If photons are deflected by a strong gravitational field, then how come photons do not have mass? [duplicate]

It has been proved and showed through experiments that light can be bent by the Sun or any other body with considerable mass. Also light is nothing but photons. So can these photons be attracted by massive bodies if they have no mass?

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marked as duplicate by Frédéric Grosshans, mbqMar 29 '12 at 13:52

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

This has been adressed ad-nauseum. Photons have energy, which is "relativistic mass" (meaning just energy divided by c^2 so that it gets units of mass) and "relativistic mass" is the source of gravity, not "rest mass". The rest mass is zero, but the energy is not, and energy is the source of gravity. There are at least two other questions here about this, but I don't remember which. – Ron Maimon Dec 30 '11 at 13:33
If photons have no mass, how can they have momentum? and Explain how (or if) a box full of photons would weigh more due to massless photons both go to the same basic point. The question is well answered by accepting that the mathematics really represent how the world works and not trying to cram the situation on to a intuition based on a less complete theory. – dmckee Dec 30 '11 at 14:47

1 Answer

You're trying to mix two theories. If you want to consider that photons are deflected by gravity, then you must consider that mass is energy.

By Einstein's special theory of relativity, the energy and relativistic mass of a body are related by $E=mc^2$. This works both ways. A massive body has energy, and a body with energy has mass. A photon has energy $h\nu$, so it has (relativistic) mass $\frac{h\nu}{c^2}$. Note that it still has 0 rest mass--rest mass is $\frac{E\sqrt{1-v^2/c^2}}{c^2}$. It will be deflected by gravity, but only a tiny bit (due to its tiny mass). And no, in General Relativity, acceleration due to gravity is not independent of mass as Galileo thought.

In General relativity, gravity works by not exactly being a force, but more of a distortion of spacetime. Spacetime is distorted such that what you feel is straight is curved from someone else's point of view. So an astronaut in the ISS can reason that the ISS is going straight (as long as he doesn't look at the stars or at the ground), as he feels no force (this is not due to small value of g, any orbiting body feels no force, even classically). You, on the other hand, are standing on the ground, and you say that it is going in circles. This is due to the distortion of space. (I can clarify this with the rubber-sheet analogy if you wish)

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