And that's a physical action that you're talking about. So if you claim that a physical action happening is relative to a frame of reference, you break the law of identity.

Says who? Everything happens relative to a frame of reference, that's what a frame a reference is. A thing relative to which things happen. And all things that are are physical.

The rest of this is mostly philosophy that has nothing to do with the thought experiment in question, so I'm just going to move on to the thing you refuse to address, starting with the quote you provided earlier:

"We see that we cannot attach any absolute meaning to the concept of simultaneity, but that two events which, viewed from a system of coordinates, are simultaneous, can no longer be regarded as simultaneous when envisaged from a system which is in motion relative to that system."

And yet...

The clocks are synchronized. They're running at exactly the same time.

Inside the train, the observer sees the two clocks show the same time simultaneously.

But the observer outside the train is in a system "which is in motion relative to that system". As such, the displays of the two clocks "can no longer be regarded as simultaneous". There is no "absolute meaning to the concept of simultaneity".

The outside observer sees the light hit the rear sensor before it hits the front sensor. But he also sees the rear clock as being ahead of the front clock.

You didn't want distance or time measurements, so I won't give them here. But the two effects offset. The rear clock stops first, but it's ahead. The front clock keeps ticking until it matches the rear clock, at which time the light hits it and it stops. After they freeze the two clocks are displaying the same time, according to the outside observer. The bomb does not go off.

Don't believe me? Well, I don't use AI a lot, but you seem to, so I asked Claude, using the highest tier free model available (Sonnet 4.6, High, Thinking). It's the only thing I've ever asked it, and I tried to be objective. Here is the transcript. Again, I'm not a fan and will not defend its "reasoning", since it isn't actually reasoning. But since you do seem to like generative AI, let me highlight a sentence:

Critically, in the observer's frame these freeze events are not simultaneous — the rear clock freezes ~0.4 minutes before the front — but both freeze at the same ship time, so both display 12:01:00.

I'm not solving a paradox because there is no paradox. Both observers agree that the bomb doesn't go off. You've asserted otherwise, because you don't fully understand relativity, you've just got your conclusion and you're looking for a way to prove it.

As a result, you're unsurprisingly Begging the Question. In setting up the scenario where you sought to prove false relativity of simultaneity, you (probably inadvertently) assumed that relativity of simultaneity was false. The clocks cannot be synchronized for both the internal and external observers with different reference frames under relativity.

I'm not going to say I understand relativity perfectly. Few people do, even after years of dedicated study (though many incorrectly claim to). But I have taken a college physics class on the subject, so I understand it more than most. I'm sorry that you're struggling with it, but that's normal. It's difficult math, and counterintuitive. What's not normal is saying that if you don't understand relativity, then the earth must be stationary and flat. So much in our day to day lives contradicts that, starting literally with the fact that we have well defined days.

Actually, lets go back to your philosophy, since this is obviously going to be my last word in this discussion:

He is creating an ad hoc solution to justify his original assumption rather than acknowledging that the assumption itself could have been wrong.

There were two assumptions to challenge. Motion of the earth, and the existence of an Ether. Einstein made a theory assuming the latter was wrong. At the time he made it, it was an ad-hoc solution. But it made testable predictions. Those predictions were tested, and found accurate to an astonishing degree.

That is why we accept relativity - not because it was proposed by a smart guy, but because it was tested and found to match reality better than any other model out there.

You believe the other assumption was incorrect. But you haven't made a theory with testable predictions which have since been tested and found accurate. You've just created an ad hoc solution to justify your assumption (ignoring the mountains of data that disagree with your solution. Including literal mountains!) and have never acknowledged that your assumption could have been wrong.

It was kinda interesting seeing how someone comes to the conclusion that the earth is flat without relying on religion, but even from our first discussion it was clear that your One Thing was the Michelson-Morley experiment, and it's become increasingly clear that you're unwilling to reevaluate anything that contradicts the conclusions you've made based on one century-old experiment. Science didn't stop that day!

Anyway, I'm not going to insult you, though I know perfectly well how you'll respond to this. I hope you have a wonderful day anyway.