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Jan
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comment Which physical entities equal “distance times time”?
@AlfredCentauri: In a way I can understand your frustration - on the other hand I still find it useful to think about e.g. $x'=x$ in terms of "velocity equals distance" which is also unitwise not correct (L/T != L) but gives an intuition why the solution is going to be exponential.
Jan
9
comment Which physical entities equal “distance times time”?
@AlfredCentauri: Because I am interested in the $tx(t)$ part.
Jan
9
comment Which physical entities equal “distance times time”?
@AlfredCentauri: Well, I think the answer is what Carl has already mentioned: That you have a constant (which is in these cases $1$) that has a unit so that both sides are unitwise equal again.
Jan
9
comment Which physical entities equal “distance times time”?
@AlfredCentauri: I see your point but how does the simplest ode $x'=x$ make sense then?
Jan
9
comment Which physical entities equal “distance times time”?
@AlfredCentauri: Yes, I am thinking that $t$ is e.g. time, $x(t)$ (or $y(t)$) is distance and x' (or y') is velocity. I just changed the original equation because I think it gives a better intuition to use $t$ and $x(t)$.
Jan
9
comment Which physical entities equal “distance times time”?
@JohnRennie: Yes it is :-)
Jan
9
comment Which physical entities equal “distance times time”?
@JohnRennie: I edited the question accordingly.
Jan
9
revised Which physical entities equal “distance times time”?
added 225 characters in body
Jan
9
comment Which physical entities equal “distance times time”?
@DavidZ: I have also tried to find a similar question on this site before posting but haven't found one either.
Jan
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asked Which physical entities equal “distance times time”?
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comment How is the classical twin paradox resolved?
@Joshua: Well, I think it is clear from the context that we are not talking about Newtonian mechanics here ;-) And a quick Google fight decided the matter in favour of "classical twin paradox" ;-) googlefight.com/…