# Cosmological Consequences of Massive Photons

We all learned in our junior high science classes that photons are massless. This statement has resulted in a lot of confusion for laypeople. In our junior high science classes we were also taught that photons possess energy and, thanks to Einstein’s special relativity theory, energy is equivalent to mass.

I find that no matter what audience I address, all the attendees know that E = mc^{2}. It may be the only physics equation they know, but they understand that it implies mass can be converted into energy, and energy into mass.

The resolution of massless photons and the mass equivalence of photon energy is that the conversion of energy into matter requires that energy packets (photons) be accelerated to a very high velocity. (Note the c^{2} term in Einstein’s special relativity equation.)

Whenever physicists state that a photon is a massless particle, they mean that it has a “zero rest mass.” In fact, the textbook mass of any particle is its rest mass. When a particle is at rest, its relativistic mass possesses a minimum value—namely, the “rest mass.”

**Is the Photon Rest Mass Exactly Zero?**

Physicists believe the photon rest mass is exactly zero. However, they do not know that for certain. It is impossible to make any observation or do any experiment that would prove that the photon rest mass equals exactly zero.

The best that physicists and astronomers can do is to place an upper limit on a possible positive photon rest mass. Experiments and observations done so far establish that the photon rest mass, if it is nonzero, must be very tiny indeed.

**What If the Photon Had a Nonzero Rest Mass?**

Even if the photon rest mass is very tiny instead of exactly zero, serious consequences for both particle physics and cosmology could ensue. For starters, the theory of quantum electrodynamics would be in big trouble. Nobel laureate Richard Feynman called quantum electrodynamics the “jewel of physics.”^{1 }Quantum electrodynamics provides a complete integration, or unification, of classical electromagnetism with quantum mechanics and special relativity. It describes how light and matter interact in both the classical and quantum realms. If photons possess a nonzero rest mass, charge conservation would no longer be guaranteed, and the gauge invariance that is crucial for quantum electrodynamics would be lost. At least one Nobel Prize in physics would need to be rescinded.

If photons possess a nonzero rest mass, not all photons would travel at the same velocity. The velocity of light would be a function of frequency. Astronomers would face difficulties in integrating their measurements at radio wavelengths with those at optical and X-ray wavelengths. Also, these different velocities would disturb cosmic distance scales and yield a different picture of the geometry of the universe.

Another consequence of a nonzero photon rest mass is that the electrostatic force would be weaker over large distances compared to small distances. Such variations would imply that the magnetic fields of galaxies and galaxy clusters are weaker than what astronomers think. Astronomers’ galactic dynamics models would need to be revised. Such revisions would also imply adjustments in the values of cosmic density parameters, which form the foundational basis of all cosmic creation models.

A zero rest mass for the photon implies that a photon can be polarized in only two directions—the two that are orthogonal to the photon’s direction of motion. A nonzero photon rest mass means that there would be a third polarization direction—one along the photon’s direction of motion. Since our models of the cosmic hyperinflation event that occurred when the universe was younger than 10^{-33} seconds critically depend upon determining the polarization levels of the cosmic microwave background radiation (the radiation left over from the cosmic creation event—see figure 1), a nonzero photon rest mass would give a much different picture of the early history of the universe, with serious consequences for the universe’s present properties.

**Figure 1: Planck Satellite Map of the Cosmic Microwave Background (CMB) Radiation. ***Polarization measures of the CMB radiation reveal what kind of early inflation event the universe experienced.*

A nonzero rest mass for the photon affects the cosmic microwave background radiation in another way. It would affect the spectral behavior of the cosmic microwave background dipole anisotropy (see figure 2). The distortion would increase with wavelength and would lead to different conclusions about the Great Attractor and the Monster Attractor (both are dense concentrations of galaxy clusters), which astronomers have deduced are pulling our Milky Way Galaxy in a direction that explains the cosmic microwave background dipole anisotropy.

**Figure 2: Map of the Cosmic Microwave Background Dipole Anisotropy **

**Upper Limits to the Photon Mass**

The consequences of a nonzero rest mass for the photon, especially for cosmology and particle physics, are so devastating that most physicists and astronomers are persuaded that photons really are massless. However, these consequences have not stopped theoreticians from proposing alternatives to the standard cosmic creation models and the standard particle creation models based on nonzero photon rest masses. Thus, a major effort in both physics and astronomy is to develop observations and experiments to place evermore stringent upper bounds on the photon mass. I will discuss these efforts in my next blog post.

**Featured image: World’s largest photon collecting machine—Five-hundred-meter Aperture Spherical Telescope (FAST).** Image credit: www.news.cn/Xinhua

##### Endnotes

- Richard P. Feynman,
*QED: The Strange Theory of Light and Matter*(Princeton,NJ: Princeton University Press, 1988).