Geometrodynamic Foundation of Electrodynamics, in six pages

[Yablon]

Dear SPF friends:

After hundreds of pages of writing and calculating, I have a deep enough understanding of the Lorentz Force geodesics that I have been working on since December to encapsulate the high points into six pages. This short but complete overview is available for your review at:

https://jayryablon.files.wordpress.com/ ... uction.pdf

I will use this as the new introduction for my paper, and will streamline the paper as much as possible based on what really needs to be in the paper, versus what I needed to write and calculate to help me get to this point of development and understanding.

So, I would appreciate your thoughts on the following:

First, how well does this communicate the whole thesis? Any suggestions for improvement?

I am also considering submitting this is a letter to a leading journal. So, second, is this sufficient for a letter, and if not, what other details should be added?

Thanks,

Jay

[Yablon]

I have further refined the paper into a letter with behind-the-scenes assistance from Joy Christian who if you look at the SPF threads going back to when I started this research in December has been helpful and encouraging throughout. Thank you Joy! The present draft is now public at http://vixra.org/pdf/1605.0259v2.pdf.

I have also today submitted what is at the above link to one of the top letters journals in the world. I am holding my breath in the hope that this will lead to a good outcome.

Best to all,

Jay

[Joy Christian]

I have further refined the paper into a letter with behind-the-scenes assistance from Joy Christian who if you look at the SPF threads going back to when I started this research in December has been helpful and encouraging throughout. Thank you Joy! The present draft is now public at http://vixra.org/pdf/1605.0259v2.pdf.

I have also today submitted what is at the above link to one of the top letters journals in the world. I am holding my breath in the hope that this will lead to a good outcome.

Best to all,

Jay

Thank you, Jay, for thanking me in the paper.

Best of luck with the publication process.

[Q-reeus]

I have further refined the paper into a letter with behind-the-scenes assistance from Joy Christian who if you look at the SPF threads going back to when I started this research in December has been helpful and encouraging throughout. Thank you Joy! The present draft is now public at http://vixra.org/pdf/1605.0259v2.pdf.

I have also today submitted what is at the above link to one of the top letters journals in the world. I am holding my breath in the hope that this will lead to a good outcome.

Best to all,

Jay

Jay, from 1st para p7 in http://vixra.org/pdf/1605.0259v2.pdf

To be sure, these electromagnetic time dilations are miniscule for everyday electromagnetic interactions, as are special relativistic time dilations for everyday motion. So testing of dt/dτ changes for electrodynamics may perhaps be best pursued with experimental approaches similar to those used to test relativistic time dilations.

We have I believe discussed this before:
viewtopic.php?f=6&t=261&sid=97e22e3a791bf4ba3e774a4e62541992#p6359
Let me make this plain: Brillouin and others since have raked over the notion of whether electric charges interact classically other than via standard EM theory. The experimental evidence is clear - charged particle inertia thus any possible time dilation/contraction is completely unaffected of the EM potentials.
Example: dipole oscillator as clock, housed within a Faraday cage. Charge up the cage to any desired positive or negative potential, and oscillator frequency will not alter.

[Yablon]

Jay
We have I believe discussed this before:
viewtopic.php?f=6&t=261&sid=97e22e3a791bf4ba3e774a4e62541992#p6359
Let me make this plain: Brillouin and others since have raked over the notion of whether electric charges interact classically other than via standard EM theory. The experimental evidence is clear - charged particle inertia thus any possible time dilation/contraction is completely unaffected of the EM potentials.
Example: dipole oscillator as clock, housed within a Faraday cage. Charge up the cage to any desired positive or negative potential, and oscillator frequency will not alter.

Kevin,

As regards empirical data, the most compelling equation in my paper at http://vixra.org/pdf/1605.0259v2.pdf is equation (10). Everything in the bottom line of (10) is physically observed. Had someone just written (10) out of the blue without getting there from the Lorentz force (10) would still be a correct descriptor of the observed energies. So much the better that this is tied to Lorentz force and geodesic motion.

Isn't the third term on the bottom line of (10) for the Coulomb interaction energy of the mass truly observed, and thus a contributor to charged particle inertia just like all the other energies in (10)? However, equation (10) makes clear how minute the EM electromagnetic time dilation actually is. because in



we see that the deviation from 1 is based on the ratio of the EM energy to the entire rest energy which is an atomic-to-nuclear ratio.

I perused the mathematical physics paper you linked, and while it appeared to argue against time dilation, it did so without an understanding of the actual magnitude of the time dilation predicted by (10). If somebody has actually done a time dilation test to the level of precision needed and rule this out, then I guess I'd have to live with that and as Einstein would have said, God missed a terrific opportunity to use a third form of time dilation alongside of time dilation from motion and time dilation from gravitation.

Can you, or anybody, point to specific experiments conducted at the level of precision required by (10), to rule in or out the EM time dilation shown in (10)? Unless the precision of any supposedly contradictory indications was sufficient, I'd have to stand by equation (10).

Jay

[Yablon]

Let me supplement my reply to Kevin:

I did a quick online search for electromagnetic time dilation. Of interest are these links:

http://physics.stackexchange.com/questi ... e-dilation
https://en.wikipedia.org/wiki/Reissner% ... B6m_metric

So in fact EM interactions are expected to contract dilate time. And, the Reissner–Nordström metric makes clear that they do.

This does raise an interesting research project that I am afraid I will now have to take on: relating the time dilation I have derived to that of the Reissner–Nordström.

Jay

[Joy Christian]

Can you, or anybody, point to specific experiments conducted at the level of precision required by (10), to rule in or out the EM time dilation shown in (10)? Unless the precision of any supposedly contradictory indications was sufficient, I'd have to stand by equation (10).

Jay,

It would be useful if you calculated a precise number for the difference in time-dilation predicted by special relativity and by your equation (10).

If you produce such a number, then we may be able check relatively easily whether such a difference has been ruled out experimentally, or not.

Best,

Joy

[Yablon]

Jay,

It would be useful if you calculated a precise number for the difference in time-dilation predicted by special relativity and by your equation (10).

If you produce such a number, then we may be able check relatively easily whether such a difference has been ruled out experimentally, or not.

Best,

Joy

OK, let put out a simple benchmark example. Say we have two charges Q=q=1 Coulomb separated by 1 meter. The Coulomb interaction energy

J.

Yet, if the test particle has a mass m=1 kg, then the EM time dilation is:

(1)

This is a very tiny time dilation for a tremendously energetic interaction. The release of this much energy per second would yield a power of approximately 8.99 GW, which roughly approximates seven or eight nuclear power plants, or roughly four times the power of the Hoover Dam, or the power output of a single space shuttle launch, or the power of about seventy five jet engines, or that of a single lightning bolt.

For a special relativistic comparison, consider an airplane which flies one mile in five seconds, versus light which travels about one million miles in five seconds. Here, and the time dilation is only:

(2)

So the EM time dilation (1) is actually less minuscule than the SR number 2. But you need a whole space shuttle to get you near those energies. A Van de Graaff generator at the front of an auditorium in a physics lecture that makes a student's hair stand on end won't even come close to getting you an observable time dilation.

Jay

[Joy Christian]

Jay,

It would be useful if you calculated a precise number for the difference in time-dilation predicted by special relativity and by your equation (10).

If you produce such a number, then we may be able check relatively easily whether such a difference has been ruled out experimentally, or not.

Best,

Joy

OK, let put out a simple benchmark example. Say we have two charges Q=q=1 Coulomb separated by 1 meter. The Coulomb interaction energy

J.

Yet, if the test particle has a mass m=1 kg, then the EM time dilation is:

(1)

This is a very tiny time dilation for a tremendously energetic interaction. The release of this much energy per second would yield a power of approximately 8.99 GW, which roughly approximates seven or eight nuclear power plants, or roughly four times the power of the Hoover Dam, or the power output of a single space shuttle launch, or the power of about seventy five jet engines, or that of a single lightning bolt.

For a special relativistic comparison, consider an airplane which flies one mile in five seconds, versus light which travels about one million miles in five seconds. Here, and the time dilation is only:

(2)

So the EM time dilation (1) is actually less minuscule than the SR number 2. But you need a whole space shuttle to get you near those energies. A Van de Graaff generator at the front of an auditorium in a physics lecture that makes a student's hair stand on end won't even come close to getting you an observable time dilation.

Jay

Thanks, Jay.

These calculations look pretty impressive.

However, there exist some very stringent bounds on Lorentz violations from recent cosmological observations. You may want to check out those as well:

https://en.wikipedia.org/wiki/Modern_se ... e_dilation

***

[Yablon]

Thanks, Jay.

These calculations look pretty impressive.

However, there exist some very stringent bounds on Lorentz violations from recent cosmological observations. You may want to check out those as well:

https://en.wikipedia.org/wiki/Modern_se ... e_dilation

***

Thanks Joy, that is a good reference.

To be clear -- and Joy I know you realize this -- I am not predicting any Lorentz violation. I work from the view that Lorentz symmetry is not violated, which is shown by my equation (10) in http://vixra.org/pdf/1605.0259v2.pdf, but is supplemented with other sources of time dilation, namely, gravitation (of course), and EM (which is what I am arguing).

BTW, I though about Reissner–Nordström. Those are a non-issue in my paper. If one wanted to include those effects, they would go into in my equation (10), their their impact on the numbers would be far smaller than the numbers I posted this morning, because the Newton constant G is in there. Once G shows up anywhere in a calculation like this, the energies needed for detection grow astronomically huge.

Jay

[Yablon]

BTW, I though about Reissner–Nordström. Those are a non-issue in my paper. If one wanted to include those effects, they would go into in my equation (10), their their impact on the numbers would be far smaller than the numbers I posted this morning, because the Newton constant G is in there. Once G shows up anywhere in a calculation like this, the energies needed for detection grow astronomically huge.Jay

On the other hand, while we will not ever test the Reissner–Nordström (RN) effect on time dilation in a laboratory, it occurs to me that this is the place to tie my work here to black hole study:

Because I am claiming a material limit on the strength of EM interactions, I should use RN in my and see how my material limit affects black hole collapse, if at all. I suspect there is some independence because RN time dilation does not depend on the test charge but my EM time dilation does. But it is worth checking out.

Jay

[FrediFizzx]

Jay, what about slight length contraction due to EM?

[Q-reeus]

Kevin,

As regards empirical data, the most compelling equation in my paper at http://vixra.org/pdf/1605.0259v2.pdf is equation (10). Everything in the bottom line of (10) is physically observed. Had someone just written (10) out of the blue without getting there from the Lorentz force (10) would still be a correct descriptor of the observed energies. So much the better that this is tied to Lorentz force and geodesic motion.

Isn't the third term on the bottom line of (10) for the Coulomb interaction energy of the mass truly observed, and thus a contributor to charged particle inertia just like all the other energies in (10)? However, equation (10) makes clear how minute the EM electromagnetic time dilation actually is. because in



we see that the deviation from 1 is based on the ratio of the EM energy to the entire rest energy which is an atomic-to-nuclear ratio.

I perused the mathematical physics paper you linked, and while it appeared to argue against time dilation, it did so without an understanding of the actual magnitude of the time dilation predicted by (10). If somebody has actually done a time dilation test to the level of precision needed and rule this out, then I guess I'd have to live with that and as Einstein would have said, God missed a terrific opportunity to use a third form of time dilation alongside of time dilation from motion and time dilation from gravitation.

Can you, or anybody, point to specific experiments conducted at the level of precision required by (10), to rule in or out the EM time dilation shown in (10)? Unless the precision of any supposedly contradictory indications was sufficient, I'd have to stand by equation (10).

Jay

Jay, referring to your 2nd last para p6, which presents the kernel issue, no need to electrically charge clocks. My last example of dipole oscillator was a bad one since any inertial mass coupling to an external scalar potential phi will be of equal and opposite sign for the two dipole charges. A linear quadrupole oscillator overcomes that issue, but is inconvenient. All that's needed is an oscillator with large contrasts in charge-to-mass ratios. Atoms fulfill that nicely - heavy positive nucleus, light shell electrons.
We are therefore talking about measuring conceivable spectral line shifts of say a sodium lamp placed in a Faraday cage then subject to varying potential. The cage would want to be well removed from 'ground' for a clean analysis. Given the extreme sharpness of Mossbauer effect, I suppose nuclear transitions might also be viable as check.

An appeal to old Bohr atom will do for this - orbital frequency will go as √(1/m), where m is the net inertial mass of shell electron. We expect emission spectra owing to transitions between orbitals to scale accordingly. This has an important implication apart from observed spectra - but more on that later.

Your 'extreme' example in viewtopic.php?f=6&p=6444&sid=2fc4f4140427851d2b2448bd4a45a710#p6441
seems impressive but as per that last part of 2nd last para p6 in your v2 article, the sole determinant of interest here is ratio (q/m)(φ/c²), and for an electron, q/m = −1.759×10^11 C/kg. In SI units 1/c² = 1.113×10^-17s²/m², so the fractional contribution to electron inertial mass reduces to just δm/m = φ(-1.96×10^-6), with φ in volts.

Not at all difficult to charge up a Faraday cage to several million volts using e.g. a Van de Graaff generator. Are we expecting a dramatic shift in spectral emissions?

Which leads to one more thing, hinted at earlier. As always you are careful to make sure in the derivations everything conforms to conservation of energy. YET - if m can vary by simply immersing in an exterior equipotential (charged Faraday cage), atomic orbitals will expand or shrink accordingly. Not strictly according to √(1/m) for arbitrarily large applied φ, since as m -> 0, SR comes into play, operating on the 'normal' mass component such that things never go 'tachyonic'. In accordance with your eqn (10) in fact. Phew! But even a slight alteration in orbital size implies alteration of the net electrostatic + KE energy. Given the Faraday cage external charge is oblivious to goings on of neutral atoms within, implication is energy can be created and destroyed rather conveniently. Heat up a body external to cage, quickly transport it inside, and capture the shifted spectral emissions as it cools down. Get the idea here?
Anyway, a heap of possible other schemes could be invoked, but - as a patent guy - I'm sure you'll know what to do!

[Yablon]

Jay, what about slight length contraction due to EM?

Fred, absolutely, yes. I have focused on time dilation but there is also a length contraction and the structure for this is exactly the same as in special relativity. To review and summarize:

In SR the time dilation factor is and the four velocity is where has the speed of light in its time component, and the ordinary velocity in its three space components. So the time dilation factor also dilates the three space components.

In my geometrodynamic electrodynamics the time dilation / contraction factor is and the four velocity is of the same form .

So when you have both motion and electromagnetic interaction, the four-velocity then becomes:

with the two factors multiplied. And with gravitation where at rest the complete four velocity is:

.

Multiplied by this gives you a mechanical (as opposed to canonical) energy-momentum

,

and the time component of this:



is my equation (10). The canonical momentum which appears in my equation (8) is then .

If you think about it, this is simply special relativity for motion as first presented by AE in 1905 in Does the inertia of a body depend upon its energy-content?, but extended into special relativity for motion plus electrical interaction. Unless somebody else has written down my equation (10) before, this is simple yet an important step forward in science, and it is entirely independent of how I got it this from the derivation of the Lorentz Force motion from a minimized variation. I could write this up and submit somewhere it in a one-page paper.

Jay

[Yablon]

Jay, referring to your 2nd last para p6, which presents the kernel issue, no need to electrically charge clocks. My last example of dipole oscillator was a bad one since any inertial mass coupling to an external scalar potential phi will be of equal and opposite sign for the two dipole charges. A linear quadrupole oscillator overcomes that issue, but is inconvenient. All that's needed is an oscillator with large contrasts in charge-to-mass ratios. Atoms fulfill that nicely - heavy positive nucleus, light shell electrons.
We are therefore talking about measuring conceivable spectral line shifts of say a sodium lamp placed in a Faraday cage then subject to varying potential. The cage would want to be well removed from 'ground' for a clean analysis. Given the extreme sharpness of Mossbauer effect, I suppose nuclear transitions might also be viable as check.

An appeal to old Bohr atom will do for this - orbital frequency will go as √(1/m), where m is the net inertial mass of shell electron. We expect emission spectra owing to transitions between orbitals to scale accordingly. This has an important implication apart from observed spectra - but more on that later.

Your 'extreme' example in viewtopic.php?f=6&p=6444&sid=2fc4f4140427851d2b2448bd4a45a710#p6441
seems impressive but as per that last part of 2nd last para p6 in your v2 article, the sole determinant of interest here is ratio (q/m)(φ/c²), and for an electron, q/m = −1.759×10^11 C/kg. In SI units 1/c² = 1.113×10^-17s²/m², so the fractional contribution to electron inertial mass reduces to just δm/m = φ(-1.96×10^-6), with φ in volts.

Not at all difficult to charge up a Faraday cage to several million volts using e.g. a Van de Graaff generator. Are we expecting a dramatic shift in spectral emissions?

Which leads to one more thing, hinted at earlier. As always you are careful to make sure in the derivations everything conforms to conservation of energy. YET - if m can vary by simply immersing in an exterior equipotential (charged Faraday cage), atomic orbitals will expand or shrink accordingly. Not strictly according to √(1/m) for arbitrarily large applied φ, since as m -> 0, SR comes into play, operating on the 'normal' mass component such that things never go 'tachyonic'. In accordance with your eqn (10) in fact. Phew! But even a slight alteration in orbital size implies alteration of the net electrostatic + KE energy. Given the Faraday cage external charge is oblivious to goings on of neutral atoms within, implication is energy can be created and destroyed rather conveniently. Heat up a body external to cage, quickly transport it inside, and capture the shifted spectral emissions as it cools down. Get the idea here?
Anyway, a heap of possible other schemes could be invoked, but - as a patent guy - I'm sure you'll know what to do!

Kevin,

Very interesting idea about Mossbauer effect, https://en.wikipedia.org/wiki/M%C3%B6ssbauer_effect. And yes, the time dilation will be greater for electrons over protons. In all varieties of circumstances this will be driven by a factor of or about about 1836 to 1. So one might find some way to use protons as a reference against which one measures electron time dilation. Also, mathematically, I like that the Mossbauer recoil equation is:



Take the derivative with respect to the gamma energy and we have:



which is precisely the energy ratio that is at the heart of my EM time dilation with . So the math could be made compatible. I / we need to think about the physics.

I have certainly thought a lot about how you would detect this EM time dilation in an experiment. As much as using the Coulomb interaction between two charged bodies creates a clear theoretical picture of what we are looking for, I can't help but feel this is an impractical approach. In our myriad of technological instruments there are few if any practical devices that make use of static charges. Everything, pretty much, makes use of currents which entail the flow of charges. And there is good reason: while one Coulomb of charge is incredible large, 1 Ampere of current which flows one Coulomb per second is eminently practical and used all the time without blowing up the room. So I have been thinking of the magnetic forces between parallel (or anti parallel) current flows and about some type of nano-scale device that can be designed to do the experiment. But, as you point out, there are likely a heap of schemes. The challenge is that it is a very small effect, with the numbers I gave earlier in this thread.

Whoever does design and perform the first experiment to confirm the EM time dilation in equation (10) of my http://vixra.org/pdf/1605.0259v2.pdf will of course have my eternal gratitude for doing so. And if you look at (10), again, how could God have passed up the opportunity to do this alongside of special and general relativistic time dilation? It has to be right!

Jay

[Q-reeus]

...I have certainly thought a lot about how you would detect this EM time dilation in an experiment. As much as using the Coulomb interaction between two charged bodies creates a clear theoretical picture of what we are looking for, I can't help but feel this is an impractical approach...

Jay - I disagree with that assessment, but first an admission.... By likening the situation to a mechanical oscillator where only the mass varied, I made a careless assumption last time in stating atomic emission frequencies would go as √(1/m). A visit to e.g. http://hyperphysics.phy-astr.gsu.edu/hbase/hyde.html makes it clear the variation is straight proportionality to net inertial mass m, as per Rydberg constant R. Which concurs with mesonic atoms being so much more compact and as a consequence emission spectra that much more energetic than for the normal atomic counterpart.

Other than direct proportionality to m being a more severe variation than claimed earlier, my last post stands that the proposed coupling to scalar potential should be readily measureable and that much more so in fact. Do you have any reason to doubt that as per your article eqn (10), atomic emission spectra, at least for modest applied potentials φ (up to say a few 100,000 volts) should approx vary as per δm/m = φ(-1.96×10^-6), with φ in volts? Hence m = m'(1+δm/m') = m'(1-φ(1.96×10^-6)), where m is the net mass and m' the standard electronic rest mass. Without going back and scouring the literature, offhand I think it was this sort of thing that was looked for by Brillouin et al. Maybe not.

[Yablon]

To all:

I updated by paper further, and you can now read the latest at http://vixra.org/pdf/1605.0259v3.pdf. I have accordingly updated my submission to the leading journal to which I submitted the paper last week.

Sections 1 and 2 contain the same summary overview that was in the earlier versions. More supporting detail is now provided in newly-added sections 3 through 7.

Section 3 is a greatly-consolidated derivation of the Lorentz force for the variational minimization. The includes more emphasis on the gauge condition which I realized was needed as a result of feedback received several week ago from this forum, now called the "geodesic gauge."

The reason I added to this paper is that I felt it important to explore this geodesic gauge more fully. That is the purpose of sections 4 and 5, which reveals a new "Lagrangian / action" gauge as well. This is NEW material not previously posted.

Then, after writing about the gauges, I felt that I should elaborate the main line of development that gets me to the electrodynamic time dilation and contraction, and to the associated empirical energies. That is section 6. This consolidates to about 3 pages, derivations that had previously been spread over 20 or more pages in my earlier humongous paper. Clarity is always good, and now I do have clarity.

Section 7 is a one-paragraph conclusion.

Comments, discussion, food fights, etc., are always welcome.

Jay

[Q-reeus]

To all:

I updated by paper further, and you can now read the latest at http://vixra.org/pdf/1605.0259v3.pdf. I have accordingly updated my submission to the leading journal to which I submitted the paper last week....
Comments, discussion, food fights, etc., are always welcome.

Jay

From last part of 7. Conclusion, p18 of current v3 Vixra article:

Experimental observation of a change in the rate at which time flows for charged bodies in electromagnetic fields an accordance with (7.1) would therefore confirm this geometrodynamic foundation for classical electrodynamics in four spacetime dimensions.

Sorry Jay but in all likelihood there will be a rejection from any mainstream journal referee or editor. At least for the main reason given in my earlier posts - the proposed coupling to the scalar potential in particular should have long been observed as dramatic shifts in atomic emission (and absorption) spectra. As mentioned, searches for such or similar effects have long ago been done and came out negative. And as also raised before, any such coupling implies failure of energy-momentum conservation. Owing to e.g. implied changes in atomic dimensions thus net energy - 'virtual muonic atom' orbital contraction if φ +ve, or inverse if φ -ve (made a sign error in my last post). Yet with zero back-reaction (neglecting utterly infinitesimal gravitational coupling) on the causative agent. That is, an electrostatically charged Faraday cage or some such arrangement.
Still, I might be wrong so will be interesting to find out how you do fare.

[Yablon]

Sorry Jay but in all likelihood there will be a rejection from any mainstream journal referee or editor. At least for the main reason given in my earlier posts - the proposed coupling to the scalar potential in particular should have long been observed as dramatic shifts in atomic emission (and absorption) spectra. As mentioned, searches for such or similar effects have long ago been done and came out negative. And as also raised before, any such coupling implies failure of energy-momentum conservation. Owing to e.g. implied changes in atomic dimensions thus net energy - 'virtual muonic atom' orbital contraction if φ +ve, or inverse if φ -ve (made a sign error in my last post). Yet with zero back-reaction (neglecting utterly infinitesimal gravitational coupling) on the causative agent. That is, an electrostatically charged Faraday cage or some such arrangement.
Still, I might be wrong so will be interesting to find out how you do fare.

Well Kevin, what if we are already observing this time dilation effect but simply have not attributed it as such?

One calculation I have not put in the paper yet -- and I am debating it -- is this:

Take a Coulomb interaction with , but now take and to be individual electrons . Then with being the Compton wavelength of the electron, the time contraction is:



My present (6.11) says that the canonical momentum is related to the mechanical momentum via , so that for this electron example:



So mechanical momenta are raised into canonical momenta by a factor with includes the "anomalous" of Schwinger that is central to the electron magnetic moment. And this carries forward to a general relation between mechanical and canonical variables.

Now, to be transparent, I have been aware of this calculation for months, and have been looking to formally tie this to the electron magnetic moment. And to also be clear, once we talk about individual electrons interacting near their Compton wavelengths we are crossing the boundary from classical to quantum theory, so needs to be seen as an expected value for separation, which also gives the time flow rate an expected value and sets up energy time uncertainty because this means there must also be a statistical standard deviation . But, fundamentally, for single charge quanta -- electrons and protons most notably -- all canonical quantities are related to mechanical quantities at average separations for individual charge quanta equal to their Compton wavelengths via the factor

.

So while I have not yet formalized this connection -- though I can produce this factor by considering electron self-interaction -- I have a sneaking suspicion that these time dilations are already at the heart of observed "anomalous" behaviors even though presently unrecognized as such, and that the observed anomalies are merely reflecting this canonical-to-mechanical ratio.

The reason this is not in the paper is that I have not fully formalized this, and because I cannot get into this without also branching into the quantum issue of time uncertainty, and I see all of this as Part II of this work and want to first get Part I firmly planted. But I would love to hear thoughts as to how to introduce this even if not formalized, in a way that will not cause more problems than it solves.

Jay

[thray]

Jay,

You write, "I cannot get into this without also branching into the quantum issue of time uncertainty ..."

I think 'branching' is exactly correct, which brings up the issue of mathematical completeness -- we know with certainty the timestamp at which an event happens, and not where the next timestamp will be. We also know that it will NOT be within R^3 or any Euclidean linear representation of space. The reason is simple:

The topological space S^3 is identical to S^2 + S^2 (or S^2 X S^2), differing from R^3 by a point at infinity. Because S^2 is is a 3-dimensional quantum, it cannot include 4-dimension spacetime -- conventional QM explains this as collapse of the wave function, and discards the role of time, or rather, calculates it out of existence.

Preserving time is tricky thing. Hess-Phillip use timelike-correlated parameters, enlarging the measurement space to the limit of 4 dimensions. Joy Christian's framework envisions an undivided world connected continuously in 4 dimensions by an 8-dimension Hopf fibration. Both have built-in time reversibility, an absolute requirement for compatibility with special and general relativity.

So it seems reasonable to me that " ... we are already observing this time dilation effect ..." if <r> is degenerate, and time nonlinear. This eliminates the boundary between classical and quantum theory.

Because the wave function is non-collapsing, predicting where the next timestamp will occur is tantamount to showing the precise point at which separability of S^2 elements takes place, that is, where <r> becomes degenerate due to time dilation.

Tom