Of Particular Significance

On Two Feynman Quotes

Hi again, @juangrga and @7MikeH7. I started to compose a long twitter thread, but it got too long, and may require revision anyway as I learn more, so I decided to put it here.

Thanks for pointing out these Feynman quotes, which are historically very interesting. Aside from their general interest, they also highlight why explaining science to non-experts is so challenging.

After all, Feynman was a genius, and I am not, so who am I to contradict him? But even geniuses make statements that do not stand the test of time — because they lack knowledge that emerges later. That’s why we respect, but do not worship, our ancestors’ remarks.

Even Einstein, for instance, changed his mind about how to think about mass & about aether during his life, and went back & forth on whether gravitational waves actually exist (ending up with the wrong conclusion.)  So old quotations have to be understood in historical context. (And don’t get me started about Bohr! Amazing physicist, but please let’s not spend too much time on his view of particle-wave duality.)

[Added: In those same days, Feynman would have told you that renormalization in QED is about removing infinities. But it isn’t. It took Wilson in the 1970s to understand what it really is… and he got a Nobel prize for that, too.]

Although I can’t access the Feynman texts right now and explore the context and the equations in more detail, it seems Feynman is drawing intuition from the particle path integral methods that he invented, applied in relativistic quantum *mechanics*, which works particle by particle. This methodology does not extend to quantum field theory (QFT), which is the language of modern particle physics. In QFT the path integral is over fields, not particles, and particles may not even exist. At best they are an epiphenomenon. 

One consequence is that the physical electron or photon you measure in experiment is not the one that appears in Feynman’s particle path integral, which implicitly assumes the particle has no interactions with other quantum objects. To understand how this works requires the language of renormalization, which was not fully clear until the 1960s and 1970s.  It makes it impossible to directly transfer Feynman’s statements about his path-integral electrons to physically observable ones. [As for the Dirac quote, that I have to study; *nobody* uses that language or intuition today, and I’m not sure what result of Schrodinger is being referred to, it has long ago dropped off the quantum physics map. Again, certain weird things happen in relativistic quantum mechanics that never show up in quantum field theory.]

Again, without the equations I can’t be certain, but I believe that Feynman in the photon quote may be calculating the photon “propagator”, and his statements about “short times” implies that we, in retrospect, should understand his statement as applying to a virtual photon. [To be confirmed]

The language Feynman himself introduced for “real” and “virtual” particles is useful, but it is very easy to over-interpret.  Real particles can be observed in experiments. Virtual ones can have all sorts of strange properties, such as negative mass-squared, negative energy, etc. Such virtual particles can indeed have any mass and travel at any speed.  However, they only appear inside calculations, and never in experiments. 

My view is that virtual particles are best viewed as a math technique, not as physical objects.  Why? First, in some QFTs (such as those that describe a metal at a phase transition) there are no particles at all. In others, the particles that appear in experiments are not the ones whose fields appear in the path integral.  (Protons, for instance.)  Feynman’s methods can’t be used in such situations.  Second, if you do the calculations in a different way, not using Feynman’s methods, the very notion of “virtual particle” may disappear altogether.  For instance, in computer calculations of the mass and structure of the proton, virtual quarks and gluons never appear anywhere in the calculation, and so they can’t in any way be essential to the way one understands the physics. By contrast, real particles do appear in these calculations, which is essential if one is to calculate the mass of such a particle! Virtual particles are also absent from the calculational methods that have been developed over the past 10 years by Arkani-Hamed and his physics and math collaborators, such as his most recent, https://arxiv.org/abs/2401.00041.

So I think Feynman, in these quotes, is providing an interpretation of the math that he invented as a calculational approach to QED. I view it as over-interpretation, but that’s no criticism of Feynman; we only recognize it as such in hindsight. This is why I was unaware of the quotes that you found.  Modern experts don’t learn all the details of relativistic quantum mechanics today, because in the end that approach doesn’t work, and isn’t general enough, to make all the predictions for particle physics. Only quantum field theory is general enough. Feynman, like everyone else around him, couldn’t have known that until the 1970s.

Finally, any interpretation, including the ones we use today, is subject to revision and controversy. That is why, in the end, physics is done using math, not words. Math makes unambiguous predictions for experiments. Words don’t… and neither do intermediate steps in a math calculation [cf. the Dirac quote that supposed motion at light-speed is unobservable… we’ve learned over the decades to be highly suspicious of things that you can’t directly observe.]

So in the end, the best I can tell you is this. (1) Feynman is out of date, as all of us will someday be, and you cannot read old scientific texts as though they are religious texts; they will all contain unfortunate interpretations that did not stand the test of time, and sometimes outright errors. (2) No verbal, intuitive interpretation of physics is unique. The best I can do is to try to tell you clearly the one that I use and why I use it.  Unfortunately, other authors will offer different ones, *even when we completely agree on the equations and how to use them.*

This makes life tough for non-experts, but it’s an insoluble problem.  Experts will look at the same math differently.  They will mostly agree on some things, one being that the Feynman path integral for particles (i.e. relativistic quantum mechanics) does not universally apply in QFT. And they will agree on the predictions of the math, even if they view what’s happening *inside* the math with different physical intuition.

[Note added: Clearly, @juangrga, you disagree with the premise, which is that the Standard Model, a QFT, is a successful theory of nature, and that a theory such as QCD is a complete theory. I do not understand your logic but am happy to hear what it is.]

Happy to discuss further.

2 Responses

  1. Please elaborate in a future post on what renormalization *really* is. That would make a great post to distinguish it from the outdated picture that still gets repeated.

    Thank you for the yeoman’s work of pointing out where the field’s understanding of a topic has shifted over the years.

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