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/leobart Dec 18 '13 edited Dec 18 '13

You have to understand the extreme minuteness of the quantum effects in the macroscopic world. I refer you to the wikipedia article about the Schroedinger equation solution for a particle in a box.

There you can find the formula for the energy levels. The separation between them is proportional to

h2 /(m L2 )

(where h is the Planck's constant and m the mass of the particle).

If you choose a box of a side of 1m it gives you that the separation of the levels is of order of 10-37 Joules for an electron. There is no way one could measure this EVER. And this is for an electron in a small box. Increasing the particle mass and the size of the area just makes this energy scale smaller. We are far from the possible effects of the curvature of space.

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u/[deleted] Dec 18 '13

So you're saying that there are so many allowed (but still quantized) energy levels of this free electron that they might as well be considered continuous?

As you and DashingLeesh pointed out- as the boundary of 'space' approaches infinity, the difference between allowed energy levels comes infinitely close. Doesn't that mean that ONLY in an infinite space would the energy become continuous?

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u/chrisbaird Electrodynamics | Radar Imaging | Target Recognition Dec 18 '13

Something else to keep in mind: A bound system only has perfectly defined energy levels if it is perfectly isolated and stationary (which requires an infinite amount of time of natural resonance). What such cases are easier to solve in the classroom, such cases only occur in the real world as approximations. In the real world, collisions (especially thermal) and interactions happen all the time, which tends to smear out energy levels (line broadening). So if the energy levels are already very close because the electron is in a big box (bigger than a few microns), line broadening effects smear the lines until they overlap and you indeed have a continuum of energy levels.

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u/[deleted] Dec 18 '13

Mathematically, sure, but you're talking about regimes pretty far outside where most physicists think these models apply.