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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?

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  • $\begingroup$ If you think about wavefunctions and finite potentials then it's always "spread out". You need whatever theory comes after QFT to say more. $\endgroup$
    – user21433
    Jul 11, 2014 at 7:24
  • $\begingroup$ Due to some downvotes and my newbiness, any assistance (from anyone) in pointing out how to make this a better question (or "what's wrong with it") would be appreciated. What may be causing downvotes so I can attempt to address. As Jeff Atwoods said, "No, you may not ask “plz send me the code” questions, but if you do, we will explain to you, in a friendly and professional way, what you did wrong." :) $\endgroup$ Jul 11, 2014 at 16:21
  • $\begingroup$ I have not down voted, but the fuzziness of the question might have annoyed someone. Fuzziness as far as physics goes, i.e. it is not just size that separates quantum mechanical from classical. Also you do not say exactly what you mean by "spread out". My answer is in terms of physics as we know it now. $\endgroup$
    – anna v
    Jul 11, 2014 at 16:46

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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

hup

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.

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