Question: What is the mass of a photon?
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The answer to this question is dependent on your definition of mass. If your definition of mass is based on the concept of rest mass or invariant mass, then the mass of a photon is zero. Hence, photons are sometimes said to be massless. However, there is no experiment that can establish the photon’s rest mass to be exactly zero. Experimental physicists can only place limits on it. On the other hand, if your definition of mass is based on the concept of relativistic mass or effective mass, then the mass of a photon is dependent on the energy it possesses. According to Einstein’s principle of mass-energy equivalence, the mass of the photon is equivalent to its energy. Thus, its mass can be calculated by using the equation, m = E/c2. If the energy of the photon is hf, then its mass is hf/c2.
As another alternative, one may include the concept of Meissner mass (non-zero photon mass). This is related to the Meissner effect in which magnetic fields penetrate a finite distance into a superconductor. For example, Wilczek (2005) explains that “[a]n unusual but valid way of speaking about the phenomenon of superconductivity is to say that within a superconductor the photon acquires a mass. The Meissner effect follows from this. Indeed, to say that the photon acquires a mass is to say that the electromagnetic field becomes a massive field. Because the energetic cost of supporting massive fields over an extended volume is prohibitive, a superconducting material finds ways to expel magnetic fields (p. 241).”
How would Feynman answer?
Feynman may answer this question from the perspectives of rest mass and relativistic mass, as well as discuss problems of defining photon’s mass as shown below.
1. Rest mass of a photon:
Based on the concept of rest mass, Feynman mentions that “The masses given here are the masses of the particles at rest. The fact that a particle has zero mass means, in a way, that it cannot be at rest. A photon is never at rest, it is always moving at 186,000 miles a second (Feynman et al. 1963, section 2–4 Nuclei and particles).” This concept of mass can be mathematically represented by m0, and its value is Lorentz invariant. In other words, the rest mass of a photon does not change with the inertial frame of reference of an observer.
2. Relativistic mass of a photon:
Feynman may also provide an answer based on the concept of relativistic mass or Einstein’s principle of mass-energy equivalence. In Volume I of The Feynman Lectures on Physics, he explains that “[i]n the Einstein relativity theory, anything which has energy has mass — mass in the sense that it is attracted gravitationally. Even light, which has an energy, has a “mass.” When a light beam, which has energy in it, comes past the sun there is an attraction on it by the sun. Thus the light does not go straight, but is deflected. During the eclipse of the sun, for example, the stars which are around the sun should appear displaced from where they would be if the sun were not there, and this has been observed (Feynman et al. 1963, section 7–8 Gravity and relativity).” However, the relativistic mass is dependent on the inertial frame of reference of an observer.
In Volume II of The Feynman Lectures on Physics, Feynman elaborates that “[a] photon of frequency ω0 has the energy E0 = ℏω0. Since the energy E0 has the relativistic mass E0/c2 the photon has a mass (not rest mass) ℏω0/c2, and is ‘attracted’ by the earth. (Feynman et al. 1964, section 42–6 The speed of clocks in a gravitational field).” Although the speed of a photon is constant, the photon’s frequency may vary with the inertial frame of reference of the observer. That is, the relativistic mass of the photon may be increased or decreased and this can be explained by using Doppler’s effect.
3. Problems of defining a photon’s mass:
Feynman might discuss problems of defining (or determining) a photon’s mass by sharing his discussion with a physicist in Paris: “In this connection, I would like to relate an anecdote, something from a conversation after a cocktail party in Paris some years ago. There was a time at which all the ladies mysteriously disappeared, and I was left facing a famous professor, solemnly seated in an armchair, surrounded by his students. He asked, ‘Tell me, Professor Feynman, how sure are you that the photon has no rest mass?’ I answered ‘Well, it depends on the mass; evidently if the mass is infinitesimally small, so that it would have no effect whatsoever, I could not disprove its existence, but I would be glad to discuss the possibility that the mass is not of a certain definite size. The condition is that after I give you arguments against such mass, it should be against the rules to change the mass.’ The professor then chose a mass of 10-6 of an electron mass.
My answer was that, if we agreed that the mass of the photon was related to the frequency as ω = (k2 + m2)1/2, photons of different wavelengths would travel with different velocities. Then in observing an eclipsing double star, which was sufficiently far away, we would observe the eclipse in blue light and red light at different times. Since nothing like this is observed, we can put an upper limit on the mass, which, if you do the numbers, turns out to be of the order of 10-9 electron masses. The answer was translated to the professor. Then he wanted to know what I would have said if he had said 10-12 electron masses. The translating student was embarrassed by the question, and I protested that this was against the rules, but I agreed to try again.
To conclude, the rest mass of a photon is zero, whereas its relativistic mass is dependent on the photon’s frequency and the observer’s inertial frame of reference.
References:
1. Feynman, R. P., Morinigo, F. B., & Wagner, W. G. (1995). Feynman Lectures on gravitation (B. Hatfield, ed.). Reading, MA: Addison-Wesley.
2. Feynman, R. P., Leighton, R. B., & Sands, M. (1963). The Feynman Lectures on Physics, Vol I: Mainly mechanics, radiation, and heat. Reading, MA: Addison-Wesley.
3. Feynman, R. P., Leighton, R. B., & Sands, M. (1964). The Feynman Lectures on Physics, Vol II: Mainly electromagnetism and matter. Reading, MA: Addison-Wesley.
4. Wilczek, F. (2005). In search of symmetry lost. Nature, 433(7023), 239-247.