Can the speed of light be considered an absolute?

[neopolitan]

A simple question, but maybe not so simple to answer.

If the speed of light is relative, to what it is it relative? If it is absolute, against what is it absolute?

It occurs to me that the speed of light could be considered to be absolute, in and of itself, and that every other speed (or rather velocity) can be considered relative to:
1. the rest frame against which the velocity is measured, and
2. the "absolute" speed of light (in the direction of the velocity being considered).

The velocity of another inertial frame, when compared to our inertial frame, could be seen to "compress" the range of velocities from 0 -> c, relative to and in terms of the other inertial frame, into the range v (inertial frame) -> c, relative to and in terms of our inertial frame.

Mathematically it works, does it have any physical validity?

 

[HallsofIvy]

"If the speed of light is relative, to what it is it relative? If it is absolute, against what is it absolute?"

To some observer, of course, the same way any speed is relative to some observer.
It happens, according to experimental evidence, that all observers arrive at the same value for light. If you want to call that "absolute", fine with me. For me to understand what you mean by that, you will have tell us "against what is it absolute?" (or, more precisely, what you mean by "absolute").

 

[neopolitan]

HallsofIvy,

I am not sure that a simple question deserves such a reply but I agree that the term "absolute" is possibly misleading.

I often see the speed of light being referred to as the "ultimate speed limit" or some such. It's clear that when you talk about a mass that you can't reach the speed of light (because of the escalating energy requirements) but when considering a photon "fired" within my inertial frame which is in motion relative to your inertial frame, both you and I will "see" that photon travel at the speed of light, c. Similarly if you "fire" a photon in your inertial frame, we will still both "see" that photon travel at the speed of light.

Making the assumption that the photons are fired parallel to the relative motion, we will see the photons at different frequencies - shifted by an amount related to the magnitude of the difference in velocity between our inertial frames. The fact remains, however, that no matter what inertial frame either of us may have, the photons "fired" by either of us or by anyone or anything else will travel at c, relative to any inertial frame.

So, rephrasing a little, while we can't point to any "absolute rest" is it at all valid to point to an "absolute maximum speed", or "ultimate speed limit"?

neopolitan

By the way, when you say " To some observer, of course, the same way any speed is relative to some observer" surely you realize this is disingenuous. The speed of light is very special, in that it is a speed which has the same value to any observer in any inertial frame. Compare with "the speed of a bullet" or even "the speed of sound" - if I fire a bullet on a train in motion, the speed of bullet relative to me is not the same as the speed of the bullet according to you at the station. The doppler effect of the sound of the gun's report heard on the station is due to an actual speed difference, this is not the same effect as with frequency shift associated with firing a photon under the same circumstances.

 

[robphy]

When one says that "the simultaneity of two given events is absolute" in Galilean relativity, it means that all inertial observers agree that those events are simultaneous. Mathematically, this can be expressed by saying that the eigenvectors of the Galilean boost transformations are spatial vectors (the t=constant 4-vectors). That is to say, such a transformation maps a t=constant displacement vector into a proportional (in fact, the same [although the base point may have shifted]) t=constant displacement vector. [Note that the corresponding eigenvalue is equal to 1. So, one can also say that "spatial length [between two simultaneous events] is absolute".]

The eigenvectors of the Lorentz boost transformations are a pair of light-like (a.k.a. null) vectors. Specifically, such a transformation maps the forward light-ray's lightlike 4-vector into a proportional lightlike 4-vector, and similarly for the backward ray. So, by analogy, one can say that "the velocity of light [in the forward and backward directions] is absolute" in Special Relativity. [FYI: The two eigenvalues are the Doppler factors. So, their frequencies and energies are not absolute.] Of course, the Lorentz Transformations preserve the square-norms of all 4-vectors... so, in particular, all lightlike 4-vectors are mapped to lightlike 4-vectors. So, one can say that "the speed of light is absolute" in Special Relativity.

In both the Galilean transformations and the Lorentz transformations, there are no timelike eigenvectors. This means that there is no sense of "absolute rest", as to be expected in a "theory of relativity".

My $0.02

 

[neopolitan]

Section 16-3 of Volume 1 of "The Feynman Lectures on Physics", Transformation of Velocities applies. The whole chapter is available on-line: http://mafihe.hu/~bnc/feynman/Volume_1/Feynman_Lectures_on_Physics_Volume_1_Chapter_16.pdf

While the validity of using the term "absolute" may be suspect, but it does seem that to be completely accurate all secondary velocities* must be stated in terms of the velocity of the inertial frame against which the secondary velocity is referenced - and the speed of light. Naturally, when the inertial frame being considered has a negligible velocity in comparison to the speed of light, or the secondary velocity is negligible in comparison to the speed of light, then you can pretty much ignore the effect.

Thanks for people's input.

neopolitan

* By secondary velocity I mean the velocity of something within an inertial frame different to your own, which has its own velocity relative your "rest" frame.