A Possible explanation for muon g-2 anomaly: Gravity?

[George Jones]

they have the two camps of opinion

This just collapsed to the single camp that the effect is negligible.

 

[Arman777]

This just collapsed to the single camp that the effect is negligible.

Well, vmarko indeed argues exactly as I did, but as I said, I've not done the calculation myself, and I think one should confirm it by a proper QFT calculation too. On the other hand, I don't see something that looks obviously wrong.

Vmarko added in his recent post on the site,

"It appears that I was wrong regarding my comment to the response of Chris Polly. Namely, in experiment, the a.m.m. is not being determined from equation (44) but from equation (8). The authors correctly point out that this is calculated using the skewed value of $γ$ which appears to be a valid remark given the GR correction term in (40). So I decided to calculate the variation of (8) with respect to $γ$ taking into account (40), to see what happens when the value of $γ$ is slightly shifted. And indeed, the variation turns out to be proportional to $β$ x $E$
as well, as Chris wrote. So Chris is right that this effect is weighted with the magnitude of the electric field, which is apparently small enough to suppress the GR correction beyond the experimental resolution.

In the end, it appears that the correction term in (45) and in Table 3 is really just a numerical coincidence."

 

[ohwilleke]

So sad. Refutations are coming in from all directions to these papers. It appears that they have at least two distinct flaws. One related to the relative strength of the B and E fields in the experiment and another more general objection related to GR.

 

[mfb]

It means the muon g-2 discrepancy is still there. That is interesting as well.

 

[vanhees71]

Ok, if there are calculational and interpretational shortcomings in these papers, then it's likely to be wrong :-(.

 

[Vanadium 50]

Ok, if there are calculational and interpretational shortcomings in these papers, then it's likely to be wrong

Yes, but apart from that...

 

[Urs Schreiber]

So sad. Refutations are coming in from all directions to these papers. It appears that they have at least two distinct flaws. One related to the relative strength of the B and E fields in the experiment and another more general objection related to GR.

I imagine a proper discussion of QFT corrections due to a background gravitational field ought to proceed in direct analogy to the well-known discussion of QFT corrections due to a background electromagnetic field as in the Lamb shift.

This should require evaluating vertex corrections to lepton-graviton Feynman amplitudes (a concept that is curiously missing from the discussion of the three articles cited in #19). But this must have been considered before. (?)

Digging around, I find

• F. del Aguila, A. Culatti, R. Munoz-Tapia, M. Perez-Victoria,
  "Supergravity corrections to $(g-2)_{\mathrm{lepton}}$ in differential renormalization",
  Nuclear Physics B 504 (1997) 532-550
  hep-ph/9702342

which (on the first page of its introduction) points to

• [13]
  F.A. Berends, R. Gastmans,
  Phys. Lett. B55 (1975) 311

as:

This seems relevant.

Now, I haven't seen that Berends-Gastmans article yet. Maybe the reference [13] is garbled, or my spire-search foo is lacking. Might anyone have a copy?

 

[Urs Schreiber]

Now,I haven't seen that Berends-Gastmans article yet.

Sorry, got it now:

• F. A. Berends, R. Gastmans
  "Quantum gravity and the electron and muon anomalous magnetic moment"
  Phys. Lett. B55 Issue 3
  Feb 1975 311-312
  https://doi.org/10.1016/0370-2693(75)90608-5

Okay, I see, these authors do not consider corrections due to a background field, just the 1-loop gravity corrections due to these diagrams:

So it's not directly relevant to the claim cited in #19.

But nevertheless, it seems to me that if one wanted to study that effect in #19, it's this kind of QFT computation that should be used.

 

[ohwilleke]

A short new pre-print from a Wellington, New Zealand based physicist posted three days after the original papers concludes that these papers are flawed:

In three very recent papers, (an initial paper by Morishima and Futamase, and two subsequent papers by Morishima, Futamase, and Shimizu), it has been argued that the observed experimental anomaly in the anomalous magnetic moment of the muon might be explained using general relativity. It is my melancholy duty to report that these articles are fundamentally flawed in that they fail to correctly implement the Einstein equivalence principle of general relativity. Insofar as one accepts the underlying logic behind these calculations (and so rejects general relativity) the claimed effect due to the Earth's gravity will be swamped by the effect due to Sun (by a factor of fifteen), and by the effect due to the Galaxy (by a factor of two thousand). In contrast, insofar as one accepts general relativity, then the claimed effect will be suppressed by an extra factor of [(size of laboratory)/(radius of Earth)]^2. Either way, the claimed effect is not compatible with explaining the observed experimental anomaly in the anomalous magnetic moment of the muon.

Matt Visser, "Post-Newtonian particle physics in curved spacetime" (February 2, 2018).

There is also an official statement from the g-2 collaboration:

The response from the g-2 collaboration (from the spokesperson Chris Polly):

Our spokes already replied to the authors since they made a mistake in the final conclusion. While the additional effect in the bxE term they calculate is 2ppm, they then attribute this full term to be the change in g-2. However, they forgot that that additional contribution needs to be weighted by the relative strength of the bxE term which is 1330ppm of the B field. So even if their calculation was correct, the actual contribution is 2ppm*1330ppm=2ppb. That’s negligible for the ongoing experiments measuring to ~100ppb precision. And this argument does not even involve any judgement on the validity of the additional term they calculate.

and from the same source http://www.science20.com/comments/206921:

Re: Gravitational Effects Explain Muon Magnetic Moment Anomaly A

Regardless of whether or not the GR is correct, the authors make an error at the end of their paper by failing to take the relative strengths of the E and B fields used by the experiment into account. The vast majority of the muon precession is driven by the B-field while the E-field is only a small perturbation. The maximum E-field experienced by a muon in the g-2 storage ring is 30kV/5cm while the B-field is 1.5T. That means betaXE is very small compared to B...to be precise betaXE is 1300 parts per million (ppm) compared to B. So, in their treatment they find an additional modification to the coefficient in front of the betaXE term that shifts the value of the coefficient by 2ppm. Therefore, the overall impact on the anomalous magnetic moment extracted by the experiment would change by 2ppm x 1300 ppm = 2.7 parts per billion (ppb), which is well below the 500ppb error on the BNL experiment and the 140ppb error targeted at Fermilab. This is actually an overestimate since we used the maximum E-field a muon can experience in the g-2 ring in the calculation. If you cannot find anywhere in the paper where they state the average magnitudes of E and B observed by muons in the experiment, then you know there is a problem. For instance, they would find the same correction arising from the betaXE term would apply to the experiment proposed at J-PARC even though the novel design of that experiment has E=0 by construction.

There also also many comments in the blog posts that have covered this development and some have updates to their body texts or follow up posts.

 

[mfb]

I moved six posts from this thread into this thread as they have the same topic and don't fit well in the other thread.

 

[Demystifier]

From Aharonov-Bohm effect, we know that sometimes in QM the potential itself (not its derivative) has a physical role. The gravitational redshift in classical GR is also formulated in terms of the potential (not its derivative). Could it be that something similar is happening here?

 

[mfb]

From Aharonov-Bohm effect, we know that sometimes in QM the potential itself (not its derivative) has a physical role.

Even there it is only the difference. Gauge symmetry stays, and adding a constant term to the potential is a trivial gauge symmetry everywhere.

The gravitational redshift in classical GR is also formulated in terms of the potential (not its derivative)

Yes, there something moves from A to B.

 

[Demystifier]

Even there it is only the difference. Gauge symmetry stays, and adding a constant term to the potential is a trivial gauge symmetry everywhere.Yes, there something moves from A to B.

Well, maybe the correction to g-2 from $g_{\mu\nu}\neq\eta_{\mu\nu}$ really depends on $\phi(R)-\phi(\infty)$, where $r=\infty$ corresponds to the point where $g_{\mu\nu}=\eta_{\mu\nu}$, and the authors work in the gauge in which $\phi(\infty)=0$.

 

[Demystifier]

I am trying to understand what could possibly be wrong with their calculation. Eq. (2) in paper I is general covariant. From that they derive Eq. (4). The second line of Eq. (4) contains only the derivative of the potential, so it should not be problematic. The potential itself appears only in the first line, which vanishes when the EM fields ${\bf E}$ and ${\bf B}$ vanish. This suggests that there could be something wrong with their calculation of ${\bf E}$ and ${\bf B}$. Indeed, they do not state how ${\bf E}$ and ${\bf B}$ are defined. I suspect that they define ${\bf E}$ and ${\bf B}$ as the corresponding components of $F^{\mu\nu}$ in (2), but if they do, that's wrong. In general, electric and magnetic field are defined covariantly as (see https://arxiv.org/abs/1302.5338 )
$$E^{\mu}=F^{\mu\nu}o_{\nu}$$
$$B^{\mu}=-\tilde{F}^{\mu\nu}o_{\nu}$$
where $o_{\nu}$ is the 4-velocity of the observer. In a gravitational background, the velocity $o_{\nu}$ also depends on the potential, which might cancel the dependence on the potential in the first line of (4). Someone should do a detailed calculation to check it!

 

[mfb]

Well, maybe the correction to g-2 from $g_{\mu\nu}\neq\eta_{\mu\nu}$ really depends on $\phi(R)-\phi(\infty)$, where $r=\infty$ corresponds to the point where $g_{\mu\nu}=\eta_{\mu\nu}$, and the authors work in the gauge in which $\phi(\infty)=0$.

If that would be true, we would be back at the Sun/galaxy question.

 

[Demystifier]

If that would be true, we would be back at the Sun/galaxy question.

You are right. Now I suspect that their calculation could be wrong due to the reason explained in #64 above.

 

[Demystifier]

I have found a rather trivial error in their paper, so I have written a short paper on it:
http://lanl.arxiv.org/abs/1802.04025

 

[vanhees71]

• [13]
  F.A. Berends, R. Gastmans,
  Phys. Lett. B55 (1975) 311

as:

View attachment 219802

This seems relevant.

Now, I haven't seen that Berends-Gastmans article yet. Maybe the reference [13] is garbled, or my spire-search foo is lacking. Might anyone have a copy?

https://doi.org/10.1016/0370-2693(75)90608-5

 

[Urs Schreiber]

https://doi.org/10.1016/0370-2693(75)90608-5

Yeah, I had found in #58, right after my first message. Sorry for the trouble.

 

[Urs Schreiber]

I have found a rather trivial error in their paper, so I have written a short paper on it:
http://lanl.arxiv.org/abs/1802.04025

Great. Trivial or not, you seem to be the first to actually identify the error, instead of just making broad comments about the plausibility of the result.

 

[Vanadium 50]

ou seem to be the first to actually identify the error

No, see message #43, point (2).

He is however, the first to put it on the arXiv.

 

[PAllen]

I also hinted at the source of error in my post #33. Demystifier carried out and verified this idea (presumably independently arrived at), and posted it.

 

[Urs Schreiber]

No, see message #43, point (2).

Hm. If you are serious about pointing out the mistake in a computation, and maybe taking credit for it, you should produce something that looks like a computation.

 

[Urs Schreiber]

I also hinted at the source of error in my post #33. Demystifier carried out and verified this idea, and posted it.

Hm. This forum has "physics" in its title, and there is a button for typesetting formulas with each comment box. If you have an insight, and would like credit for it, make it a unambiguous derivation in formulas. That's how physics is communicated ever since it stopped being called "natural philosophy".

I agree that it seems a bit of a stretch to promote an elementary manipulation of a few lines to an arXiv preprint, but at least it's a formal mathematical manipulation that rises to the standards of argument in modern physics, and not just an essay with hints.

 

[PAllen]

Hm. This forum has "physics" in its title, and there is a button for typesetting formulas with each comment box. If you have an insight, and would like credit for it, make it a unambiguous derivation in formulas. That's how physics is communicated ever since it stopped being called "natural philosophy".

I agree that it seems a bit of a stretch to promote an elementary manipulation of a few lines to an arXiv preprint, but at least it's a formal mathematical manipulation that rises to the standards of argument in modern physics, and not just an essay with hints.

I have no intention to imply credit. Use of the word hint was deliberate. If I had chosen to follow through on my suggestion, and post the calculation, only then would I claim credit.

 

[mfb]

That's how physics is communicated ever since it stopped being called "natural philosophy".

That typically doesn't include web forums. There are some exceptions, and we do realize that some professional communication happens outside the traditional ways, but putting it on arXiv and linking to it is better than posting it here exclusively.

 

[Vanadium 50]

something that looks like a computation.

I would say that's a description of the Nikolic paper. Looks like a computation. What it is not is a corrected calculation of the Morishima et al. papers. What it is has three parts:

1. A short restatement of the Morishima argument.
2. The statement "they seem to tacitly assume that time t in [1] is physical time. However, it is merely a coordinate time."
3. The derivation of gravitational time dilation of Schwarzschild.

The only original part is #2, as #1 comes from Morishima and #3 is a century old.

 

[Urs Schreiber]

The only original part is #2, as #1 comes from Morishima and #3 is a century old.

I guess I see your point. But I would want to suggest generally, to you and other contributors here on PF, to try a more professional style of discourse, more formulas and also (not relevant here but elsewhere) more citations for claims. Over on Mathematics.StackExchange and MathOverflow it is completely common to write a non-original formula if that is the answer to some question. Formulas are simply the language in which to speak in physics and mathematics, even if one is just recalling ancient insights. In all the informal chit-chat here, you can't expect us (not me at least) to spot your technical insight hidden in an essay that looks no different than many other opinions being voiced and forgotten.

Here, it would have been easy for you to settle the issue for good if you had used accurate notation.

 

[Demystifier]

A new paper on the subject appeared
https://arxiv.org/abs/1803.01395
but it seems that the authors have not understood what Visser and me objected.

 

[Shahaf Yefet]

Hi!

I find this too abstract. How can we apply this, at the very least, to SAGR?

I believe Dorigo did not take into account that gravity is none-constant...

Perhaps if he'd reverse the algorithm he'd get a more approachable result

 

[Jimster41]

So is the conclusion t
hat there can't be an effect on the moment based on gravitational potential or just not one based on earth's? Or is there still an opening for some connection between the anomaly and the overall gravitational potential of the experiment. I'm trying to reconcile @mfb 's initial comment that the Sun's effect would be bigger and then there was one about the galactic potential. Is any complex interplay between all the relevant potentials ruled out or just unclear, or expected to be either be way too small or way too large?

The line in @Demystifier 's paper on pg 2 "For horizontal motion we have dr=0" kind of left me hanging. Is dr for all potential's =0? Is the particle moving horizontally w/respect to all potentials? Isn't the metric a combination of Earth's and the Sun's.

 

[mfb]

I think the general conclusion is that only higher order effects (like differences of the gravitational potential within the experiment) might contribute. The gravitational potential should not contribute - and if it would, then the effect would be much stronger than observed because the Sun and the galaxy would be more important.

 

[Jimster41]

Just a follow up to this thread - which was pretty interesting and left me with a ton of questions (@MTd2 post #25 especially gave me a cartoon I couldn't get out of my head). I found these papers in my travels as I tried (fairly unsuccessfully) to answer them.

I gather there is not currently a perfect fully GR equation solution to a realistic scenario (n charged spinning massive bodies)? Wiki says the two body problem is still unsolved really.

In hindsight of course it's not surprising. But when you are looking at science from the bleachers you always think, "well surely they can calculate that... like they do everything else". I don't know how realistic the proposal for a relativistic positioning system in the first paper is is but it is a pretty intriguing model - like could you use a set of Schwarzschild solutions that radio each other under some dynamic to explore a real GR context? [Edit] What I mean is - what does a quantum mechanical observer know about its metric if it is caught up in a system of like three spinning massive objects all telling it what to do (what space-time is like). How does it resolve a metric? I mean can it just... add them up?

https://arxiv.org/abs/1603.00127
Epistemic relativity: An experimental approach to physics
Bartolomé Coll
(Submitted on 15 Dec 2017)
The recent concept of relativistic positioning system (RPS) has opened the possibility of making Relativity the general standard frame in which to state any physical problem, theoretical or experimental.
Because the velocity of propagation of the information is finite, epistemic relativity proposes to integrate the physicist as a real component of every physical problem, taking into account explicitly what information, when and where, the physicist is able to know. This leads naturally to the concept of relativistic stereometric system (RSS), allowing to measure the intrinsic properties of physical systems. Together, RPSs and RSSs complete the notion of laboratory in general relativity, allowing to perform experiments in finite regions of any space-time.
Epistemic relativity incites the development of relativity in new open directions: advanced studies in RPSs and RSSs, intrinsic characterization of gravitational fields, composition laws for them, construction of a finite-differential geometry adapted to RPSs and RSSs, covariant approximation methods, etc. Some of these directions are sketched here, and some open problems are posed.

Comments: 19 pages; 12 figures; in Relativistic Geodesy: Foundations and Application. Proceedings of 609 WE-Heraeus Seminar (2016)
Subjects: General Relativity and Quantum Cosmology (gr-qc)
Cite as: arXiv:1712.05712 [gr-qc]
(or arXiv:1712.05712v1 [gr-qc] for this version)

https://arxiv.org/abs/1603.00127
Gravitational Effects on Measurements of the Muon Dipole Moments
Andrew Kobach
(Submitted on 1 Mar 2016 (v1), last revised 14 Apr 2016 (this version, v2))
If the technology for muon storage rings one day permits sensitivity to precession at the order of 10−8 Hz, the local gravitational field of Earth can be a dominant contribution to the precession of the muon, which, if ignored, can fake the signal for a nonzero muon electric dipole moment (EDM). Specifically, the effects of Earth's gravity on the motion of a muon's spin is indistinguishable from it having a nonzero EDM of magnitude dμ∼10−29 e cm in a storage ring with vertical magnetic field of ∼ 1 T, which is significantly larger than the expected upper limit in the Standard Model, dμ≲10−36 e cm. As a corollary, measurements of Earth's local gravitational field using stored muons would be a unique test to distinguish classical gravity from general relativity with a bonafide quantum mechanical entity, i.e., an elementary particle's spin.
Comments: 5 pages; corrected calculation, qualitative results unchanged
Subjects: High Energy Physics - Phenomenology (hep-ph); High Energy Physics - Experiment (hep-ex)
DOI: 10.1016/j.nuclphysb.2016.08.011
Cite as: arXiv:1603.00127 [hep-ph]
(or arXiv:1603.00127v2 [hep-ph] for this version)

 

[mfb]

As comparison: The current limit on the muon EDM is 2*10^-19, E989 tries to reach 10^-21.

Gravitational fields don't add linearly in GR. While we don't have analytic solutions to many interesting cases, numerical simulations work well.