I was getting it jumbled up with the magnetic moment of the electron, which is predicted by the SM (well, the QED part anyway), to be slightly different to the 'classical' prediction.
Experiment measurement of this is accurate to one part per billion, and is consistent with the QED prediction.
The electroweak bits of the SM predict the W & Z bosons, along with their masses, which have also been measured, to around 1 part per 10,000, and match SM predictions.
EDIT: last but not least, the Higgs Boson was also predicted by SM, with a ballpark figure for it's mass, and other properties (how often it decays into photons, W bosons, quarks etc). So far all measurements of these properties are consistent with SM predictions.
Correct me if I'm wrong, but the standard model makes no prediction for the masses of any of the fundamental particles. To my knowledge, they are all input parameters. It might put certain bounds on them, but in the end they are all not predicted by the standard model itself.
This is seen as one of the big issues with the standard model, that it does not actually explain a lot of the characteristics of the fundamental particles like their couplings and masses.
For the W & Z bosons, their masses are derived from 3 other 'free parameters' of the SM.
The Higgs mass is indeed a free parameter, but the SM wouldn't work of it's mass was greater than 200 GeV or so. The Higgs interacts with other particles of mass, and the strength of interaction is proportional to the Higgs mass, it influences certain processes (like W boson scattering), the rate at which these happen would deviate from experimental observation if Mhiggs was over 200 GeV.
That's why the LHC was such a big deal, it reached the energies required for direct observation of sub-200 GeV Higgs, so it would either find the SM Higgs, or rule it out and invalidate the SM. Unfortunately the former seems to have happened.
Indirect constraints on Higgs mass in SM (a bit technical, slide 6 chart is the key one, strongly influenced specs & mission of the LHC)
https://indico.lal.in2p3.fr
It comes from the magnetic moment of the electron being measured and then run through more than 10k Feynman diagrams. The second part wouldn't work if QED didn't.
I can't tell whether you are agreeing or disagreeing with me. Let's make it easier. Do you agree or disagree with the following statement: The value of the fine-structure constant is not predicted by any physics theory.
Given what? If a theory gives you a well-defined relation between the magnetic moment of the electron and the fine structure constant, you can measure either one and then compute the other one. Which one is "predicted" is just a convention.
Eq. (13) in [1] is a prediction of the electron's magnetic moment given the fine structure constant. Eq. (15) in [1] is a prediction of the fine structure constant given the electron's magnetic moment. For the purposes of that paper (testing QED) it turns out to be more convenient to use Eq. (15).
> There is a most profound and beautiful question associated with the observed coupling constant, e – the amplitude for a real electron to emit or absorb a real photon. It is a simple number that has been experimentally determined to be close to 0.08542455. (My physicist friends won't recognize this number, because they like to remember it as the inverse of its square: about 137.03597 with about an uncertainty of about 2 in the last decimal place. It has been a mystery ever since it was discovered more than fifty years ago, and all good theoretical physicists put this number up on their wall and worry about it.) Immediately you would like to know where this number for a coupling comes from: is it related to pi or perhaps to the base of natural logarithms? Nobody knows. It's one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by man. You might say the "hand of God" wrote that number, and "we don't know how He pushed his pencil." We know what kind of a dance to do experimentally to measure this number very accurately, but we don't know what kind of dance to do on the computer to make this number come out, without putting it in secretly! — Richard Feynman, Richard P. Feynman (1985). QED: The Strange Theory of Light and Matter. Princeton University Press. p. 129. ISBN 978-0-691-08388-9.
I have never seen a physicist put that particular number on a wall (these days, the cosmological constant would be a better bet). I am vaguely aware of numerological attempts (some collected in [1]) to "explain" why 137 is "special", none of which has ever led anywhere.
As far as I can tell, the fascination with it got started by the number being close to an integer, and maybe the remark in [1] that "In ancient Hebraic language letters where used for numbers, and Cabbala is the word corresponding to 137" played a role. But we know that it isn't an integer, and that it runs [2] like any coupling constant in QFT, so at best you could marvel about it taking on some particular value at some particular interaction energy, which would mean... what? I dunno. As Feynman also said [3],
You know, the most amazing thing happened to me tonight... I saw a car with the license plate ARW 357. Can you imagine? Of all the millions of license plates in the state, what was the chance that I would see that particular one tonight? Amazing!
Your latest comment seems to be replying to someone with a fascination with the specific number 1/137, which I do not have, and some related tangents. I'll try to refocus the points of contention between us.
This whole thread started because the top comment said that a physics theory predicted the value of the fine-structure constant. Which is wrong, as the fine-structure constant is one of fundamental constants of the universe and one _whose value is not predicted by any theory_.
At this stage, two claims are in tension.
The first is your claim, that QED predicts the fine-structure constant once you measure the magnetic moment of the electron using several thousand Feynman diagrams.
The second claim is Feynman, himself, literally writing in his book titled _QED_, that we have no idea how to predict the value of this constant.
Could it be that Feynman overlooked the fact that he, himself, predicted the value of the fine-structure constant? He thought that not being able to predict its value was such an unsolved problem as to call it "one of the greatest damn mysteries of physics"? That "all good theoretical physicists put this number up on their wall and worry about it"?
The long and the short of it is that I think you're missing something much deeper. Yes, _once you measure_ something that has a tight coupling with the fine-structure constant, you now know the value of the fine-structure constant. But, before you made that measurement you DO NOT KNOW and further CANNOT PREDICT the value of the fine-structure constant. If you could, you'd be able to claim your own Nobel prize.
> This whole thread started because the top comment said that a physics theory predicted the value of the fine-structure constant.
Yes.
> Which is wrong
No. I even provided you with the reference to the paper in question. Did you even try to read it?
> as the fine-structure constant is one of fundamental constants of the universe and one _whose value is not predicted by any theory_
This is where you go wrong, and where you misunderstand Feynman's point.
The correct statement is that all respectable theories of physics (to date), including the Standard Model, include an irreducible number of values which must be plugged into them "by hand". In other words, once you've written down your theory, there are some parameter values in it about which the theory itself gives you no guidance; you could give them different values, and the theory would still work. It would just be describing a universe with different properties than ours. In order to make it describe our universe, you need to get those values from experiment.
Feynman's point is that we don't have a theory without at least some such parameters (even string theory, which he disliked, has the string tension, and it skirts the need for more by randomly picking a vacuum, which sets the values of low energy theory "constants"). It is not that the fine structure constant has some particular status as "more fundamental" than others.
The choice of constants which you can determine by experiment is constrained by the theory, but generally not locked down completely; you can choose your set of constants, as long as they are independent, i.e. as long as measured constant #1 can not be determined by plugging measured constant #2 into the theory and doing some calculation. If constant #1 can be computed given the theory and constant #2, then they are not independent, and the choice between them is arbitrary; a convention.
The choice between fine structure constant and magnetic moment of the electron is one such arbitrary choice. Given one of them and the Standard Model, you can compute the other. And It turns out that it's actually more convenient to do it this way: measure the magnetic moment, then compute the fine structure constant. There is no reason at all to regard the fine structure constant as more of an "input to the model" than the magnetic moment, as you claimed at the start of this thread.
Needless to say, Feynman knew all this perfectly well. You are just taking away the wrong message from an attempt to popularize the topic. "QED" was a popular book, not a graduate text.
> The correct statement is that all respectable theories of physics (to date), including the Standard Model, include an irreducible number of values which must be plugged into them "by hand". In other words, once you've written down your theory, there are some parameter values in it about which the theory itself gives you no guidance; you could give them different values, and the theory would still work. It would just be describing a universe with different properties than ours. In order to make it describe our universe, you need to get those values from experiment.
100% yes.
> It is not that the fine structure constant has some particular status as "more fundamental" than others.
Agreed, as I wrote above "as the fine-structure constant is one of fundamental constants of the universe", it's in a class of fundamental constants (or one of the irreducible values to be plugged in to use your phrasing).
> If constant #1 can be computed given the theory and constant #2, then they are not independent, and the choice between them is arbitrary; a convention.
Sure. You can choose one input over the other once you have made at least one other measurement.
Are you arguing something like, "there are X irreducible inputs to the Standard Model. For any particular input, a, you might be able to swap it out for a different one, g, so that you still have X irreducible inputs, but now they are a different set. Therefore, because we swapped a for g, a is not a fundamental constant"?
1) > ...physicists ... reserve the use of the term fundamental physical constant solely for dimensionless physical constants that cannot be derived from any other source.
2) > Fundamental physical constants cannot be derived and have to be measured.
And 3) its classification of the fine-structure constant as a fundamental physical constant?
> Are you arguing something like, "there are X irreducible inputs to the Standard Model. For any particular input, a, you might be able to swap it out for a different one, g, so that you still have X irreducible inputs, but now they are a different set.
That's part of what I'm saying. Some trivial examples from the Standard Model are the choice of angles you use to parametrize the CKM and PMSN matrices, Weinberg angle vs electroweak gauge couplings and the scale at which you choose to fix those couplings.
Maybe it will help to call the prediction of values for one such set of parameters from the values of another such set of parameters a "horizontal prediction": you have one theory T, a value a_A of some parameter A, and you predict a value b_B of some other parameter B: B_b = T(A_a). It is "horizontal" because A is no more fundamental than B; you could equally well use T to predict A_a from B_b.
y = T(x) is of course the general form of any prediction of anything at all from theory T.
The reason you saw fit to "correct" walru1066 is that you implicitly expanded "prediction" to "prediction from a more fundamental theory". That's too long to write, so I'll call it a "vertical prediction": you have a more fundamental theory F with some set of parameters A and a less fundamental theory L with some set of parameters B, and you predict B from A using F: B = F(A). It is "vertical" because F is more fundamental than L.
How do we know that F is more fundamental than L, and not just an equivalent description of the same theory? That's easy: because the set A is smaller than the set B. :)
walrus1066 mentioned a prediction of the fine structure constant, and he was right; that's what's done in [1] (I'm pretty sure he was remembering that paper, but not the exact reference; who does?). It's a horizontal prediction. Like all proper predictions, it only works if the theory works, so it is a perfectly valid test of the theory (the topic of his post).
You saw "prediction" and expanded it to "vertical prediction", but that was never mentioned or intended.
I do not take issue with the full phrasing of it, which you snipped out. The complete sentence is
Other physicists do not recognize this usage, and reserve the use of the term fundamental physical constant solely for dimensionless physical constants that cannot be derived from any other source.
In other words, there is no consensus about whether dimensional quantities can be called "fundamental physical constant". The reason is obvious: once you've settled on a system of units (if you are doing fundamental physics, presumably natural units [2]), you can always turn any dimensional quantity into a dimensionless one combined with a fixed dimensional factor.
I can imagine a parallel to this thread in that context: Somebody posts "the mass of the electron is a fundamental constant of the Standard Model", you reply "no it's not, it's dimensional, so it's not fundamental", and I end up writing a long post explaining that you can factor it into a dimensionless Yukawa coupling and a dimensional Higgs expectation value, so it's really fine to call it fundamental even by your definition (i.e. we do not currently have a more fundamental theory which predicts the mass of the electron, unless you are happy with it being a random value).
Regarding this part of your question,
> Fundamental physical constants cannot be derived and have to be measured.
I have no problem with the first part of that sentence (can't be derived; that would require having a more fundamental theory) but the "have to be measured" is subject to interpretation. If you take it to mean directly measured, it's really too restrictive (just have a look at what really goes into determining the properties of short-lived elementary particles). If you allow for measuring some quantities and performing a bunch of calculations on the general form of a horizontal prediction (the only kind possible within the confines of a single theory) then fine.
As for "classification of the fine-structure constant as a fundamental physical constant", I have no problem with it (at the current state of knowledge).
