# Is the speed of light constant to all observers?

I was curious, is the speed of light in a vaccum really constant to all observers no matter their speed or movement? Is it possible for someone to somehow see light travel slower?

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DaveC426913
Gold Member
Yes.
No.

Dale
DaveC426913
Gold Member
OK, technically the correct answer is: if Einsteinian SR is wrong.

The constancy of the speed of light in a vacuum is a postulate of SR.
i.e. SR assumes it to be true, and lays out what that world would look like.
To a high degree of detail, it looks like our universe looks, so it is a very accurate model - far more so than any competing theory so far.

Ibix
I was curious, is the speed of light in a vaccum really constant to all observers no matter their speed or movement?
Yes, to the best of our ability to measure.
Is it possible for someone to somehow see light travel slower?
Kind of. You can prepare unusual single photon states that don't propagate at the speed of light, but this is (roughly speaking) because they correspond to expanding waves and the average speed of an expanding wave is always lower than the wave speed. It's cheating, in a sense. And (in any sense) it doesn't change the invariance of ##c##.

Yes, to the best of our ability to measure.
Kind of. You can prepare unusual single photon states that don't propagate at the speed of light, but this is (roughly speaking) because they correspond to expanding waves and the average speed of an expanding wave is always lower than the wave speed. It's cheating, in a sense. And (in any sense) it doesn't change the invariance of ##c##.
Also, apparently things can't go faster than the speed of light, but apparently galaxies far away travel faster than the speed of light, how is this possible?

https://www.space.com/33306-how-does-the-universe-expand-faster-than-light.html

stevendaryl
Staff Emeritus
I was curious, is the speed of light in a vaccum really constant to all observers no matter their speed or movement? Is it possible for someone to somehow see light travel slower?
Just a slight correction: Speed is only meaningful for an inertial, cartesian coordinate system. If you are using a curved coordinate system, then the quantity ##\frac{dx}{dt}## will not necessarily be ##c##.

Ibix
Ibix
Also, apparently things can't go faster than the speed of light, but apparently galaxies far away travel faster than the speed of light, how is this possible?
Because the word "speed" can mean multiple different things in relativity, broadly related by being the rate at which the distance between two things grows in some sense or other. The speed limit only applies to local measurements. So you will never, under any circumstances, see anything overtake a pulse of light (excepting the odd "slow" photon states I mentioned above).

But once you try to measure the speed of something that isn't right next to you, there isn't a unique way to do this. And there isn't necessarily a restriction on the speed you can obtain - because it's not the same thing as the local measurement.

As a trivial example, turn 360° on the spot. In a frame where you were stationary, Alpha Centauri just moved about twenty five light years in a circle, in only a second or two. Relativity doesn't break. The reason for supra-luminal recession speeds is harder to explain without maths, but it's a similar effect.

SiennaTheGr8 and stevendaryl
Because the word "speed" can mean multiple different things in relativity, broadly related by being the rate at which the distance between two things grows in some sense or other. The speed limit only applies to local measurements. So you will never, under any circumstances, see anything overtake a pulse of light (excepting the odd "slow" photon states I mentioned above).

But once you try to measure the speed of something that isn't right next to you, there isn't a unique way to do this. And there isn't necessarily a restriction on the speed you can obtain - because it's not the same thing as the local measurement.

As a trivial example, turn 360° on the spot. In a frame where you were stationary, Alpha Centauri just moved about twenty five light years in a circle, in only a second or two. Relativity doesn't break. The reason for supra-luminal recession speeds is harder to explain without maths, but it's a similar effect.
So it's not really going faster than the speed of light, is it?

Also, just as a side question, I know this isn't really related to physics, but,
A good answer is at https://www.space.com/33306-how-does-the-universe-expand-faster-than-light.html Oops...that's the same link you posted. Did you read it? If there is something you don't understand, could you tell us what it is?
I don't understand how the universe expands faster than the speed of light, if nothing can surpass light. That's all.

Ibix
So it's not really going faster than the speed of light, is it?
To the extent that "really" means anything, yes, really it is moving faster than light, by some measures.
I don't understand how the universe expands faster than the speed of light, if nothing can surpass light.
Because "nothing can travel faster than light" isn't true for all definitions of speed in curved spacetime. As V50 points out, the article you linked explains in some detail.

PeterDonis
Mentor
2019 Award
Because "nothing can travel faster than light" isn't true for all definitions of speed in curved spacetime.
This way of putting it might be confusing. A better way to put it would be: the coordinate speed of things (including light) can exceed ##c## in some coordinates, and/or in curved spacetime (note that this can happen even in flat spacetime in some coordinates). But nothing can move outside the local light cones, i.e., nothing can move faster than a ray of light at the same location and moving in the same direction. So nothing can move "faster than light" in the actual physical sense that matters in contexts where "nothing can move faster than light" is a useful rule.

Ibix
This way of putting it might be confusing.
I'm not sure your way is any less confusing to a beginner, but it's certainly a more precise statement than my answer.

I understand that light is measured as C in all frames so that if you are standing on earth and a spaceship flies by the light will be blue shifted on the approach and red shifted while it is leaving, but in all cases the light given off will travel at speed C from the ship to you. It is not effected by the speed of the spaceship. However, wouldn't you calculate that the spaceship and the light are not separating at the speed of light? as in on the approach, the light is only out passing the spaceship at C - the spaceships velocity? and when the spaceship is leaving the distance between the light and spaceship is increasing by more than C? (This is all from the perspective of earth) The spaceship perspective, however, would measure the speed of light to be C due to length contraction and time dilation. is this all correct?

jbriggs444
Homework Helper
2019 Award
However, wouldn't you calculate that the spaceship and the light are not separating at the speed of light?
Right. However, the number you get for such a "rate of separation" is not a relative velocity. That is, it is not the velocity of the one thing in the rest frame of the other.

Mister T
Gold Member
So it's not really going faster than the speed of light, is it?
A better expression of that idea is to say that if there were a race between it and a beam of light in a vacuum, the beam of light would always win.

@jbriggs444 The part I am trying to understand is why wouldn't people in the ship wouldn't notice light traveling faster from front to back versus back to front. The only thing i can think of is that it is impossible for it not to be a round trip (impossible to do only one way experiments). This would allow length contraction to hide it.

Nugatory
Mentor
@jbriggs444 The part I am trying to understand is why wouldn't people in the ship wouldn't notice light traveling faster from front to back versus back to front. The only thing i can think of is that it is impossible for it not to be a round trip (impossible to do only one way experiments). This would allow length contraction to hide it.
As far as the people in the ship are considered, there is no time dilation or length contraction. They and all parts of the ship are at rest and the flash of light is moving at speed c relative to both the front and back. The calculation is easy: the clocks at both ends of the ship are synchronized because they're at rest relative to one another; so take the time at which the light arrives at one end, subtract the time at which it was emitted at the other end and we have the flight time; the distance traveled is the length of the ship; divide one into the other and we have the speed. The numbers are the same whether the flash is travelling from front to rear or rear to front.

(The ship people also believe that the rest of the universe is moving relative to them, and is length-contracted and time-dilated, but that's irrelevant to their measurement of the speed of the light flash. However, this length contraction time dilation, along with the relativity of simultaneity, are how the ship people explain the otherwise puzzling to them fact that everyone else in the universe also finds that the light flash was moving at speed c).

Good question, I have been thinking about the same subject. I wonder what would happen to a photon trapped inside a black hole or somehow stopped by any kind of gravitational force. I don't have autorithy to affirm anything, but my suggestion is that sometimes the speed of light will not be constant to anyone.

Ibix
I wonder what would happen to a photon trapped inside a black hole or somehow stopped by any kind of gravitational force.
Light is never stopped in the sense you mean. It's true that light can be trapped at the surface of a black hole, but to anyone in a position to investigate the event horizon is moving outwards at lightspeed (which is one explanation of why you can't cross the horizon outwards - you can't catch it). So light trapped at the event horizon will, indeed, pass an observer at lightspeed despite being trapped.

Spacetime geometry near a black hole is fun.

Light is never stopped in the sense you mean. It's true that light can be trapped at the surface of a black hole, but to anyone in a position to investigate the event horizon is moving outwards at lightspeed (which is one explanation of why you can't cross the horizon outwards - you can't catch it). So light trapped at the event horizon will, indeed, pass an observer at lightspeed despite being trapped.

Spacetime geometry near a black hole is fun.
Check lab experiments that stopped photons using fluids and crystals I think that this idea of constant speed of light is over... (it's not constant when influenced by a gravitational field and when manipulated by other means)

Ibix
Check lab experiments that stopped photons using fluids and crystals I think that this idea of constant speed of light is over...
The speed of light in materials is variable, yes. That's been known at least as far back as Fermat, who died in 1665. It's the speed of light in vacuum that is invariant.

Edit: I have my doubts about "stopped", too. Do you have a reference for that?

Nugatory
Mentor
Check lab experiments that stopped photons using fluids and crystals I think that this idea of constant speed of light is over.
You are misunderstanding what people mean when they say that the speed of light is constant. We are talking about the speed of light in a vacuum here, and no one is expecting or suggesting that the speed of light in a medium is necessarily ##c##. This qualification is so well understood that people generally leave it off.
.. (it's not constant when influenced by a gravitational field)
Again, you are misunderstanding what is meant by saying that the speed of light is constant. If a flash of light passes you, you will measure its speed to be ##c## regardless of whether you're moving or not, and regardless of whether there is a gravitational field present. The "non-constant" speed that you're thinking of is what is called a "coordinate velocity" and it has no physical significance - it's just an artifact of the way that we assign times and positions to distant events in a curved spacetime.
(For an example of why a coordinate velocity lacks physical meaning, you might consider a simpler situation in which the fallacy of taking the speed seriously is more obvious: If we choose coordinates in which you and I are at rest then alpha centauri, four light years away, moves in a circular path around the earth; this path has a length of more than 24 light years, yet alpha centauri makes it all the way around in a mere 24 hours, yielding a coordinate velocity several thousand times greater then the speed of light. Note that despite this enormous "speed", alpha centauri is never going to win a race with a flash of light).

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The speed of light in materials is variable, yes. That's been known at least as far back as Fermat, who died in 1665. It's the speed of light in vacuum that is invariant.

Edit: I have my doubts about "stopped", too. Do you have a reference for that?

Nugatory
Mentor
(This is a good time to remind everyone about the Physics Forums rules about acceptable sources and personal theories. The mission statement is also worth a read)

This googling exercise will find many non-technical descriptions of these experiments in question, but these oversimplified descriptions are not acceptable references under the physics forums rules. There's a reason for this: If you run down the actual peer-reviewed papers describing the real physics, you will find that these popular explanations written for laypeople are incomplete to the point of being misleading (often they've glossed over the crucial distinction between phase and group velocities). In any case, they can't be used to support your argument here - you'll need to cite the peer-reviewed papers for that.
By logic if it's influencing curvature it's possible to influence the speed too...
That logic works (with a bit of tweaking to phrase it more precisely) for coordinate velocities, but as I said above.... we aren't talking about coordinate velocities here.

DaveC426913
Gold Member
Check lab experiments that stopped photons using fluids and crystals
The postulate - and topic under discussion - is that the speed of light in a vacuum is constant. We know there are ways of slowing it down in media.

(it's not constant when influenced by a gravitational field and when manipulated by other means)
Yes it is, when in a vacuum.

By logic if it's influencing curvature it's possible to influence the speed too, you can imagine a situation in which a photon travelling at constant speed reaches a point of coincidence of gravitational fields and it can't take a destination, it would be stucked in vacuum without movement because there wouldn't be a dominant force,
No. It does not work like this. If opposing gravitational fields cancel out - indeed, anytime net gravity is essentially zero - it just goes straight.

And even when it doesn't go straight, its speed is still c.