In my last blog post I described the consequences for particle and cosmic creation models if the photon, rather than possessing a zero rest mass, actually had a small nonzero rest mass. The consequences are sufficiently severe that most physicists and astronomers believe that the photon really must have a zero rest mass. However, they lack the experimental and observational tools to prove that the photon indeed has a zero rest mass or an upper limit on its rest mass. This implies that none of the consequences I described in my last post are of concern in any physical or astronomical context. Thanks to recent measurements, all that has changed.

During the last several years and even weeks, astronomers and physicists have developed new tools that now place strong limits on the maximum possible value of the photon rest mass that, to a significant degree, alleviate concerns about the consequences I raised. Better yet, the new tools can potentially be made much more robust within the next few years. I will devote the remainder of this blog post to describing the new tools, the limits established so far, and the limits that will be forthcoming.

Wavelength Independence of Light’s Velocity
As I explained in my previous blog post, if the photon has a nonzero rest mass, that mass implies that the velocity of light will be a function of the frequency or wavelength of the light. If scientists can place strict constraints on the limits of the fractional variation of the velocity of light with respect to frequency, those limits will translate into an upper bound constraint of the rest mass of the photon.

In one study, several pulsar measurements indicated that light’s velocity was constant to within 10^-20 throughout the ultraviolet, visible, and near infrared parts of the pulsar spectra.¹ This constancy limit corresponded to an upper limit on the photon rest mass = 3 x 10^-46 grams. (For comparison, the electron rest mass = 9.11 x 10^-28 grams.) In a later study, observations of bursts from the gamma ray burst object GRB 980703 covering the range from radio to gamma ray wavelengths yielded an upper limit on the photon rest mass = 4.2 x 10^-44 grams.²

Possible Deviation from Coulomb’s Law
We might remember Coulomb’s Law from our junior high science education. Coulomb’s Law states that, just like with gravity, electromagnetism obeys an inverse square law. That is, the magnitude of the electromagnetic force declines with the square of the distance from the source of the electromagnetic force. However, if the photon rest mass is not zero, the electromagnetic force declines at a greater rate than that predicted by the inverse square law. The most sensitive laboratory measurement of possible deviations from Coulomb’s Law establishes that the photon rest mass must be less than 8 x 10^-48 grams.³

Torsion Balance Experiments
The best of these experiments uses a rotating torsion balance to detect the product of the square of the photon rest mass and the ambient cosmic magnetic fields. A team of four Chinese physicists used this method to obtain an upper limit on the photon rest mass = 1.2 x 10^-51 grams.⁴ However, another team comprised of one American and two Chinese physicists pointed out that uncertainties in the magnetic field levels of the Coma Cluster of galaxies and the Milky Way Galaxy reduce the upper limit to 2.6 x 10^-50 grams.⁵ Yet another team demonstrated that uncertainties in the homogeneity of the magnetic fields and plasma densities of the Coma Cluster and the Local Group of galaxies make the 2.6 x 10^-50 gram limit optimistic at best.⁶

Fast Radio Bursts
Fast radio bursts (FRBs) are the newest discovered phenomenon in astronomy. FRBs are high-energy transient radio pulses that last for only a few milliseconds. While many FRB objects have been found, astronomers have observed only one such object with repeating FRBs.

Thirteen months ago a team of six astronomers pointed out that the frequency time delays in FRBs—if the distance to the FRB object is known—can be used to place an upper limit on the photon rest mass. That same team used data from FRB 150418 to establish that the photon rest mass can be no greater than 3.2 x 10^-47 grams.⁷ Using data from FRB 121102, the same team later determined that the photon rest mass must be less than 3.9 x 10^-47 grams.⁸ In addition, two Chinese astrophysicists, in a paper that appeared just two weeks ago, used a Bayesian analysis of a catalog of FRBs to constrain the photon rest mass to less than 8.7 x 10^-48 grams.⁹

Pulsars
Pulsars are highly magnetized neutron stars or white dwarfs that emit a focused beam of electromagnetic radiation. This radiation is seen only when the beam is pointing toward Earth in the same way a beam of light from a lighthouse can be seen only when the beam is pointed in the observer’s direction.

If the photon has a nonzero rest mass, it will distort the “dispersion measure” of pulsars. The pulsar dispersion measure refers to the broadening of the sharp, or highly focused, pulse when the pulsar is observed over a certain bandwidth of wavelengths as opposed to just a single wavelength. Pulses emitted at higher frequencies (shorter wavelengths) arrive earlier than those emitted at lower frequencies (longer wavelengths).

By determining a limit on the distortion of pulsar dispersion measures, astronomers can establish an upper bound on the photon rest mass. Four astronomers did just that through their measurements of radio pulsars in the Large and Small Magellanic Clouds. They established that the photon rest mass cannot be greater than 2.0 x 10^-45 grams.¹⁰ While their limit was ten thousand times lower than previous constraints based on the Crab Nebula pulsar, it ranked about a hundred times inferior to limits established from FRBs.

All pulsars are neutron stars except for one object, AR Scorpii. AR Scorpii is a binary pulsar that contains a white dwarf and a red dwarf (see featured image). The discovery of the pulsing nature of the white dwarf was announced at the beginning of this year.¹¹ Astronomers do not directly observe the highly focused light beam from the white dwarf pulsar. The pulsation they see occurs when the focused beam from the white dwarf sweeps across the surface of the red dwarf. The red dwarf reprocesses the beam into the observed electromagnetic energy. You can watch a short video of an artist’s impression of the pulsing nature of both the white dwarf and the red dwarf components of AR Scorpii here.

The AR Scorpii pulsar gets its energy from its spindown, not from accreting any material from its red dwarf partner. If photons have nonzero rest mass, the spindown rate of the AR Scorpii pulsar will be lower than for the zero rest mass case. Measurements made by two astronomers yield a stringent upper limit for the photon rest mass.¹² Assuming a vacuum dipole spindown for the AR Scorpii pulsar, the photon rest mass must be less than 6.3 x 10^-50 grams. If the spindown arises from a fully developed pulsar wind, the photon rest mass must be less than 9.6 x 10^-50 grams. Realistically, the spindown behavior will be between these two extremes. Therefore, the two photon rest mass limits bracket the true photon rest mass upper limit.

Future Prospects 
The upper limit value of 7–8 x 10^-50 grams for the photon mass from measures of the spindown of the AR Scorpii white dwarf pulsar is the most stringent limit, to date, within the secure methods. However, several white dwarfs with magnetic fields ranging from one million to one billion Gauss with periods on the order of an hour are now known to exist.¹³ Observations of the spindown behavior of these white dwarfs could easily push the upper limit for the photon mass below 1 x 10^-51 grams.

A method based on the solar wind magnetic field recently has been refined to where it very likely has become a secure method for constraining the photon rest mass. The best measurements show that the photon rest mass must be less than 8 x 10^-52 grams.¹⁴ Finally, the galactic magnetic field structure, if mapped to sufficient precision and certainty, could establish a limit for the photon rest mass below 1 x 10^-52 grams.¹⁵

Secure Creation Models
With an upper bound on the photon rest mass as low as 7–8 x 10^-50 grams and potentially much lower, no astronomer, physicist, or any other member of the human race needs to worry about the validity of cosmic or particle creation. Thus, any possible extremely tiny rest mass for photons poses no threat to the biblical creation model for the universe and the particles that comprise it.

Endnotes

1. Z. Bay and J. A. White, “Frequency Dependence of the Speed of Light in Space,” Physical Review D 5 (February 15, 1972): 796–99, doi:10.1103/PhysRevD.5.796.
2. Bradley E. Schaefer, “Severe Limits on Variations of the Speed of Light with Frequency,” Physical Review Letters 82 (June 21, 1999): 4964–66, doi:10.1103/PhysRevLett.82.4964.
3. R. E. Crandall, “Photon Mass Experiment,” American Journal of Physics 51 (August 1983): 698–702, doi:10.1119/1.13149.
4. Jun Luo et al., “New Experimental Limit on the Photon Rest Mass with a Rotating Torsion Balance,” Physical Review Letters 90 (February 26, 2003): id. 081801, doi:10.1103/PhysRevLett.90.081801.
5. Laing-Cheng Tu, Jun Luo, and George T. Gillies, “The Mass of the Photon,” Reports on Progress in Physics 68 (January 2005): 77–130. The relevant comments are made on page 109. doi:10.1088/0034-4885/68/1/R02.
6. Alfred Scarff Goldhaber and Michael Martin Nieto, “Problems with the Rotating-Torsion-Balance Limit on the Photon Mass,” Physical Review Letters 91 (October 3, 2003): id. 149101, doi:10.1103/PhysRevLett.91.149101.
7. Luca Bonetti et al., “Photon Mass Limits from Fast Radio Bursts,” Physics Letters B 757 (June 10, 2016): 548–52, doi:10.1016/j.physletb.2016.04.035.
8. Luca Bonetti et al, “FRB 121102 Casts New Light on the Photon Mass,” Physics Letters B 768 (May 10, 2017): 326–29, doi:10.1016/j.physletb.2017.03.014.
9. Lijing Shao and Bing Zhang, “Bayesian Framework to Constrain the Photon Mass with a Catalog of Fast Radio Bursts,” Physical Review D 95 (June 19, 2017): id. 123010, doi:10.1103/PhysRevD.95.123010.
10. Jun-Jie Wei et al., “New Limits on the Photon Mass with Radio Pulsars in the Magellanic Clouds,” Research in Astronomy and Astrophysics 17 (February 2017): id. 13 (2017), doi:10.1088/1674-4527/17/2/13.
11. D. A. H. Buckley et al., “Polarimetric Evidence of a White Dwarf Pulsar in the Binary System AR Scorpii,” Nature Astronomy 1 (January 23, 2017): id. 0029, doi:10.1038/s41550-016-0029.
12. Yuan-Pei Yang and Bing Zhang, “Tight Constraint on Photon Mass from Pulsar Spindown,” Astrophysical Journal 842 (June 8, 2017): id. 23, doi:10.3847/1538-4357/aa74de.
13. D. T. Wickramasinghe and Lilia Ferrario, “Magnetism in Isolated and Binary White Dwarfs,” Publications of the Astronomical Society of the Pacific 112 (July 2000): 873–924, doi:10.1086/316593.
14. Liu Lin-Xia and Shao Cheng-Gang, “Re-estimatation of the Upper Limit on the Photon Mass with the Solar Wind Method,” Chinese Physics Letters 29 (November 2012): id. 111401, doi:10.1088/0256-307X/29/11/111401.
15. D. D. Ryutov, “Constraints on the Photon Mass from the Galactic Magnetic Field Structure,” Plasmas in the Laboratory and the Universe: Interactions, Patterns, and Turbulence, AIP Conference Proceedings 1242 (June 2010): 1–10, doi:10.1063/1.3460125.

Subjects: Big Bang Theory, Inflation, Relativity, Laws of Physics, Origin of the Universe, Particle Physics, Universe Design