Photons and the Aharonov Bohm Effect

Bound on the Photon Charge from the Phase Coherence of Extragalactic Radiation

Brett Altschul

PRL 98, 261801 (2007)

URL: http://link.aps.org/abstract/PRL/v98/e261801


The conclusion of this paper will come as a surprise to very few people: the photon probably doesn't have a charge. Altschul, from Indiana University, has deduced an upper bound on the photon charge that is 32 orders of magnitude less than the electron charge (46 if photons have both a positive and a negative charge). It is his analysis rather than his conclusion that I found interesting.

Altshcul's analysis starts from the observation that we can use interferometry to study astrophysical objects. Basically, one collects light from the same source at two different receivers. By studying the interference between the signals at the two receivers, one can obtain information about the source object. For this to work, the light from the source must be coherent --- i.e., the phase difference between two photons traveling along the same path must be small compared to the phase difference they acquire due to the path difference between the two receivers.

Altschul points out a source of phase difference that does not immediately come to mind: the Aharonov-Bohm Effect. If photons have a charge, then photons at the two detectors of an interferometer will acquire a phase difference that depends on the magnetic flux through the triangle made up of the two detectors and the source. (The assumption here is that a charged photon would interact with an external electromagnetic field exactly the same way an electron does.) The fact that interferometry works means the Aharonov Bohm phase small. (Conservatively, Altschul interprets "small" as "less than one".)

Making order of magnitude estimates for the interstellar magnetic field and using the baseline of the Very Long Baseline Interferometry Space Observatory Program (VSOP) with a source distance of 1 Gpc (about 3 billion light years), Altschul places an upper bound of 10^{-32} on the ratio of the photon charge to the electron charge.

The small bound is possible because of the huge distances involved in astronomical observations. It's almost like running a lab experiment designed to probe the Aharonov Bohm effect for 3 billion years --- that's a lot of data!

If the photon can have both positive and negative charges (like electrons) or positive, negative, and neutral charges (like pions), then the bounds are even tighter. This is because the Aharonov Bohm phase is proportional to the charge of the particle. If a particle with positive charge and a particle with negative charge travel along the same path, they acquire equal and opposite phases. If photons have two charges, the fact that interferometry works places an upper limit of 10^{-46} on the ratio of photon and electron charges.

The major source of uncertainty in this analysis is the current lack of understanding regarding interstellar magnetic fields. Perhaps Altschul's study will inspire new methods of studying these fields using interferometry.

As I said, the fact that the one can place a very small upper bound on the photon charge is not surprising. The fact that it can be done by analyzing the Aharonov Bohm effect is.

Altschul mentions a couple interesting facts about the theory of photons. First, the problem of the photon mass has been studied much more than that of photon charge. He mentions three theories of photon mass (Proca, Higgs, and Stuckleberg). I've never heard of the third. He also points out that not much is known about the consequences of charged photons. This is surprising, given the large number of models studied in quantum field theory --- many of which have little relevance to the physical world as revealed by experiments. It sounds like the kind of problem one might find at the end of a chapter in Peskin and Schroeder.