# Can light travel faster than the speed of 300,000,000m/s?

98operate
Hello, I am just curious about this physics question.

I understand the light can travel 300,000,000 m/s in vacuum but if air, water, or something else would interact with it light will move slower.

Here are some questions
Using the example when a boat is moving 40 m/s and a ball is shot at 90 degrees upward it would return back to the original spot on the boat because the ball is also moving at 40m/s.
If a car is moving 30 m/s and has it's headlights turned on, assuming nothing else is effecting it wouldn't the light be moving at 300,000,030 m/s?

Another question is if light was shot into a planet that had nothing affecting the light except its gravity will light travel faster than 300,000,000 m/s, if it doesn't then wouldn't that mean that gravity doesn't effect it?

The reason I was perplexed about this question was because I did not understand how come light was being eaten by the black hole, If the speed of light was not affected by the black holes gravity then it would shoot pass it, but if it doesn't wouldn't that mean there is a possibility of causing the speed of light to move faster than 300,000,000 m/s?

## Answers and Replies

Science Advisor
Homework Helper
welcome to pf!

hello 98operate! welcome to pf!
If a car is moving 30 m/s and has it's headlights turned on, assuming nothing else is effecting it wouldn't the light be moving at 300,000,030 m/s?

no, you have to use the special relativity velocity-addition formula, see http://en.wikipedia.org/wiki/Velocity-addition_formula#Special_theory_of_relativity

w = (u + v)/(1 + uv/c2)​

obviously, if v = c, then w = (u + c)/(1 + u/c) = c, whatever u is
Another question is if light was shot into a planet that had nothing affecting the light except its gravity will light travel faster than 300,000,000 m/s, if it doesn't then wouldn't that mean that gravity doesn't effect it?

The reason I was perplexed about this question was because I did not understand how come light was being eaten by the black hole, If the speed of light was not affected by the black holes gravity then it would shoot pass it, but if it doesn't wouldn't that mean there is a possibility of causing the speed of light to move faster than 300,000,000 m/s?

light travels at speed c only according to a local observer

if the space-time geometry changes, a distant observer will measure the speed of light as different from c

GW Leibniz
Hi 98operate!

You ask an interesting question. In case tiny-tim's answer was difficult to follow, let me try to answer more conceptually (though perhaps with less precision). If photons were classical objects, like the ball in your example, then you would be correct. To someone who is treading water and observing the boat go by at 40m/s, the ball would be also be moving at 40m/s, while to an observer on the boat, the ball would be at rest (aside from the up-down motion). In other words, if you asked the question "How fast is the ball moving?," different observers would have different answers.

What is really interesting about light is that it doesn't work like that. Every observer, no matter how fast he or she is moving with respect to the light source, will measure the same speed of light. This is not only counter intuitive, it leads to all of the 'strange' consequences of special relativity. In order for two observers moving away from one another to measure the same speed of light, they have to have different experiences of the passage of time. That's why a clock inside a high speed airplane runs a little slower than an identical clock sitting on the surface of earth. (This is also the basis of the twin paradox, which you might find interesting: http://en.wikipedia.org/wiki/Twin_paradox).

Your intuition about black holes is also interesting, it points toward general relativity. If I am sitting on the surface of earth, and you are floating in outer space in a synchronous orbit (so that we are maintaining a constant static distance between us), and we shot equally powerful cannons at one another, the cannon ball I shoot should take a lot longer than the cannon ball you shoot, since gravity will slow mine down and speed yours up. But if we shoot lasers at each other simultaneously, and we checked our watches to see how long it takes to receive the other's laser, they would have to take the same amount of time, because we both must measure the same speed of light. The only way that can happen is if my watch runs slower than yours. That seems pretty counter intuitive, but experiments have confirmed that if you have two identical clocks, the clock that is closer to a massive body will run slower than the clock that is farther from the massive body.

For these reasons, the clocks inside our GPS satellites need to be adjusted for both effects. On the one hand, they are moving pretty quickly with respect to someone sitting (or driving a car) on the surface of the earth, which causes their clocks to run a little slower. On the other hand, they are at a higher gravitational potential, which causes their clocks to run a little faster. The two effects don't cancel one another out, as the former effect is stronger than the latter effect, but if we didn't take both into account, the satellites would be off by miles.

Neat, eh?

Science Advisor
Hi 98operate!
On the one hand, they are moving pretty quickly with respect to someone sitting (or driving a car) on the surface of the earth, which causes their clocks to run a little slower. On the other hand, they are at a higher gravitational potential, which causes their clocks to run a little faster. The two effects don't cancel one another out, as the former effect is stronger than the latter effect, but if we didn't take both into account, the satellites would be off by miles.
While I'm not sure if it's not just my reading comprehension messing with me, it looks to me like you've mixed up the strength of the two effects - the latter is stronger(-7 microseconds/day for SR effect vs +45 microseconds/day for GR effect).
http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html

GW Leibniz
Whoops, you are right! Mixed them up.

Staff Emeritus
Science Advisor
Homework Helper
Another question is if light was shot into a planet that had nothing affecting the light except its gravity will light travel faster than 300,000,000 m/s, if it doesn't then wouldn't that mean that gravity doesn't effect it?
There are other ways light can be affected without changing speed. For example, its wavelength or direction of travel could change, and it would still travel at a speed of c.

Science Advisor
In general relativity, it's tricky to define the velocity of something that is not at the same place/time as the observer. Light falling into a black hole can seem to move faster than c from the perspective of an observer who is outside the hole and uses the wrong coordinate system. But the light falling into the black hole can't move faster than c relative to something else falling into the black hole which happens to cross paths with the light.

Someone correct me if I'm wrong, but I think the correct way to measure the velocity is to measure the velocity of the light relative to a killing vector field which is parallel to the observer's motion. Or perhaps a less abstract method would be to perturb the observer's motion so that it will fall into the black hole and cross paths with where the light used to be. Trace out the free-fall orbit to the crossing point. Measure the relative velocities between the observer after free-fall and the light. Undo the initial perturbation. Now the relative velocity of the light ought to equal c, if I understand things correctly. Because gravity doesn't accelerate anything in the framework of GR. It merely twists the coordinate system around.

98operate
Wow! Sorry for the late response my laptop had to be repaired. Thanks so much for the response though, especially GW Leibiniz for the more conceptual part and tiny-tim for the formula as well! So in the end I guess the speed of light 300,000km/s can't be surpassed.
Was the twin paradox actually something that happened with actually twins? I have heard about how astronauts do seem to age a lot less due to this paradox.

Mentor
Time dilation is not strong enough to be measured with a pair of human twins. The best we can do (which is still pretty good!) is identical clocks.

Science Advisor
Homework Helper
yup … it was done in the 1971 Hafele–Keating experiment (and many others later), with caesium atomic clocks, comparing a stay-at-home clock with one on a commercial aircraft, see http://en.wikipedia.org/wiki/Hafele–Keating_experiment
I have heard about how astronauts do seem to age a lot less due to this paradox.

this probably comes from http://en.wikipedia.org/wiki/Time_dilation
astronauts come back from missions slightly younger than they would be if they had stayed on earth​
… but this ageing is far too small to be detected in any way … wikipedia might as well say …
dogs come back from running round the park slightly younger than they would be if they'd stayed at heel!

hav0c
i would like to suggest that this question should be added to the FAQ. :D Even i've seen it come up a lot

Nessdude14
Wow! Sorry for the late response my laptop had to be repaired. Thanks so much for the response though, especially GW Leibiniz for the more conceptual part and tiny-tim for the formula as well! So in the end I guess the speed of light 300,000km/s can't be surpassed.
Was the twin paradox actually something that happened with actually twins? I have heard about how astronauts do seem to age a lot less due to this paradox.

The "twin paradox" is just a hypothetical scenario to show problems with the consequences Einstein's special theory of relativity. This "paradox" is resolved with Einstein's general theory of relativity. This consequence of Einstein's theories has been given the name "time dilation," and its predictions have been tested and proven to be accurate, so it's not actually a "paradox" but a real physical effect.