Why would the time coordinate (t) be NOT invariant under translations, but invariant under Galilean transformations? I thought it should be invariant under both
Here is what I'm tying to understand:
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asked Sep 8, 2019 at 19:02
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$\begingroup$ Can you write what happens to $t$ under each of these transformations? $\endgroup$– AccidentalFourierTransformCommented Sep 9, 2019 at 1:40
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$\begingroup$ Could you help / elaborate / point me in the right direction? I wouldn't have asked my question had I known the answer to your question (I'm not saying this in a bitter tone, this is really how I feel). $\endgroup$– An Ignorant WandererCommented Sep 9, 2019 at 2:23
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$\begingroup$ The question you added at the bottom is too vague to answer without knowing exactly how your textbook defines “translations”. The word “translations” can be shorthand for “spatial translations”, “time translations”, or. “spacetime translations”. $\endgroup$– G. SmithCommented Sep 9, 2019 at 4:26
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$\begingroup$ Given the N answer, it is apparently referring to time translations or spacetime translations but not spatial translations. $\endgroup$– G. SmithCommented Sep 9, 2019 at 4:31
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$\begingroup$ @G.Smith Yes that was the problem thank you for clarifying. $\endgroup$– An Ignorant WandererCommented Sep 9, 2019 at 16:35
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1 Answer
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In your previous question, the answer that you accepted clearly and correctly stated that $t’=t$ for both spatial translations and Galilean transformations. So time is invariant under both those kinds of transformations.
If you are now asking about time translations, well, time shifts by a constant under a time translation so it is obviously not invariant under them.
