known, before relativity came up, that fields are contracted during motion (Fitzgerald, Lorentz, Lodge, Heaviside etc). This comes fundamentally from the limited velocity of light by which field changes propagate. If it is now stated that not the field shrinks but space itself shrinks, this is of a different quality. And I doubt (as e.g. Lorentz did until the end of his life in the 1930ies) that this is a practical approach.

You cannot change definitions

I do not change definitions. But I try to show that the classical understanding of space and time was a practical one (not my invention), and that it is more related to a physical (instead of geometrized) understanding of the world to assume e.g. the contraction of objects rather than the contraction of space. Because we have very concrete physical causes for the contraction of objects; we do not have any similar for space.

 

[Hurkyl]

Originally posted by Albrecht:
Formally what I am doing is just a mathematical transformation of the theory of Einstein into something different, which gives us the possibility to understand it as physical phenomena. So the results will not be different.

May I take your last post as an admission that this claim is incorrect?

 

[Albrecht]

Originally posted by Hurkyl
May I take your last post as an admission that this claim is incorrect?

No, it is meant that both statements are equivalent.

Assume history would have been different: First a physical theory of relativity would have been developed. Then Einstein would have appeared and transformed this physical theory into a "geometrized" theory for which he used the idea of a curved spacetime. - Such transformation can of course be inverted.

History was, however, different. Einstein was first and created the geometrized theory as the first one. Now I have entertained to do the inverted transformation back to physics.

The results which can be proven by the experiment should be the same in both cases.

Originally posted by Ambitwistor
I mean, take a piece of string, sweep out a curve of fixed radius with it... .

How do you fix the radius? How do you measure the circumference? You will have to use some kind of mechanical (or optical) equipment. This equipment undergoes changes in a gravitational field. So there cannot be an independent measurement of the space itself.

Now I can ignore all your claims that your theory predicts gravitational effects, like influencing the orbits of planets.

No, why should that be? I repeat the point: we do not need a specific theory of gravity. Gravity is explained in one part by classical physics (the refraction process) and in the other part by our present knowledge of particle physics (i.e. the internal oscillation of particles) which was not accessible to Einstein.

This variable light speed theory you have concocted is not a "fact", and it is not ordinary refraction, either.

The variance of the speed of light near a big object is an experimentally proven fact. Shapiro and his followers have made very precise measurement of it.

The cause of it is most probably the interaction of the particle (photon...) with the field of the other forces inside the object. This has, of course, still to be quantized. But I see good chances to do that. Einstein on the other hand has not at all given a cause for the change of the light speed. The "curved space" is only another wording to state the result.

The equivalence principle applies to everything, not just light-like objects.

Of course, I said that. In the equation which I have derived, there is that factor between 1 and 2 which depends on the speed of the object. (And a factor very close to 1 causes the perihelion shift). But the result does not depend on properties of the object, that is the essential point of the equivalence principle.

An axiom of Newton's theory is that F = GMm/r2. From that you can derive the equivalence principle. An axiom of Einstein's theory is that objects in gravitational motion along geodesics.

Both axioms you mention are "equivalent" to the equivalence principle. So one has the choice which version to take formally as the axiom.

The point is that although you can "easily" derive properties of black holes in Newtonian gravity, they do not behave like black holes in Einsteinian gravity --- and they also do not behave like black holes in nature.

That was my question: How behave black holes in nature? Which experiment exists that shows it with sufficient precision?

This has been observed astronomically: the accretion disks outside black holes vanish abruptly close to the hole.

My question was: where is the experiment which is precise enough to decide about the factor of 1.5 ?

 

[Hurkyl]

No, it is meant that both statements are equivalent.
...
The results which can be proven by the experiment should be the same in both cases.

You miss my point. Your derivation of the location of the circular photon orbit yields a different location than GR's derivation. You even consider it a "good point to decide which way is correct."

So how can your pet theory be equivalent to GR when it makes testably different predictions?

The variance of the speed of light near a big object is an experimentally proven fact.

I don't think you understand what this means in the context of GR. What is varying is coordinate velocity. If you know classical physics, this should be at least somewhat familiar under the name generalized coordinates; the derivative of your coordinate position is, in general, not your velocity.

And, incidentally, the coordinate velocity of light will generally be dependant on the direction in which the light is travelling, so you cannot simply assign a speed of light value to each point in space. (if you want to be equivalent to GR)

In fact, I had an idea very similar to yours when I was in high school, and I abandoned it because of this directional dependance. A "density of space" type model simply cannot be compatable with GR.

 

[Albrecht]

Originally posted by Hurkyl
Your derivation of the location of the circular photon orbit yields a different location than GR's derivation. You even consider it a "good point to decide which way is correct."

My derivation of the photon orbit used an approximation for large r. Sorry for the mistake.

But anyhow: What about "testable ... predictions"? When or where was the Schwarzschild radius ever quantitatively tested in an experiment??

Except the results that I derive in my website and the perihelion shift (which I will add): which statement of GR were ever quantitatively tested?

And: what means "pet theory"? I do not find it in my dictionary.

And, incidentally, the coordinate velocity of light will generally be dependant on the direction in which the light is travelling, so you cannot simply assign a speed of light value to each point in space. (if you want to be equivalent to GR)

It is not my intention to be equivalent to the formalism of GR. It is my intention to provide those results identically which are experimentally proven.

My textbooks about GR say that the velocity of light only depends on the location, not on the direction. I will check that.

Originally posted by Ambitwistor
It doesn't matter whether the space is "really curved" or all your measuring instruments are changing in a way that makes it look curved: if the ratio comes out other than ð&, then space is defined to be curved.

No, this is the difference I mean. It is the difference between the relativity of Einstein and the one of Lorentz and Poincare. For a contraction of an object we know physical causes (the behaviour of the fields). For the contraction of space we do not have any physical causes. Ii is just philosophy.
Similarly the fact of dilation. The reduction of the frequency of periodic processes follows directly and very physicall from the internal oscillations of elementary particles. In contrast to this is the statement of the dilation of "time" again purely philosophy.

If you want to explain these gravitational effects by a variable light speed, fine, but you still need a theory.

We have this theory already: Classical optics and particle oscillation. The deflection of light follows quantitively correct from the refractiton and from the internal oscillations of elementary particles.

The reason that Einstein developed his version of relativity was caused by the fact (from today's view) that he could not know about particle physics. When he developed relativity it was not even certain that atoms really exist. - This was the historical reason. Historically also the cultural situation in Germany of that time which promoted Einstein compared to the other physicists (like Lorentz and Poincare). - Sometimes it can be useful to know the history.

Speculation ignored. Try again if you ever develop a theory.

The curvature of space and time is the most scpeculative and most vage (and logically never provable) theory which exists.

Both axioms have the equivalence principle as consequences.

Newton's equation F = G * m*M/r^2

states that m is also the inertial mass. This statement *is* the equivalence principle.
I have derived it. Who else?

 

[elas]

Surely you should not be argueing over the things Einstein got right, but over the things he got wrong.

Relativity does not give a correct explanation of the observed rotatation of stars around the galatic centre. Neither (according to Enc. Brit.) does it give an acceptable explanation of the transmission of light between galaxies (see: Enc. Brit. Unsolved problems of physics).

 

[Albrecht]

Originally quoted by Ambitwistor
If two interpretations lead to the same physics, then it is a philosophical opinion which interpretation one likes -- it is not a matter of physics.

The slowing down of clocks etc. is the consequence of the internal rotation of elementary particles, which is a fact. The assumption that "time" itself slows down is a statement, nothing more.

When Copernikus stated the helio-centric view of the planetary system, the next question was: why do the planets orbit the sun? The answer of Rene Descartes was: It is a fundamental law in this world that everything has the tendency to orbit. In contrast to him Newton did have a law of motion and a theory of gravity. - Wasn't the latter the real physics?

Einstein told us that the time is slowing down with motion as a fundamental law of physics. This is very similar to Descartes. Main stream physics is still lacking the correspondence to the step of Newton.

You have no field equation which predicts, given a particular source configuration, what the speed of light as a function of position will be.

The field equations descibe how the speed of light is reduced. Not why. The answer to the "WHY" would be physics.

Einstein's version of relativity explains particle physics quite well, in the form of quantum field theory.

So, why do we not know what the origin of mass is? Why do we deal with odd thoughts like the Higgs fields? Even if the Higgs theory would be true, it is not able to tell what the mass of e.g. the electron is?

So we know very little about this. Einstein founded relativity ca. 100 years ago. He died ca. 50 years ago. He did not know these problem and could have not answers to it.

Newton. Einstein.

Lets begin with Newton. In his equation F = G * m*M/r^2 Newton had to assume that m is the inertial mass of an object and works as well for gravity. This assumption is the assumption of the equivalence principle.

How can mass cause a gravitational acceleration? Elementary particles have, according to the standard model, no mass by it's own. Mass is a dynamic process within the particle which is dominated by the strong force, in a certain configuration of it`s constituents. Why does the strong interaction cause a gravitational acceleration just in a specific configuration? Who anwers this? Or, to speak with Einstein, why should this specific configuration cause the space to get curved? Ever heard an answer??

Originally prosted by elas
Surely you should not be argueing over the things Einstein got right, but over the things he got wrong.

We have too many open questions. My textbooks say that Einstein's gravity is in conflict with particle physics (QM). No one knows the origin of mass. (There I have in fact a theory, in contrast to main stream physics, which works quantitatively correct
http://www.ag-physics.org/rmass )
There is in fact still to do a lot in physics.

It does, if you accept the existence of dark matter

Dark matter is real guesswork. It shows a bit how helpless present astronomy is when they attempt to explain the expansion of the universe.

 

[elas]

You do not have an explanation of "why" the speed of light is reduced, and you don't even have an equation that will predict, in general, how it is reduced.

The speed of light is directly related to field elasticity.

So, why do we not know what the origin of mass is?

Mass originates from the reduction of the vacuum force. the rest energy of the mass and the vacuum force at a given point is always equal to the same quantity, (constant).

Why do we deal with odd thoughts like the Higgs fields?

Because no one applied the Law of Economy to Quantum Physics.

How can mass cause a gravitational acceleration?

It does not. Gravitational acceleration is caused by the vacuum force.

We need to be able to predict the orbits of bodies

Of course we do and if you read the reports on the rotation of galaxies you will know that this is where GR fails completely. The outer stars are orbiting 5 to 6 times faster than GR predicts, and should (according to GR) be flying off out into space.
GR also fails to predict the observed gravitational relationship between galaxies within a group of galaxies. Add to this its failure to predict the observed universal expansion and tell me please, what is left of GR?

 

[spacetravel101]

If I remeber correctly, the rotation of the outer stars is directly a function of the super massive black holes at the center of every galaxy.

 

[elas]

If I remeber correctly, the rotation of the outer stars is directly a function of the super massive black holes at the center of every galaxy.

A Black Hole is just another vacuum field where the density of the force carrier is high due to a high vacuum force. You can get some idea of how this works from my explanation of atomic structure; simply repeat the process on a larger scale.
This is the beauty of of the Vacuum Model in that every structure from quark to black hole can be seen to be a repitition of a single structural building process, nature simply repeats itself in different volumes and densities in order to produce the variety we observe (and are part of).
Given that vacuum is a negative quantity and the force potential of the mass has a positive quantity then at any given point

Vacuum force plus latent energy force equals zero

This applies to all fields regardless of changes in volume and density.

If you then look at my explanation of movement you can see that the greater the density of the force carrier the greater the drag it applies to movement of the vacuum field. Given that photons pass through vacuum fields of other particles (including gravitons) then one can understand how the speed of light is controlled by nature.

An imbalance in the number of particles in two or more adjacent groups creates an imbalance in the vacuum fields, given rise to so-called magnetic action, in reality there is no separate magnetic force it is a variation of vacuum force.

This concept of a vacuum theory does not invalidate current theory, it changes the way current theory is explained, thereby allowing the question of how and why to be answered.
So far it seems to be the relativity groups who are trying to develope a vacuum theory to replace the unsatisfactory relativity theory. But particle and quantum physics groups need to wake up to the fact that if we want a T.O.E. then vacuum theory is the simplest way forward. Black Hole and String theories are an unwarrented distraction. Particle and quantum physicists already have all the data needed to build a vacuum theory, relativity groups do not.

 

[Albrecht]

Originally quoted by Ambitwistor
(What is the "internal rotation of elementary particles", anyway? Intrinsic spin?) Time dilation is empirically independent of any known property of particles.
...
When all physical processes are observed to take place more slowly, that is the definition of "time slowing down".

From the Dirac equation it follows that the electron performs an internal oscillation with c. (This causes the spin and the magnetic moment of it). From the dependency of the gyromagnetic relation from the mass of an elementary particle, it can be concluded that this fact, the internal oscillation with c, is universal for all elementary particles.

If now a particle is moved then the oscillation frequency has to slow down to keep the oscillation velocity at c in relation to the observer or to the frame at rest. This follows simple from the theorem of Pythagoras which leads directly to the Lorentz factor. You find the calculation in detail in my website http://www.ag-physics.org/rtime

All objects are built by elementary particles. That makes this behaviour universal. In such situations it happens easily that humans take it as a universal property of nature. But making physics should mean to find the details.

A similar phenomenon is the equivalence of mass and energy. Both are different physical parameters. As another consequence of the similar structure of all elementary particles our measurement show this equivalence. But we loose information if we mix both parameters.

Newton merely gave a more precise statement of a body's tendency to orbit; he didn't specify a mechanism any more than Descartes did.

The following happened in sequence:
1. Copernicus detected that the planets orbit the sun (only the fact, nothing more)
2. Kepler gave us a kinematic law which described the relation between radius, angular velocity and period of their motion
3. Newton presented a dynamic law from which 2. can be derived.

This is the normal step-wise development of physical understanding.

Regarding GR we are somewhere between step 1 and step 2.
Step 3 is still completely open.

You are confused. The strong interaction does not dictate mass or gravitational acceleration. The Higgs mechanism dicates mass, and a theory of gravity dictates the resulting gravitational field of that mass.

I have shown (on my web site) that the inertial mass results from the strong interaction and the internal structure of an elementary particle. According to this, the mass depends on the size of a particle. I applied this to the electron: From it's magnetic moment the radius of the electron can easily be calculated. If I take this radius and insert it into my formula, it yields the correct mass of the electron with a residual deviation of 0.1% . (This is because I ignored electric effects). - To my understanding this is a good proof of this model.

It is true that there are still physicists who believe in the Higgs theory. This will continue for another ca. 3 years from now. Then the LHC at Cern will be finished and will have started operation. And people will have to realize that they do not find Higgs bosons even at that energy. - Anyway, even if the Higgs theory should be working, it is obviously not able to provide results like the one mentioned above for the electron.

Originally quoted by elas
Mass originates from the reduction of the vacuum force.

Can you please explain how this works, of correspondingly what "vacuum force" is?

GR also fails to predict the observed gravitational relationship between galaxies within a group of galaxies.

Astronomy has these problems to explain the motion of galaxies and the expansion of the universe in general. The assumption of dark matter is an attempt to find an answer. To my opinion it is very probable that gravitation does not depend on the mass but on the number of elementary particles and on their fields. That would mean that also neutrinos can give a considerable contribution to the gravitational field.

For our planetary system we do not notice this. It does not cause a large numerical error if we assume that the mass is the origin of gravity. The objects in our system have a very similar composition.

 

[elas]

You never say anything real about physics

All the work on the opening page of my website is based on graphs constructed using 'Emsley's' 'Tables of Elements', a standard work in Particle Physics, the author being on the staff of Cambridge University, a world leader in Particle and Quantum Physics. A large number of the quantities used were found by experiment; the rest are predicted from known quatities. This is reality as far as we know it.

The interpretations I make are new and therefore do not contradict current theory since current theory makes no such interpretations, it deals only with predictions. I am not concerned with prediction, but with structure. My work explains observed structure and therefore is an attempt to explain the reality of particles and wave structure .

There is a world of difference between prediction and reality and I am the one dealing with reality. On that basis I challenge you to justify the statement you made, which is quoted above at the start of my reply.

 

[Brad_Ad23]

Predictions are observations which may be made. Any theory must make these, and these predictions MUST match all previous observations as well, or do a damn good job convincing us why the way we observed something was flawed. You have yet to do this. Example: The claim that two particles orbit each other with the speed of light. This is absolutely forbidden by Special Relativity, which is extremely well verified. You need to get a better understanding of the physics before you can be justified in saying that you are correct.

 

[elas]

Predictions are observations which may be made. Any theory must make these

Correct.

Relativity predicts the speed of galatic rotation and is out by 500%.
Relativity predicted the expansion of the universe and got it completely wrong.
Relativity predicted the radius of a black hole and was out by 900%.

Astrophysicist think Relativity will be replaced by either a vacuum or string theory.

I am using particle physics to predict that it is a vacuum based theory that will win this debate. The observations needed to justify my claim have already been made, they just need intelligent interpretation.

 

[Albrecht]

Originally posted by Ambitwistor
The Dirac equation doesn't actually say that. It does say something about spin, but it doesn't say it's due to any "internal oscillation".

I did not evaluate the Dirac equation by myself. But the Austrian Erwin Schrödinger has evaluated it short time after it was published. And he stated that it follows from the Dirac equation that the electron oscillates internally with the speed of light c. This result was to my knowledge never questioned by the physical community. David Hestenes (Arizona) e.g. used it as a basis for his theoretical work on electrons.

The purpose of the Dirac equation was to take relativity into the wave function. To my opinion Dirac has inadvertently found the cause of (special) relativity. I just continue from that point.

What are you talking about? GR has a dynamic law from which 2 can be derived: the Einstein field equation.

Wasn't it clear that this is an analogy? Newton could derive the orbital motion from gravity. Now we have to derive gravity from something more fundamental. That is still an open issue.

Ah, the last refuge of the crackpot: "I can't prove them wrong, but history will vindicate me."

I do not keep it open for an unpredictable future. We have only to wait for a limited time to clarify the Higgs issue.

You never say anything real about physics, just a bunch of claims you make up and never support. You haven't produced a theory of gravity, and you haven't produced a theory of elementary particles.

I have leaned that a theory is the better, the fewer assumptions are necessary for it. My intention is to show that classical physics and a quite simple particle model are sufficient to explain relativity (and in the other case the origin of mass).

I can derive the equivalence principle from my (simple) assumptions and I can also,using the same model, derive the mass of a particle from it's other parameters. I do not know any alternative approach which is doing this.

Once again, groundless speculation with no testable theory to back it up.

(This quote was with reference to a composition dependency of gravity)

The investigations which have been made in the 1980ies to investigate the assumption of a "fifth force" gave some indication to a possible dependency of the gravitational constant on the composition of the gravitational objects. This result is not very significant but could show the direction, where a further investigation could be useful.

Originally posted by Brad_Ad23
The claim that two particles orbit each other with the speed of light. This is absolutely forbidden by Special Relativity, which is extremely well verified.

It is just the contrary. Did you realize that the two basic particles are mass-less? Where is then the conflict to Special Relativity?

My approach is conflict-free in contrast to the normal conclusions from the Dirac function. The Dirac function is normally interpreted in the way that the electron itself is making an orbital oscillation with c. This interpretation has two problems:

1. As the electron as a whole has a mass, it cannot move with c
2. An object, which orbits on it's own, is a permanent violation of the momentum law.

The standard answer of main stream physics to this conflict is, that this process is subject to QM and as such not understandable by the human brain with normal imagination.

If you accept my particle model, both conflicts disappear and the process is easily accessible by our imagination.

 

[FZ+]

It is just the contrary. Did you realize that the two basic particles are mass-less? Where is then the conflict to Special Relativity?

The idea that they are orbiting - ie. accelerating.

 

[Albrecht]

Originally posted by FZ+
The idea that they are orbiting - ie. accelerating.

Sorry, is this a comment or a question?
I am not sure if I understand what you mean.

 

[elas]

you forgot to mention that all of your responses have nothing to do with the known laws of physics

All my responses are based on atomic data used in Particle Physics. I do not seek to change the Laws of Physics, but to enforce them. My argument is that the Law of Economy (Occam's Law) has not been applied with sufficient vigour. If doctors treatd medical science the way physicists treat Quantum Physics they would all be doing time for malpractice.

By the way, "what is left of GR" is the dozens of experiments that which have verified GR's predictions to high precision.

Then why did 'Scientific American' feel that the dissatisfaction with 'GR' was sufficient to warrent a special issue on this issue; dealing largely with the need for change. The articles are all by experts in their field.

It only gives the wrong prediction if you assume that all the mass-energy in the universe is luminous. But we know that is not the case; the question is just a matter of, how much of it is non-luminous, and why?

The last article I read on this subject stated that the latest observation proved that the maximum possible quantity of dark matter was insufficient to make up the difference in orbital speeds.

Your comments on equations are so wide of the agreed rules on "What constitutes a new theory" as to be unworthy of a reply.

 

[Albrecht]

Originally posted by Ambitwistor
I need not remind you again that one or two calculations demonstrate nothing.

I have many calculations, but at least 2 of them (origin of mass and derivation of the equivalence principle) are not available from existing theories.

And that works for all particles? Or even all Dirac particles? If it doesn't, your theory is wrong.

It works for all leptons and for all quarks.

On conferences I have asked particle theorists what will happen if no Higgs bosons are found. The answer: We will have to re-think large areas of our physics. - Are we prepared for that?

I think Brad_Ad23's point was just that massless particles in special relativity can travel only in straight lines, and therefore cannot orbit.

If you look to my web site, the basic particles are bound to each other by a multipole field. This makes them orbiting at a fixed distance (which is of course subject to relativistic contraction).

But your theory is not consistent with special relativity anyway.

On the contrary, my model defines special relativity. It is in detail in http://www.ag-physics.org/relat

No, Albrecht, that is your nonsense interpretation.

The interpretations which I have cited about the oscillation within an electron and the difficulty to understand them are copied from David Hestenes, who has done a lot of theoretical work about the electron and particularly it's "Zitterbewegung".

You may give him a call and tell him that he has written "nonsense". Have fun!

 

[russ_watters]

Originally posted by elas
Then why did 'Scientific American' feel that the dissatisfaction with 'GR' was sufficient to warrent a special issue on this issue; dealing largely with the need for change. The articles are all by experts in their field.

Could you cite it? All I could find was this (about SR):

After a century, Einstein's special theory of relativity, which describes the motion of particles moving at close to the speed of light, has held up remarkably well.

I do not seek to change the Laws of Physics, but to enforce them.

Um... ahh, nevermind. You probably already know.

 

[Albrecht]

Originally posted by Ambitwistor
You can predict the masses of all particles from first principles? What do you get for the values?

If I know either the size or the magnetic moment, the mass follows from it. The formula is given e.g. in http://www.ag-physics.org/electron

There are non-Higgs theories that have tried to account for mass, too, like technicolor. They may experience a renaissance.

Do they work?

Fields, multipole or not, do not deflect massless particles in special relativity.

There is no conflict with special relativity if a massless particle moves with c on an orbit.

A theory with a variable speed of light isn't SR.

True. But that was not the point.

The point was that 2 massless ("basic") particles orbiting each other fulfill - besides the field contraction already known before Einstein - the conditions for being the origin of special relativity.

 

[Albrecht]

Originally posted by Ambitwistor
But that is not an independent prediction of mass; it's a relation between mass, charge, and magnetic moment: no different than the Dirac equation, which also does not predict the masses of the elementary particles.

Did Dirac find the equation
m = h(bar)/r*c ? Can you please give me a reference for your statetment?

I have presented this origin of mass, which uses the fact that every extended object must behave inertially, at 6 physical conferences till now. During the very engaged discussions no one has ever stated that this idea or the formula which I derived was previously found by somebody else.

Yes, there is. Special relativity says that a massless particle must move in a straight line.
...
Special relativity does not permit massless particles to orbit each other.

Please give me a reference which states this. I have presented this model to some of the German top researchers in relativity. No one has ever stated this. And I do not see where the conflict could be.

 

[Albrecht]

Originally posted by Ambitwistor
No, but that's irrelevant. You don't have an independent measurement for r; you have to derive it from the magnetic moment. Thus, to determine m, you need to know the charge and magnetic moment of the electron, which is the same as what Dirac needed.

The Basic Particle model does not tell why an electron exists. It provides the dependencies of it's parameters. It derives the dependency from basic assumptions.

The Dirac equation on the other hand describes the situation correctly using the QM formalism. It does not explain why it is as it is. If Dirac would explain the origin of mass, nobody would look for Higgs bosons.

If tomorrow it would be measured that the electron has a different mass or a different spin or a different mag. moment, the Dirac function could be easily adapted. But the Basic Particle model would in that case be void. The model does not have free parameters in this respect.

Are you denying that, in special relativity, photons always travel along null geodesics of Minkowski spacetime?

I do not talk about photons, but about particles which are really massless.

If the photon is bound into an orbit, this will be a classical dynamic process using the dynamic mass of the photon. The basic particle has no mass / no energy even if moving with c. Mass (and energy) is caused by the configuration of a pair of basic particles. This is the essential assumption of this model.

And also: The configuration of a pair of basic particles constitutes special relativity. Below that level (i.e. below the level of an elementary particle) there is consequently no relativity

 

[spacetravel101]

All this talk and no real progress. Do look up where others are going.
I found this website,
http://www.faraday.ru/faraday_english.html,

if it is true I haven't found anything comparable to this in the West.

 

[QuantumNet]

I thought the Schwarzschild Radius was due of relativistic effects.


M = black hole mass

a = MG(1-(v/c)²)^½/r² = MG(1-(MG/(rc)^2))^½/r² =c

But this results in MG/c whatever you do.