Speed of Light in Free Space - Einstein's Second Principle

[abdossamad2003]

hello everyone
According to Einstein's second principle of relativity:
"The principle of the constancy of the speed of light: The speed of light in free space has the same value c in all inertial reference frames"
Does free space mean vacuum? Is this principle not valid in the air and the measured speed of light in air is different from the perspective of each observer?

 

[malawi_glenn]

Yes, in vacuum.

In air, you have to account for index of refraction

 

[DaveC426913]

"Light in air is 1.0003 times slower than light in a vacuum, which slows it all the way down from 299,792,458 meters per second to 299,702,547 meters per second. "
- Google

...and the measured speed of light in air is different from the perspective of each observer?

No. All observers (in the same atmospheric density) will agree on their measured speeds of light.

 

[Ibix]

No. All observers (in the same atmospheric density) will agree on their measured speeds of light.

No they won't, because it isn't doing $c$, not quite. Different observers will, therefore measure different speeds. This includes an observer doing approximately 99.9997c with respect to the atmosphere who will see the light wave as stationary (briefly, before turning into a cloud of plasma due to friction).

Is this principle not valid in the air and the measured speed of light in air is different from the perspective of each observer?

The principle always applies - that is, $c$ is always invariant. But light does not always travel at $c$.

 

[robphy]

It’s really not about light but about maximum signal speeds.

 

[DrGreg]

Is this principle not valid in the air and the measured speed of light in air is different from the perspective of each observer?

No. All observers (in the same atmospheric density) will agree on their measured speeds of light.

Incorrect. The speed of light in air depends on the speed of the air relative to the observer.

For light parallel to the motion of the air, the formula$$\frac{u + v}{1 + uv/c^2}$$applies, where $u$ is the speed of the air relative to the observer, $v$ is the speed of light in air relative to the air (about $c/1.0003$), and $c$ is the speed of light in vacuum.

 

[DaveC426913]

Sorry. I interpreted the OP's question to mean "all observers" are in the same rest frame of the atmosphere. (Which is a dumb interpretation, since that's a trivial scenario.) I did not adequately generalize the scenario.

Others have made a better, more generalized interpretation and provided appropriate explanations.

 

[Mister T]

hello everyone
According to Einstein's second principle of relativity:
"The principle of the constancy of the speed of light: The speed of light in free space has the same value c in all inertial reference frames"
Does free space mean vacuum? Is this principle not valid in the air and the measured speed of light in air is different from the perspective of each observer?

That was quite some time ago. Almost 120 years. As far as we know today, as was known in Einstein's time, light in a vacuum travels at speed $c$. It's the speed $c$ that's invariant.

Anything traveling at any speed less than $c$ could be traveling at different speeds for different observers.

 

[Lord Jestocost]

But light does not always travel at c ...

Light “per se” travels always at $c$.

When light travels through media like water or glass or air, it merely appears to slow down. The apparent slower speed is the result of the superposition of two radiative electric fields: (1) the incoming light, traveling at speed $c$, and (2) the light re-radiated by the atoms in the medium in the forward direction, traveling at speed $c$, too. The re-radiated light stems from the oscillating charges driven by the incoming light. The superposition of (1) and (2) shifts the phase of the resulting radiation in a way that would occur if light - so to speak - were genuinely to go slower in media.

To understand how the apparent or effective speed of light in media comes about, I recommend to read chapter 31 “The Origin of the Refractive Index” in “The Feynman Lectures on Physics, Volume I". On Bruce Sherwood’s homepage (https://brucesherwood.net/) you find an article “Refraction and the speed of light” dealing with this question, too.