I just learned some interesting news from Tommaso Dorigo’s blog. Go there for more details, but the news is the claim in these three papers that, accounting for GR effects on the precision measurement of the muon anomalous magnetic moment, the three sigma difference between experiment and theory goes away.

This sort of calculation needs to be checked by other experts in the field, and provides an excellent example of where you want good peer review. Presumably we’ll hear fairly soon whether the result holds up (the papers are not long or complicated). If this is right, it’s a fantastic example of our understanding of fundamental physics at work, with the muon g-2 experiments measuring something they weren’t even looking for, a subtle effect of general relativity.

Also interesting will be the implications for the ongoing experiment at Fermilab trying to achieve an even more precise g-2 measurement. I’m wondering whether there is any way for them to isolate the GR effect on their measurement.

The significance of this is that (setting aside questions about the neutrino sector), the muon g-2 measurement is the most prominent one I’m aware of where there has been a serious (three sigma) difference between experiment and Standard Model theory. This has often been interpreted as evidence for SUSY extensions of the SM. Projects producing “fits” that “predict” SUSY particles with masses somewhat too high to have been seen yet at the LHC use the g-2 anomaly as input. Tommaso ends by asking what happens to these fits if the g-2 anomaly goes away.

**Update**: For some recent things to read about the g-2 anomaly, before this latest news, see here and here.

**Update**: Rumor about a problem with this calculation here.

**Update**: According to this comment and this one, the g-2 collaboration has identified a problem with the calculation, making the predicted GR effect unobservably small. If the authors agree, presumably we’ll soon see a corrected version of the paper(s).

Looking for more information about this, I ran across two blogs I hadn’t seen before. String theorist Joe Conlon of Oxford has a blog called Fickle and Freckled. Not much there besides a posting supporting Brexit and denouncing the fact that nearly all of his colleagues disagree with him, which he fears will cost the university money. A second one is string/SUSY phenomenologist Mark Goodsell’s Real Self-Energy. Goodsell seems to be a Lubos fan, dealing with the current g-2 story by linking to his discussion and denouncing the authors as “effectively crackpots”. He also seems to be unhappy with a certain blogger:

I regularly read two or three physics blogs, since they report on the latest news (and rumours). Now, one of these blogs is very popular whose ostensible purpose is to persuade people that string theory is a misguided research topic. Obviously, this is something I disagree with. However, it also talks a lot about high-energy physics generally, and being rather well-connected it can be quite informative and useful. However, it pretty much uniformly takes a very pessimistic line about all concrete ideas for new physics. It is difficult to overstate how damaging this has been, in making physicists and scientists in neighbouring fields depressed about the future of high-energy physics, and opposing this trend is one of the reasons I would like to blog …

Goodsell has devoted his career to string and SUSY phenomenology, and seems to feel that this is the “future of high-energy physics”, and I’m responsible for making people discouraged about it. Perhaps he should stop advertising Lubos and denouncing crackpots, instead pay attention to the negative results from the LHC and the evidence they provide that his research program is a failure. Blaming his problems on me for pointing them out isn’t going to make them go away.

**Update:** As mentioned in the comments, Matt Visser now has a preprint criticizing the calculation in these articles.

I cannot read Tommaso’s article. Somehow it is being redirected to other stuff and I only see the abstract.

Bernhard,

I’ve seen that problem before on that website. For me right now it seems to be working properly. Another thing to try would be

http://www.science20.com/tommaso_dorigo

then the correct blog posting. If someone sees the problem you mention, perhaps they could report it to the website owner, saying what the page is that they are being incorrectly redirected to.

Peter,

Thanks. I read it now and also (diagonally) read the articles. Whoever peer reviews those articles has a huge responsibility on his hands. It’s almost like reading a standard textbook calculation (even if a hard one) that is surprising nobody had such an idea before.

Delicious. Llewellyn Thomas must be smiling somewhere. I wonder if the electron magnetic moment could be measured in a storage ring, as opposed to a Penning trap, to see if the same effect arises.

Isn’t it a bit suspiciuous that the GR correction happens to cancel the anomaly down to 0.1 sigma difference between the expected vs observed?

Hmm, they claim the shift is due to absolute value of gravitational potential. But the gravitational potential GM/R due to the Sun is more than 10 times larger at the radius of Earth’s orbit than Earth’s own gravitational potential on its surface. Its probably premature to get excited.

Also such effect would almost certainly violate the equivalence principle, if one can distinguish space-time curvature from uniform acceleration with a local experiment.

Because the earth is in free fall around the sun, the equivalence principle says the solar gravitational field has no effect on a local terrestrial measurement.

If I understand the paper this could be a tiny effect caused by the likewise tiny GR space-time curvature by the gravitational field of the the earth. We know of course that this tiny space-time curvature is crucial for the working of the GPS. Question: If that is true what’s the big deal if the GR space-time curvature of the earth gravitational field leads to other effects?

I went through the papers and it seems a tree-level contribution from Earth’s gravitational field cancels out from all relevant quantities, except the ‘muon magic momentum’ term, which is used to calculate g-2. This apparently explains the anomaly.

Personally, I think this result will hold up. The calculations are pretty straightforward. If there is any inconsistency, it’ll be found in no time.

I haven’t read the original calculation of g-2, but people are usually thorough about these things. So all of this is pretty surprising.

According to the papers, the new effect does not depend on the gravitational field, but on the gravitational potential. It would be breakthrough if it could be measured by local g-2 experiments. One could even claim a bigger g-2 anomaly due to the gravitational potential of the sun and of the galaxy. Let’s see if they missed some term that cancels the putative effect.

A,

I don’t want to spoil your excitement, but people have measured gravitational potentials for quite a while using atomic clocks. There are even portable clocks that can measure the gravitational potential of the earth with a resolution of about 70 cm.

Bernd,

Atomic clock experiments measure only gravitational potential difference between different locations. The effect in muon experiment is claimed to be proportional to the gravitational potential in that location (and not for example proportional to the gravitational potential gradient i.e. local acceleration).

Does anyone know what Schwarzschild coordinate system Morishima and Futamase are using in Eq.(3) in paper no. 1?

The claimed resolution of the g-2 anomaly is asserted to depend on the *absolute* gravitational potential on the surface of the Earth.

Insoafar as one believes this claimed result, one is not working in general relativity,

and has explicitly violated Einstein’s equivalence principle.

Insoafar as one believes this claimed result, the effect of the Sun exceeds that of the Earth by a factor 15, and worse, the effect of the Galaxy exceeds that of the Earth

by a factor 2000.

(Gravitational potentials at the surface of the Earth, as opposed to gradients, behave somewhat unexpectedly: the Galaxy dominates over the Sun, which in turn dominates over the Earth’s self gravity.)

On the other hand, insofar as one claims to be working with general relativity, then one should take note of the Einstein equivalence principle, whereby *absolute* gravitational potentials do not matter, and it is only potential differences that show up in laboratory physics.

The fractional corrections due to GR as compared to SR are of order

(Riemann tensor) x (size of laboratory)^2

With a little work this fractional correction turns into

(gravitational potential) x [ (size of laboratory) / (radius of Earth) ]^2

Overall, either way this proposal for resolving the g-2 anomaly fails:

1) Either you violate general relativity,

but then the effect of the Galaxy dominates and is 2000 times too big.

2) Or you work within general relativity, and then the effect is suppressed

by the overwhelmingly small factor

[ (size of laboratory) / (radius of Earth) ]^2.

So unfortunately this claimed resolution of the g-2 anomaly is not going to work.

The authors claim that the effective muon magnetic moment is related to the one without gravity by μ_eff(muon)≃ (1+3φ/c^2) μ(muon), where φ is the gravitational potential.

It seems hard to believe

(1) that this formula does not contain potential differences, because potentials can be changed by a constant or by a change of coordinate system;

(2) that this formula doe not contain a term that depends on the orientation of the experiment with respect to the height coordinate z.

They do “assume that the motion is confined in the horizontal plane and the

magnetic field is applied vertically” (Part III, after Eq 27). But as Matt stated, they confuse the gravitational potential generated by earth with the minuscule gravitational potential difference in the laboratory (or else claim violation of the equivalence principle).

Apparently the error is more subtle that we speculated. In the very end of the Part III they correctly conclude that “Therefore, the relative magnitude of the contributions of the gravity gradient and the electromagnetic interaction is f∇φ / fEM ≃ 1.5 × 10^−15 which shows the gravity gradient contribution is 10^−15 times smaller than the electromagnetic interaction…”

It is the post-Newtonian effects that they conclude wrongly (as the sentence continues “… and is even 10^−5 times smaller than the post-Newtonian effects.”)

Beautiful! 🙂 Textbook GR, elementary calculation, this could have been an exercise for a graduate student (I might even give it to my students as an exercise). I haven’t checked all minuses and factors of 2, but if the details of the calculations in the papers don’t contain any mistakes, this represents an amazing lesson in GR for everyone!

As UltraDoofus noted, the kill comes in the equation (40) in 1801.10246, where the velocity of the muon (encoded in $\gamma$) is tuned to the “magic” value so that the term proportional to electric field becomes zero. From there, one reads off the value of the anomalous magnetic moment, and equations (44) and (45) compare it to the value of the a.m.m. without the GR correction term. And according to the table 3, this GR correction term has precisely the correct value to account for the $3.6\sigma$ discrepancy between experiment and the SM calculation. This is just way too good to be a coincidence. 😀

On the one hand, I do understand why GR has always been a blind spot in the minds of hep-ph and hep-ex folks (and maybe even some hep-th folks as well). But on the other hand, in face of a $3.6\sigma$ discrepancy in a high-precision experiment, the fact that nobody even _bothers_to_think_ of checking the GR contribution (while string theorists are on an all-out hunt for supersymmetry contributions) is just unbelievable! This result is a proper slap-in-the-face to all hep-* folks, to go back into the classroom and learn some GR.

Also, a small spoiler — while the first two papers are nice and instructive, one doesn’t really *need* to read them, 1801.10246 is quite enough to make the point. 😀

Best, 🙂

Marko

Bill,

The Schwarzschild metric used is defined in Appendix B.

Matt Viser,

The experimental apparatus is at rest with respect to the earth, as analyzed. To include the solar gravitational effect, one would have to include the accelerations with respect to the sun as well (since the earth is in free fall around it). However, there’s no need to go to all that trouble, since the two precisely cancel per the equivalence principle. Ditto for the galaxy.

Various,

The analysis explicitly assumes a Schwarzschild geometry, so the corresponding fields are “baked in”. Completely analogously, one can express the gravitational blue-shift of such a geometry solely by the potential of the receiving station.

With all that said,

I am not certain of the result. It seems they are suggesting the “magic gamma” was not selected quite correctly. I doubt the exact value was calculated for the experiment, but rather the result of some extremum search. I look forward to more authoritative discussion of this matter.

vmarko,

Don’t you see a problem that they use gravitational potential of the earth ϕ (and not its’ derivative)? It is claimed that a constant rescaling of the time and space coordinates could be made so that ϕlab = 0, and there is no Post-Newtonian contribution.

Off topic, but it’s going around social media that Joe Polchinski passed away yesterday following his battle with cancer. He was 63.

marko,

After looking at the papers again, I’m gonna have to curb my enthusiasm. I think they messed up while taking the post-Newtonian approximation.

As others have pointed out, the bare potential (gauge dependent) shouldn’t appear in any observables. Only ‘g’ or its gradients can satisfy the equivalence principle. So the actual gravitational corrections are likely far too small cancel the anomaly.

Art,

1) The apparatus is not in free fall wrt to the Earth’s field, which is why the experiment can only detect the local acceleration, ‘g’, and its gradients.

2) The redshifted/blueshifted frequency is a dot product between two vectors. So it’s gauge independent.

3) Their argument about the magic momentum doesn’t stand either. Because it’s also gauge independent.

This discussion, while interesting, is completely irrelevant. 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.

Matt Visser,

Is it obvious that the factor in (2) suppresses the effect? The muons are relativistic (gamma ~ 30) so SR effects are of order 1, the ratio of the storage ring radius to the earth radius is about 10^-5, and the correction only needs to be a few parts per billion.

OK, actually more like 10^-6, but still in the ballpark. Also it must depend on the mass density of the earth somehow (if the earth were a neutron star, the effect would be much bigger)?

G.S.

Yes, I was sorry to see that news. I never met Polchinski and my own indirect interactions with him were rather unfortunate. Rest in Peace.

Ok, maybe I should respond to some of the issues people have raised here, just for the sake of clarity.

First, in the Newtonian approximation of GR, it is a quite standard thing to choose the boundary condition $\phi(\infty)=0$ for the potential. The authors have defined $\phi(r)$ in the sentence below equation (4), and it is obvious that they use this boundary condition to set the zero-level of the potential. Given this, the potential itself becomes observable. If anyone is uncomfortable by this, feel free to substitute (throughout the paper) every appearance of $\phi(r)$ by $(\phi(r) – \phi(\infty))$, which is invariant with respect to adding a constant. This doesn’t change the result in any way.

Second, the gravitational potentials of the Sun doesn’t play a role. In Newton-speak, this is because it is canceled by the corresponding centrifugal potential, coming from the fact that the Earth revolves around the Sun. In Einstein-speak, this is because the Earth follows a free-fall trajectory, and is thus in a locally inertial frame, so according to the equivalence principle it feels no pull from the Sun (and the tidal forces are too small over the size of the apparatus). The same statements hold for the galaxy. Note that the apparatus does *not* freely fall in the gravitational field of the Earth (as opposed to the Sun and the galaxy), but is being “pushed” off its geodesic trajectory upwards by the floor of the lab. This is an electromagnetic effect (spiced up by the Pauli exclusion principle), despite being described by the gravitational potential $\phi$, in Newtonian language. This force is real, we all feel it when we stand up, and it has nothing whatsoever to do with any violation of the equivalence principle.

Third, one should distinguish the contribution coming from the potential $\phi$ and the contribution coming from the gradient of the potential, $\nabla\phi$. These are different, and the latter is much smaller than the former, as explained in Appendix C of the paper. Thus the gradient can be neglected, while the potential itself should not. The authors correctly showed due diligence to discuss this, I see no problem there.

Finally, regarding the response from Chris Polly, the relevant statement in the paper is this: ” If the $\gamma$ was experimentally tuned to minimize the electric field

contribution, the quantity $a^{mod}$ might have been measured.”. That is to say, the experiment may contain a systematic error, depending on their procedure for tuning the value of $\gamma$. I don’t know the details of the measurement process(es), but this doesn’t seem to have anything to do with the absolute magnitude of the electric field, since the $\beta\times E$ term in (40) multiplies *both* the a.m.m. and the correction, so it cancels out of equation (44). Or maybe I misunderstood what Chris wanted to say. 😉

I hope this clears things up a little.

RIP Joe Polchinski.

HTH, 🙂

Marko

Marko,

I am grateful that you explained the topic in a such understandable way.

Pingback: La gravitación de la Tierra podría explicar la anomalía en el momento magnético del muón | Ciencia | La Ciencia de la Mula Francis

Given the claims that the preprint fails to explain the anomaly by orders of magnitude, I’m amazed there isn’t some pretty simple dimensional analytic/O(mag) argument that shows this whole idea of GR affecting so subtle a phenomenon in QFT was always a non-starter.

vmarko,

I don’t know about this result, but let me just say that gravitational (and GR) effects are not unknown to accelerator physicists at all. The field has been taking these things into consideration and even I (not an accelerator physicist) happened to be at such a seminar. The rumor says that g-2 is already half way in writing an answer, as is by now kind of evident from comments above.

In case of the first article, another way to look at this “potential” effect, note that the factor in formula (4) comes from time dilation, and it is known that gravitational time dilation is, to the first order, proportional to differences of potentials. Since here only one location of comparison is explicitly mentioned, i.e. on the Earth’s surface, the other location of comparison is naturally set at the infinity, and the constant cancels out. Hence, there is no contradiction in having pure potential. I was surprised that initially people jumped in with such conclusions, especially when this can be check almost on paper, with possible help from Mathematica.

Also, formula (5) contains mistakes. Surely, the overall factor should be gamma, not its inverse, and, I think, terms in brackets should have opposite signs. Seeing such things on page 2, I am not surprised that they may have forgotten a numerical factor.

Pingback: Possible explanation for muon g-2 anomaly: Gravity? | Page 2 | Physics Forums - The Fusion of Science and Community

Matt Visser’s response to the original postings has appeared on hep-ph/gr-qc: “Post-Newtonian particle physics in curved spacetime” arXiv:1802.00651.

Julius, the difference with the potential at infinity will be relevant when some experiment will be done there. Local experiments cannot measure the local gravitational potential. This was also discussed in arXiv:1802.00651 by Matt Visser.

OK, so it seems the odds against the article being correct are now rather low, given the comments from experts, but the unprofessional reactions towards the authors are really sad. They are not crackpots – they wrote a paper that an experimental collaboration felt the need to respond to. However flawed, which I’m in no position to judge, this is all part of doing science. One wants to avoid making public mistakes, but this is not always possible.

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 $\gamma$, 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 $\gamma$, taking into account (40), to see what happens when the value of $\gamma$ is slightly shifted. And indeed, the variation turns out to be proportional to $\beta\times E$ 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. 🙁

Best, 🙂

Marko

A,

time dilation is not a local event. To the first order it depends on the difference of potentials, and the further apart they are measured, the bigger the effect. If one dislikes time at infinity, then by coordinate transformation time can be brought to a finite distance from Earth. In practice this is what we do for experiments on the ground, since we, are sitting in a potential well, together with our atomic clocks. Maybe what is confusing is the usage of the gradient notion, and I use the differential gradient definition, not some macroscopic difference.

In the first paper, they compare Eqs. (4) and (19) to their Minkoswki counterparts to extract the effective magnetic moment of the muon. But this comparison is only valid in the locally inertial frame of the lab. (e.g. Fermi coordinates).

If one assumes that they are using a locally inertial frame in Eq. (3), then the metric has to be Minkowski at the lab, and the potential vanishes there. Eq.(9) is then “trivial”. The first correction from GR will thus come from variations of the potential (i.e. of the metric), as explained by Matt Visser in his short paper.

If on the other hand one uses Schwarzschild coordinates (as they do), then one is not allowed to extract the magnetic moment from Eqs. (4) and (19).

Their calculations seem correct to me, it is their physical interpretation of these calculations that one must be cautious with.

Hello Peter,

in all three papers, the Schwarzschild metric is approximated with respect to the small parameter ε = 1/c …

This is not correct.

The expansion parameter is usually dimensionless (such as e.g. the ratio υ/c, or the fine structure constant α).

And the expansion shall be finite when ε = 0. But in their case, it’s infinite!

Anyway, perturbation expansions are not based on dimensional quantities such as c, because with a change of units c can take any value you want – large or small…

Funny, in all three papers, it is stated that they use units where c = 1.

🙂

Usually Φ/c^2 is considered small for approximations of the Schwarzschild metric, but this gives the Newtonian limit.

Has anyone checked if their derivation of the approximate post Newtonian metric is correct?

Does it occur to anyone that the authors could have contacted the muon g-2 collaboration privately, to discuss their findings? I asked a friend (member of the collaboration) about this and his reply was that expert theorists rapidly identified the error and this formed the basis of the reply by the collaboration.

arxiv,

Ideally they should have asked for feedback from experts and the muon collaboration privately before posting the papers. In practice though it is very understandable that they would choose to “shoot first and ask questions later”. Especially since they seem to be young unestablished people and therefore likely to get minimal credit if their work happened to be scooped “by coincidence” (not) by someone prominent while they were doing the private consultations…

(I had an experience of exactly that, although concerning a much smaller result, as I’m sure many others have had too. As a young nobody I found a result of some significance in a specialized subfield of hep theory – although no big deal in the general scheme of things – and thought I better seek feedback and confirmation from experts before posting the paper… Without getting into the details, the upshot was that I ended up sharing credit for it with 2 others, both of whom were more senior, so my paper was always 3rd and last when that work was cited thereafter… One of the others was an eminent senior person who ended up with the bulk of the credit – not so much because he tried to grab it but because the community just felt more comfortable with him having it, i.e. the Matthew effect in action.)

Regarding the current papers, if the result doesn’t hold up (which seems to be the case now) I hope the authors still get credit for boldness, creativity, and giving us something interesting to think about!

arxiv etc. What was required was feedback from theorists. It would be a little odd that authors should feel they have to go through an experiment to get this. For theory feedback, the arxiv is the most appropriate choice. There is also no guarantee that the expert theorists engaged by the collaboration would have worked as quickly as they did when the papers appeared in the arxiv. A response to the authors’ work may well have been placed on the back-burner for quite a while.

In general, I prefer these issues to play out in the open. I admire the authors for taking a chance. Yes, they were left with egg on their faces; that’s life. I certainly don’t see them as crack pots, as has been alleged (unless someone can come up with more evidence than is provided by this particular issue). At the very least we’ve all learned that GR plays effectively no role (no surprise) in the muon g-2 measurement and we’ve also been reminded that there is a first rate experiment which may resolve one of the big puzzles in particle physics.

X and Rob,

It is a simple matter of courtesy. The authors explicitly claimed to offer a resolution of the muon g-2 anomaly. It is a simple courtesy to contact the collaboration “We have performed a calculation which we believe resolves the muon g-2 anomaly. We enclose a preprint of our analysis for your comments. We look forward to your reply.”

#1

The collaboration might ignore the authors. Post a preprint with a statement “We have communicated our results to the collaboration, but to date they have not replied.”

#2

Post a preprint and send a copy to the collaboration at the same time. Include a statement “We have sent a copy of our results to the collaboration and will update our post if and when we receive a reply.”

But at a minimum

demonstrate that they made a good faith effort to communicate with the collaboration.arxiv,

The problem is that a genuinely good faith effort to communicate with the collaboration before posting the papers would require giving them at least 3 days to respond, and that is enough time to be “coincidentally” scooped.

E.g. in this scenario, in the case that the result happened to be correct:

The collaboration forwards the papers to their theory expert, who spends an hour or two on them and gets very excited – doesn’t see any immediate flaw in the arguments but still needs to check more carefully. He mentions his initial impression and excitement to someone, who mentions it to someone else, and the rumor quickly spreads among a circle of experts.

One of them, person A, hears the rumor and remembers that he had actually thought about calculating the gravitational contribution to the muon anomaly, and vaguely planned to do it at some point (as a fun exercise; he was sure the contribution would be negligible). Well, since he had the idea, and planned to do the calculation, “why should I just sit here now and let that unknown Japanese group get all the glory” he thinks this to himself. “So he puts everything else aside and immediately gets to work…does the calculations and posts the paper within 24 hours.

(Perhaps person A adds a note at the end of his paper saying that while this work was in preparation he heard from person B that a Japanese group had informally circulated a paper on this topic, although having not seen the paper he doesn’t know if their approach and result is the same…)

In my view it would be fine if the authors send an email to the muon collaboration to point out their paper and solicit feedback once they posted the paper. And for all we know they might have actually done this.

“why should I just sit here now and let that unknown Japanese group get all the glory” he thinks this to himself. “So he puts everything else aside and immediately gets to work…does the calculations and posts the paper within 24 hours.

That’s just sad, that these are modern scientists. When Einstein received Bose’s manuscript he did not say “why should I just sit here now and let that unknown Indian get all the glory”.

It is obvious the authors did not contact the collaboration, or the collaboration would not have worded their reply as they did. It costs the authors nothing to include a statement in their preprint that they had contacted the collaboration. They did not, as the response of the collaboration makes clear.

It is a simple matter of civil behavior.

All,

I think the question of whether they should have contacted the experiment has now been properly beaten to death. In any case, in retrospect it seems to me the authors made the more general mistake of not consulting a theorist more expert than themselves in the subtleties of GR calculations. Yes, there’s always a danger that if you talk to experts about your ideas they may get stolen, but on the other hand, if you don’t you’re likely to not find out what the problems are with your ideas until it is too late.

X, Peter etc. Futamese is not a junior person. He is one of the best GR theorists in post-Newtonian business. You can check out his past works.

Peter,

“mistake of not consulting a theorist more expert than themselves in the subtleties of GR calculations”

They did not make any mistakes with regards to GR, their calculations are textbook-level proper. The only thing they did wrong was to suggest an interpretation of the experiment that turned out to be wrong. And even in doing that they used careful phrasing, like ”If the $\gamma$ was experimentally tuned to minimize the electric field contribution, the quantity $a^{mod}$

might have beenmeasured” (emphasis mine). I cannot think of a more toned-down formulation of that statement (which turned out to be wrong in the end).BTW, it is not really common practice to include statements like “we contacted the experimental collaboration, but they didn’t reply yet” into a paper or a preprint. I have never seen any such statements in any paper whatsoever.

HTH, 🙂

Marko