🏅 Top traders

@ScottLawrence @JosephNoonan

A few other people have chimed in and have no objections resolving as yes, so please go ahead and do so. I have no objections.

"from what you're writing it sounds like you're using a different definition of "5 sigma" than we are. Does your definition match Plasma's discussion above? If not, what is it?"

I agree with his definition, let me explain.

"A 5 sigma result isn't an inherent property of some set of data - it's a comparison between data and a prediction. Pointing out that the data wouldn't be 5 sigma if it was compared to a different prediction doesn't make it insufficient to produce a 5 sigma result when compared to the prediction that was actually made."

I agree with this exactly. So then what point was I trying to make? Let me give a slightly absurd example. Imagine one of the authors of the paper had done a calculation using Newtonian mechanics, and then wrote that the the comparison between the data and [the Newtonian] prediction exceeded 5 sigma. This would be a 5 sigma result, but not "the" 5 sigma result we care about. The OP question description reads

"Will the new data be sufficient to cross the 5 sigma threshold, the standard for statistical significance in physics?"

but because a 5 sigma result isn't an inherent property of some set of data the above question is underspecified. This leaves open this leaves open the question of *which* 5 sigma result we are talking about. Arguably, the 5 sigma result reported yesterday is not one worth caring about (just like a Newtonian one would not be worth caring about).

On the other hand, the most straightforward interpretation of the OP question refers strictly to whatever result was reported yesterday, and questions about whether or not we should care about the result are irrelevant to the resolution of the market.

"The 5 sigma discrepancy still tells us something useful (the prediction was wrong, meaning that we've either done the calculations wrong, put inaccurate measurements into it, or the Standard Model is wrong).'

Yes, I think the argument made here is a good one. My level of confidence in my initial arguments was mediocre to start with, and I wanted to solicit opinions to see if anybody else found them convincing. A couple other no holders have had no objections with resolving yes - so I think you should go ahead and do so.

@Soren OK, glad we are on the same page.

I will summarize my position here:

The title of this questions asks if the Muon g-2 collaboration will announce a 5 sigma result. This did happen.

But the body of the question asks if the new data "will be sufficient to cross the 5 sigma threshold." By the admission of the authors, they seem to be saying that the new data is not "sufficient" because it is based on an incomplete analysis. So this did not happen.

I would split it 50-50, or wait for the upcoming analysis. I am, of course, biased 😂 . I may also be misunderstanding the paper (I did not look at in depth), and am open to contrary arguments.

@Soren

By the admission of the authors, they seem to be saying that the new data is not "sufficient" because it is based on an incomplete analysis.

This is a very stretched interpretation. The description asks whether the new data would be sufficient for a 5 sigma result, which it is, according to the paper. When you say it is "not 'sufficient'", you don't say what you think it is insufficient for, but clearly you don't mean that it's insufficient for a 5 sigma result. You seem to just be saying that it's insufficient to provide conclusive evidence of a discovery, which is true but also not what this market asked about.

I definitely won't split it 50-50, the only reason I was considering a PROB resolution was the argument that, "It shouldn't count as a real 5 sigma result since it's based on a flawed theoretical calculation." But so far, I am not really convinced by any of the arguments on that side to not just count it as a YES.

@JosephNoonan

"When you say it is "not 'sufficient'", you don't say what you think it is insufficient for, but clearly you don't mean that it's insufficient for a 5 sigma result."

I do mean that; garbage in, garbage out. If you have a bad theory then the data can be "sufficient" for a 5 sigma result, but if we are talking about the standard for statistical significane in physics then the data is only sufficient for a 5 sigma result if the best currently known theory is used. A back of the hand calculation wouldn't suffice, for example. If you expect a more complete analysis based on the same data to no longer yield a 5 sigma result, then the data is insufficient for a 5 sigma result.

I would just give more time for the other no holders to respond - they haven't even been given a day yet. If they agree it should be resolved as yes, then I won't complain.

@Soren no, the result is a 5-sigma result. A result does not need to debunk the standard model to be significant. The result falsifies the available theory predictions (maybe with some special treatment for BMW).

The result is not significant with respect to the SM, because we don't have a reliable SM calculation. But the question did not mention the standard model.

Moreover, I can't help but point out that yesterday, it wasn't unheard of for people to say "well maybe with some more statistics on all sides, these issues will disappear". In other words, as of yesterday, the world was consistent with "the theory calculations are all pretty much okay, we just got remarkably unlucky". Or better yet, "the usual lattice calculations are okay, BMW is a fluke, and the first fermilab experiment underestimated their uncertainties". Or whatever mix of these ideas you want.

Of course there was some tension in this world view, but it wasn't 5-sigma tension. Today it is.

@ScottLawrence There's an argument to be made for a PROB resolution on the grounds that this market was particularly susceptible to misinterpretation by outsiders, who read it as "will BSM physics be found this week". (I think the 25% probability before the announcement was quite low, given how incredibly boring the announcement felt.)

I won't complain, but in general I'm against this, because I like having the norm of crisp, pedantic resolutions, and caveat bettor (or whatever the latin should be).

@Soren @zzlk @ScipioFabius did y'all genuinely bet thinking---consciously---that the question was about the gap with SM? If that's true, and if @JosephNoonan resolves YES, I think it's fair enough if I send you back a good fraction of what you lost. Looks like that was 10, 45, 30, respectively. So I'll offer M$6 to @Soren , M$27 to @zzlk , and M$18 to @ScipioFabius (if I did arithmetic right).

@ArmandodiMatteo you, at least, should have known better. You're on your own :)

@ScottLawrence No, I can't honestly say that I was consciously thinking that. I genuinely believe there is some ambiguity whether or not this is "actually sufficient" to be a 5 sigma result, but it doesn't seem like my arguments have been very convincing to either of you two.

The amount of mana is small, so I am not very worried about it.

@Soren

if we are talking about the standard for statistical significane in physics then the data is only sufficient for a 5 sigma result if the best currently known theory is used

A five sigma result is a five sigma result. It's a purely statistical comparison between two values, and it's still statistically significant as a refutation of the old theory even if outdated theoretical predictions are used. In this case, the data weighs against the theoretical calculations (which are currently the best ones - the "updated" calculations mentioned in the paper haven't actually been performed) at the 5 sigma level.

If you expect a more complete analysis based on the same data to no longer yield a 5 sigma result, then the data is insufficient for a 5 sigma result.

A 5 sigma result isn't an inherent property of some set of data - it's a comparison between data and a prediction. Pointing out that the data wouldn't be 5 sigma if it was compared to a different prediction doesn't make it insufficient to produce a 5 sigma result when compared to the prediction that was actually made. I think you are maybe misunderstanding what the issue with the current 5 sigma result is. There is no problem with the data from the muon g-2 experiment or the way it was analyzed. The problem is that, it is 5 sigma away from a certain prediction of the muon g-2, but that prediction may not actually be as close as we thought to the value that the muon g-2 would have if the Standard Model were true. The 5 sigma discrepancy still tells us something useful (the prediction was wrong, meaning that we've either done the calculations wrong, put inaccurate measurements into it, or the Standard Model is wrong). It's just that it doesn't immediately justify the conclusion that the Standard Model got it wrong.

I'll give others the chance to respond, but I don't actually think this is very ambiguous. Maybe my original comment after the result came out gave the impression that it was more ambiguous than it actually is, but really I just wanted to give people the chance to object before I resolved it.

@Soren I want people to feel that market resolution proceeds fairly; I want this site to remain friendly for as long as possible; I care particularly about the quality of physics markets here. Even when the amount of mana at stake is small, I'd rather people be happy.

I was gonna write more about the 5-sigma thing but @JosephNoonan just did a better job than I possibly could have. Props.

@Soren from what you're writing it sounds like you're using a different definition of "5 sigma" than we are. Does your definition match Plasma's discussion above? If not, what is it?

@ScottLawrence I was not consciously thinking that.

I have no objections to this resolving as yes.

There don't seem to be any objections to the YES resolution. I'm planning to resolve soon. Do the NO bettors @zzlk @ArmandodiMatteo @ScipioFabius @Soren have any objections?

@JosephNoonan I would object to resolving right now. The question asks "is the new data sufficient." The paper released today seems to say that once the entire analysis is done, the result likely won't be >5.0sigma. In other words, the new data is not sufficient. I would wait for the updated prediction to be released.

@Soren This market is about what would be announced today, not what will be announced when all analysis is complete. I have a different market about whether the result will be 5 sigma once the entire experiment is complete.

.

@JosephNoonan no objections!

From the paper released today:

While a comparison between the Fermilab result from Run-1/2/3 presented here, aµ(FNAL), and the 2020 prediction yields a discrepancy of 5.0σ, an up-dated prediction considering all available data will likely yield a smaller and less significant discrepancy.

This seems like a YES to me, but I could see the argument that it shouldn't count since they acknowledge that it is based on a flawed theoretical prediction, and that it probably wouldn't be 5 sigma against a more accurate prediction. However, they haven't actually produced an updated prediction, so I can't resolve based on the value they hypothetically would have gotten if the theoretical results were clarified before the experimental results were released.

I will probably resolve this YES, but I will wait to hear arguments from anyone who thinks I should resolve to a high probability instead due to the slight ambiguity.

@JosephNoonan my interpretation was yes. It's a five sigma result with the theory result at this time. I don't think that it should matter---for this market---that the theory result is widely believed to be flawed.

@JosephNoonan can you link the paper please?

@ScipioFabius https://muon-g-2.fnal.gov/result2023.pdf

@JosephNoonan Hmmm. The question description reads "Will the new data be sufficient to cross the 5 sigma threshold?" Meanwhile curent sigma is 5.0, but results are "an up-dated prediction considering all available data will likely yield a smaller and less significant discrepancy." So if the current data yields 5.0, but "all available data" will push this lower, then wouldn't it be less than 5.0?

@JosephNoonan I guess does "Will the new data be sufficient to cross the 5 sigma threshold, the standard for statistical significance in physics?" refer to "an up-dated prediction considering all available data" ? I haven't looked at the paper, so what does "all available data" refer to?

@Soren The "new data" referred to in the description is the data from Runs 2 and 3 of the Fermilab muon g-2 experiment. That data was indeed enough to push the previous 4.2 sigma result to the 5 sigma threshold. The issue is that it's 5 sigma away from the most recent theoretical calculation, that calculation is likely flawed, such that the 5 sigma result would disappear if a better calculation were made.

The "updated prediction" referred to in the paper is one that hasn't actually been made yet. The paper is just stating that, when an updated prediction is made, it will likely be closer to the experimental result than the current prediction. The reason for that is that the theoretical prediction isn't actually purely theoretical - it depends on some other measured values, and those measurements have recently been called into question. In particular, the values of electron to hadron and electron to muon cross sections used in the calculation of the predicted value both disagree with more recent data and analysis, and an updated estimate of these values would probably put the theoretical prediction more in line with the measured value.

@JosephNoonan Of course the other reason the theory value will "probably" move towards the experimental value is that most folks' prior is heavily on "this ain't new physics". Meaning that, if the theory is done right, one expects the two to agree---even without already knowing about aspects of the theory calculations that are untrustworthy.

@ScottLawrence Actually, that's not the only reason. There are some calculations using lattice QCD that give a different value for the hadronic terms than the prediction used by Fermilab. Those calculations give a prediction that agrees with the experimental results:
/TomBouley/will-the-results-of-fermilabs-muon

@JosephNoonan Yeah sorry, I didn't mean to imply that that was the only reason. Just that in the absence of the BMW results, it would still be reasonable to expect more careful theory work to bring the two into agreement.