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 travel alongside a beam of light, it would have the same speed regardless of how fast you are travelling relative the 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.