A couple of days ago, Ram Rao (A Crank Learns Physics) asked a pair of very interesting questions — do phonons exist, and are phonons particles? I gave a preliminary answer, but would like to add some further comments based upon a paper of Eugene Wigner’s that I happened across. So here is a revisit of the topic. The original dialogue is to be found in the comments to my prior post, “Observing the Positron”. I will repeat most of that here, with additional insights that I’ve gained from reading the Wigner paper. That Wigner paper is “Invariance in Physical Theory”, December 1949, Proceedings of the American Philosophical Society, vol 93 number 7, pp 521-526.

Ram Rao asked… Do phonons exist? Or rather, are Phonons particles? In fact, what exactly are the differences between particles, quasiparticles and virtual particles?

Let me say right off, that I am not an expert in particle physics, or materials science, or other specialties which are pertinent to this question, nor am I expert in thousands of other fields! Someday I will know more than I know now, and my opinion may change. But here is the best I can do based upon reading to date and reflection.

My original response…

We have to understand what is meant by the phrase “(some generic class noun phrase) exists”. I think it means pretty much the same as “phonons are observables”. Not that we are necessarily capable of making those observations — ie, in general, we may not have (yet) constructed machinery to make observations of some class of hypothesed observables, When we do construct such machinery, it may be indirect, and depend as much upon reasoning as upon direct sensation. Eg, we “know” positrons exist by interpreting cloud chamber photographs, just as we know electrons exist via other lab apparatus such as charged oil drop experiments, travel of beta particles through vacuum, etc.

So can we observe phonons? They are, for practical purposes, waves. And, going back to the ocean, no-one denies that waves exist. Walk into a sailor’s bar and claim that waves do not exist! But, as known, a wave crest (until it breaks) is not the same water particles moving. The wave exists, but its materialization as water molecules is changing.

I think it is partly a matter of choosing a coordinate domain for speaking about an observable. Not just a reference frame, but also perhaps another distinctive type of coordinates — like phase space. If, in such a coordinate domain, we can find a frame which is the “proper” frame of an observable, in which it is “at rest” with constant coordinates (the origin), then it becomes reasonable to speak of that observable not only existing, but being a particle.

Something like Descartes’ “Cogito, ergo sum” — “I think, therefore I exist”. If a phonon is able to say “I am stationary, the world is moving around me” (in some coordinate domain of choice) then the phonon, an observable, can consider itself a particle.

To that response I would now add something based upon Wigner’s article. He discusses (pp 523-524) the difficulty, in quantum physics, of establishing the form of the physically important operators. Except, when dealing with an elementary particle, “whose states are formed by the superposition of the states of a single invariant set.” He then goes on: “As a result, the possible equations of elementary particles can easily be enumerated and some progress has been made recently also toward the invariant theoretic determination of the operators for the most important physical quantities.” And, further, he says this, which can be taken as a definition of an elementary particle:

“The property which makes a particle elementary in the sense of the above statement is that it shall have no internal coordinate, which would permit an invariant division of its states into two or more groups. It is certainly no accident that all elementary particles, including the light quantum, obey irreducible equations and hence form elementary systems in the above sense.”

That is a good reminder of what it means to be an elementary particle — a definition in terms of its description via irreducible equations. So, are (some) phonons not just particles, but elementary particles?

I’ve been reading papers of Eugene Wigner in connnection with another project, and he is worth your attention. If one does not wish to delve into the scientific details too deeply, Wigner also wrote several articles of general interest. If one is looking for insights into the ideas of physics, his writings are a terrific resource. It is often said that physics is the poetry written at the interface between mathematics and matter. Wigner is one of our best poets.

Best wishes,
Ken Roberts
08-Mar-2014

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