A light wave and a sound wave travelling together

[freshnfree]

If we could imagine a medium that could slow down light quite significantly, if a sound wave and a light wave were both passing through this medium, would the sound wave see the light wave passing by at the speed that light passes through that medium or would it see it passing by at the speed for that medium minus the speed of the sound wave for that medium?

 

[Drakkith]

Considering that outer space isn't a perfect vacuum, and so the index of refraction isn't exactly 1, it seems to me that you could replace the sound wave with an observer moving at high velocity through the medium and make this more like a standard SR thought experiment.

 

[Dale]

If we could imagine a medium that could slow down light quite significantly, if a sound wave and a light wave were both passing through this medium, would the sound wave see the light wave passing by at the speed that light passes through that medium or would it see it passing by at the speed for that medium minus the speed of the sound wave for that medium?

The speed of light in a medium is not invariant. In a medium it is dragged around by the medium just like sound, this is called Fresnel drag. So if the speed of sound in a medium were equal to the speed of light in that same medium (I suspect that is not true for any medium) then they would go at the same speed.

 

[GeorgeDishman]

Water has a refractive index of 1.33 so slows light to ¾c. Fizeau's experiments with light in flowing water are one of the early tests that confirmed SR. Slowing to a lower speed such as that of sound would not introduce any new effect.

 

[Nugatory]

If we could imagine a medium that could slow down light quite significantly, if a sound wave and a light wave were both passing through this medium, would the sound wave see the light wave passing by at the speed that light passes through that medium or would it see it passing by at the speed for that medium minus the speed of the sound wave for that medium?

Neither. It would be $(u-v)/(1-uv)$ where $u$ and $v$ are the speeds of light and sound in the medium (and I'm measuring distances in light-seconds and time in seconds so that $c=1$ to keep factors of $c^2$ from cluttering up the equation). This is just the formula for relativistic velocity addition and it is consistent with Fizeau's 1850 experiment mentioned by @GeorgeDishman above. If $u$ and $v$ are both small compared with $c$ (not just "slowed significantly") then the formula reduces to $u-v$, which is the speed of light for that medium minus the speed of the sound wave for that medium.

A key point is that it is the speed $c$ that is special, not whatever speed light happens to be moving at. In fact, it's a historical accident that we call the special speed $c$ "the speed of light" instead of something else. We had measured the speed of light centuries before we had any idea that the universe had a special speed, so when we discovered that there was a special speed and that it was equal to the measured speed of light in a vacuum which we already knew, it was natural to call it "the speed of light".

 

[Dale]

In fact, it's a historical accident that we call the special speed c "the speed of light" instead of something else.

Yes, it would be nice if we could shift towards calling it the "invariant speed" but the historical usage is quite strong.

@freshnfree you may want to look at this page, which gives the best discussion of the speed of light and the speed of sound.

http://mathpages.com/rr/s2-04/2-04.htm

 

[William Nelso]

It's not really a well-defined question since the medium breaks lorentz invariance so that there is a-priori no simple way to compute what observers in different states of motion will see. The observers, and all of their measuring apparatus, are moving through the medium and they will be affected by the medium in ways highly dependent on both the type of apparatus and the nature of the medium. It is only in vacuum that any simple connection exists between observations made in different states of motion, as described by special relativity.

 

[Nugatory]

It's not really a well-defined question since the medium breaks lorentz invariance so that there is a-priori no simple way to compute what observers in different states of motion will see. The observers, and all of their measuring apparatus, are moving through the medium and they will be affected by the medium in ways highly dependent on both the type of apparatus and the nature of the medium. It is only in vacuum that any simple connection exists between observations made in different states of motion, as described by special relativity.

This is true, and in that sense the answers that I and other have been providing in this thread are based on some idealizing assumptions. However, it turns out these assumptions are good enough for many interesting experiments (Fizeau's, for example) and violate no laws of physics so give us an OK thought experiment.

The breaking of Lorentz invariance is also indisputable - but the whole point of OP's thought experiment is to understand the consequences of having broken Lorentz invariance.