Is the speed of light actually constant or just always measured to be the same?

[Ken Natton]

I do think that the OP is talking about the speed of light rays. However, I see no consequence for this thread of understanding this thread to be about either light rays or the limit speed, as they are supposed to be equal and the validity of relativity is not questioned here. What answer do you think would change with the interpretation of the question?

Well okay, and perhaps my intervention has added nothing, I apologise if so. Clearly I was not successful in defusing the argument which is what I presumed to be doing. My perspective was just this – for someone who has a view of the reality in which they live that might be described as Newtonian mechanical – even though they themselves might not even know what that term means – it is a big struggle to understand how it can be possible for two different observers, one of whom is stationary and the other of whom is moving at some significant proportion of the speed of light, to both observe the same beam of light and measure its velocity to be the same. For such a person, grasping how it can be that all reference frames are relative and yet the speed of light is constant for all observers requires a fundamental shift in their understanding of the reality in which they live. Falling out over minute details about the speed of propagation of electromagnetic waves seems to me to be getting bogged down in a detail that is less than entirely essential.

 

[harrylin]

Well okay, and perhaps my intervention has added nothing, I apologise if so. Clearly I was not successful in defusing the argument which is what I presumed to be doing. My perspective was just this – for someone who has a view of the reality in which they live that might be described as Newtonian mechanical – even though they themselves might not even know what that term means – it is a big struggle to understand how it can be possible for two different observers, one of whom is stationary and the other of whom is moving at some significant proportion of the speed of light, to both observe the same beam of light and measure its velocity to be the same. For such a person, grasping how it can be that all reference frames are relative and yet the speed of light is constant for all observers requires a fundamental shift in their understanding of the reality in which they live. Falling out over minute details about the speed of propagation of electromagnetic waves seems to me to be getting bogged down in a detail that is less than entirely essential.

There is no need at all to change your views of reality - the early inception of relativity was fully based on a Newtonian view of reality! A classical understanding about the speed of propagation of electromagnetic waves is compatible ("only apparently irreconcilable", as Einstein put it) with relativity*. What needed to be abandoned was Newton's theory according to which measurements of time and length are "absolute". Examples of physicists who maintained the "old" view of reality are Lorentz, Langevin and perhaps Dirac (Einstein's opinion is a bit unclear, and it flip-flopped somewhat).

Cheers,
Harald

* http://www.fourmilab.ch/etexts/einstein/specrel/www/
PS: in the QM section the - for me surprising - view is advanced that a classical view of EM propagation is also quite compatible with QM.
- https://www.physicsforums.com/showthread.php?t=474537

 

[ApplePion]

<<Light always travels at c. Period. >>

Not in General Relativity.

 

[ApplePion]

<<FAQ: Is the speed of light equal to c even in an accelerating frame of reference?
The short answer is "yes.">>

Actually, the answer is "No". In such a frame, a ficticious gravitational field would exist, and the metric would be non-Lorentian.

 

[DrGreg]

<<FAQ: Is the speed of light equal to c even in an accelerating frame of reference?
The short answer is "yes.">>

Actually, the answer is "No". In such a frame, a ficticious gravitational field would exist, and the metric would be non-Lorentian.

Did you bother to read the long answer?

The long answer is that it depends on what you mean by measuring the speed of light...

...Silly conclusions like this one can be eliminated by specifying that c has a defined value not in all experiments but in local experiments. The Sagnac effect is nonlocal because the apparatus has a finite size. The observed effect is proportional to the area enclosed by the beam-path. "Local" is actually very difficult to define rigorously [Sotiriou 2007], but basically the idea is that if your apparatus is of size L, any discrepancy in its measurement of c will approach zero in the limit as L approaches zero.

So the speed of light is always c locally (i.e. measured over a short enough distance), but not necessarily "remotely".

 

[ApplePion]

<<So the speed of light is always c locally >>

That is not the case. One need not use Lorentzian coordinates locally.

 

[Passionflower]

<<So the speed of light is always c locally >>

That is not the case. One need not use Lorentzian coordinates locally.

You are incorrect ApplePion, locally the speed of light is always c. Of course strictly local there is no speed as a speed can only be measured between two distinct points. But in the limit it will be c even in curved spacetimes.

 

[WannabeNewton]

For pseudo - Riemannian manifolds you can say that on a local enough scale the space - time metric reduces to the minkowski metric.

 

[ApplePion]

<<You are incorrect ApplePion, locally the speed of light is always c>>

You can set up various different local coordinate systems. The ones where the metric is Lorentzian you have a speed of c. If it is not Lorentzian, the speed is not necessarily c.

For example, if you set up a local coordinate system where it is c, I can make a coordinate transformation x' = 2x, and in the primed coordinate system the speed of light is c/2.

I am actually not creating a pointless quibble. By appealing to these "local" coordinate systems where the speed is c, you are stripping the physics of physical meaning. This will be clear from the following analogy. You can always set up a coordinate system where something is not moving (e.g. making a Lorentz transformation to a frame where the object is at rest). So from your perspective that the speed of light is always c because a coordinate transformation can make it so, one could argue that all objects are at rest. It should be obvious that the statement "All objects are at rest" is bad.

 

[ApplePion]

<<For pseudo - Riemannian manifolds you can say that on a local enough scale the space - time metric reduces to the minkowski metric>>

And a coordinate transformation can always be made so that a particular person has a height of 6. But it is not good to from this conclude "Everyone's height is 6".

 

[ApplePion]

Since you think that the speed of light is always c, because one can make a local coordinate transformation to a locally Lorentzian metric, then... since you can always make a local coordinate transformation to make the affine connection vanish you must logically also think that the gravitational field is always zero.

So do you want to take the position that there is no such thing as a gravitational field?

 

[harrylin]

[..] I am actually not creating a pointless quibble. By appealing to these "local" coordinate systems where the speed is c, you are stripping the physics of physical meaning. This will be clear from the following analogy. You can always set up a coordinate system where something is not moving (e.g. making a Lorentz transformation to a frame where the object is at rest). So from your perspective that the speed of light is always c because a coordinate transformation can make it so, one could argue that all objects are at rest. It should be obvious that the statement "All objects are at rest" is bad.

Maybe not really bad, but poor yes (in the sense of empoverished). For example, Einstein's prediction of gravitational lensing was based on considering the speed of light as measured non-locally. That it's always c locally lacks physical information and can even be misleading.

 

[AstrophysicsX]

I woke up this morning thinking about special relativity. I read last night that light is always traveling at light speed, relative to anything. But there's a paradox. What about light, relative to light? Doesn't that mean that photons could travel at an undefined, infinitesimal speed? (Which seems impossible, but you never know when it comes to physics.) Any help?

 

[ApplePion]

I woke up this morning thinking about special relativity. I read last night that light is always traveling at light speed, relative to anything. But there's a paradox. What about light, relative to light? Doesn't that mean that photons could travel at an undefined, infinitesimal speed? (Which seems impossible, but you never know when it comes to physics.) Any help?

You are trying to introduce an inertial frame where one photon is at rest, and to describe the motion of a second photon in that frame.

The problem is that you cannot make a Lorentz transformation that would make that first photon at rest.

continued

 

[ApplePion]

continued

Here though is something you can do.

Consider an object moving at 99 percent of the speed of light. Ask what a photon looks like in that guy's frame.

To make that guy become at rest yiou need to make a Lorentz transformation to make him at rest. Just use the usual Lorentz transformation, with v/c in the formula being .99. That will do it.

So what is the photon doing in that frame? In the original frame the photon moves along the worldline x= ct. Now go use the Lorentz Transformation with .99 and transform x to x' and t to t'. After you do that divide x' by t'. You will get c. So in the new frame the photon moves at the speed c. Had you used .999 or .99999 instead of .99 the same thing would happen. Indeed, the Lorentz transformation was constructed specifically so that you would always get "c" regardless of what value you chose for v/c in the Lorentz Transformation.

 

[harrylin]

I woke up this morning thinking about special relativity. I read last night that light is always traveling at light speed, relative to anything. But there's a paradox. What about light, relative to light? Doesn't that mean that photons could travel at an undefined, infinitesimal speed? (Which seems impossible, but you never know when it comes to physics.) Any help?

That's a sloppy way of saying it - perhaps it led to a misunderstanding.
Light is always traveling at light speed as measured with (and relative to) any standard inertial reference system. I would not call that "anything". No reference system can co-move with a photon in vacuum.

As a matter of fact, the "closing" speed of two light rays relative to each other with respect to any such system can be up to 2c. [1, 2]

The details have already been explained by ApplePion.

[1] section 3 of http://www.fourmilab.ch/etexts/einstein/specrel/www/
[2] http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/FTL.html#2

Cheers,
Harald