special relativity - Why does speed of light have to be constant?

My question is not about why speed of light has a particular constant value which has been sufficiently addressed in other questions on SE already. I want to know whether the fact that speed of light has to be constant is a consequence of other fundamental laws of Universe, or is it just a fundamental law itself.

My motivation for asking this question is thinking about Special Theory of Relativity. One way of understanding why time dilation and length contraction happen is to look at it from the perspective of constancy of speed of light. Alice who is on the moving source of light and Bob, a fixed observer see the speed of light as constant. In order for Alice to see the speed of light as a constant value, time slows down and length expands (in forward direction) thus keeping the speed constant.

In the course I'm doing, the Professor tells that this constancy of speed of light could be more generally referred to as, "Principle of wave constancy". That is, the speed of any wave is a property of the medium (and thus it remains constant). So, the speed of a wave in water, for example, remains constant even if the source of the waves (say a paddle keeps moving). Frequency and wavelength may change but the speed remains constant. In a similar fashion, light is an electromagnetic wave and thus its speed is constant. And the constant speed is defined by the medium (which happens to be vaccum i.e., no medium for light).

My questions are twofold now -

1. Is the above reasoning correct to explain why speed of light is constant? (i.e., thinking of it as constancy of any wave in general)


2. Theoretically, could there be other waves that could travel through vaccum at a different speed? If yes, time dilation and length contraction will have to be different.

I'd appreciate it if the answer is kept non-technical (essential math is okay). More importantly, I request you to try and explain without using General Theory of Relativity. Because I'm thinking how the scientific understanding by 1905 had already knew that speed of light has to be constant.

Answer

Is the above reasoning correct to explain why speed of light is constant? (i.e., thinking of it as constancy of any wave in general)

I would say no, although I'm sure you could argue for it if you defined you terms carefully. I just don't think it's good to put light waves and other waves on the same footing. First, light does not need a medium to travel through. Second, according to SR, light behaves much different than waves such as sound in air. I will explain.

Let's say I'm moving near but less than the speed of sound in air relative to the air itself. I emit a sound wave. Since the speed of sound is constant relative to the medium, I will practically be riding right next to this sound wave. In my own frame, I will observe the speed of my sound wave to be very slow, since I am moving just a little less faster than it.

Now let's say I take off in my spaceship near the speed of light. Then I turn on my ship's headlights. According to my own reference frame, I won't be practically riding along with the light I just emitted. I will see it move away from me at the speed of light relative to me.

And this is where SR breaks away from the behavior of sound waves. Sound waves move relative to the air they move through. Their speed is defined relative to the medium. You could argue that the medium serves as an absolute frame. But light does not have this property. There is no absolute frame we can use.

I want to know whether the fact that speed of light has to be constant is a consequence of other fundamental laws of Universe, or is it just a fundamental law itself.

This is held to be a postulate of SR, but whether or not it is a fundamental law is somewhat subjective, and the answer could change based on what we end up discovering about the universe in the future. According to SR it is a fundamental property of the universe. But maybe we will discover more that explains why this happens. Then that explanation will be the fundamental explanation of the universe.

I will note that your title question isn't answerable with physics. Nothing has to be any way. Why does mass have to warp space-time? Why does the universe have to have more than two fundamental forces? There isn't anything saying it has to be this way. But it is.

Theoretically, could there be other waves that could travel through vaccum at a different speed?

I believe the answer here is no, but I have to admit I can't think of a good reason. Even if there was, I'm not sure it would ruin SR. I believe it would just mean that the particle associated with this wave would need to have mass, but then I'm not sure it could propagate without a medium. I'm not sure about all of this though.