High School Is the speed of light constant to all observers?

[TheQuestionGuy14]

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

 

[DaveC426913]

Yes.
No.

 

[DaveC426913]

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 vacuum 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 $c$.

 

[TheQuestionGuy14]

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]

I was curious, is the speed of light in a vacuum 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]

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.

 

[Vanadium 50]

how is this possible?

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?

 

[TheQuestionGuy14]

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]

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.

 

[Justin Hunt]

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]

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.

 

[Herman Trivilino]

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.

 

[Justin Hunt]

@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]

@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 traveling 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).

 

[uservt2018]

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.

 

[uservt2018]

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]

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).

 

[uservt2018]

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?

I have read about an experiment of Lene Hau about this, Google more and you will find news about German scientists using crystals to completely paralize photons... what I think is that the speed of light will not be constant even in vacuum when a gravitational field influences it. This is not proven, however it's about logics for me. It is well spread that the gravitational force influences the curvature of light, even Einstein has a famous experiment about it. By logic if it's influencing curvature it's possible to influence the speed too, you can imagine a situation in which a photon traveling 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, I would imagine this as a tangible point of circles or something like this. This situation could be manipulated if the gravitational field is artificial (an imaginary situation), I could make the photon accelerate or decelerate creating or erasing the fields. Just think about it...

 

[Nugatory]

(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)

I have read about an experiment of Lene Hau about this, Google more and you will find news about German scientists using crystals to completely paralize photons...

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]

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 traveling 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.

 

[Ibix]

There are at least three different things one can call the "speed of light".

The first is the speed of light in a medium. This is variable. Hau's experiment is a modern and extreme example in a Bose Einstein condensate (which I wouldn't call a crystal, by the way), but the effect was well known long before Einstein. For example, Fermat was able to derive Snell's Law from the principle of least time.

The second thing is the coordinate speed of light. This is also variable. Shapiro delay is an example. But this is an effect analogous to looking at the shadow of a rod on bumpy ground - it will most certainly be curved, and regularly spaced notches on the rod may well be irregularly spaced on the shadow. This is an effect of the shape of the ground (analogous to your choice of coordinates), not the rod itself (analogous to the 4d path of a light ray).

Finally, there's the locally measured speed of light in vacuum. This is not variable. All observers will always see light pass them at c. Even in the presence of gravity, spacetime is locally flat (this is the meaning of the equivalence principle), so gravity does not have any effect on this measurement.

No one disputes that the first two are variable. But the last one cannot be variable in general relativity.