sol invictus
Philosopher
- Joined
- Oct 21, 2007
- Messages
- 8,613
Try again and actually use the Lorentz transformation, Johan. Including the off-diagonal terms. Write down the four-vector coordinates, in the ground rest frame, of the two flashes and of the "light arrives at detector" event. Transform these three coordinates into the train rest frame. Look at the result.
That is impossible - Johan is mathematically incompetent. But his mistake here is more basic, it's a mistake in logic. He thinks that because Δt=Δt', there cannot be time dilation or length contraction.
But this is obviously wrong. Δt is a length divided by a speed. If one clock measures a contracted length, and the other is running slow, they can (and do) agree.
And indeed, in either frame K or K', that's exactly what happens - one captain measures a contracted length with a normal clock, while the other measures a non-contracted length with a slow clock. Of course which is which depends on whether we describe things from K or K', but in either case all physical results are identical.
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