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Is there a smallest unit of time, like there is a smallest unit of matter?
J.T Foster, Nanton, Alberta Canada
We don't really know how time behaves on very small scales. At scales under about 10^-44 sec, the combined effects of gravity and quantum mechanics aren't really describable by the known laws of physics. There are attempts to figure this out (string theory) but these are still speculative. We do not yet know how to make an experiment to test the predictions of string theory.
It is not clear that there is a smallest unit of matter, or that if there is one, we'd have a way of detecting it. Certainly the numbers of each kind of particle are quantized, but we do not know about all of the particles that there are. Some can have very small masses (like the neutrinos), and others are most likely massless, such as the photon. Experiments have not found any evidence for photon mass and have set very strict upper bounds on what it could be, and our current favorite theories explain why the photon is massless (of course these'd have to be modified if we ever measured a photon mass). You can make a collection of photons with as little energy as you like.
There is a mass (around 10^-4 grams) called the "Planck mass" associated with the time scale on which we don't know the laws. Roughly speaking, it's the mass of a black hole the size of a Planck time times the speed of light.
Mike W. (and Tom J.)
(published on 10/22/2007)
Follow-up on this answer.