High School Why is the constant speed of light so unique?

[PLAGUE]

TL;DR

Doppler shift shows that speed of sound is same even if the source is moving. Then why don't we consider it of the same importance as the constant speed of light?

I was studying doppler shift yesterday and found out that the speed of sound wave remains the same even if the source is moving. To compensate that, the wavelength and frequency are adjusted. I know that this is also true for light which results in red and blue shift. Then why in special relativity, this constant speed of light is given so much importance?

Or, is it entirely some different topic? My knowledge of Michelson-Morley experiment doesn't give me any clue whatsoever.

 

[A.T.]

TL;DR: Doppler shift shows that speed of sound is same even if the source is moving.

Only in the rest frame of the medium you have sound propagating at the same speed in all directions.

Light propagates at the same speed in all directions in all inertial frames.

 

[Ibix]

As A.T. says, the speed of sound is constant with respect to the medium. In air it's about $330\mathrm{ms^{-1}}$, but if you are running at $10\mathrm{ms^{-1}}$ (congratulations, that's a good 100m time) you will measure the speed of the wave as between $320\mathrm{ms^{-1}}$ and $340\mathrm{ms^{-1}}$, depending if the wave is moving in the same or opposite direction to you, or at an angle.

We initially assumed this would be the case for light when wave solutions to Maxwell's equations were found and we realised the speed of such waves was the speed of light. Michelson and Morley carried out an experiment to detect the variation in the speed of light due to the Earth moving in different directions through light's medium (named "the ether"), but found no variation. Light had the same speed no matter what direction the Earth was moving, different from the sound case I described above. That kicked off a series of attempted explanations and experiments that ruled the explanations out one by one until Einstein came up with relativity. In relativity, the speed of light is always $c$ for all inertial frames - its frequency and wavelength and direction of travel may vary depending on how you are moving, but its speed doesn't.

Odd as that sounds, it turns out that you can have one speed that is invariant like that. And the resulting theory simplifies to Newtonian physics as long as you never experiment with anything travelling anywhere near that speed - which is why it took us two centuries to notice Newton was subtly wrong. It also turns out that anything massless (such as light waves and gravitational waves) travel at that invariant speed - which is why the speed of light is important to relativity.

 

[FactChecker]

TL;DR: Doppler shift shows that speed of sound is same even if the source is moving.

It's not. The speeds of sound and light are fundamentally different.
The speed of sound relative to the moving source, measured by that source, is not the same as it is relative to a stationary object, measured by the stationary object. In fact, an airplane which exceeds the speed of sound actually goes past the sound that it has made.

Then why don't we consider it of the same importance as the constant speed of light?

The speed of light, relative to any inertially moving object, is measured the same (speed = c) by that object.

 

[Janus]

The basic idea for the SOL in a vacuum is that it is invariant. Its speed relative to you as measured by you is always the same. So in the case of Doppler shift, this results in a different equation than one for sound.
For sound, you use the form of (Vm±Vr)/(Vm±Vs), where Vm is the speed of sound in the medium, Vr the speed of the receiver with respect to the medium, and Vs, the speed of the source with respect to the medium. This will result in different answers if the source is stationary with respect to the medium, vs. when the receiver is stationary, even if the velocity difference between the two are the same.
For light, however the form is Sqrt((1+v/c)(1-v/c)), where v is the relative velocity between source and receiver, and c is the SOL. All that matters is the relative speed between the two, and not which one you consider as "moving".

 

[Herman Trivilino]

I was studying doppler shift yesterday and found out that the speed of sound wave remains the same even if the source is moving. To compensate that, the wavelength and frequency are adjusted. I know that this is also true for light which results in red and blue shift. Then why in special relativity, this constant speed of light is given so much importance?

The speed of light is not just constant, it's also invariant. Meaning that if you were to travel alongside a beam of light, it would have the same speed regardless of how fast you are travelling relative to the source.

The same is not true of a sound wave. If you are moving alongside a sound wave you will observe that its speed relative to you will vary according to how fast you are moving relative to the source.

For an extreme example, suppose you are moving at the speed of sound relative to the source. The sound wave will appear stationary to you.

You could never do such a thing with a beam of light in a vacuum because no matter how fast you move relative to the source, the light beam will move away from you at the same speed. You could therefore never catch it, and you could therefore never even move at the speed of light.

 

[Pencilvester]

you will observe that its speed relative to you will vary according to how fast you are moving relative to the source.

For an extreme example, suppose you are moving at the speed of sound relative to the source. The sound wave will appear stationary to you.

This depends on the details of a given scenario and is not true in general, no? In the case of your extreme example, I could specify that I am standing outside (with negligible winds) watching a loud jet pass me by at the speed of sound (i.e. I’m moving at the speed of sound relative to the source). With these details, the sound waves won’t appear stationary to me— they’ll appear to be moving at the speed of sound.

The generally applicable statement, as @A.T. and @Ibix mentioned, is that it’s speed relative to the medium (and direction) that determines how fast the sound waves appear.

 

[Herman Trivilino]

This depends on the details of a given scenario and is not true in general, no?

I should have described your motion as being relative to the medium rather than relative to the source.

In the case of your extreme example, I could specify that I am standing outside (with negligible winds) watching a loud jet pass me by at the speed of sound (i.e. I’m moving at the speed of sound relative to the source).

What's the source? If you're listening to the sound of the loud jet, the jet is the source. If it moves past you then you are not moving relative to the source.

The generally applicable statement, as @A.T. and @Ibix mentioned, is that it’s speed relative to the medium (and direction) that determines how fast the sound waves appear.

But the speed of the sound wave will be different for listeners moving at different speeds.

Look, here's the point I'm making. When you move relative to a sound wave you measure different speeds for that wave.

When you move relative to a light wave in a vacuum, or more precisely the source of that light wave, you will always measure the same speed for that wave.

That's the answer to your the original query about special relativity and the speed of light.

 

[PeroK]

Look, here's the point I'm making. When you move relative to a sound wave you measure different speeds for that wave.

In what way had that point not already been made (several times) by previous posters?

That's the answer to your original query about special relativity and the speed of light.

@Pencilvester is not the OP!

 

[Herman Trivilino]

In what way had that point not already been made (several times) by previous posters?

I don't know. But here is the full quote ...

Look, here's the point I'm making. When you move relative to a sound wave you measure different speeds for that wave.

When you move relative to a light wave in a vacuum, or more precisely the source of that light wave, you will always measure the same speed for that wave.

Sorry if it's repititious.

@Pencilvester is not the OP!

Okay, thanks for letting me know. I made an edit.

 

[PeterDonis]

If it moves past you then you are not moving relative to the source.

Um, what? If the jet is the source and it is moving past you, then you are moving relative to it.

 

[Herman Trivilino]

Um, what? If the jet is the source and it is moving past you, then you are moving relative to it.

Oh, yeah. What a flub. I fixed it.

 

[Pencilvester]

I should have described your motion as being relative to the medium rather than relative to the source.


What's the source? If you're listening to the sound of the loud jet, the jet is the source. If it moves past you then you are not moving relative to the source.


But the speed of the sound wave will be different for listeners moving at different speeds.

Look, here's the point I'm making. When you move relative to a sound wave you measure different speeds for that wave.

When you move relative to a light wave in a vacuum, or more precisely the source of that light wave, you will always measure the same speed for that wave.

That's the answer to your the original query about special relativity and the speed of light.

I was never disagreeing with the main point you were trying to make; I was only pointing out the minor mistake in your statement about how different people measure different speeds of sound.

I’m unclear on the purpose of your reply. Is there something I said that you thought was incorrect? Or were you just concerned that I wasn’t aware of the invariance of the speed of light and how that invariance makes it fundamentally different from the speed of sound in some medium?

 

[PeterDonis]

I’m unclear on the purpose of your reply. Is there something I said that you thought was incorrect? Or were you just concerned that I wasn’t aware of the invariance of the speed of light and how that invariance makes it fundamentally different from the speed of sound in some medium?

This subthread is getting off topic. Please don't speculate about another poster's motives. You are not the only one in this thread, and Herman Trivilino has acknowledged that you're not the OP and that the OP question is not one that you asked.

 

[A.T.]

When you move relative to a sound wave you measure different speeds for that wave.

When you move relative to a light wave in a vacuum, or more precisely the source of that light wave, you will always measure the same speed for that wave.

I find this comparison confusing:
- For sound you talk about "moving relative to the wave". (Whatever that means)
- For light you talk about "moving relative to the source". (Persumably after realizing that "moving relative to a light wave" makes no sense, as light has no valid reference frame).

Did you mean "moving relative to the source" in both cases? If yes, then the counter example by @Pencilvester in post #7 applies.


As the @PLAGUE correctly noticed:
The source motion is irrelevant for propagation speed of both: sound and light. So the dependency (or lack of it) on the source motion is not what distinguishes sound and light.

The difference between sound and light is rather:
- A sound wave (in a uniform medium) has the same propagation speed in all directions, only in the rest frame of the medium.
- A light wave (in vacuum) has the same propagation speed in all directions, in all inertial frames.

 

[cianfa72]

As the @PLAGUE correctly noticed:
The source motion is irrelevant for propagation speed of both: sound and light. So the dependency (or lack of it) on the source motion is not was distinguishes sound and light.

The difference between sound and light is rather:
- A sound wave (in a uniform medium) has the same propagation speed in all directions, only in the rest frame of the medium.
- A light wave (in vacuum) has the same propagation speed in all directions, in all inertial frames.

I believe the key point in the last bullet is (all) inertial frame. This is defined such that light propagation (coordinate) speed is isotropic w.r.t. it. In a non (standard) inertial frame this is no longer true.

 

[Herman Trivilino]

I find this comparison confusing:
- For sound you talk about "moving relative to the wave". (Whatever that means)
- For light you talk about "moving relative to the source". (Persumably after realizing that "moving relative to a light wave" makes no sense, as light has no valid reference frame).

Yup, I agree. I bungled it up. I was trying to make the statements of the speed of light to that of sound as comparable as possible, but my attempts failed. That's why I spoke of speed relative to light, which of course is nonsense.

Did you mean "moving relative to the source" in both cases? If yes, then the counter example by @Pencilvester in post #7 applies.

Yes. That's why I changed the statements. But the change didn't fix it, just introduced another error.

As the @PLAGUE correctly noticed:
The source motion is irrelevant for propagation speed of both: sound and light. So the dependency (or lack of it) on the source motion is not was distinguishes sound and light.

Very true and relevant.

The difference between sound and light is rather:
- A sound wave (in a uniform medium) has the same propagation speed in all directions, only in the rest frame of the medium.
- A light wave (in vacuum) has the same propagation speed in all directions, in all inertial frames.

Yes, that's very good. It correctly addresses the point I was trying to make that the speed of sound is constant, but but varies according to the motion of the observer, whereas the speed of light in a vacuum is both constant and invariant.

I'm under the impression that that issue was at the core of the OP's quandary.

 

[Herman Trivilino]

For sound you talk about "moving relative to the wave". (Whatever that means)

You could, for example, have a way of measuring the pressure such that you can identify the location of a high pressure region (a wave front) and then somehow measure it's speed relative to you. That is, at least in principle, possible.

 

[pervect]

You could, for example, have a way of measuring the pressure such that you can identify the location of a high pressure region (a wave front) and then somehow measure it's speed relative to you. That is, at least in principle, possible.

Measuring pressure is certainly possible. Even in Newtonian mechanics, pressure is only as simple as a single number when the pressure is the same in all directions (i.e. isotropic). I could say more about how anisotropic pressures wind up being represented, but I think that would drift off from the main point I want to make here.

The main point I want to make is that interpreting the physical pressure measurements as a wave is a matter of interpretation and the reason for being cautious. There is one special case where the interpetation is fairly solid. This is the case when the pressure follows a particular differential equation, called the wave equation, https://en.wikipedia.org/wiki/Wave_equation

$$\frac{\partial^2 P}{dt^2} = k^2 \left( \frac{\partial^2 P}{\partial x}^2 + \frac{\partial^2 P}{\partial y^2 + \frac{\partial^2 P}{\partial z}^2$$

Sound waves and light waves in the simplest cases can both be modeled by this wave equation, in the case of light waves the partial differential equations it satisfies are called Maxwell's equations. The solution of Maxwell's equations in a vacuum is that both the electric and magnetic parts of the light wave satisfy the wave equation, just as the sound waves do.

For the simple wave equation above, it's possible to interpret the pressure (or light) as moving like a wave, a wave that keeps its shape. But there are difficulties with the idea when the wave doesn't keep it's shape - the decomposition of the wave into various "moving parts" is not acatually physical, it's an interpretation.

The typical example of where problems can arise is interpreting the phase velocity, https://en.wikipedia.org/wiki/Phase_velocity. Phase velocities can notoriously exceed the speed of light - as can other non-physical entities, like the path of a laser pointer being swept across the moon from Earth.