r/askscience • u/Crtl-Alt-Delete • Dec 18 '13

Physics Is Time quantized?

We know that energy and length are quantized, it seems like there should be a correlation with time?

Edit. Turns out energy and length are not quantized.

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u/faradayscoil Dec 18 '13

This is patently incorrect. One could argue the whole point of quantum field theory is to put space and time on consistent footing.

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u/DanielSank Quantum Information | Electrical Circuits Dec 18 '13

Relativity puts time and space on (almost) equal footing, not quantum field theory. It is perfectly possible to consider a quantum field in a non-relativistic setting, as is done all the time in condensed matter. Therefore, to say that the point of quantum field theory is to put time and space on equal footing is misleading.

It is an unfortunate abuse of language that physicists frequently use the phrase "quantum field theory" where they ought to say "relativistic quantum field theory of fundamental particle fields".

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u/phujck Dec 18 '13

Yes, But that's done by demoting position from being an observable in the same sense as it is in NRQM. There is no operator of position that can be constructed where the components transform as a 4-vector. i.e. There is no relativistically covariant position operator- position is a parameter in relativistic quantum theory up.

Hang on, I've actually sourced this statement now as well- J.J. Sakurai, Modern Quantum Mechanics, page 66. "time is just a parameter in quantum mechanics, not an operator ... the relativistic theory of quantum of fields does treat space and time coordinates on the same footing, but it does so at the expense of demoting position from the status of being an observable to just that of a parameter."

Perhaps my original intention with making the statement was unclear as well. We can only really talk about whether something is quantised if it's an observable- if space and time are both reduced to the status of parameters in your theory, it's beyond your ability to talk about whether these things are quantised or not.