In 2006 I asked my first question on a physics forum. I couldn't understand the difference between a sound wave and a light wave as it pertained to relative velocity. Of course I got nothing but nasty, snarky, condescending, general and irrelevant answers from Wiki-like sources to my question which set the tone of my attitude towards physics forums to this day. I understood a source could not force a sound or light wave any faster through it's medium, the wave's velocity was always the same relative to its medium. Any velocity of the source or a receiver would manifest itself in the altered frequency of the wave. Years later I learned this was not completely true for sound waves. Although a car approaching you with it's horn blaring couldn't force the sound to reach you any sooner, you could run towards the sound or a strong wind behind the car could make the sound cover the initial distance between you and the start of the sound wave in less time than if you didn't move or if the wind wasn't blowing. Same distance in less time meant the wave's velocity relative to you increased.
The same was true for the source's relative velocity to the sound wave. Although it couldn't push the sound wave's velocity relative it its medium any faster, the source's relative velocity to the medium would allow it to catch up with the wavefronts or a strong wind behind the car could reduce the car's relative velocity to the wavefronts. The source's velocity relative to the wave altered because its velocity relative to the medium altered while the wave's relative velocity to its medium did not. The key understanding here is there are 2 relative velocities to consider: the relative velocity of the wave to its medium and the relative velocity of the source or receiver to the wave's medium.
The permittivity and permeability characteristics of space make it an electromagnetic medium that allows for the propagation of electromagnetic waves. Sound is a mechanical wave in a material medium. Space, ideally, is a vacuum devoid of material for sound to propagate through but that doesn't mean it is not a medium for light to propagate through. Water has material but light uses the electromagnetic field of water to propagate through it at 75% the speed of light. We will be considering water and vacuum mediums for light to understand the relative velocities of sources and receivers to those mediums to address the main difference between sound and light waves wrt relative velocity.
The main question is this: If you can run towards a sound wave and increase its velocity relative to you, why does relativity say you can't run towards a light wave and increase its velocity relative to you? Just like for the sound wave, your motion towards the wave cuts down the initial distance between you and the wave which allows the wave to reach you in less time just as though you were standing still and the wave's relative velocity had increased to reach you in less time. This addition of velocities definition of relative velocity just ignores the fact not only the time has changed but so has the distance. If instead of choosing the initial distance over final time as the definition of relative velocity you chose final distance over final time, you'd get a completely different answer.
It's the same for light, your velocity towards the light allows the light to reach you sooner so the relative velocity should increase if you use the formula of initial distance over final time. But relativity has changed the rules, there is no relative velocity greater than c so your relative velocity to c can't add or subtract from c. This is enshrined in the relative velocity combination law. But at the same time this does not mean the light doesn't take longer to reach you if you're moving away from it or less time if you're moving towards it.
So how do you resolve this paradox? Well you come up with the idea that the distance between you and the light is contracted by your velocity just as your time is dilated so that the velocity of light remains the same in the spacetime warp your velocity is creating. And from there the history of science fiction begins to the delight of movie goers everywhere.
In the only course I took on relativity, Brian Greene's on worldscienceu.com, the photon is treated like a baseball instead of a wave. While a wave's velocity can't be affected by the velocity of the source that launched it, a baseball's velocity can be. So using perfect logic, a photon baseball's velocity can't be increased or decreased by a train's motion unlike it would be in a Newtonian universe. Of course this is total nonsense because light doesn't behave like a baseball but it's crucial to selling relativity. Let's look at the train example to see what I mean.
A train is whizzing into a station and as the middle of the platform aligns with the middle of the station, a light beam is sent from the middle to both ends of the train. From inside the train, the light hits both ends simultaneously but from outside the train, the back is moving toward the light so the light reaches it sooner. The front of the train is moving away from the light so the light has to cover more distance in more time to reach the front. I don't see where the train's motion creates a spacetime warp to conserve c from all perspectives when c is simply the distance covered in the time it takes to cover it. No magic here but I'll show you where the magic really is. It's not in the train's relative velocity to light directly, it's in the train's relative velocity to the medium of light.
Let's consider the train example using sound waves. As the middle of the train aligns with the middle of the platform, an air horn goes off inside the train but a firecracker goes off outside the train's middle. Since the air is motionless within the train, the air horn will hit both ends simultaneously from the train's perspective but the sound of the firecracker will hit the back end first because the back end is moving towards it while the firecracker noise will take more time to reach the front because it has to travel a greater distance in more time to reach the front. However if the same experiment had been done using an open boxcar, there would be no difference between when the airhorn or the firecracker noises reach the ends of the train because it's about the train's relative velocity to the medium, not to the sound directly.
So how is light different? If the train was a giant vacuum bottle travelling through a vacuum, there would be no difference whether the train was a vacuum bottle or open to the outside vacuum. There's no medium to move relative to. There's no vacuum wind. This is what the MMX proved. If the train let off a red light inside the train and a blue light outside the train, the outside perspective would see both the blue and red lights hit the back simultaneously before they both hit the front simultaneously later. From inside the train's perspective, both red and blue lights would hit the front and back of the train simultaneously. This could never happen in the airhorn and firecracker example because of the relative velocity of the train to the sound medium.
Let's do the intermediate example of a water filled train going through water. (This is actually the Fizeau experiment.) Light is no longer going at c through this medium but 75% c. The train's velocity will actually be a factor this time between an open box car and a sealed train version because it can have a relative velocity to the medium. However, the addition of the velocities is not straight Newtonian additive but the combined relative velocity is according to the relativistic combo law. So there's nothing magical about the nature of light at all, the magic happens when things bump up against the universe's max speed limit.
Edited by ralfcis, 22 May 2019 - 08:10 AM.