### If light has no mass, why is it affected by gravity?

• Rahul Singh

3 years ago

Light doesn’t accelerate in a gravitational field, which things with mass would do, because light has a universally constant velocity. Why is that exception? Light is affected by gravity in general, that's why there's gravitational lensing. Why would gravity from black holes be any different? You might be interested in How can gravity affect light?, Why doesn't gravity speed up light? and Speed of light in a gravitational field? on the Physics SE.  Great, now it's just a bunch of confusing answers. **Gravity bends space-time, the medium through which light travels.** @Mazura I'd formulate it more directly: **Gravity _IS_ the bending of space-time** Photons have no *rest mass* -- they never rest, do they. But each existing photon has the mass which is equivalent to its energy ($m = \frac{E}{c^2}$, or $\frac{\hbar*\nu}{c^2}$).

• 3 years ago

Another way to answer this question is to apply the Equivalence Principle, which Einstein called his "happiest thought" (so you know it has to be good). The equivalence principle says that if you are in an enclosed box in the presence of what Newton would call a gravitational field, then everything that happens in that box must be the same as if the box was not in a gravitational field, but accelerating upward instead. So when you release a ball, you can imagine the ball is accelerated downward by gravity, or you can imagine everything but the ball is accelerated upward, and the ball is simply being left behind (which, ironically, checks better with the stresses you can easily detect on every object around you that are not present on the ball, including the feeling you are receiving from your bottom right now).

Given that rule, it is easy to see how light would be affected by gravity-- simply imagine shining a laser horizontally. In the "left behind" reference frame, we see what would happen-- the beam would start from a sequentially higher and higher point, and that raising effect is accelerating. So given the finite speed of light, the shape of the beam would appear to curve downward, and the beam would not strike the point on the wall of the box directly opposite the laser. Therefore, this must also be what is perceived from inside the box-- the beam does not strike the point directly across from the laser (as that point is getting higher then the point across from it where the light was emitted), and its path appears to curve downward. Ergo, light "falls."

Indeed, this is the crucial simplification of the Equivalence Principle-- you never need to know what the substance is, all substances "fall the same" because it's nothing happening to the substance, it is just the consequences of being "left behind" by whatever actually does have forces on it and is actually accelerating.

Incidentally, it is interesting to note that even in Newtonian gravity, massless objects would "fall the same" as those with mass, but to see it requires taking a limit. Simply drop a ball in a vacuum, then a lower mass ball, then a lower still mass. All objects fall the same under Newtonian gravity. So simply proceed to the limit of zero mass, you will not see any difference along the path of that limit. Nevertheless, Newtonian gravity doesn't get the answer quite right for the trajectory of light in gravity, because Newtonian physics doesn't treat the speed of light correctly. Well, Newtonian gravity, $F = \frac{Gm_1m_2}{r^2}$ certainly goes to zero force when the mass is zero. @CarlWitthoft, *F = ma* also goes to zero when the mass is zero. Applying zero force to zero mass gives you any acceleration you wish. I'm torn with this answer... it just explains *that* light is affected by gravity (by way of a thought experiment, no less). The OP knew that already - he wanted to know *why* (which is a can of worms, sure...). The equivalence principle is not the reason for the light behaving its way, it is just a didactic helper... @AnoE : it isn't a can of worms. It's simpler than you think. It seems however that a lot of GR textbooks were written before the Einstein digital papers were online, and don't explain it as simply as Einstein did. @JohnDuffield, ok, my comment was a bit flippant maybe. But in an accepted answer, I would at least like to see curved spacetime mentioned. Or a mention that all massless things always move at the speed of light. Again, the E.P. is a "principle" - it is a thought experiment, not the physical *reason* for light behaving as it does. @AnoE - Newtonian physics had no answer to why gravity apparently acts instantaneously, with the force proportional to the product of the masses divided by the square of the distance. It's an *ad hoc* explanation. General relativity explains that (and also explains where that Newtonian model falls short), but it does not explain why the speed of light is (locally) constant, nor does it explain what makes space-time curve. Quantum mechanics has similar issues with "why" questions. Physics answers "what" questions. "Why" questions are the purview of metaphysics, philosophy, and religion. I'm not sure one can draw any significant distinction between "didactic helpers" and all of physics. But I think it's fair to say that the equivalence principle is only part of the issue-- it tells you why light "falls the same" as everything else, but by itself it doesn't tell you why *anything* falls-- for that, you need something that involves the gravitational acceleration in some way. That's where the spacetime curvature comes in, but that's a much harder issue than "why light falls like other things"-- as long as you already know that other things do fall. @DavidHammen and KenG, good points, that's the direction I wanted to allude to with my comments. (N.B. OP does use the GR tag in his question.) It's interesting to me that a good part of the existing answers (except this one) talk a lot about black holes - OP does not mention black holes, and those are an edge case anyways. I don't feel qualified to write a helpful answer myself, but will keep watching... @David Hammen : my answer below is correct. Look at those Einstein quotes, I didn't make them up. Science is not a democracy. All the downvotes in the world won't make a right answer wrong, or vice versa. @AnoE : there's no problem in mentioning curved spacetime provided you don't say light follows the curvature of spacetime. And there's no harm saying massless things move at the speed of light, provided you don't say the speed of light is constant. Einstein was clear about why light curved - because the speed of light is spatially variable. As for the equivalence principle, yes, it isn't the physical reason for light behaving as it does. In fact it's something of a myth. I've written about it, see this. I was confused by you "bottom" comment till Irealised that you were a physicist and that my "bottom" was the underneath of my feet (am reading this standing up!) Oh! I figured I could assume sitting, must be more careful! Note that we probably can't ever explain _why_ light is affected by gravity. We can explain how GR predicts that light will bend in the presence of massive objects, and as far as we can tell, it seems that light bends exactly as much as GR says it will. But we have no proof that GR is **the truth**, and even if GR were **the truth**, we probably never would have any proof. This is how scientific theories work in general.