General comment: I think that the questions and comments by grav-universe are well posed and should be encouraged. Maybe they can be improved, refined, but at no rate should they be treated dismissively.
In this line, sorry, DH, let me fight your dismissals.
On the one hand, you admit that your approach is not based on any physical reason, on any physical hypothesis about the “whys”:
D H said:
Special relativity and general relativity are kinematic theories: They explain what happens, but not how/why it happen. They describe mathematically what is to be expected but do not say how those interactions come to be. Talking about the "fabric of space-time" is in a sense attributing a "how" without any underlying mechanism.
As I expressly mentioned, I think that such approach is perfectly legitimate. Working on the basis of postulates, for which the reason is not specified, is a common and acceptable method. Afterwards observation confirms or not and that is it. “Whatever works”, like the film says. I never said that is ridiculous.
However, on the other hand, you want to live in the best of the worlds. You want to dismiss grav-universe because he looks for reasons, but when you discuss with me you want to asseverate that you do have some physical reasons for your postulates. I do not know why but you do think that the ether is a ridiculous candidate for that purpose, don’t you? And then you find a better candidate:
D H said:
The assumption that the speed of light is the same to all inertial observers is clearly motivated by Maxwell's equations. That the speed of light is the same to all observers is right there in Maxwell's equations.
Maxwell's equations differ markedly from the mathematical description of all other wave phenomena in one key aspect. The speed at which other waves propagate depends on the speed of the observer with respect to the transmission medium. That is not the case in Maxwell's equations. The speed at which electromagnetic propagate is c, period. The speed of the observer does not appear in those equations.
You are mistaken. As you yourself noted, Maxwell believed in an ether. And he believed that the speed of light of his equations was c only in the ether frame. A different thing is that Einstein realized that, if c were to vary depending on the reference frame, that might be a threat to the principle of relativity. Why so is a subtle issue whose discussion we can skip for the time being. (After all, the speed of sound is different in all frames moving relative to the air and nobody thinks that such fact ruins the principle of relativity…) Anyhow, he rightfully found that contradiction. And that is why he postulated that c is the same for all observers. By doing so he did not simply repeat Maxwell’s laws. He added a new postulate to them, one that reconciles them with relativity. I do not think this is controversial.
Conclusion:
- Yes, today's mainstream science does not care for the why of SR, it just provides a mathematical description.
- The so called LET is exactly the same as that plus an attempt at providing a why (by reference to the ether).
- This ether model, as you yourself accept, has a didactic value = it helps to better visualise the consequence of the formulas.
- Does it have a predictive value? In my opinion, it might have one in cases where absurd consequences fit within the math. For me an example of this is time travel: even if the formulas admitted it, I think it is absurd and I rely for this purpose on the conceptual foundation that the ether model provides. But that is another and a long story... The point is that the ether model does not only help to understand the math, it also puts boundaries to its meaning.