Black Holes, Gravity, and Photon Mass

May I just make an observaton? In almost all discussions of Black Holes for a lay audience, the statement is made that: "Gravity is so strong that mot even light can escape". For those of us with a LITTLE Physics education (High School) this eventually starts to niggle because "Photons have no mass to be attracted by Gravity" -- so why is even the unbridled Gravity of a Black Hole attractng photons? Of course, when I relearn my General Relativity and put aside Sir Isaac Newton, temporarily, I remember that Gravity is not PULLING at all, but warping Space! So ... even a massless photon has to "run downhill" in the distorted Space which (n a Black Hole) is an extended spiral into the Singularity. This is SO DAMN OBVIOUS to professional Physics Communicators that they feel no need to restate it every time, but are happy with the bald: "Gravity is so strong not even light can escape". So, this is just an appeal to you Physics pro's not to forget to remind us layfolk WHY the Photons are trapped -- without their nonexistent "Mass" being pulled by Gravity!
- 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(E²-p²c²)/c², 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)