What happens to "large objects" within very small time periods? What can we say about the state of "large things" within very small time periods?  While reasonable (or "useful") divisions between classical and quantum physics are usually made  in terms of size, can a similar division be made in terms of time?  If so, what scale of time would that be?
For example, suppose someone is "sitting at a desk".  During very small time periods we cannot specify exactly where all the particles of the body are, right?  Does that mean that the body (and everything else for that matter) is statistically "spread out" in small time periods?
 A: For large objects what happens is decoherence

In quantum mechanics, quantum decoherence is the loss of coherence or ordering of the phase angles between the components of a system in a quantum superposition. One consequence of this dephasing is classical or probabilistically additive behavior. Quantum decoherence gives the appearance of wave function collapse (the reduction of the physical possibilities into a single possibility as seen by an observer) and justifies the framework and intuition of classical physics as an acceptable approximation: decoherence is the mechanism by which the classical limit emerges from a quantum starting point and it determines the location of the quantum-classical boundary. Decoherence occurs when a system interacts with its environment in a thermodynamically irreversible way. This prevents different elements in the quantum superposition of the total system's wavefunction from interfering with each other. Decoherence has been a subject of active research since the 1980s.

So time, as a variable entering both classical and quantum mechanical equations is the classical time as we know it, and "nothing" happens because classical time can be as small as needed.
An other way of looking at it is that  h_bar defines the region where quantum mechanical equations should be involved, either in time or in space

In that case if dt becomes very small the energy of the system will become undefined. For classical dimensions h_bar is effectively zero and there is no constraint.
