# Black Holes, Gravity, and Photon Mass

*Most recent answer: 01/07/2017*

- Dr Hugh R Johnston (age 60)

L3 6LL

That is in part a good point. Nevertheless, part of the confusion is due to a different way in which physicists communicate poorly. The word "mass" has two distinct meanings. One is the so-called rest mass, or invariant mass, sqrt(E^{2}-p^{2}c^{2})/c^{2}, where E is energy and p is momentum. Photons have zero rest mass. That's not the "mass" that enters into the gravitational effects, however, even before you consider spacetime warping. What enters in is the *inertial* mass, the m that you multiply velocity **v** by to get momentum **p**. Light does have inertial mass, because it has non-zero momentum and finite velocity, as Maxwell already knew in the 19^{th} century. So even in a classical picture you'd expect light rays to bend in a gravitational field.

(For background see https://van.physics.illinois.edu/qa/listing.php?id=16351.)

The problem comes up when you worry about how gravity can speed them up or slow them down, when Maxwell's equations say they travel at fixed speed. Worrying about that problem led Einstein to General Relativity. Ultimately you're right- you need that spacetime warping to explain why nothing can escape from a black hole. But it's not because "massless" photons would not be affected by gravity.

It's interesting that for mild gravitational effects bending light rays, the extra effect due to the full warped spacetime picture just doubles the bending that you would get just from the effect of gravity on the inertial mass of the photons.

Mike W.

*(published on 01/07/2017)*