# Time dilation in an electromagnetic potential

• Creator

#### Creator

We all realize time dilates in a gravitational potential. Is there any evidence to suggest there is time dilation in an electromagnetic (vector or scalar) potential??

Creator

Creator said:
We all realize time dilates in a gravitational potential. Is there any evidence to suggest there is time dilation in an electromagnetic (vector or scalar) potential??
I don't know about actual evidence. But to the extent that electromagnetic field represents energy - such as two charges separated by a distance - it has mass = E/c^2 which has gravitational effect.

Creator said:
We all realize time dilates in a gravitational potential. Is there any evidence to suggest there is time dilation in an electromagnetic (vector or scalar) potential??

Creator
Are you thinking of some kind of equivalence principle argument so that when a photon leaves a region with a large vector potential, the photon is red shifted? I suspect the linearity of Maxwell's equations may defeat you. Along the way with the equivalence principle you'll need to decide whether a charge at rest in a uniform gravitational field radiates. If conceptual arguments don't defeat you then there is the tiny coupling of electromagnetic fields and curvature with Einstein's equations that will defeat any measurements today.

The Newtonian potential is in the gtt and for the charged, spherical black hole (Reissner Nordstrom solution), it goes as 2M/r and Q*Q/r*r. This solution, apart from weak field approximations, is about the only one where the Newtonian potential shows up in general relativity. Here a simple vector potential goes as Q/r. So you might think you get a time dilation going as the square of the vector potential, but you haven't got a flat metric to make this simple square. Further you have the problem of gauge changes for the vector potential that should not produce any time dilation.

Rob Woodside said:
Are you thinking of some kind of equivalence principle argument so that when a photon leaves a region with a large vector potential, the photon is red shifted?

Ummm; I'm not referring to an equivalence principle since I'm referring to a gravitational field-FREE region, in which there is only the EM potential, Rob and Calculex.
(I knew this was going to happen when they diverted my post from 'electromagnetics' to 'relativity'.)

However, your idea (Rob) is conceptually somewhat similar to what I had in mind for the possible detection of time dilation in such a grav. field-free region. For example, a photon passing into the region of vector potential and, while in the region, instead of the photon being frequency shifted, it is wavelength shifted, which is, I believe, an equivalent method of measuring time dilation. Some ideas in this area may be helpful.

Creator Creator said:
Ummm; I'm not referring to an equivalence principle since I'm referring to a gravitational field-FREE region, in which there is only the EM potential, Rob and Calculex.
(I knew this was going to happen when they diverted my post from 'electromagnetics' to 'relativity'.)

However, your idea (Rob) is conceptually somewhat similar to what I had in mind for the possible detection of time dilation in such a grav. field-free region. For example, a photon passing into the region of vector potential and, while in the region, instead of the photon being frequency shifted, it is wavelength shifted, which is, I believe, an equivalent method of measuring time dilation. Some ideas in this area may be helpful.

Creator The linearity of Maxwell's equations will defeat you. E/m fields pass through one another unimpeded and consequently pass through vector potentials unimpeded (no change in wavelength or frequency).

Rob Woodside said:
The linearity of Maxwell's equations will defeat you.
If the gravitational equations were linear would that preclude grav. time dilation?

I'm interested in the possibility of time dilation in the magnetic vector or electric scalar potential, whatever the means of detection. I only suggested EM waves in the region as one possible method of detection; if that's not possible is there some other means that would show definitively no such dilation can possibly occur?

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E/m fields pass through one another unimpeded and consequently pass through vector potentials unimpeded (no change in wavelength or frequency).

I understand, but there is a phase change in EM waves & particles passing though differing (or changing) electromagnetic potentials. Whether that fits your definition of 'unimpeded' is not as important to me as the quantum mechanical reason it MAY be related to time dilation.

Creator

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Creator said:
If the gravitational equations were linear would that preclude grav. time dilation?

The idea for gravitational time dilation came from asking what happens to light as it escapes a gravitational potential. A massive particle looses kinetic energy and slows down as it does so. What can light do if it must travel at c? With the photon idea and E=hf, the light could loose energy by red shifting. The frequency of a photon is the clock rate of the emitting atom. Ergo, clocks tick more quickly down a gravitational potential. This argument is a delicate dance over contradictory ideas (start with flat space and homogeneous clock rates to get variable clock rates?) and only gets credibility in general relativity or with the Pound Rebka experiment. The argument should also work with gravitons, if any are ever found. If the gravitational field equations were linear, then one could superpose fields, keeping wavelength and frequency invariant and in this case there would be no red shifting on leaving a bound gravitational field.

Creator said:
I'm interested in the possibility of time dilation in the magnetic vector or electric scalar potential, whatever the means of detection. I only suggested EM waves in the region as one possible method of detection; if that's not possible is there some other means that would show definitively no such dilation can possibly occur?

As another poster pointed out you seem to be confusing gravitational potential which is an energy per unit mass with electromagnetic vector potential in units of energy per unit charge. Any time dilation occurring will be due to the energy carried by the electromagnetic field and the ansatz gravitational potential it consequently carries. Classical Electromagnetism happens in a flat space with linear fields that superpose and do not affect each other. Consequently the wavelength and frequency of light is invariant no matter what other electromagnetic fields are present. Einstein Maxwell theory permits a time dilation but that is due to Maxwell's stress energy tensor that the electromagnetic field carries and is just the usual gravitational time dilation applied to electromagnetic fields.

Creator said:
I understand, but there is a phase change in EM waves & particles passing though differing (or changing) electromagnetic potentials. Whether that fits your definition of 'unimpeded' is not as important to me as the quantum mechanical reason it MAY be related to time dilation.

Creator

E/m waves do NOT undergo any phase change passing through electromagnetic potentials. This only happens when the waves interact with matter (e.g. a quarter wave plate). The only particles that have phases are quantum particles and we are talking about the phase of the wave function. Even today people will say that the electromagnetic potential is unphysical as it is defined only up to the gradient of a scalar function and it is only the electric and magnetic fields that are measurable and physical. So it was a shock when Aharanov showed that the wave function's phase could be altered by the presence of a vector potential (with no electromagnetic field) and that this phase change would show up in a two slit experiment. You are mixing a poisonous confusion of gravity, electromagnetism and quantum mechanics.

There's actually been quite a bit of theoretical work on electromagnetic time dilation already. I have a rather crude approach to it myself in a draft paper at:
http://www.riverrock.org/~howard/QuantumTime13.pdf
but there are more sophisticated developments by Apsel and by Van Holten (see their papers in the bibliography of mine).

One interesting thing that drops out of my version is that the phase frequency shift for different energy levels given by the Schrodinger equation is shown to be mathematically identical to gravitational time dilation in the stationary case. Thus gravitational time dilation can be viewed as a quantum effect.

Both Apsel and my version predict that a muon will have its lifetime altered by an electrostatic potential. There is some support for this in negative muon lifetimes in matter (see the Apsel paper on that). Whether they are true or not, this prediction is definitely testable with existing equipment. I think I could run the experiment for under $100K (need a medium size Van De Graaff generator (about$20K), one or more muon lifetime devices (about \$5K each), and access to any old accelerator that can produce a single-polarity muon beam. Neither of our theories are gauge-invariant (but they are, rather counter-intuitively, CPT-invariant, as I discuss in my paper). But then, the universe is not gauge-invariant. The Aharonov-Bohm effect proves that.

Van Holten sees the theory as having the same gauge-invariance as the Maxwell equations, which means the above would not work. His version requires extremely strong magnetic fields (say 5 GT), which are way beyond the reach of present equipment (1T is common, 10T is doable, 100T would be expensive). You might see such a field around a magnetar or neutron star. The energy density of such a field would be denser than solid lead. So we won't be testing this on Earth any time soon, but astronomy might be able to get some evidence one way or the other.

I indirectly tested my (and Apsel's) theory in June 2010 using the giant VDGG at Boston Museum Of Science, but the indirect test did not show any violations of gauge-invariance. So either the whole theory is wrong, or only Van Holten's version is right, or my indirect test was too indirect and missed something essential. I'm planning another (different) indirect test at MOS possibly as soon as this winter. After that it's time to look for funding for the direct test.

Some of the strongest electric potentials we see in nature are in nuclei. If there were an electrical analog of gravitational time dilation, then gamma rays emitted by nuclei would be observed with a frequency shift. Mössbauer spectroscopy works to within about 1 part in 1011, and for a moderately heavy nucleus like Fe, the electrical potential is on the order of 107 V, so I think any such effect would be limited empirically to about 10-18 V-1.

There is no known technology for doing this yet.

If there were an electrical analog of gravitational time dilation, then gamma rays emitted by nuclei would be observed with a frequency shift.

It's not at all clear to me that this would apply to all versions of the theory, so I think your statement is probably false as a universal. However this might provide a way to test some versions of the theory.

The problem is that nuclei are very heavy, and the dilation predicted by Apsel and myself is proportional to the ratio of energies. So for (say) a 57Fe nucleus with a mass (=energy) of 56.93u = 53 GeV and a charge of 26, putting it in a potential of 2 MV would change its energy by 52 MeV and be predicted to change its decay lifetime by about 1 part in 1000. It would not necessarily change the frequency emitted by the decay, since the difference between the energy levels might not have been altered and energy is conserved.

This is why I think muons are ideal for testing the effect. They are the lightest particles that decay. With a mass of 105.7 MeV and a charge of 1, a 2 MV potential would be predicted to change their lifetime by about 1 part in 53. I already know I can measure this with relatively inexpensive equipment. I just need access to a source of single-type muons (cosmic ray muons are mixed + and - and unfortunately not very suitable).

However, I'll have to think about this some more. Van Holten's version definitely predicts slightly different dilation for a spin-up vs spin-down nucleus in a strong magnetic field, so the extreme sensitivity of Mössbauer spectroscopy might provide a direct test there if the numbers work out. This could potentially get around his requirement for ridiculously strong magnetic fields. A field of 1 to 10 Tesla might be enough.

Some of the strongest electric potentials we see in nature are in nuclei. If there were an electrical analog of gravitational time dilation, then gamma rays emitted by nuclei would be observed with a frequency shift. Mössbauer spectroscopy works to within about 1 part in 1011, and for a moderately heavy nucleus like Fe, the electrical potential is on the order of 107 V, so I think any such effect would be limited empirically to about 10-18 V-1.

Wouldn't the frequency shift occur within the atom, on the way out from the nucleus? It would appear that the frequency can only be measured locally. 107 V probably behaves as a multiplier, so given identical external environments, I would say that the observed shift should be 0 (measuring emissions from different nuclei in the same external environment) even if there is a shift inside the nucleus we cannot observe.

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H_A_Landman, PF has rules https://www.physicsforums.com/showthread.php?t=414380 about where to submit posts about personal theories -- they aren't supposed to be submitted in the regular forums. If you want to discuss Van Holten and Apsel's papers, please post the journal references here rather than expecting people to go to your site and get them out of the references of your own paper. It would also be helpful if you could find a URL where they are freely available; otherwise people (including me) who don't have electronic access to journals can't discuss them with you. I suspect that you're misunderstanding or misinterpreting some GR papers on electrovac solutions.

It's up to you whether you want to have a discussion just of the van Holten and Apsel papers, which we can do here, or your personal research, which would have to be in the Independent Research forum.

If you want to discuss Van Holten and Apsel's papers, please post the journal references here rather than expecting people to go to your site and get them out of the references of your own paper. It would also be helpful if you could find a URL where they are freely available; otherwise people (including me) who don't have electronic access to journals can't discuss them with you.

 D. Apsel, ”Gravitational, electromagnetic, and nuclear theory ”, International Journal of Theoretical Physics v.17 #8 643-649 (Aug 1978) DOI: 10.1007/BF00673015
 D. Apsel, ”Gravitation and electromagnetism”, General Relativity and Gravitation v.10 #4 297-306 (Mar 1979) DOI: 10.1007/BF00759487
 D. Apsel, ”Time dilations in bound muon decay”, General Relativity and Gravitation v.13 #6 605-607 (Jun 1981) DOI: 10.1007/BF00757247
 W.A. Rodrigues Jr., ”The Standard of Length in the Theory of Relativity and Ehrenfest Paradox”, Il Nuovo Cimento v.74 B #2 199-211 (11 April 1983)
 L.C.B. Ryﬀ, ”The Lifetime of an Elementary Particle in a Field”, General Relativity and Gravitation v.17 #6 515-519 (1985)
 R.G. Beil, ”Electrodynamics from a Metric”, Int. J. of Theoretical Physics v.26 #2 189-197 (1987)
 J.W. van Holten, ”Relativistic Time Dilation in an External Field”, NIKHEF-H/91-05 (1991)
 J.W. van Holten, ”Relativistic Dynamics of Spin in Strong External Fields”, arXiv:hep-th/9303124v1, (24 March 1993)

I don't have free access to journals either, but managed to get all of these through friends. Let me know if you want any.

Sorry for violating the guidelines, I'll try not to do it again. The problem is that as far as I know my paper is the only survey of the field and it took me 3 years to find all the references I have now. (This stuff is so obscure that, until I contacted them, Apsel and Van Holten had never heard of each other!) My sense (now) is that if my paper were viewed as a survey paper it would be OK to discuss here, but if it was viewed as original research then it's not. It's a little of both, which makes things awkward.

I suspect that you're misunderstanding or misinterpreting some GR papers on electrovac solutions.

I've discussed this by email with both Apsel and Van Holten, so I'm pretty sure that I don't misunderstand their positions at least. I have some trouble seeing how Van Holten gets from his equations (which on the surface seem isomorphic to Apsel's and hence NOT gauge-invariant) to his belief in the gauge-invariance of the effect, but I am quite certain that that is how he sees it.

I will admit, however, that I can't (yet) follow all of the math in all of the above papers, and I'm not always able to judge how sound they are. In particular, I have a lot to learn before I can understand the use of Finsler spaces in Beil's paper.

The only one that's freely available online is J.W. van Holten, ”Relativistic Dynamics of Spin in Strong External Fields”, arXiv:hep-th/9303124v1 , so I took a look at that. It talks about a time dilation effect (eq. 18 on p. 5) of $\Delta t/t \approx (d\cdot E+\mu \cdot B)/m$ (with c=1) that sounds much too small to be measurable in practice, and it's also an effect that's completely different from what the OP described in #4, with $\Delta t/t \propto \phi$.

Is there a paper in a refereed journal that relates more directly to the OP's $\Delta t/t \propto \phi$ version? That version seems implausible to me, since (1) it violates C invariance; (2) it requires the introduction of a new universal constant with units of inverse volts, which means that it can't be derived from known physical principles; and (3) I think the constant is constrained to be extremely small, for the reasons given in #9.

Maybe you should start a separate thread if you want to discuss the $\Delta t/t \approx (d\cdot E+\mu \cdot B)/m$ version. But we're probably going to have very little luck getting a discussion going on the other references you gave in #14, since they're not freely available online.

van Holten ... talks about a time dilation effect (eq. 18 on p. 5) of $\Delta t/t \approx (d\cdot E+\mu \cdot B)/m$ (with c=1) that sounds much too small to be measurable in practice, and it's also an effect that's completely different from what the OP described in #4, with $\Delta t/t \propto \phi$.

I think all versions can be viewed as saying that $\Delta t/t = \Delta E/E$, at least for $\Delta E$ small compared to $E$. I don't believe that this formula can be correct for large $\Delta E$ because it gives absurd results for $\Delta E < -E$. It could at best be the linear approximation to a non-linear reality, much like the weak-field approximation to gravitational time dilation.

The differences between theories come in how you calculate $\Delta E$. Van Holten only uses fields (in the paper you have), while Apsel uses the 4-potential.

Do you think it would be appropriate to post just the "History" section of my paper here? It summarizes all the papers in about a page and includes many of the key equations.

the ... $\Delta t/t \propto \phi$ version ... violates C invariance

Could you explain this in a little more detail? I believe that neither theory violates CPT invariance, which as far as we know is the only absolute one. So I don't understand why you're making this claim or how you might be justifying it.

I think all versions can be viewed as saying that $\Delta t/t = \Delta E/E$, at least for $\Delta E$ small compared to $E$. I don't believe that this formula can be correct for large $\Delta E$ because it gives absurd results for $\Delta E < -E$. It could at best be the linear approximation to a non-linear reality, much like the weak-field approximation to gravitational time dilation.

The differences between theories come in how you calculate $\Delta E$. Van Holten only uses fields (in the paper you have), while Apsel uses the 4-potential.
Does your E mean electric field? Energy?

Do you think it would be appropriate to post just the "History" section of my paper here? It summarizes all the papers in about a page and includes many of the key equations.
I think a more appropriate place for that would be the independent research forum.

Could you explain this in a little more detail? I believe that neither theory violates CPT invariance, which as far as we know is the only absolute one. So I don't understand why you're making this claim or how you might be justifying it.
Under charge reversal, $\phi$ reverses sign, but time dilation doesn't, so $\Delta t/t \propto \phi$ is not consistent with C symmetry, which is an exact symmetry of GR coupled to electromagnetism. (I don't think CPT is relevant, since we're talking about classical field theories, not QFT.)

Since the gravitational field is can be represented using Einsteins Relativity Eq. Well the EM field can also have some curvature effect on the fabric on space so in effect yes. It would. because intense Em fields can produce gravitational fields which in turn has a gravitational potential..

Since the gravitational field is can be represented using Einsteins Relativity Eq. Well the EM field can also have some curvature effect on the fabric on space so in effect yes. It would. because intense Em fields can produce gravitational fields which in turn has a gravitational potential..

Yes, this makes sense. This gives an effect proportional to the square of the field, so it doesn't violate C symmetry; it follows directly from known principles; and it doesn't require the introduction of a mysterious new universal constant. It has also been tested indirectly, in the sense that there is empirical evidence that EM fields do interact gravitationally:

Kreuzer, Phys. Rev. 169 (1968) 1007
Bartlett and van Buren, Phys. Rev. Lett. 57 (1986) 21
Will, "Active mass in relativistic gravity," Ap. J. 204 (1976) 234, http://articles.adsabs.harvard.edu//full/1976ApJ...204..224W/0000224.000.html
Will, "The Confrontation between General Relativity and Experiment," http://relativity.livingreviews.org/Articles/lrr-2006-3/ [Broken], 2006

But this doesn't seem to be the same as what Creator and H_A_Landman were referring to.

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Does your E mean electric field? Energy?
Energy

Under charge reversal, $\phi$ reverses sign, but time dilation doesn't, so $\Delta t/t \propto \phi$ is not consistent with C symmetry, which is an exact symmetry of GR coupled to electromagnetism.

Under charge reversal, the charges of all particles in the universe are reversed, which necessarily also reverses all electric potentials. The $\Delta E$ for each particle is therefore unchanged, and so is the dilation. It's proportional to BOTH $\phi$ and $q$ and they both flip.

Energy
Isn't a shift in the period that goes like $\Delta t/t \approx -\Delta E/E$ expected simply because quantum-mechanically E=hf? But that isn't time dilation unless $\Delta t/t$ is the same for all particles, charged or uncharged.

Under charge reversal, the charges of all particles in the universe are reversed, which necessarily also reverses all electric potentials. The $\Delta E$ for each particle is therefore unchanged, and so is the dilation. It's proportional to BOTH $\phi$ and $q$ and they both flip.

I think Creator was hypothesizing a time dilation effect, so it would apply to uncharged particles, e.g., gamma rays emitted from a nucleus would be frequency-shifted in proportion to the electric potential. That would violate C symmetry, since a gamma ray emitted from an anti-iron nucleus would have a shift in the opposite direction compared to a gamma ray emitted from an iron nucleus.

Isn't a shift in the period that goes like $\Delta t/t \approx -\Delta E/E$ expected simply because quantum-mechanically E=hf?

Well, there's no minus sign. Higher energies oscillate faster. But yes, that's one path into these theories. In essence, the phase frequency is each particle's local clock. Or in Apsel's words, "the physical time associated with the trajectory of a classical particle is related to the beats of the quasi-classical quantum mechanical wave function associated with the particle".

But that isn't time dilation unless $\Delta t/t$ is the same for all particles, charged or uncharged.

None of the theories I've mentioned satisfies that definition of time dilation. Van Holten's dilation depends on the spin orientation in a magnetic field; spin up and spin down are dilated oppositely. Apsel's also depends on charge and electric potential.

None of the theories I've mentioned satisfies that definition of time dilation. Van Holten's dilation depends on the spin orientation in a magnetic field; spin up and spin down are dilated oppositely. Apsel's also depends on charge and electric potential.

I think we're talking about two different things here. In the example of the nucleus emitting gamma rays, I'm talking about the gamma rays, not the nucleus.

Yes they are two different things. Of course strong EM fields have mass and cause gravity (the 5 GT magnetic field postulated in Van Holten's paper would have a density greater than lead!), and gravitational potential causes time dilation in the usual GR way. But this is an indirect effect, not a direct one. And it doesn't depend at all on the EM properties of the thing being dilated.

When I talk about EM time dilation, I mean theories in which the EM field or potential ITSELF causes time dilation in a way which a lump of uncharged matter of equal mass would not. The refs I posted all have this property. In some of them, positive and negative particles (or spin up/spin down particles) may be dilated in opposite directions; the rate of time flow for a particle may depend not only on its frame of reference but also on its EM properties.