# Speed of light versus pull of gravity - Is $c$ really the limit? [duplicate]

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The understanding I have is that the speed of light is considered to be the highest attainable speed in physics. Of course there are theories of tachyons but since those haven't been proven we'll dismiss them for this statement. So, thinking mathematically, the speed of everything else is relative to the maximum value (using this logic I've always had an issue with believing there IS a max value instead of just infinity).

Using this line of thinking, how is it possible for some force to be able to overcome this universal constant? For example, the gravity of a black hole. Shouldn't that at most be able to equal the amount of force carrying a photon (or other body traveling at the speed of light) in the opposite direction? By this logic the only place that gravity could possibly even match the speed of light is at the center of the singularity, so it wouldn't trap any photons at all that weren't generated at that exact point.

I guess my point is that mathematically speaking, the largest "number" is infinity, and you can't have "infinity minus one" so why should the absolute largest possible speed be able to be influenced at all, let alone in a way that it can be completely negated and then some? Doesn't that completely invalidate $c$ as being the fastest possible speed? Perhaps it's just the fastest speed we've observed?

People far smarter than me have developed these theories and built whole areas of physics off of them, so I don't expect to be right. But can someone please explain to me why that's wrong?

## marked as duplicate by Kyle Kanos, Ali, ACuriousMind♦, Qmechanic♦Aug 14 '14 at 20:41

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• Re: "Shouldn't that at most be able to equal the amount of force carrying a photon (or other body traveling at the speed of light) in the opposite direction?": You do know that a photon moving at constant velocity doesn't have to be acted on by any forces, right? – jhobbie Aug 14 '14 at 13:01
• The answer is simply: The pull of gravity is no speed. You conflate forces with accelerations with speeds. Distinguish among these more carefully, and the question goes away. – ACuriousMind Aug 14 '14 at 13:15
• Thing you are able to observe or measure can't be infinity. – Berry P J Aug 14 '14 at 14:48
• Possible duplicates: physics.stackexchange.com/q/937/2451 , physics.stackexchange.com/q/5456/2451 and links therein. – Qmechanic Aug 14 '14 at 14:52
• It is not true, that c is thought of as "the highest attainable velocity" in physics. c is simply the same velocity in all inertial coordinate systems (that's an experimental result that has not been violated by nature, as far as we know). One can, however, easily construct examples and build experiments, in which phase velocity v_ph exceeds c by far. Now, if you do a Lorentz transform on v_ph, it may still be >>c in another coordinate system, but it will be numerically different from its value in the original one, so unlike c, v_ph is not a constant. – CuriousOne Aug 14 '14 at 18:50

## 1 Answer

You're using cartoon physics. There's no "force carrying a photon". Photons will happily move on their own, without any external force being applied. This is basic Newtonian physics: F=0 <=> a=0 <=> dv/dt=0 <=> v(t) = v(0)