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.
Tuesday, July 10, 2007
Wednesday, July 4, 2007
Relativity on the Table-Top
Dirac Equation and Quantum Relativistic Effects in a Single Trapped Ion
L. Lamata, J. Leon, T. Schatz, and E. Solano
PRL 98, 253005 (2007)
URL: http://link.aps.org/abstract/PRL/v98/e253005
In this article, the authors demonstrate the experimental possibility of simulating a Dirac Hamiltonian in an atomic system. In short, they propose a table-top experiment that would probe the effects of a relativistic system.
The requirements are relatively modest. To simulate the (1+1)-D or (2+1)-D Dirac equation, one needs a two-level atomic system; for the (3+1)-D Dirac equation, one needs a 4-level system. Three types of couplings are also required:
• Carrier Interaction -- a resonant coupling between two of the internal atomic states (such as a laser tuned to the transition frequency).
• Jaynes-Cummings Interaction -- couples two internal states with a vibrational mode of the center of mass. An upward transition between internal states is accompanied by the destruction of a phonon.
• Anti-Jaynes-Cummings Interaction -- also couples two internal states with a vibrational mode, but the frequency is tuned so that an upward transition between is accompanied instead by the creation of a phonon.
When the phases of the laser fields used to generate the above interactions are appropriately tuned, the effective Hamiltonian for the two-level or four-level system is identical in form with the free Dirac equation. By varying the couplings, one can tune the effective particle mass and velocity of light.
The authors dedicate a lot of space to a discussion of Zitterbewegung, which is a rapid oscillatory motion of an electron about its mean position. It was predicted in 1930 by Schrodinger, but has not yet been observed experimentally. For electrons, the amplitude of the oscillations is on the order of 10^{-13} m, and the frequency is on the order of 10^{21} Hz. In addition, Zitterbewegung is an effect of the single-particle Dirac equation. There is some controversy over whether or not the effect persists in QED.
The authors point out that by controlling the effective electron mass and the effective speed of light, one should be able to bring the amplitude and frequency of the oscillations into an experimentally accessible range. Another point they don't mention: even if the effect does not occur for real electrons, the dynamics of their atomic system are (in theory) accurately described by a single-particle Dirac equation. Whether or not real electrons jitter around, the trapped ions on their desks should.
The authors mention a few other relativistic effects that might be simulated: by controlling the particle mass, one could observe something akin to the Higgs mechanism for mass generation; one could simulate the Klein paradox, in which particle-hole pairs are created in a strong potential; one could simulate a (1+1)-D axial anomaly, the lower-dimensional counterpart of the chiral anomaly in (3+1)-D.
The possibility of tuning the parameters of the Dirac equation is interesting. However, such simulations of relativistic systems is a bit perplexing. A similar situation exists in the theory of graphene and carbon nanotubes, where the low-energy excitations are described by a Dirac equation. On a very fundamental level, the simulation can't be right. So how far can one push the analogy?
How similar are a pseudospinor and a spinor? Electron spin has to do with angular momentum, but pseudospin has nothing to do with it. The simulated system can't have pseudospin-orbit coupling, but the Dirac equation can.
How effective is an effective speed of light? In the table-top simulation, nothing prohibits the electron or the center of mass of the ion system from exceeding the effective speed of light. What then? Would the authors claim they were simulating tachyons?
In the Klein paradox, where are the holes going to come from? No corresponding anti-cesium ion is going to materialize in the trap.
It would be quite interesting to probe these unphysical effects in a trap and see exactly how the effective Dirac physics breaks down.
A final note: This was a well-written paper, but I must criticize the authors for a particular choice of phrase. On page 2, they refer to the "notorious analogy" between the Dirac equation and the effective Hamiltonian of the trapped ion. Jesse James was notorious. The three-body problem is notoriously difficult. An analogy between Hamiltonians is not "famous or well known, typically for some bad quality or deed."
L. Lamata, J. Leon, T. Schatz, and E. Solano
PRL 98, 253005 (2007)
URL: http://link.aps.org/abstract/PRL/v98/e253005
In this article, the authors demonstrate the experimental possibility of simulating a Dirac Hamiltonian in an atomic system. In short, they propose a table-top experiment that would probe the effects of a relativistic system.
The requirements are relatively modest. To simulate the (1+1)-D or (2+1)-D Dirac equation, one needs a two-level atomic system; for the (3+1)-D Dirac equation, one needs a 4-level system. Three types of couplings are also required:
• Carrier Interaction -- a resonant coupling between two of the internal atomic states (such as a laser tuned to the transition frequency).
• Jaynes-Cummings Interaction -- couples two internal states with a vibrational mode of the center of mass. An upward transition between internal states is accompanied by the destruction of a phonon.
• Anti-Jaynes-Cummings Interaction -- also couples two internal states with a vibrational mode, but the frequency is tuned so that an upward transition between is accompanied instead by the creation of a phonon.
When the phases of the laser fields used to generate the above interactions are appropriately tuned, the effective Hamiltonian for the two-level or four-level system is identical in form with the free Dirac equation. By varying the couplings, one can tune the effective particle mass and velocity of light.
The authors dedicate a lot of space to a discussion of Zitterbewegung, which is a rapid oscillatory motion of an electron about its mean position. It was predicted in 1930 by Schrodinger, but has not yet been observed experimentally. For electrons, the amplitude of the oscillations is on the order of 10^{-13} m, and the frequency is on the order of 10^{21} Hz. In addition, Zitterbewegung is an effect of the single-particle Dirac equation. There is some controversy over whether or not the effect persists in QED.
The authors point out that by controlling the effective electron mass and the effective speed of light, one should be able to bring the amplitude and frequency of the oscillations into an experimentally accessible range. Another point they don't mention: even if the effect does not occur for real electrons, the dynamics of their atomic system are (in theory) accurately described by a single-particle Dirac equation. Whether or not real electrons jitter around, the trapped ions on their desks should.
The authors mention a few other relativistic effects that might be simulated: by controlling the particle mass, one could observe something akin to the Higgs mechanism for mass generation; one could simulate the Klein paradox, in which particle-hole pairs are created in a strong potential; one could simulate a (1+1)-D axial anomaly, the lower-dimensional counterpart of the chiral anomaly in (3+1)-D.
The possibility of tuning the parameters of the Dirac equation is interesting. However, such simulations of relativistic systems is a bit perplexing. A similar situation exists in the theory of graphene and carbon nanotubes, where the low-energy excitations are described by a Dirac equation. On a very fundamental level, the simulation can't be right. So how far can one push the analogy?
How similar are a pseudospinor and a spinor? Electron spin has to do with angular momentum, but pseudospin has nothing to do with it. The simulated system can't have pseudospin-orbit coupling, but the Dirac equation can.
How effective is an effective speed of light? In the table-top simulation, nothing prohibits the electron or the center of mass of the ion system from exceeding the effective speed of light. What then? Would the authors claim they were simulating tachyons?
In the Klein paradox, where are the holes going to come from? No corresponding anti-cesium ion is going to materialize in the trap.
It would be quite interesting to probe these unphysical effects in a trap and see exactly how the effective Dirac physics breaks down.
A final note: This was a well-written paper, but I must criticize the authors for a particular choice of phrase. On page 2, they refer to the "notorious analogy" between the Dirac equation and the effective Hamiltonian of the trapped ion. Jesse James was notorious. The three-body problem is notoriously difficult. An analogy between Hamiltonians is not "famous or well known, typically for some bad quality or deed."
Subscribe to:
Posts (Atom)
