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### Photon charge experiment $(document).ready(function() { // The supplied crossmark code loads this inline before jqplot has finished unitialising, they then unregister the // jQuery causing much hilarity - doing it after page load is safer, we chain all of our requests to hopefully avoid // any kind of race condition var cachedScript = jQuery.cachedScript; cachedScript("https://ajax.googleapis.com/ajax/libs/jquery/1.4.4/jquery.min.js", { success: function () { cachedScript("https://ajax.googleapis.com/ajax/libs/jqueryui/1.8.7/jquery-ui.min.js", { success: function () { var s = document.createElement('script'); s.type = 'text/javascript'; s.src = 'http://crossmark.crossref.org/javascripts/v1.3/crossmark.min.js'; document.body.appendChild(s); } }); } }); }); USD 10.1119/1.4793593 View Affiliations Hide Affiliations Affiliations: 1 Department of Physics, Seattle University, 901 12th Avenue, Seattle, Washington 98122 a) Electronic mail: kimw@seattleu.edu Am. J. Phys. 81, 436 (2013) /content/aapt/journal/ajp/81/6/10.1119/1.4793593 ### References • A. Hankins, C. Rackson and W. J. Kim • Source: Am. J. Phys. 81, 436 ( 2013 ); 1. 1. E. Williams, J. Faller, and H. Hill, “ New experimental test of Coulomb's law: A laboratory upper limit on the photon rest mass,” Phys. Rev. Lett. 26, 721724 (1971). http://dx.doi.org/10.1103/PhysRevLett.26.721 2. 2. R. E. Crandall, “ Photon mass experiment,” Am. J. Phys. 51, 698702 (1983). http://dx.doi.org/10.1119/1.13149 3. 3. L. B. Okun, “ On the charge of the photon,” e-print arXiv:hep-ph/0505250v1. 4. 4. L. B. Okun, “ Photon: History, mass, charge,” Acta Phys. Polon. B37, 565574 (2006). 5. 5. L. de Broglie, “ Sur une analogie entre l’électron de Dirac et l'onde électrogmagnetique,” Compt. Rend. 195, 536537 (1932); 5. L. de Broglie, “ Sur le champ électromagnetique de l'onde lumineuse,” Compt. Rend. 195, 862864 (1932). Available at http://archive.org/details/ComptesRendusAcademieDesSciences0195. 6. 6. W. A. Perkins, “ Neutrino theory of photons,” Phys. Rev. 137, B1291B1301 (1965). http://dx.doi.org/10.1103/PhysRev.137.B1291 7. 7. A. L. Akhiezer and M. P. Rekalo, “ Electric charge of elementary particles,” Sov. Phys. Usp. 17, 864874 (1975). http://dx.doi.org/10.1070/PU1975v017n06ABEH004402 8. 8. J. Beringer et al., “ Review of particle physics,” Phys. Rev. D 86, 010001 (2012). http://dx.doi.org/10.1103/PhysRevD.86.010001 9. 9. B. Altschul, “ Bound on the photon charge from the phase coherence of extragalactic radiation,” Phys. Rev. Lett. 98, 2618011 (2007). http://dx.doi.org/10.1103/PhysRevLett.98.261801 10. 10. G. Cocconi, “ Upper limit for the electric charge of the photons from the millisecond pulsar 1937+21 observations,” Phys. Lett. B 206, 705706 (1988). http://dx.doi.org/10.1016/0370-2693(88)90723-X 11. 11. G. Raffelt, “ Pulsar bound on the photon electric charge reexamined,” Phys. Rev. D 50, 77297730 (1994). http://dx.doi.org/10.1103/PhysRevD.50.7729 12. 12. G. Cocconi, “ Upper limits on the electric charge of the photon,” Am. J. Phys. 60, 750751 (1992). http://dx.doi.org/10.1119/1.17082 13. 13. V. V. Kobychev and S. B. Popov, “ Constraints on the photon charge from observations of extragalactic sources,” Astro. Lett. 31, 147151 (2005). http://dx.doi.org/10.1134/1.1883345 14. 14. C. Sivaram, “ Upper limit on the photon electric charge from the cosmic microwave background,” Am. J. Phys. 63, 473 (1995). http://dx.doi.org/10.1119/1.17918 15. 15. C. Caprini and P. G. Ferreira, “ Constraints on the electrical charge asymmetry of the universe,” J. Cosmol. Astropart. Phys. (02 ) 0061 (2005). http://dx.doi.org/10.1088/1475-7516/2005/02/006 16. 16. Y. K. Semertzidis, G. T. Danby, and D. M. Lazarus, “ New laboratory technique for measuring the photon charge,” Phys. Rev. D 67, 0177011 (2003). http://dx.doi.org/10.1103/PhysRevD.67.017701 17. 17.The original work by L. Grodzins, D. Engelberg, and W. Bertozzi, published in the Bull. Am. Phys. Soc. 6, 63 (1961), is presently unavailable. However, some details of their experiment are concisely summarized in a review article.7 18. 18. R. W. Stover, T. I. Moran, and J. W. Trischka, “ Search for an electron-proton charge inequality by charge measurements on an isolated macroscopic body,” Phys. Rev. 164, 15991609 (1967). http://dx.doi.org/10.1103/PhysRev.164.1599 19. 19. B. Altschul, “ Astrophysical bounds on the photon charge and magnetic moment,” Astropart. Phys. 29, 290298 (2008). http://dx.doi.org/10.1016/j.astropartphys.2008.02.006 20. 20. A. M. Grassi Strini, G. Strini, and G. Tagliaferri, “ Attività sperimentale a Milano nell'ambito di studi di fattibilità di un rivelatore interferometrico a masse libere di onde gravitazionali,” Atti del IV convegno nazionale: Relatività Generale e Fisica Della Gravitazione. 121126 (1980). 21. 21. A. M. Grassi Strini, G. Strini, and G. Tagliaferri, Looking for the Scattering of Photons by a Quasi-Static Electromagnetic Field (University of Milano, 1977) (unpublished). 22. 22. C. E. Wieman and L. Holdberg, “ Using diode laser for atomic physics,” Rev. Sci. Instrum. 62, 120 (1991). http://dx.doi.org/10.1063/1.1142305 23. 23.Replacing the modulation of the electric field with that of a magnetic field , one also retrieves the upper limit of the photon charge obtained by Semertzidis et al.,16 which was reported to be 8.5 × 10−17e. 24. 24. C. Sivaram and K. Arun, “ Bounds on photon charge from evaporation of massive black holes,” e-print arXiv:1003.3818v1. 25. 25. W. J. Kim, M. Brown-Hayes, D. A. R. Dalvit, J. H. Brownell, and R. Onofrio, “ Anomalies in electrostatic calibrations for the measurement of the Casimir force in a sphere-plane geometry,” Phys. Rev. A 78, 02010114R (2008). http://dx.doi.org/10.1103/PhysRevA.78.020101 26. 26. W. J. Kim and U. D. Schwarz, “ Potential contributions of noncontact atomic force microscopy for the future Casimir force measurements,” J. Vac. Sci. Technol. B 28, C4A17 (2010). http://dx.doi.org/10.1116/1.3294709 27. 27. A. R. Hambley, Electronics, 2nd ed. (Prentice-Hall, Upper Saddle River, 2000), pp. 809812. 28. 28. E. D. Greaves, An Michel Rodríguez, and J. Ruiz-Camacho, “ A one-way speed of light experiment,” Am. J. Phys. 77, 894896 (2009). http://dx.doi.org/10.1119/1.3160665 29. 29.Our total experimental cost including all of the major electronics and components needed for the experiment is about$12,200. This includes the laser, laser components and controllers, breadboard for mounting, quadrant photodetector, PZT, oscilloscope, function generator, lock-in amplifier, high voltage power supply, and other miscellaneous components. This total cost assumes that there is no equipment available on hand already and that all components will need to be purchased brand new for the experiment.
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## Figures

Fig. 1.

Schematic of deflection of a “charged” photon inside a parallel-plate capacitor where the electric field is directed downward in the -direction.

Fig. 2.

Schematic diagram of the experimental setup. The strength of the electric field / across the parallel plates is modulated with the upper plategrounded, and the subsequent light “deflection” is measured from the lock-in output.

Fig. 3.

Calibration for the lock-in amplifier at a modulation frequency of 250 Hz. The larger the voltage applied to the PZT drive, the greater its displacement and hence the larger the output response from the lock-in. Care is taken not to drive the PZT with a negative voltage (an offset voltage is applied to ensure the modulation signal is always positive). Similar calibration data are also obtained at different modulation frequencies from 100 to 250 Hz.

Fig. 4.

Schematic of a Michelson's interferometer (top) and interference patterns (bottom). The intensity resulting from an interference between two light beams, one traveling directly into the photodiode and the other traveling a longer distance and being reflected from a mirror attached to the PZT. As the PZT moves the intensity varies from minimum (destructive) to maximum (constructive) with a visibility larger than 90%. Periodicity of , where nm enables a direct calibration of the PZT's applied voltage to the actual position displacement.

Fig. 5.

Circuit diagram of a relaxation oscillator (top) and period measurements (bottom). The period of the relaxation oscillator is proportional to the external capacitance: . A motorized actuator moves one of the plates thereby changing their separation distance. The absolute distance is not known , and measured data are fit to a function , where pF in the limit of , is a point of contact to be determined from the fit, and is the relative position of the actuator. Finally, β contains the information regarding the effective size of the plate as well as the permittivity constant in between.

Fig. 6.

Schematic diagram to determine the speed of light (top) and phase change versus distance (bottom). The laser used in our experiment is modulated at 15 MHz and is split into two different paths. Delay times associated with different travel lengths are then measured in terms of phase changes between two photodetectors. A linear fit to the data leads to m/s. Modulation frequencies ranging from 1 to 15 MHz are used, leading to similar results.

## Tables

Table I.

Status of upper limits on the photon charge. There have been several laboratory tests to constrain the photon charge, three employing electric fields and the most recent laboratory test involving magnetic deflection. Even the best laboratory limit is about ten orders of magnitude weaker than the limit obtained from charge asymmetry in the CMB data, which is the least stringent bound among those based on astrophysical observations.

/content/aapt/journal/ajp/81/6/10.1119/1.4793593
2013-05-20
2013-12-12

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