Is a photon's mass zero or not?

Please answer just this question, then we can keep discussing.

As you know, whether a photon has mass depends on what you mean by "mass." I.e. it depends on how the term "mass" is defined. The following relationships are true

Let m = proper mass and M = inertial mass (aka relativistic mass aka mass)

For particles or closed systems we have

m is the magnitude of 4-momentum

M = |

**p**/

**v**| = m/sqrt(1 - v^2/c^2)

Proper mass of photon = 0

Relativistic mass of photon is not zero but has the value M = p/c. E = pc for photon so p = E/c. Therefore M = (p/c)/c = E/c^2

You can find this defined and explained in many relativistic texts such as the following (the following texts use m as inertial mass and not proper mass)

**Special Relativity**, A. P. French, MIT Press, page 20

Let us now try to put together some of the results we have discussed. For photons we have

E = cp

and

m = E/c^2

(the first experimental, the second based on Einstein's box). Combining these, we have

m = p/c

**Relativity: Special, General and Cosmological,** Wolfgang, Oxford Univ., Press, (2001), page 120

According to Einstein, a photon with frequency f has energy hf /c^2, and thus (as he only came to realize several years later) a finite mass and a finite momentum hf/c.

**Introducing Einstein's Relativity,** Ray D'Inverno, Oxford Univ. Press, (1992), page 50

Finally, using the energy-mass relationship E = mc^2, we find that the relativistic mass of a photon is non-zero and given by m = p/c.

Combining these results with Planck's hypothesis, we obtain the following formulae for the energy E, relativistic mass m, and linear momentum p of the photons:

E = hf m = hf/c^2 p = hf/c

Also found in

**Concepts of Mass In Contemporary Physics and Philosophy,** Max Jammer, Princeton University Press

The same thing is found in Alan Guth's lecture notes from his course at MIT, the

**Early Universe.**Were you aware of the fact that some physicists define M in this way in recently published relativity texts?