When it comes to the weak nuclear force and why it is weak, there’s a strange story which floats around. It starts with a true but somewhat misleading statement:
- The weak nuclear force (which is weak because its effects only extend over a short range) has its short range because the particles which mediate the force, the W and Z bosons, have mass [specifically, they have “rest mass”.] This is in contrast to electromagnetic forces which can reach out over great distances; that’s because photons, the particles of light which mediate that force, have no rest mass.
This is misleading because fields mediate forces, not particles; it’s the W and Z fields that are the mediators for the weak nuclear force, just as the electromagnetic field is the mediator for the electromagnetic force. (When people speak of forces as due to exchange of “virtual particles” — which aren’t particles — they’re using fancy math language for a simple idea from first-year undergraduate physics.)
Then things get worse, because it is stated that
- The connection between the W and Z bosons’ rest mass and the short range of the weak nuclear force is that
- the force is created by the exchange of virtual W and Z bosons, and
- due to the quantum uncertainty principle, these virtual particles with mass can’t live as long and/or travel as far as virtual photons can, shortening their range.
This is completely off-base. In fact, quantum physics plays no role in why the weak nuclear force is weak and short-range. (It plays a big role in why the strong nuclear force is strong and short-range, but that’s a tale for another day.)
I’ve explained the real story in a new webpage that I’ve added to my site; it has a non-technical explanation, and then some first-year college math for those who want to see it. It’s gotten some preliminary comments that have helped me improve it, but I’m sure it could be even better, and I’d be happy to get your comments, suggestions, questions and critiques if you have any.
[P.S. — if you try but are unable to leave a comment on that page, please leave one here and tell me what went wrong; and if you try but are unable to leave a comment here too for some reason, please send me a message to let me know.]
11 Responses
I’ve seen more than 5 books and more than 10 articles saying that high mass and uncertainty principle makes weak force weak. I think I’ve read a few published articles saying that. Are they all wrong?
And one more question. I can easily understand that virtual particle is a mathematical tool. However, what about virtual particles resulting quantum vacuum/Casimir effect? Are they more meaningful virtual particles. or what?
Are these actual physics textbooks, or books/articles about physics written for non-experts? Usually physics textbooks don’t even both to calculate it because it’s an easy calculation; and they never say “uncertainty principle”, they just calculate the answer correctly, using methods that alluded to late in my article.. The relation between the short range and the particle’s mass is correct, but as I showed in the math part of this article, it’s an indirect relation, not a direct one (as illustrated in Fig 2); it’s the stiffness term (which physicists usually call a “mass term”, even though it does not give the field any mass, just its particles) that is responsible for both.
Most of the books/articles written for the public are indeed wrong on this point, because they borrow from past books and employ pedagogical techniques that “everyone” uses, never worrying about whether there might be better and more accurate methods of explaining things. That’s why I was motivated to write the article.
If you’re curious about my credentials on this point, I have taught quantum field theory for 30 years and was trained by Michael Peskin (author of the most popular textbook on quantum field theory for several decades) and by Lenny Susskind (an expert in quantum field theory and string theory.) The point that I have discussed in this article is, in fact, a very elementary one [which is why the math is comprehensible to advanced first-year undergraduates.]
This is unusual. When it comes to why the strong nuclear force is short-range, the story is far from elementary, and I will not be able to lay out all the math in a similar way.
As another source: David Tong, a good friend of mine, is an excellent teacher and is writing a wonderful set of physics texts. David, like most of my colleagues, puts more weight on virtual particles as a teaching tool than I do. But if you look at how he introduces the subject of short-range forces (he takes a simpler case than the weak nuclear force, but the math in this context is the same) he first explains it on pages 67-68 of https://www.ippp.dur.ac.uk/~mspannow/files/Tong_QFT.pdf , equations 3.64-3.68 plus a little discussion, using exactly the undergraduate math that is in my article, with the additional techniques of Fourier transforms that typically undergraduates run into in second or third year math/physics.
Now, why does David emphasize the virtual particles in the rest of his text much more than I do in this article? Because he is teaching a course to graduate students who are going to have to do calculations far more complex than the ones needed to show the force is short range. It is absolutely not true that everything the weak nuclear “force” does (now using the term generally, not only as a push or pull) can be understood using first-year undergraduate math. If you want to understand why neutrons decay as they do and calculate their lifetime, of if you want to understand some of the rare processes involving bottom quarks, or many other things, you need graduate-level math. Usually the simplest method for these calculations involves Feynman diagrams, in which “virtual particles” are part of the method and the jargon. And if you look forward in David’s text, you will see that all of the math is unfamiliar.
But if you only want to understand why the force is short range, that is a non-quantum effect and easy to understand — as shown in David’s equations 3.64-3.68.
Thank you very much for this kind explanation! I see your point.
What I mentioned earlier was an article like this: ( https://faculty.washington.edu/seattle/physics541/%202010-reading/virtual-4.pdf ) It says “don’t take this too literally” at least, but anyway, I think you are saying the approach of the article is misleading and wrong.
And again, my second question. What about virtual particles resulting quantum vacuum/Casimir effect? Do you think these also should not be taught? and should we take quantum vacuum also as the effect of quantum fields themself, not mentioning virtual particles?
Yes, I disagree with the pedagogical approach and the conceptual baggage shared by Mr. Jones (whom I don’t know personally.) He is well-meaning, and certainly well-trained, and he’s not “wrong”, strictly speaking; but I think the pedagogical strategy he takes makes certain things sound much more mystical and amazing than they are, which distracts from the things that really are amazing. My field has a long and unfortunate history of doing things like this, and that’s why so few people actually understand how it really works, which is true not only among non-experts but among semi-experts too.
There are no calculations that involve virtual particles that cannot be done in other ways. Virtual particles are part of the Feynman diagram calculational technique; they allow you to calculate real effects, but they are not themselves observable. If you do the calculation of quantum vacuum effects/Casimir effects etc using lattice gauge theory (i.e. numerical simulation of quantum field theory), virtual particles never appear in the calculation. I do not think that objects that appear in certain calculation techniques but not in others should be ascribed the kind of physical significance that we ascribe to things we actually measure, such as real electrons. Furthermore, virtual particles violate all sorts of rules (such as being tachyons) that no physical objects should ever violate, so there are many reasons to understand that they are not physical, and they are not particles.
On top of this, there are many field theories in which Feynman’s methods do not work at all. Yet there are still quantum vacuum and Casimir effects in these theories, and they can still be calculated. You don’t ever need to say “virtual particles” to understand these effects.
However, one *should* teach virtual particles as part of teaching how to do calculations using Feynman’s techniques. I’m not saying they should never be taught. I’m saying we should not over-emphasize them and give the impression that they are part of the physics; they are part of a math technique. When they are at their most physical, they are still just classical (i.e. non-quantum) or almost-classical physics rewritten into fancy language. I’ll give an example of this soon.
Actually there’s another point that maybe I should make on this blog. Ordinary integrals, such as the integral of exp[-(x^2 + a x^3 + b x^4)], can be computed using Feynman’s techniques. There are “virtual particles” in the calculations; the diagrams are exactly the same as what appear in quantum field theory. This makes it clear that these are just part of a calculation; if you do the integral numerically on a computer, you never even see the virtual particles appear.
Huh. I was a while ago, but I remember being taught this phib as an undergraduate – I never had any cause to doubt it even if the “exchange of virtual bosons” thing never quite made sense to me. Looks like I was unknowingly inveigled into – as you put it – the cult of Feynman Diagrams!
I was taught this also. But I’d also already been taught about Green functions in an honors undergraduate course on electromagnetism that used Jackson’s book (with no quantum physics), so I recognized (without anyone saying so) that this was just different language for exactly the same idea, expressed in momentum space instead of position space and wrapped in Feynman jargon. After all the “Feynman propagator” is literally a Green function, albeit with an unfamiliar boundary condition. (Any great quantum field theorist, such as Vadim Kaplunovsky at UTexas, will tell you this;) and I was taught quantum field theory by the great theorists Larry Yaffe, Ann Nelson and Leonard Susskind, along with Michael Peskin (my advisor) who had written a book about it.
Is the stiffness of the W and Z fields due to their interaction with the Higgs field?
Yes. For a brief discussion of the basic conceptual framework, you can read what I wrote here: https://www.quantamagazine.org/how-the-higgs-field-actually-gives-mass-to-elementary-particles-20240903/ . You”ll find the complete story, laid out carefully but non-technically, in my book. If you want a somewhat more mathematical discussion at the level of first-year undergraduate math and physics, you can find it here: https://profmattstrassler.com/articles-and-posts/particle-physics-basics/how-the-higgs-field-works-with-math/ ; but note (a) there are articles that you should read first, and also (b) these articles are a decade old, and I had not yet chosen to use the term “stiffness” (or “wavicle”) back then, so the language is slightly different (though it should still be clear from context.)
I loved your statement that it is the field, not imaginary particles, that mediate force. I have never been able to wrap my head around the concept of imaginary particles mediating force. Can you point me to a bit more detailed explanation of the subject?
Well, make sure you read my article, because so far that is the clearest explanation that I know of in the literature that doesn’t just do it all in advanced math. Read all of the side comments in the mathy section.
The point is that a virtual particle in a diagram that shows a force between two real particles (the final figure of the new article) is nothing but what is known as a “Green function”. Green functions are used to calculate forces at an advanced undergraduate level, and they are proportional to the force laws that you are familiar with. So the mathematical connection is very direct. Maybe I’ll have to write this math out for people who want to follow it closely. I’m not sure what math level you have, though, so after you’ve read the article, let me know what questions you still have.