# Could a photon travel faster than the speed of light in vacuum?

If the cosmic speed limit is the speed of light in vacuum, then what happens when a photon traveling through space meets gravity? Wouldn't gravity pull on the photon that's already traveling at max speed, thus making it ever-so-slightly faster?

• Gravity doesn't make photons move any faster, but what it does do is increase their energy i.e. it blue shifts them. May 29, 2014 at 18:05
• The event horizon inside a blackhole means no light can escape. Doesn't this mean gravity does affect photons? May 29, 2014 at 18:09
• Yes, gravity does affect photons. It blue shifts them on the way in and red shifts them on the way out. Actually gravity has all sorts of strange effects on light, but it doesn't make it travel faster than $c$. May 29, 2014 at 18:13
• Possible duplicates: physics.stackexchange.com/q/98980/2451 , physics.stackexchange.com/q/24319/2451 and links therein. May 29, 2014 at 18:16
• think about it like this: observations confirm that spatial and time coordinates of events will arrange such that, no matter how you are moving, photons will always seem to travel at the same speed locally May 30, 2014 at 1:59

No, the photon would still go at c. E = hf for a photon. E is energy, h is a special number called Planck's constant, and f is frequency (also sometimes people use v instead of f). Instead of speeding up the photon, the gravity would increase the frequency of the light. For example, a red beam of light, pulled by gravity, might have its frequency increased so that it becomes blue.

In all references frames, due to special relativity, the velocity of a photon is always the speed of light, denoted $c$. If we consider a photon in spacetime, with a metric $g_{\mu\nu}$, the situation does not change; it must travel at the speed of light. However, virtual photons are off-shell, meaning they do not satisfy,

$$E^2 = p^2c^2$$

i.e. the relativistic dispersion relation (with $m=0$), and hence may travel faster than the speed of light.

• for off shell " they may travel faster than ..." only mathematically, because they are not going anywhere, being bounded by the interaction . May 29, 2014 at 18:56
• @annav: Yes, that's the subtlety :) May 29, 2014 at 18:59

Photons travelling inbetween two parallel conducting plates (travelling in the direction parallel to the plates) will travel slightly faster than the speed of light in an ordinary vacuum (the vacuum between the plates is known as a "Casimir vacuum" which has different properties from an ordinary vacuum). This effect is known as the Scharnhorst effect. While the photons do travel faster than light, this cannot be exploited to produce a violation of causality as is shown here.

Any photon that's moving away from the milky way is travelling faster than c relative to us because the space in between is expanding. There are even galaxies that move away from us faster than c but they are beyond the horizon of the visible universe.