Measurement of the W boson mass reveals 7σ deviation from calculations
356 points by nvalis 3 years ago | 151 comments- nvalis 3 years agoSome comments from an ATLAS physicist doing W mass measurements at the LHC:
https://non-trivial-solution.blogspot.com/2022/04/do-we-have...
- cshimmin 3 years agoAs another ATLAS physicist, I can say that this is an excellent article from Prof. Schott. He is very politely arguing that "someone messed up". I'm not sure I agree so much with the point of combining the LEP experiments, which do have some tension with each other. Unless the combination is specifically taking into account correlations between uncertainties at the different experiments on the same collider (which exist, but it's really hard to handle).
Another take many people in the field are expressing is that it's simply infeasible to reliably interpret statistical models at that level (especially one that is dominated by systematic uncertainty), since they are based on approximations and assumptions e.g. that certain nuisance parameters are "nicely" distributed and uncorrelated. See e.g. comments from Prof. Cranmer [1] who is one of the folks who developed the standard statistical formalism and methods used in modern particle physics experiments.
[1] https://twitter.com/kylecranmer/status/1512222463094140937?s...
- spekcular 3 years agoWhy don't people use nonparametric methods to get around the problem of assuming certain parameters are "nicely" distributed? (Not a physicist, but curious – this seems like the "obvious" solution.)
- nabla9 3 years agoNonparametric methods are often used when the assumptions of parametric tests don't hold.
In physics experiments they want to fix the structure of the model and know the assumptions. They want to know the distribution and parameters to hold. If assumptions don't hold, they must find out why, find better assumptions and fix the model.
To say it differently: physicists are not trying to discover statistical laws. They are trying to discover physical laws trough statistics.
- nabla9 3 years ago
- spekcular 3 years ago
- slibhb 3 years ago> We observed for quite some time some features in the our data, which we could not explain. Once one of my PhD students came into my office and told that he finally figured out this feature: the protons in the ATLAS detector do not collide heads-on but under a very small angle, allowing the not interacting protons to continue their travel through the LHC on the other side of the experiment. Indeed he was right - we have not been considering this effect in our simulations, however - after some calculations and speaking to the machine experts - it turned out that this effect induces a feature in our data, which is opposite in sign that we observe; so we have been left with an effect that was twice as large and unexplained. In the end it turned out to be caused by the deformation of the ATLAS detector by its own weight of more than 7000 tons over time.
I know these people are incredibly smart and conscientious. And the standard model is extremely successful and well confirmed. But that's a lot of degrees of freedom.
- Certhas 3 years ago"I do not think, we have to discuss which new physics could explain the discrepancy between CDF and the Standard Model - we first have to understand, why the CDF measurement is in strong tension with all others."
That's... cute. I doubt it will stop the theorists from flooding the arxiv with explanaitions in the coming days/weeks. Recall what happened when there was a barely 3 sigma (local) statistical fluctuation in LHC data:
https://resonaances.blogspot.com/2016/06/game-of-thrones-750...
Edit: Thank you for posting the excellent article!
- beezle 3 years agoWaiting to see if Tammaso puts something up about it, IIRC he was a CDF member
- cshimmin 3 years ago
- chris_overseas 3 years agoDiscussed here: https://news.ycombinator.com/item?id=30948260
- andyjohnson0 3 years agoThanks. As a general reader, I found that article much more accessible than the Science article.
- bejelentkezni 3 years agoThe duality of man[0].
- bejelentkezni 3 years ago
- andyjohnson0 3 years ago
- neals 3 years agoWhat is a sigma?
- cshimmin 3 years agoI work in this field (different experiment); despite the downvotes this is a reasonable question. Reposting my comment from above, since there is confusion here (the other sibling comments are incorrect).
In particle physics, sigma denotes "significance", not standard deviation. Technically what we're quoting as "sigmas" are "z-values", where z=Phi^{-1}(1 - p), where Phi^{-1} is the inverse CDF of the Normal distribution and p is the p-value of the experimental result. So, 7 sigma is defined to be the level of significance (for an arbitrary distribution) corresponding to the same quantile as 7 standard deviations out in a Normal distribution.
- yccs27 3 years agoThis is the correct answer.
In other words, "z sigma" means: That a result like this occurs as a statistical fluke, is just as likely as a standard-normal distributed variable giving a value above z.
- sgregnt 3 years agoI would add: If the null hypothesis is true, then "the result like this... (in this case the null hypothesis is of cause that the standard model is true)
- sgregnt 3 years ago
- a1369209993 3 years ago> sigma denotes "significance", not standard deviation.
Nitpick: this is still a standard deviation in some (potentially very contrived and nonlinear) coordinate system. (As a simple example, a log-normal distribution might have a mean of 1 and a standard deviation effectively of multiplying or dividing by 2. Edit: also, multidimensional stuff might have to be shoehorned into a polar coordinate system.) But in practice you'd never bother to construct such a coordinate system, so that's more a mathematical artifact than anything useful.
- cshimmin 3 years agoNo, there is no coordinate system. This is referring to the distribution of a test statistic for hypothesis testing. It's a 1-d real scalar, and coordinate transforms don't have any meaningful statistical representation. Of course there are much higher-dimensional distributions, in all sorts of coordinate systems, involved in sampling the test statistic, but at the end of the day this is all you are left with. If you change the underlying distributions of the model, then of course you will change the test statistic distribution, but that's meaningless, since the whole point of the test statistic is to quantify an observation in the context of a given model.
Anyway, as I mentioned elsewhere, the motivation for calling it sigma is that, by construction, it maps onto the quantiles of the standard Normal distribution. So an N-sigma result will have the same p-value as N standard deviations in a Normal distribution. So you can associate "sigmas" with "standard deviations of the Normal distribution". Perhaps this is what you are trying to say, but it does not make sigma a standard deviation in any statistical sense, i.e. it is not necessarily related to the variance of the relevant distribution.
- cshimmin 3 years ago
- jxm262 3 years agooh wow, thanks for pointing this out :)
- cshimmin 3 years agoFor what it's worth, sigma is chosen for this purpose specifically to evoke the notion of "standard deviations". But quoting the std dev. directly is useless, since the distribution is unspecified. So we "convert" the statistical significance to the corresponding number of standard deviations of the Normal distribution, since that is a familiar distribution. If you like, it's another way of stating p-values, which physicists prefer because ours can have lots of zeros :)
- cshimmin 3 years ago
- yccs27 3 years ago
- throw0101a 3 years agoA unit used in statistics:
> In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values.[1]
- tempay 3 years agoThis page is likely more approachable:
https://en.wikipedia.org/wiki/68%E2%80%9395%E2%80%9399.7_rul...
- sundarurfriend 3 years agoI thought you were going to link to https://simple.wikipedia.org/wiki/Standard_deviation
The "Simple English Wikipedia" is a really underrated resource for understanding jargon outside your field.
- sundarurfriend 3 years ago
- tempay 3 years ago
- jstx1 3 years ago1 sigma = 1 standard deviation
- RosanaAnaDana 3 years agoA measurement of uncertainty.
- omginternets 3 years agoA standard deviation.
- EVa5I7bHFq9mnYK 3 years agoIt's just a way to say something has probability of 0.0000000002% while looking smart.
- WanderPanda 3 years agoIt actually is smart to compress this on an exponential scale instead of writing a large number like this :p
- WanderPanda 3 years ago
- cshimmin 3 years ago
- codezero 3 years agoHow is it that several other measurements have error bars that don’t even overlap with this one?
- CrazyStat 3 years agoError bars account for the known and quantifiable sources of uncertainty. They don't (can't) account for unknown or unquantifiable sources of uncertainty, such as aspects of the experimental design that were not properly accounted for or unpredicted/unmodeled interactions with other particles or forces.
Known unknowns and unknown unknowns, as Rumsfeld would put it.
About a decade ago I saw a very nice figure of estimates of the speed of light over time showing this effect. Unfortunately I haven't been able to find it since.
- aspenmayer 3 years agoI found something similar on page 19 of this presentation. No errors bars, but they do provide some info about the errors of various experiments.
https://www.nhn.ou.edu/~johnson/Education/Juniorlab/C_Speed/...
Edit: here’s some error bars!
https://www.researchgate.net/figure/Uncertainties-in-Reporte...
- brummm 3 years agoJust a small comment about the speed of light. The way we now define the speed of light, measuring it doesn't really make sense anymore. The speed of light is now DEFINED as 299792458 m/s and the meter definition is based on the speed of light. So in principle, one can only measure the meter and not the speed of light anymore.
- rightbyte 3 years agoIn vacuum.
- rightbyte 3 years ago
- XorNot 3 years agoIf this result turns out to be right, at least part of that confirmation will involve producing a theory which reduces down to explaining other results - either from previously unknown systematic error or interactions.
- codezero 3 years agoThanks for the reminder, this makes sense.
- aspenmayer 3 years ago
- Kinrany 3 years agoReminded me of the recent https://slimemoldtimemold.com/2022/01/11/reality-is-very-wei...
- CodesInChaos 3 years agoEven if you only consider statistical errors, there is no guarantee that the actual value is in the confidence interval. The graphs in this article seem to use 1σ bars which have a 68% chance of containing the result, assuming a normal distribution.
- CrazyStat 3 years ago
- beefield 3 years agoTalking about particle/quantum physics, is there a book/youtube channel/whatnot that would describe (some/main) experiments and results that have convinced physicists that classical physics does not work when you go small. I mean, I know about double slit experiment, but I guess it is a long journey from that to the Standard Model.
So instead of the heavy theory, I'd like to see the stuff that made people scratch their heads in the first place.
- mr_mitm 3 years agoThe first real head scratchers were the black body spectrum [0] and the fact that atoms are stable.
Rutherford [1] showed that atoms consist of a tiny, positively charged nucleus and rather large negatively charged shell. It was hypothesized that electrons are flying around the nucleus like planets around the sun. But we already knew at that point that moving charges emit radiation, which causes the electron to lose energy and move closer to the nucleus. So it should pretty much immediately collapse into a point. Bohr then showed that if you assume that only certain orbits were allowed, it works out pretty nicely. Nowadays we now that there is such a thing as a ground state, meaning the lowest amount of energy the electron can possibly have around a nucleus is enough to keep it moving.
The idea for quantizing things came from observing the black body spectrum. If you sum up all contributions classically, you get infinity. Planck tried to see what happens if you assume that energy comes in little packets instead of a continuous spectrum. He didn't have any justification for it, but it matched the observations pretty well.
- simonh 3 years agoThis is a bit old, but still excellent. https://www.youtube.com/watch?v=XYcw8nV_GTs
This is more up to date and specifically on challenges to the SM. Where is physics going? | Sabine Hossenfelder, Bjørn Ekeberg and Sam Henry https://www.youtube.com/watch?v=b8npmtsfsTU&t=2306s
- MatteoFrigo 3 years agoSee https://www.feynmanlectures.caltech.edu/I_40.html specifically Sections 40-5 and 40-6, for a discussion of why classical physics fails to explain the specific heat of gases.
As a sibling poster commented, the blackbody spectrum was also inexplicable from a classical point of view (see https://www.feynmanlectures.caltech.edu/I_41.html Section 41-2), but I think that the specific-heat problem was known before the blackbody problem.
- jrpt 3 years agoQuantum physics is a separate (but related) branch from particle physics so using the slash "quantum/particle" is mixing up two different things - which one do you really want?
Theoretical Concepts in Physics by Malcolm Longair is a mix of history and physics, by explaining how physicists came to discover their theories. I actually don't think it says much about modern particle physics though. It includes quantum mechanics.
Introduction to Elementary Particles by David Griffiths if you just want particle physics. Griffiths also has an intro book on quantum mechanics.
- beefield 3 years agoI'd be interested in all observations that make "non-classical" thinking of physics necessary. I have no deep enough knowledge to distinguish quantum physics and particle physics. So for example what is the experiment that makes us think that particles have something called spin? And what experiment makes us think that the spin can only have distinct values? And so forth.
Anyway, the books you proposed look interesting, thanks.
- beefield 3 years ago
- Splendor 3 years agoMaybe not exactly what you're looking for but these two videos discuss the results of a Fermilab experiment that hints at a crack in the standard model.
- mr_mitm 3 years ago
- mc4ndr3 3 years agoIf my calculations were off by seven standard devs I'd quit science and go skip rocks. wth
- rpz 3 years ago:) If only they spent a few billion more on the equipment maybe they’d get to six sigmas
- rpz 3 years ago
- 3 years ago
- was_a_dev 3 years agoCan anyone explain the difference between light and heavy supersymmetry? Particle physics isn't quite my field
- fallingfrog 3 years agoI would guess that unless some other team replicates this result, it's probably a measurement error somewhere. Physics can be very delicate and tricky, and it's easy to make mistakes. But, even the mistakes are opportunities for learning, so it's not a waste.
- nyc111 3 years agoDo we actually know how physicists define "mass" in this context? Because, in physics many words have technical meanings that only physicists can know. For instance, as a layman when I see the word "particle" I imagine a spherical thing with an extension in space. But a physicist would laugh at me because in physics a particle is not a particle, it can be a statistical bump in data, it can be a field, it can be a wave, anything but a spherical particle. But a physicist would call a wave a particle and see nothing wrong with it. The same goes for mass, what physicists call mass can be voltage for instance. So does anyone know what "mass" means in this context?
- cowboysauce 3 years ago> The same goes for mass, what physicists call mass can be voltage for instance.
You’re probably thinking of how a proton has a mass of 938 MeV/c^2. This is still a mass and not a voltage. 1 eV (electronvolt) is the amount of kinetic energy that an electron would have after being accelerated though an electric potential of one volt. By the mass-energy equivalence 1 eV is equivalent to a mass of ~1.783x10^-36 kg and a proton has a mass of ~1.673x10^−27 kg.
- nyc111 3 years ago> You’re probably thinking of how a proton has a mass of 938 MeV/c^2.
Yes, that’s what I was thinking. But it seems that there is a problem with the definition of the word “mass”. Clearly there are at least two definitions. First, the weight of an object. Here weight is measured and weight is called “mass”. There is no equivalence, same thing is called weight and mass. Weight and mass are synonyms. This mass has nothing to do with electricity and has nothing to do with motion.
The second definiton of mass is related to electricity and motion. It has no meaning outside electricity. In this case, they accelerate an electric current and measure its kinetic energy and call this kinetic energy “mass”. Again these words are synonyms. Why do physicists like these silly word plays so much, I have no idea.
- patrickkrusiec 3 years agoThe weight of the object is not its mass. The weight is the force an object experiences due to a gravity. You have the same mass on the Earth and the Moon, but you weigh 1/6 of your weight on Earth on the Moon because of the gravitational force is 1/6th the strength of Earth's gravitational force.
The definition of mass is subtler, but you seem to confusing units with the definition of the concept. Units are necessary because you need a scale to measure physical properties. You can't measure a length and say that it's "ten". You needs units attached like feet or meters. An eV (electronvolt) is a unit of energy. Just like a kilogram (unit of mass) originally was defined as the mass of a 10cm x 10cm x 10cm cube of water at room temperature, the eV (unit of energy) is defined as the increase in kinetic energy of an electron (which has a fixed and known charge) accelerated across 1 volt. But neither the definition of the kilogram or the eV define the concepts of mass or energy, they just merely define units, which humans chose, used to measure mass or energy.
Now how does mass and energy relate to each other? Simply put, the Special Theory of Relativity, developed by Einstein in 1905, states that mass and energy are equivalent to each other. Now the word "equivalent" has a precise but complicated meaning that I will not explain here (if you do want to understand it, take a course in special relativity). This relation is defined quantitatively by E=mc^2 (Energy E equals mass m times the speed of light c squared). Let's first look at another relationship, distance = velocity * time. This equation can be be rewritten as distance/time = velocity. If we use meters to measure distance and seconds to measure time, we can "divide" the units and define the units of velocity as a meters per second or m/s. Same thing with E=mc^2. We can rewrite the mass m as m = E/c^2, and let the units of mass be eV/c^2. Using eV/c^2 or kilograms or whatever to measure mass has no effect on the definition of the concept mass itself (which you can think of as an intrinsic property of objects independent of units which affects their behavior in known ways).
Why do physicists make all of this so complicated? They don't. It is reality that is subtle and complex and hard to understand. Because the purpose of physics is to describe reality, it has to be subtle and complicated.
- patrickkrusiec 3 years ago
- nyc111 3 years ago
- BlueTemplar 3 years agoParticle and wave are just both incomplete ways to describe things - but for some phenomena combining both gives the best results : that is the very weird domain of quantum physics.
(Like if you're trying to predict what happens when speeds approach those of light, you have to make weird relativistic corrections stemming from the observed speed of light being the same for all observers, regardless of their relative speeds.)
If you're lucky to not be in one of those weird cases, objects as spherical things with a sharp boundary in space and using the normal composition of speeds work just fine.
- cowboysauce 3 years ago
- junon 3 years agoCan someone explain this in laymen's terms?
- SpeakMouthWords 3 years agoSomeone has run an experiment, and in this experiment they created a large amount of evidence that seems to say that quite an important particle in particle physics weighs something slightly different from what we thought it should.
This is important because the weight of that particle was predicted by our generally-accepted theory of how the universe works. If the weight is different, it means the theory hasn't taken into account everything that it should.
- junon 3 years agoThank you :)
- junon 3 years ago
- SpeakMouthWords 3 years ago
- beezle 3 years agoUnfortunately I missed the webinar this afternoon, but here is the orginal press release from Fermilab, it is fairly long:
https://news.fnal.gov/2022/04/cdf-collaboration-at-fermilab-...
- 3 years ago
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- a-dub 3 years agohow much tearing apart of everything and quintuple checking goes on before publishing a result like this?
do they stand by the result or is it more of a call for "hey, come have a look at this. we can't explain it."
it's got to be anxiety inducing! (and exciting, of course)
- aaaaaaaaaaab 3 years agoOh no! Time to tweak the parameters of the standard model again!
- imtemplain 3 years ago
- imtemplain 3 years ago
- Pet_Ant 3 years agoHow do ±6.4 and ±6.9 combine to ±9.4 and not ±13.3 ?
- fulvioterzapi 3 years agoErrors do not sum like regular numbers. You want to take the square root of the sum of the squares of the errors.
sqrt(6.4^2 + 6.9^2) ≈ 9.4
You can have a look here: http://ipl.physics.harvard.edu/wp-uploads/2013/03/PS3_Error_...
- stocknoob 3 years agoThat PDF is great, thanks for sharing.
- stocknoob 3 years ago
- alephxyz 3 years agoThe variances are additive but not the std dev. Sqrt(6.4^2 + 6.9^2) = 9.4
- pif 3 years ago
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- fulvioterzapi 3 years ago
- freemint 3 years ago7 sigma is actually less than one thinks because these distributions are not normal distributions.
- cshimmin 3 years agoI work in this field (different experiment); that's not really true. In particle physics, sigma denotes "significance", not standard deviation. Technically what we're quoting as "sigmas" are "z-values", where z=Phi^{-1}(1 - p), where Phi^{-1} is the inverse CDF of the Normal distribution and p is the p-value of the experimental result. So, 7 sigma is defined to be the level of significance (for an arbitrary distribution) corresponding to the same quantile as 7 standard deviations out in a Normal distribution.
- habitue 3 years ago> Surprisingly, the researchers found that the mass of the boson was significantly higher than the SM predicts, with a discrepancy of 7 standard deviations. —JS
This is from the editor's comment at the top of the article, I'm guessing it was a mistake, but that might be why people are getting thrown off by it
- Aachen 3 years agoI'm one of those dumb people that didn't have much math or greek in school, so this weird-looking o in the title was quite literally Chinese to me. Now it turns out that people in the know also misunderstood its intended meaning because it's in a different field.
For years I've argued foreign symbols and single-letter variable names mainly seem to serve to keep a walled garden around the sciences, and this was cemented when I eventually went for a master's degree and I was expected to do this as well in compsci to get a better grade even if there is no advantage. If we could just write what we mean, I suspect people would find that more useful even if it makes it look less cultivated and more mainstream.
(To be clear, this is not criticism on the person I'm replying to, but split between the author of this specific title and most of the sciences as a whole because it's a universally supported barrier (if only ever implicitly), aside from a few science communicators.)
Edit: scrolled further in the thread. Looks like I'm not the only one, though this person at least knew to name the sigma: https://news.ycombinator.com/item?id=30955621
- cshimmin 3 years agoIt is just a convention, specifically for interpreting and presenting experimental results. We also use sigma to represent standard deviation in other contexts, of course. Sometimes it represents Pauli spinor matrices. Sometimes it's an index for spacetime tensors.
Life would be hell for any practitioner without single-letter abbreviations. In fact, we like them so much, that's why we adopted the greek letters (we ran out of alphabet). And, for better or for worse, convention runs deep in scientific literature. In practice it reduces a lot of redundancy, makes it more efficient for researchers to skim and understand results. But the cost is a years-long learning curve to break into any scientific field's literature.
FWIW, the linked article is from the journal Science, which is a technical publication. Often "sigma" is omitted in sci-comm articles, or at least is translated for the reader. They will say something like "there is a one in X million chance this is a fluke".
- nine_k 3 years agoMuch of these formulae used to be handwritten, and still are handwritten at a blackboard / whiteboard in physics classes.
It's much easier to draw a fancy symbol by hand than write several simple letters quickly and legibly, and it also takes much less space.
We've been having the privilege to write using computers for last 20-25 years, when PCs became widespread, relatively cheap, and running good enough software. And this is outside the lecture hall settings anyway.
- _moof 3 years agoIf you don't know what the Greek letter sigma means, you aren't going to know what the phrase "standard deviation" means, either. The notation isn't the issue. The issue is you can't fit stats 101 into a headline, and there's no getting around that.
- bigbillheck 3 years agoWhen you see a symbol you don't recognize, like 'σ', you can just paste it into google and it'll tell you.
I personally don't see why greek letters are such a big sticking point, there's only 24 of them, and unlike Greek children you don't have to learn them all in one go.
- ajkjk 3 years agoDon't agree with this, it took a few weeks of physics classes to get used to using greek letters as variables, and without them you'd drown in re-used letters.
- enchiridion 3 years agoI disagree with the parent post about the use of Greek letters, but it seems like a valid point worth of discussion. Certainly in the spirit of HN.
I’ve seen an increasingly worrying trend of using downvotes to voice disagreement, rather than as the intended purpose as a kind of crowd-based moderation. And before anyone lambasts me for complaining about downvotes, I’m complaining about the trend, where the above comment is just a exemplar.
- doliveira 3 years agoDo you want to go back to writing equations with words?
- LudwigNagasena 3 years agoNotation is the easiest (and a very helpful) part of physics, statistics and probably all other scientific areas. That just sounds like an excuse.
- cshimmin 3 years ago
- habitue 3 years ago
- ivad 3 years agoA measurement being 7 sigma out would still be Chebyshev bounded by 1/7^2 ≈ 0.02 I.e. the probability of it being ≥7 sigma out is interestingly at most 0.02.
- freemint 3 years agoNeat i didn't think about that. But that is less improbable then 1 in 12450197393 which is what you might get with normal distribution.
- lupire 3 years agoThat's just because Chevyshev bounds is a very weak general statement about all distributions.
High Energy Physics sigma is calibrated to match normal distribution quantiles.
- lupire 3 years ago
- lupire 3 years agoThat is not so interesting because it could be far less.
- freemint 3 years ago
- 3 years ago
- bawolff 3 years agoWhy aren't they normal? I know very little about this topic, but i would generally assume that measuring most natural phenomenon would be normal.
- cshimmin 3 years agoBasically, the result of an experiment has to be boiled down to a single numerical value, called the test-statistic. Typically the test-statistic is a (log) likelihood ratio. It is the distribution of the t.s. that must be considered when determining the significance of a measurement. Obviously the measurement itself only gives you a single value of the t.s., so you need to know the distribution to ask "does this result seem significant?". This is done by considering all the factors of random variation (statistical and systematic) that could have an effect on the t.s. Often, the distributions of these individual random factors are assumed to be Normal, but the resulting distribution considering all of their conspiring effects is very seldom normal distribution. Even in the central limit theorem, I think the distribution of the LLR ends up being something like a noncentral chi^2 distribution.
- rich_sasha 3 years agoEspecially since, isn't this an average / error of a mean estimate? So even if individual observations are non-normal, this would be a perfect place for Central Limit Theorem.
I know nothing about Quantum though, only maths.
- freemint 3 years agoBecause it's a non-linear world? And the graphs seem very obviously skewed? And it's kurtosis also seems to differ from three?
- freemint 3 years ago
- krona 3 years agoAlso not knowing anything about this topic, I'd assume it wasn't normal because we're talking about mass close to zero, and mass must be greater than zero.
- gus_massa 3 years agoThe mass in their result is 80433.5±9.4 MeV/c^2. The result of the experiment is a Gaussian like distribution. If you consider a Gaussian distribution with μ=80433.5 and σ=9.4, the probability to get a result that is less than 0 is 4E-15899105.
I filled this widget https://www.wolframalpha.com/widgets/view.jsp?id=53fa34c5c66...
And got this result https://www.wolframalpha.com/input?i=mean%3D%5B%2F%2Fnumber%...
Note in the graphic that σ is 10000 smaller than μ so the probability to get a negative result is almost zero and you can just ignore it.
- gus_massa 3 years ago
- cshimmin 3 years ago
- sdfgdf 3 years ago
- cshimmin 3 years ago
- imtemplain 3 years ago
- rybosworld 3 years agoThis could be an alien race interfering with our measurements.
- sbelskie 3 years agoI feel like I’ve read that book before but can’t recall what it was.
- sylens 3 years agoThree Body Problem
- jkhloiujlknmk 3 years agoor The Gods Themselves.
Neither is great, actually. With all due respect for Asimov, who I love.
- jkhloiujlknmk 3 years ago
- sylens 3 years ago
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- sbelskie 3 years ago
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- graderjs 3 years agoScccoooopped! :P :) xx ;p https://news.ycombinator.com/item?id=30952630
- londons_explore 3 years agoDoes it make sense to even discuss the sigma of any deviation?
When you add in the "10% chance that some scientist messed up the maths or something in the experiment", then it's impossible to ever reach 7 sigma...
- davrosthedalek 3 years agoYes. The meaning of 7 sigma is: It's very very unlikely that this is a statistical fluke, it must have a different reason (new physics, systematic error, ...)
- morelandjs 3 years agoKnown unknowns, and unknown unknowns. Still useful to quantify the known unknowns and compare significance of various events according to them.
- FabHK 3 years agoWhen you look at the graph at the bottom, several independent measurements have non-overlapping error bars, and are even on opposite sides of the Standard Model prediction. So, yeah, somewhere along the line there've been bad measurement errors...
- davrosthedalek 3 years agoSince error bars are typically +-1 sigma, you expect about 1/3 of all measurements to be further away from the true value than the error bar, if all error estimates are correct, and uncorrelated. That's actually a check a lot of doctored data fails.
- davrosthedalek 3 years ago
- mhh__ 3 years agoThis is why these measures have to be taken with a grain of salt (but are still useful).
Probability is subjective, in this case because it's dependant on the design of the experiment / quality of the analysis of that experiment to determine a p-value of a given result.
The book "Bayesian analysis in high energy physics" is a short and sweet introduction. If I got the title wrong I'll update it later.
- bawolff 3 years agoThen it would never make sense, because someone messing up somewhere is always a possibility.
I would assume that the implication is that its 7 sigma assuming the measurements were done correctly.
- TheRealDunkirk 3 years agoYeah, my thought from reading the headline was, "That's a funny way of saying we were completely wrong."
- amelius 3 years agoIf a quantity cannot be negative (such as a mass), then standard deviation isn't the best choice.
EDIT: Yes, because the Gaussian distribution extends to +/- infinity; davrosthedalek explains it best, below.
- hhmc 3 years agoA fair dice roll can only have positive values {1,2,3,4,5,6} but it has a clearly defined std deviation: sqrt(105/36) -- there's no clear reason this isn't the 'best choice' that's just a case of application.
- mhh__ 3 years agoThe point about applications is mostly valid even if theoretically unsatisfying, but I think the thing about dice rolls is basically spurious.
- mhh__ 3 years ago
- bigbillheck 3 years agoThe predicted value is so incredibly far from zero that you can pretend it's a truncated Gaussian and not see any actual difference in the results.
Alternate reply: Gaussian approximation to the binomial is perfectly valid in all sorts of cases.
- cedilla 3 years agoWhat would be a better choice?
- FabHK 3 years agoGP is probably referring to the coefficient of variation, sigma/mu (standard deviation divided by mean), which normalises out for example the unit of measurement.
However, the 7 here is basically (x - mu)/sigma, so it is normalised (in that sense), anyway.
- FabHK 3 years ago
- hhmc 3 years ago
- davrosthedalek 3 years ago