Relativity is founded upon the fact that light has no mass, and the equations prove this. However, what I am asking is how did scientists originally realize that light does not have mass? It was know that light had a speed, which is also a characteristic of classical objects forgetting relativity and that no object with mass could ever reach that speed. What led physicist to conclude that light has no mass.

  • $\begingroup$ See section 1.2 "The inverse square law or the mass of the photon" in Jackson's "Classical Electrodynamics" , 2nd edition. You can get limits to the mass of the photon that are 20 orders of magnitude smaller than the mass of the electron. $\endgroup$ – NickD Apr 11 '20 at 18:26
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    $\begingroup$ I'm voting to close this question as off-topic because it belongs to hsm.stackexchange.com $\endgroup$ – Semoi Apr 11 '20 at 18:30

The basic fact is that a non-zero mass of the photon would change the inverse square law. There are a couple of ways to do that: one is to assume that you have an inverse $(2+\epsilon)$ law and set experimental limits on $\epsilon$; the other is to assume that the potential has the Yukawa form $e^{-\mu r}/r$ where $\mu = m_\gamma c/\hbar$ and set experimental limits on $\mu$.

There are both laboratory experiments and measurements of the Earth's magnetic field that give limits for $m_\gamma < 4\times 10^{-48} g$, which is 20 orders of magnitude smaller than the mass of the electron.

These measurements validate the inverse square law at distances of order $1 cm$ to $10^9 cm$ but with additional assumptions, it can be extended down to $10^{-15} cm$.

All of this comes from Jackson's "Classical Electrodynamics", 2nd (or 3rd) ed, section 1.2.

  • $\begingroup$ Why is electric potential related to photon mass? (as assumed in yukawa potential) $\endgroup$ – Razor Oct 1 '20 at 18:49
  • $\begingroup$ @Razor: see e.g. Zee "Quantum Field Theory in a nutshell" (1st ed.), p.26. Also look for the Proca Lagrangian (e.g Jackson, 2nd ed, section 12.9). $\endgroup$ – NickD Oct 1 '20 at 19:16
  • $\begingroup$ Okay. Thank you $\endgroup$ – Razor Oct 1 '20 at 19:23
  • $\begingroup$ This is amazing! We can say that mass of photon is zero if Coulomb's law/Maxwell's laws are true! I thought that if we assume mass of photon is non-zero, relativity shows that there's some inconsistency but I guess that's not true and it indeed can have mass (if coulomb's law is false). Is there a law that we can assume to be true (like coulomb) which forces massive particles to move at speeds less that $c$? $\endgroup$ – Razor Oct 2 '20 at 9:02

The simplest way to consider this is as follows: A photon of light has momentum and velocity. You might think that because it has momentum, it must have some mass, but if you extrapolate to zero velocity (where the momentum goes to zero) you discover that a photon of light has no rest mass left over- thus demonstrating that photons are massless.


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