# Paper: A causal mechanism for gravity

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Abstract

In this speculative paper, we show that electromagnetic (EM) mass and general relativistic time dilation are sufficient to predict gravitational attraction.

## Time Dilation as Refraction

First, we consider light moving slowly through a local medium with a large refractive index; we then observe a remote light ray moving slowly in a large gravitational field due to relativistic time dilation, such that their respective apparent velocities are equal, and recognize the opportunity for a potential equivalence. Exploring this, we create a spherical refractive medium whose index varies with the distance from its center by the following:

where r is the distance from the center of the object and rs is the Schwarzschild radius of some gravitational object O with mass m which we are attempting to emulate.

What we discover is that light passing through such an object at a given radius r will behave identically as it would while passing by O at the same radius. This phenomenon, known as the optical-mechanical analogy (or more recently as F=ma optics), has been well-established and extensively studied over the last century. [ref 1-3]

As Sir Arthur Eddington wrote [ref 4] in his famous 1920 summary of General Relativity, “Space, Time and Gravitation”:

Quote

We can thus imitate the gravitational effect on light precisely, if we imagine the space round the sun filled with a refracting medium which gives the appropriate velocity of light. To give the velocity 1 − 2m/r, the refractive index must be 1/(1 − 2m/r), or, very approximately, 1 + 2m/r. At the surface of the sun, r = 697, 000 km., m = 1.47 km., hence the necessary refractive index is 1.00000424. At a height above the sun equal to the radius it is 1.00000212.

Any problem on the paths of rays near the sun can now be solved by the methods of geometrical optics applied to the equivalent refracting medium. It is not difficult to show that the total deflection of a ray of light passing at a distance r from the centre of the sun is (in circular measure)

whereas the deflection of the same ray calculated on the Newtonian theory would be

.

For a ray grazing the surface of the sun the numerical value of this deflection is

1”.75 (Einstein’s theory),

00”.87 (Newton’s theory).

The efficacy of the “F=ma optics” is without doubt, however, respective authors on the subject are careful to stress the purely analogous nature of the relationship. We would like to suggest that it isn’t an analogy at all, but rather a literal equivalence.

## EM Mass

Let us envision an electromagnetic wave, with a wavelength of 2.43 * 10-12 m, moving in a periodic cycle which takes it back upon itself such that it becomes a self-reinforcing soliton. The complete orbital path length of this EM wave is equal to its wavelength but is such that it makes a double-loop. (see Fig 1)

Such a quasi-symmetrical object, if stable, would resemble an electron. It would have a physical radius of on the order of 2.43 * 10-12 m / 4𝛑, an electric field, a magnetic dipole, and a half-integral spin [ref 5, 6]. It would also offer a physical manifestation of Einstein’s mass/energy equivalence (e.g. “releasing” the photon from its self-contained path would result in a burst equal to its “rest energy”).

## Cosmic Speed Limit

Philosophically, many of us have been mystified by the limiting nature of c. EM mass might provide a straight-forward explanation -- a photon turning back upon itself does not follow the traditional geodesic between two points. As an EM mass particle is accelerated, a larger portion of its photon’s circuit is thus spent moving in the direction of its velocity; this percentage can be arbitrarily close to, but not quite, 1. (see Fig 2)

## Transverse Waves

If we refer back to our sphere of graded refractive index, we would expect that the path of light moving radially to it would remain unaffected; only a light’s path with a transverse component would be altered. The photon of an EM mass particle moving in a closed circuit within the sphere would possess a transverse portion of its path relative to the center of the medium in a range between .5 and 1, depending upon the relative velocities of the sphere and the particle. This could manifest as relativistic mass.

## Conclusion

In this paper we have shown the connection of optics to the gravitational bending of light in a graded time dilation field. Additionally we have shown that if mass were to possess an electromagnetic nature moving in a cyclic fashion (i.e. “EM mass”) then we are able to precisely predict the gravitational behavior of that mass in the presence of such a time dilation field without invoking any other mechanism related to General Relativity. Lastly, we are able to show that this model may plausibly explain other aspects of Relativity, such as the limiting speed of light and relativistic mass. We feel that these aggregate theories provide ample potential to warrant further investigation.

References

[1]The optical-mechanical analogy for stationary metrics in general relativity; Paul M. Alsing; American Journal of Physics 66, 779 (1998); https://doi.org/10.1119/1.18957

[2] The optical-mechanical analogy in general relativity: Exact Newtonian forms for the equations of motion of particles and photons; James Evans, Kamal K. Nandi & Anwarul Islam; General Relativity and Gravitation volume 28, pages 413–439(1996)

[3] ‘‘F=ma’’ optics; James Evans and Mark Rosenquist; American Journal of Physics 54, 876 (1986); https://doi.org/10.1119/1.14861

[4] Space, Time and Gravitation; Sir Arthur Eddington; http://www.gutenberg.org/files/29782/29782-pdf.pdf

[5] Sumana Bhadra, Electromagnetic Mass Models in General Theory of Relativity: https://arxiv.org/abs/0710.5619

[6] Is the electron a photon with toroidal topology? J.G. Williamson and M.B. van der Mark, 1997; Annales de la Fondation Louis de Broglie, Volume 22, no.2, 133. http://home.claranet.nl/users/benschop/homepg2/electron.pdf

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2 hours ago, rjbeery said:

Time Dilation as Refraction

I note you use page 109 of  one of Eddington's books as a supporting reference.

In his later book, 'The Mathematical Theory of Relativity', Eddington refers to this page and provides the mathematical derivation of the formula shown. (pages 90 - 91)

He also explains why the analog system is easier to calculate (he was a great calculator in the days before computers) and warns about the difference in coordinate systems employed in this analog and the local coordinate system of GR.

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2 hours ago, rjbeery said:

we then observe a remote light ray moving slowly in a large gravitational field due to relativistic time dilation,

Gravitational fields do not slow down photons, they just-red shift them and make them bend their trajectories. Think again.

3 hours ago, rjbeery said:

Such a quasi-symmetrical object, if stable, would resemble an electron.

In no way does that resemble an electron. A bundle of EM field does not have charge, nor does it invert the sign of its probability amplitude under 2pi rotations, which is required.

16 minutes ago, joigus said:

Gravitational fields do not slow down photons, they just-red shift them and make them bend their trajectories. Think again.

In no way does that resemble an electron. A bundle of EM field does not have charge, nor does it invert the sign of its probability amplitude under 2pi rotations, which is required.

And I've missed the part where you provide a causal mechanism for gravity.

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44 minutes ago, studiot said:

I note you use page 109 of  one of Eddington's books as a supporting reference.

In his later book, 'The Mathematical Theory of Relativity', Eddington refers to this page and provides the mathematical derivation of the formula shown. (pages 90 - 91)

He also explains why the analog system is easier to calculate (he was a great calculator in the days before computers) and warns about the difference in coordinate systems employed in this analog and the local coordinate system of GR.

I'll check that out, thank-you!

18 minutes ago, joigus said:

Gravitational fields do not slow down photons, they just-red shift them and make them bend their trajectories. Think again.

In no way does that resemble an electron. A bundle of EM field does not have charge, nor does it invert the sign of its probability amplitude under 2pi rotations, which is required.

Photons do not slow down locally, I agree, but remote photons must slow down. If you're wearing a watch which uses photons as a timing mechanism, and I'm wearing the same watch but sitting far above you in a powerful gravity well, how else could I explain that your watch is ticking more slowly? You can claim that it's merely an illusion because it isn't local but that point 1) is debatable (because it's an absolute effect) and 2) irrelevant to the analogy, because prism refraction is locally absolute.

Regarding EM mass, I suggest that you read the cited references, particularly http://home.claranet.nl/users/benschop/homepg2/electron.pdf. The authors have published many peer-reviewed articles on the subject. I find it fascinating, personally.

Cheers,

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28 minutes ago, rjbeery said:

I'll check that out, thank-you!

Photons do not slow down locally, I agree, but remote photons must slow down. If you're wearing a watch which uses photons as a timing mechanism, and I'm wearing the same watch but sitting far above you in a powerful gravity well, how else could I explain that your watch is ticking more slowly? You can claim that it's merely an illusion because it isn't local but that point 1) is debatable (because it's an absolute effect) and 2) irrelevant to the analogy, because prism refraction is locally absolute.

Regarding EM mass, I suggest that you read the cited references, particularly http://home.claranet.nl/users/benschop/homepg2/electron.pdf. The authors have published many peer-reviewed articles on the subject. I find it fascinating, personally.

Cheers,

I was about to tell you about your mistake with the ticking clocks, to do with absorption and re-emission, and elaborating on your messing up red-shift with slowing down. But it would be wasted on you, as there's no one reading at the other end. I close with a quasi self quotation:

Gravitational fields do not slow down photons, they just-red shift them and make them bend their trajectories. Read some relativity books.

And a literal self-quotation:

59 minutes ago, joigus said:

And I've missed the part where you provide a causal mechanism for gravity.

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15 hours ago, rjbeery said:

What we discover is that light passing through such an object at a given radius r will behave identically as it would while passing by O at the same radius.

This is valid only for spherically symmetric, non-rotating and uncharged gravitational sources in an otherwise empty universe, i.e. in spacetimes that are approximately Schwarzschild. It cannot be generalised to any other case, which is why it is not suitable as a general model of gravity.
General Relativity on the other hand represents a general constraint on the metric, i.e. it constrains what form the geometry of spacetime can take, given appropriate initial and boundary conditions. It thus works as a model for gravity regardless of the precise nature of its sources, in any given purely classical scenario.

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15 hours ago, joigus said:

I was about to tell you about your mistake with the ticking clocks, to do with absorption and re-emission, and elaborating on your messing up red-shift with slowing down. But it would be wasted on you, as there's no one reading at the other end.

The red-shifting/blue-shifting only occurs with movement which is radial to the gravity source. The difference in the apparent velocity of photon movement in various gravity wells, which is perpendicular to the gravity source, cannot be due to "slower or faster re-emission" from atoms because it is independent of distance traveled.

In other words, a photon travelling 1 light-second "up here" may take 2 light-seconds "down there", but then a photon travelling 10 light-seconds "up here" would take 20 light-seconds "down there". I don't think anyone believes that the emitting atom down there is actually holding on to that photon just long enough to give the illusion that the photon's future speed has been reduced.

15 hours ago, joigus said:

And I've missed the part where you provide a causal mechanism for gravity.

The causal mechanism is the time dilation field refracting the EM mass.

4 hours ago, Markus Hanke said:

This is valid only for spherically symmetric, non-rotating and uncharged gravitational sources in an otherwise empty universe, i.e. in spacetimes that are approximately Schwarzschild. It cannot be generalised to any other case, which is why it is not suitable as a general model of gravity.

I believe it does generalize. What we call space-time curvature in GR can simply be reframed as a time dilation field, and the effects of gravity are already accounted for.

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Gravitational time dilation is relative.
It is only apparent when comparing the emission ( frequency/wavelength ) from two differing depths of the Gravitational potential well.
IOW, one 'signal' has to climb/descend to the height/depth of the other for the comparison to be made.
You cannot circumvent that ( no mixed frames ).

Edited by MigL
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4 minutes ago, rjbeery said:

The causal mechanism is the time dilation field refracting the EM mass.

Sorry, I didn't see the geodesic equation, I didn't see Einstein's equations derived, I didn't see the equivalence principle, I didn't see the Newtonian limit, I didn't see gravitational horizons, FRW or DeSitter universes or any other cosmologies, I didn't see vacuum energy, I didn't see dark matter, or red-shift, I didn't see a thing that even remotely reminded me of gravity, except in the title and Eddington's paper.

I suggest you change your mindframe: Try to prove yourself wrong. If you always try to prove yourself right, you're always going to find a way to be right.

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12 minutes ago, MigL said:

Gravitational time dilation is relative.
It is only apparent when comparing the emission ( frequency/wavelength ) from two differing depths of the Gravitational potential well.
IOW, one 'signal' has to climb/descend to the height/depth of the other for the comparison to be made.
You cannot circumvent that ( no mixed frames ).

Gravitational time dilation is absolute. Take two identical watches which (let's say) use photons for timing, and place one more deeply in a gravitational well. It is not an illusion that the one in the gravitational well clocks more slowly. It has nothing to do with the wavelength of the the timing photons. Pound-Rebka only applies to radial movement.

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How do you know it ticks more slowly until you bring them together to compare ?
Frequency and wavelength are a 'signal', and are used as 'timing', or a clock, if you will.

Edited by MigL
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5 minutes ago, joigus said:

I suggest you change your mindframe: Try to prove yourself wrong. If you always try to prove yourself right, you're always going to find a way to be right.

That's why I'm here, friend. I'm asking for feedback. I've provided the references for my paper, and those references seem pretty thorough. The concept of "F=ma optics" has been studied for over a century, and the derivation is well established. The concept of EM mass is relatively new (~30 years) but still has many papers published in high-profile journals.

4 minutes ago, MigL said:

How do you know it ticks more slowly until you bring them together to compare ?

It doesn't matter how we compare. Bring the lower one up, bring the higher one down. Both parties use telescopes. Morse code. Carrier pigeons. We wait a year, there's a difference in time passed. Wait 100 years and that difference is 100 times greater.

If you don't believe that gravitational time dilation is an absolute phenomenon then, with respect, I don't think you'll have much to add to this conversation. The corrections made to the GPS satellites to account for gravitational time dilation are there for a reason.

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42 minutes ago, rjbeery said:

If you don't believe that gravitational time dilation is an absolute phenomenon then, with respect, I don't think you'll have much to add to this conversation. The corrections made to the GPS satellites to account for gravitational time dilation are there for a reason.

How do you define 'absolute'?

For any object moving, you set clocks and systems of laser beams going back and forth to measure positions and time intervals (the latter calculated taking into account how much the signals delay in reaching the observer, it's not 'subjective' time we're talking about; it's not 'when I see the object.') Now, let's call them dt, dx, dy, dz. The so-called proper time of the moving object, in Special Relativity, and with the proper generalization, in General Relativity too, is,

$d\tau^{2}=dt^{2}-dx^{2}-dy^{2}-dz^{2}$

For what observer? For all inertial observers! Now, that's what I would call invariant (I'd never say 'absolute'.) And in order to do that, you need a system of signals, as they're trying to tell you. You need a way to bring it all together, so to speak. For a photon, the proper time is always zero, so photons have no internal clocks. While, seen from the 'outside' in empty space, they always go c.

Edited by joigus
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32 minutes ago, rjbeery said:

Gravitational time dilation is absolute. Take two identical watches which (let's say) use photons for timing, and place one more deeply in a gravitational well. It is not an illusion that the one in the gravitational well clocks more slowly. It has nothing to do with the wavelength of the the timing photons. Pound-Rebka only applies to radial movement.

It is relative in that it depends on the relative difference in gravitational potential.

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26 minutes ago, Strange said:

It is relative in that it depends on the relative difference in gravitational potential.

Agreed, but everyone would agree that the clock in a deeper gravity well is clocking more slowly. Bringing the clocks together for comparison is irrelevant (unlike the twin paradox, for example).

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3 minutes ago, rjbeery said:

Agreed, but everyone would agree that the clock in a deeper gravity well is clocking more slowly. Bringing the clocks together for comparison is irrelevant (unlike the twin paradox, for example).

That is not what "absolute" means.

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7 minutes ago, Strange said:

That is not what "absolute" means.

No problem, what word would you prefer I use? Time dilation is not illusory, and does not require a local meeting of clocks to reconcile. All observers would agree on the existence of clocking differentials in various gravity wells.

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3 minutes ago, rjbeery said:

No problem, what word would you prefer I use? Time dilation is not illusory, and does not require a local meeting of clocks to reconcile. All observers would agree on the existence of clocking differentials in various gravity wells.

What's wrong with "relative"?

Time dilation due to relative speed is not illusory either. So I'm not sure what distinction you are trying to make.

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11 minutes ago, rjbeery said:

All observers would agree on the existence of clocking differentials in various gravity wells.

All observers also agree on the invariance of c ;  something has to change.
Frequency, or wavelength, of the signal.
Hence, red or blue shift.

That was simple, wasn't it ?

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8 minutes ago, Strange said:

Time dilation due to relative speed is not illusory either. So I'm not sure what distinction you are trying to make.

As I said, everyone would agree that a clock in a deeper gravity well clocks more slowly than one higher up. This is not true of two clocks merely in relative motion. The latter is dependent on the frame of the observer, and the former is not. The clocking rate is relative between the clocks, but that differential is absolute for all observers.

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2 minutes ago, rjbeery said:

As I said, everyone would agree that a clock in a deeper gravity well clocks more slowly than one higher up. This is not true of two clocks merely in relative motion. The latter is dependent on the frame of the observer, and the former is not. The clocking rate is relative between the clocks, but that differential is absolute for all observers.

If you take Myclock - Yourclock, the difference has a different sign for the two observers.

And neither one can say theirs is "the" correct one

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5 minutes ago, MigL said:

All observers also agree on the invariance of c ;  something has to change.
Frequency, or wavelength, of the signal.
Hence, red or blue shift.

That was simple, wasn't it ?

Hi MigL, I reiterate my last point that I don't think you'll have anything to add to this discussion if you believe this. Observers all agree on the local invariance of c, but the wavelength of photons in a light-clock do not determine its clocking rate. A remote light-clock which is clocking more slowly than mine due to gravity is doing so because the photons in it are literally moving more slowly.

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1 hour ago, rjbeery said:

Gravitational time dilation is absolute. Take two identical watches which (let's say) use photons for timing, and place one more deeply in a gravitational well. It is not an illusion that the one in the gravitational well clocks more slowly. It has nothing to do with the wavelength of the the timing photons. Pound-Rebka only applies to radial movement.

There's a reason for that. Only radial movement gets you to a different gravitational potential.

Your use of "absolute" here is not in keeping with how relativity uses it. Pick different terminology.

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4 minutes ago, rjbeery said:

Hi MigL, I reiterate my last point t[...]

Before re-iterating too much, I would suggest you re-read what people are telling you, and then re-think for a change.

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1 minute ago, swansont said:

Your use of "absolute" here is not in keeping with how relativity uses it. Pick different terminology.

In the context of my discussion with MigL and Joigus, I'm using "absolute" to differentiate clocking rates in different gravity wells from what they apparently believe to be "relative' effects. What would be more appropriate? Unqualified? Indisputable?

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