A light wave and a sound wave travelling together

In summary: I think it's fair to say that, if you break Lorentz invariance by assuming that light travels at a speed that is not invariant (i.e., by introducing a medium), then you are left with a theory that is pretty much the same as special relativity except that you need to use a different velocity addition formula for the speed of light in that medium. This is the essence of the discussion so far.In summary, the participants in the conversation discuss the effects of a hypothetical medium that could slow down light and how it would affect the speed of light and sound as well as the principles of special relativity. They also mention past experiments that have tested these concepts. Overall, the conversation highlights the importance of the speed of
  • #1
freshnfree
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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?
 
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  • #2
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.
 
  • #3
freshnfree said:
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.
 
  • #4
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.
 
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  • #5
freshnfree said:
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".
 
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  • #6
Nugatory said:
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
 
  • #7
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.
 
  • #8
William Nelso said:
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.
 

1. What is the difference between a light wave and a sound wave?

A light wave is an electromagnetic wave that can travel through a vacuum or transparent mediums, while a sound wave is a mechanical wave that needs a medium, such as air or water, to travel through.

2. Can light and sound waves travel together?

Yes, light and sound waves can travel together, but they have different speeds and properties. Light waves travel much faster than sound waves and can travel through a vacuum, while sound waves require a medium to travel through.

3. How do light and sound waves interact with each other?

Light and sound waves can interact with each other in various ways. For example, light can cause sound waves to vibrate and produce sound, and sound waves can cause light to bend or scatter.

4. Can light and sound waves cancel each other out?

Yes, light and sound waves can cancel each other out under certain conditions. This phenomenon is called destructive interference, where the waves are out of phase and their amplitudes cancel each other out.

5. What are some practical applications of light and sound waves traveling together?

One practical application is in optical communication, where light waves are used to transmit information, while sound waves are used to modulate and amplify the signal. Another application is in medical imaging, where light and sound waves are used together to create images of the body's internal structures.

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