B Does E=mc^2 apply to gravitational potential energy?

[vanhees71]

I think historically that this issue was the motivation for Noether’s theorem

Yes, Noether analyzed the topic thoroughly in carefully analyzing both what we nowadays call global symmetries and local (gauge) symmetries. The latter are the relevant case for the issue with energy in GR, and that makes it so complicated. The particular problem of GR which makes it more complicated than in SR is that the global symmetry, responsible for "time-translation invariance", only leads to pseudotensors for the corresponding Noether charge-current density, not tensors in the sense of the generally covariant formalism.

 

[H_A_Landman]

No, it can be viewed as a purely classical effect. There is no need to bring QM into it at all.

I said "can", not "must be". What you're saying does not contradict anything I said.

That experiment does not say what you claim. It says that the gravitational potential can be included as a potential in the Schrodinger equation just like any other potential (e.g., the Coulomb potential). That is not the same as what you claim.

Please do not hijack someone else's thread with questionable claims.

I am claiming that the COW experiment confirms that a neutron higher in a gravitational potential has a higher frequency of phase oscillation, exactly as predicted by QM. Are you really calling that questionable?

 

[PeterDonis]

I said "can", not "must be".

You're quibbling over words. Gravitational time dilation is not a "purely quantum" effect. Unless you have a theory of quantum gravity lurking somewhere that the rest of us don't know about.

I am claiming that the COW experiment confirms that a neutron higher in a gravitational potential has a higher frequency of phase oscillation

No, that's not what you claimed. You claimed that this result of the COW experiment somehow proves that gravitational time dilation is a "purely quantum" effect. Which is a different claim than the (true) claim that the COW experiment shows that gravitational potential is included in the Schrodinger equation just like any other classical potential.

You also claimed:

there is no actual change in frequency from gravitational redshift

Which is correct: energy at infinity is a constant of geodesic motion. And therefore, if you want to apply $E = \hbar \omega$ for a quantum object, so is "frequency at infinity". Which means, as you also correctly said, that the apparent difference in frequency of quantum objects at different heights is due to the difference in the observer's clocks at those heights, not to any difference in the quantum object being observed. But all these things are not the same as "gravitational time dilation is a purely quantum effect".

 

[vanhees71]

The experiment with neutrons in the gravitational field of the Earth (over a "reflecting ground") has been done with high precision. The result for the measured energy levels is precisely as expected from the corresponding standard problem treated in the QM 1 lecture:

https://www.nature.com/articles/415297a (I can't find a legal freely available link for this)

Here's another paper on the same measurement, available also from arXiv:

https://doi.org/10.1103/PhysRevD.67.102002
https://arxiv.org/abs/hep-ph/0306198

 

[PeterDonis]

The result for the measured energy levels

Note that these energy levels are energy levels of bound states in a "potential well" created with a mirror. So measurements of these energy levels are not measurements of "gravitational time dilation" for neutrons. They are measurements of whether the gravitational potential works like any other potential in the Schrodinger equation to determine bound state energy levels.

 

[H_A_Landman]

My main point in answer to the original question was merely "it is not entirely unreasonable to ascribe a slightly increased mass to an object when it is higher up in a gravitational potential" than you are, with the caveat that you need to be careful how you use that mass. The negative of that would be "it is entirely unreasonable", even with caveats, which I don't think is a defensible position. I never claimed (and do not think) that it is the best way to formulate the problem, but even though it's clunky, you can make it work.

Gravitational time dilation is not a "purely quantum" effect.

My claim was "GTD can be viewed as a purely quantum effect", so if you're disputing that then your claim must be "GTD can not be viewed as a purely quantum effect". But it's just high school algebra to see that the frequency shift predicted by QM is exactly the same (to first order) as the frequency shift predicted by GTD (in the low-speed weak-field "Newtonian" limit). If you assume that those are independent and unrelated effects, then you need to apply both, which gives the wrong answer by a factor of 2. But if you see them as different ways of describing the same effect, then you can either use the time-dependence of the Schrödinger equation, or you can use the GTD formula; they each give the same (correct) answer. If you do the former, it looks like a purely quantum effect (which oddly does not depend on the magnitude of h); if you do the latter, it looks like a purely classical effect. Your claim is that only the latter is valid, which leaves you responsible to explain why the former gets the right answer even though you claim it's completely wrong.

Unless you have a theory of quantum gravity lurking somewhere that the rest of us don't know about.

That's not required. All this stuff pops up in published semi-classical unified theories going back 40+ years. They're widely ignored, but as far as I can tell their fundamentals are correct. I don't know whether they would be easier or harder to quantize than GR; no one has tried.

the COW experiment shows that gravitational potential is included in the Schrodinger equation just like any other classical potential.

I completely agree, but treating all classical potentials equally inescapably implies that there is a time dilation associated with every classical potential (not just gravity), which is not something that most people accept. Mainstream physics is self-contradictory on this point, so it can't possibly be 100% right. Experiments to test for the predicted EM time dilation were first proposed in 1979 but have never been performed; I'm trying to get one run at PSI in late 2021 (if COVID permits and I don't get laughed out of the review process). So maybe we'll know for sure in a year or two.

If you want to continue this, we should take it offline. We've already "hijacked" too much and are wandering farther off-topic.

 

[Dale]

My claim was "GTD can be viewed as a purely quantum effect", so if you're disputing that then your claim must be "GTD can not be viewed as a purely quantum effect". But it's just high school algebra to see that the frequency shift predicted by QM is exactly the same (to first order) as the frequency shift predicted by GTD

This doesn’t work. Without a quantum theory of gravity it doesn’t make sense to claim that gravitational time dilation can be derived purely quantum mechanically.

We don’t even know if a quantum theory of gravity will obey the equivalence principle. I suspect that the high school algebra derivation you allude to would require that, although without an actual reference it is impossible to know. IMO, bringing the equivalence principle without a quantum theory of gravity that obeys the equivalence principle already makes it semi-classical, not purely quantum.

Your claim is that only the latter is valid, which leaves you responsible to explain why the former gets the right answer even though you claim it's completely wrong

It is up to you to support your claim, not up to others to refute it.

Have you a professional scientific reference that makes the claim “GTD can be viewed as a purely quantum effect”?

 

[PeterDonis]

treating all classical potentials equally inescapably implies that there is a time dilation associated with every classical potential

It implies no such thing. The Schrodinger equation says nothing whatever about time dilation. It's a limited, non-relativistic model.

All this stuff pops up in published semi-classical unified theories going back 40+ years.

Please give references.

Mainstream physics is self-contradictory on this point

Nonsense. Please stop posting misinformation.

Experiments to test for the predicted EM time dilation were first proposed in 1979

Please give a reference.

I'm trying to get one run at PSI in late 2021 (if COVID permits and I don't get laughed out of the review process). So maybe we'll know for sure in a year or two.

If you get a paper published giving the results, then we can discuss it here.

If you want to continue this, we should take it offline. We've already "hijacked" too much

You mean you have hijacked too much. I have no desire to continue this subthread because I didn't start it and have no interest in it. The only reason I have responded to your posts is to correct misstatements (and now to ask for references to back up unsupported statements). So if you stop posting in this subthread, I will too.

 

[H_A_Landman]

Fine. If you want the full machinery of this class of theories, then in my opinion the best references are:

• Apsel, D., “Gravitational, electromagnetic, and nuclear theory.”, Int. J. of Theoretical Physics 17 643-649 (1978)
• Apsel, D.,“Gravitation and electromagnetism.”, General Relativity and Gravitation 10 297-306 (1979)
• Apsel, D., “Time dilations in bound muon decay.”, General Relativity and Gravitation 13 605-607 (1981)
• Rodrigues Jr., W.A., “The Standard of Length in the Theory of Relativity and Ehrenfest Paradox.”, Il Nuovo Cimento 74 B 199-211 (1983).
• Ryff, L.C.B., “The Lifetime of an Elementary Particle in a Field.”, General Relativity and Gravitation 17 515-519 (1985).
• Beil, R.G., “Electrodynamics from a Metric.”, Int. J. of Theoretical Physics 26 189-197 (1987).

Apsel (1979) contains the first experiment proposal.

https://www.researchgate.net/publication/333878154_The_magnitude_of_electromagnetic_time_dilation just strips that stuff down to a very elementary level, and may be of less interest. But, it does include other references and some historical analysis. Feel free to rip it to shreds, but not here. You have my contact info.

 

[PeterDonis]

in my opinion the best references are

Thank you for the references. That will close out this subthread.

 

[vanhees71]

Note that these energy levels are energy levels of bound states in a "potential well" created with a mirror. So measurements of these energy levels are not measurements of "gravitational time dilation" for neutrons. They are measurements of whether the gravitational potential works like any other potential in the Schrodinger equation to determine bound state energy levels.

Exactly, but wasn't this the point of the debate? Perhaps I don't understand, what the issue is here... Of course, I've not claimed that this has anything to do with time dilation. It's just a non-relativistic model after all.

 

[PeterDonis]

wasn't this the point of the debate?

No. The poster I was responding to was claiming that that experiment was a measurement of gravitational time dilation for neutrons. As you agree, it isn't.

 

[vanhees71]

Of course not...