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This is taken from Rindler's Special Relativity:

Any effect whose speed in vacuum is always the same could have used to derive the Lorentz Transformation, as light was used in our derivation. Only one transformation can be valid, so it follows that all such effects (weak gravitational waves, ESP?) must propagate at the speed of light.

I understand that the speed $c$ could be used as the speed of a generic effect which always propagates at that same speed in vacuum. But, I don't understand why only one transformation is valid; can someone explain this to me?

Kyle Kanos
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nightmarish
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1 Answers1

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When you have a transformation from one frame to another, this tells you how measurements with meter sticks and stopwatches in one frame relate to measurements with meter sticks and stopwatches in another frame.

If you had one transformation based on lightspeed, you'd get a relationship between measurements with meter sticks and stopwatches in one frame relative to measurements with meter sticks and stopwatches in another frame.

If you had a different transformation based on gravityspeed, you'd get a different relationship between measurements with meter sticks and stopwatches in one frame relative to measurements with meter sticks and stopwatches in another frame.

But if two frames measure the same situation, there is a fact of the matter about their relationship. So there can['t be two different transformations.

Let's be really clear about these relationships. You can make measurements in one frame (with your meterstick and stopwatch), and then using the transformation rules you can predict what a different observer (frame) would measure with their metersticks and their stopwatches. Then you compare with what they actually measured and see that they measured what you predicted.

They can also predict what you measured based on using what they measured and the reverse transformation. So these are real predictions about one frame based on another frame. The predictions are actually confirmed, so there can't be two different transformations.

Timaeus
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