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

[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