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I am aware of how the laws of physics are invariant with a time reversal transformation, so that (ignoring entropy) a film of billiard balls running backwards cannot be differentiated from one running forwards.

What about a film of billiard balls running in fast-forward motion? Ignoring relativistic effects, I think that there would be no way to tell the playback speed.

OK, then imagine that one of the billiards were made out of delicate, thin glass, and that in the regular play-back film the motions are slow enough that it does not break. Playing the film in fast-forward motion, the delicate ball still would not break despite being hit by very fast-moving ones. Does this mean that Newtonian physics is not invariant under fast-forwarding? Is there a way of expressing this mathematically (analogous to saying t goes to -t for time reversal)? And finally, since the glass ball does not break, is this violation of intuition an illusion having to do with entropy, like with running a film in reverse, or is there some kind of modification that needs be made to the forces of the molecular bonds under fast-forward motion to prevent the glass from shattering?

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  • $\begingroup$ You would be able to tell it was fast forwarded. Objects of a known mass would seem to exert a much greater gravitational force than predicted by Newtonian mechanisms. For instance, a dropped object on Earth would fall much faster. Knowing the mass of Earth, we could use Newtonian gravity to figure out the amount of fast-forward $\endgroup$ – Jim Jul 29 '14 at 14:17
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The laws of physics themselves will be unchanged, but in a problem such as the one you mention there will be some parameters with dimensions that determine what happens. This is in fact the same question as asking what happens if you change the unit of time you use: speeding up by a factor of 60 is the same as measuring in minutes rather than seconds. Then $g$, the local acceleration due to gravity, changes its value by a factor of $60^2=3600$ to around 3500 metres per minute squared, rather than 9.8 metres per second squared. The slowed down video looks like the same physics, but with the strength of gravity much greater.

There may be many other parameters that you will have to adjust in a similar manner: resistive properties of air, for example, or material properties of objects. Or if you are worried about relativity, the speed of light!

Note that this all applies equally well if you "zoom in" and look on shorter distance scales too, though the scalings required will be different depending on the units of your quantities.

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