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Jonathon

This is a question best answered by a real expert such as Prof S. Hawkings or Prof. Kip Thorne, but I will do my best.

Time is thought to be continuous, not discrete or quantised. So there is no smallest, indivisible, unit of Time. Quantum Theory deals with particles and their properties and the consequences of Wave-Particle Duality, it does not tackle the question of what time is. That is more the realm of Grand Unified Theories or Quantum Gravity. Very little is understood of these yet. Why do we think Time is continuous though?

If Time where quantised, that is events moved in small discrete steps, then all particles would have to be synchronised across the entire Universe. If it was not then how would two events be aware of each other. To illustrate my point lets assume that there is a smallest unit of time that can occur, delta-t. Two events occur and their quantum clocks are out of phase by a time t, less than delta-t. The information from the two events spreads out at the speed of light, called a light-cone. The two light cones eventually interact but they will not be aware of each other. One particle will always be `in between' steps of time when the other signals it. So, parts fo the Universe will not be aware of other parts of the Universe. This breaks causality and is not allowed by General Relativity.

There is though a smallest unit of time below which we can not know
what happens. This is called the Planck Time and is equal to about 10^{
-34} seconds. It is a consequence of the Heisenberg Uncertainty principle
that says; the uncertainty in energy (of a particle) times the uncertainty
in time is greater than or equal to plancks constant divided by (four times pi).
This shows that if we measure an event that lasts for the planck time or less,
we know nothing about its energy and hence its state. This is not to say that
time is quantised or that time has no meaning below this limit, just that
we can not measure it.

If you are unaware of Quantum Mechanics (QM) or the Heisenberg Uncertainty Principle, there are many links on the Web about QM and many, many text books written about it. The only link I found specifically showing the derivation of Heisenbergs principle is to be found here.

Try the links in the MadSci Library for more information on Physics.

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