# Does light travel at the speed of light?

I can't figure out why it should. Here's what I'm thinking:

- Light is affected by the gravity, and gravity is the interaction between masses, so surely light must have mass in some form.

- Light has no mass, but has energy depending on the frequency of the photon. By E = mc^2, photons with higher frequency should have more mass, and therefore should surely move slower. I have heard of observations though from far out in space (can't remember any specifics, sorry) where two photons from the same event but of different frequencies will be detected at the same time, surely indicating that the energy of the photons does not affect the velocity.

- If light has mass, then surely it cannot travel at the true speed of light.

Thank you

If light had mass then no it wouldn't travel at c, but it doesn't. In E = mc^2 the m is rest mass and since light is never at rest m = 0.

The correct equation is E^2 = (pc)^2 + (mc^2)^2.

For light m = 0, so we use the pc bit which is momentum. Light is affected by gravity however but will change frequency not speed.

If light had mass then no it wouldn't travel at c, but it doesn't. In E = mc^2 the m is rest mass and since light is never at rest m = 0.

The correct equation is E^2 = (pc)^2 + (mc^2)^2.

For light m = 0, so we use the pc bit which is momentum. Light is affected by gravity however but will change frequency not speed.

Thanks, that's a very clear answer. So if gravity only affects the frequency, how does, say, a black hole, pull light in? Would it squash the wavelength to 0, or even make it negative?

Pengwuino
Gold Member
Remember, gravity is an interaction between anything with energy, not just mass. So photons still attract gravitationally.

Cleonis
Gold Member
how does, say, a black hole, pull light in?

The way that a gravitational sink (such as a black hole) affects light is not a counterpart of how matter is afffected.
If you fire a rocket upwards and it doesn't have enough velocity then gravity causes it to make a U-turn. That is a form of 'pulling in'. For light there is no such U-turn scenario. There is no such thing as slowing down light.

If the light is emitted outside the event horizon then the light will escape. There is an energy cost to travelling out of the gravitational sink. The closer to the event horizon the light was emitted, the stronger the redshift.

So, expressed mathematically, in the limit of emission arbitrarily close to the event horizon, you get for light having travelled out that the frequency goes to 0, and correspondingly the wavelength goes to infinitely long.

About the statement: 'there is no such thing as slowing down light'. At every altitude above the black hole's event horizon you can measure the local speed of light, and it will always come out the same: c.

Drakkith
Staff Emeritus
Here's a thought I had the other day on this while talking to my roomate.

If gravity is the bending of spacetime, then inside a black hole's event horizon all space is curved so that it all leads back to the black hole correct? If so, would light being emitted behind the event horizon be similar to something like rolling a ball up one side of a skateboard U ramp? The ball initially goes up, but it eventually reaches a point where the vertical velocity is zero and it only has some horizontal velocity (analogy to light losing energy before it falls back in a black hole), so it curves and comes back down the ramp.

Would light act this way at all? IE if a photon heads nearly straight up out of the black hole, its path in spacetime is curved in such a way that it simply gets turned right back around (kind of like the ball on the ramp, but it never slows down) and falls back in?

ZapperZ
Staff Emeritus
I can't figure out why it should. Here's what I'm thinking:

- Light is affected by the gravity, and gravity is the interaction between masses, so surely light must have mass in some form.

- Light has no mass, but has energy depending on the frequency of the photon. By E = mc^2, photons with higher frequency should have more mass, and therefore should surely move slower. I have heard of observations though from far out in space (can't remember any specifics, sorry) where two photons from the same event but of different frequencies will be detected at the same time, surely indicating that the energy of the photons does not affect the velocity.

- If light has mass, then surely it cannot travel at the true speed of light.