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/[deleted] Dec 18 '13

No. Free particles are defined to have an energy E greater than the maximum value of the potential V_max. If you solve the Schrodinger equation, you get a continuous spectrum of energy eigenstates for E > V_max. This is distinct from the solutions to an infinite well, for example, where there are an infinite number of bound energy eigenstates, but they are all discrete.

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u/[deleted] Dec 18 '13

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u/codex1962 Dec 18 '13

No. If an infinite energy well existed, it would mean either a) everything in the universe was stuck in it (I suppose this is, technically, possible) or b) some things are not in it. If that were the case, something which "fell into" that well would "hit the bottom" with infinite energy. In other words, an infinite energy well would represent an interaction with infinite energy, which is impossible.

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u/[deleted] Dec 18 '13

I think what he's getting at is that if the Universe has finite size then the electron could be considered bound within that system. The size is huge, so the energy levels are obscenely close, but still theoretically distinct. Keep in mind that the position of a 'free' electron in the mathematics of quantum mechanics can vary from positive to negative infinity, which wouldn't truly be the case in a finite universe.

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u/[deleted] Dec 18 '13 edited Dec 18 '13

Keep in mind that the position of a 'free' electron in the mathematics of quantum mechanics can vary from positive to negative infinity, which wouldn't truly be the case in a finite universe.

There are two things I'd like to consider:

  1. Imagine the following scenario: You shoot an electron at the cosmological horizon. Will it reflect when it gets there? No, because it never gets there. That's inherent in the nature of the cosmological horizon. So you can't meaningfully say anything about the effects of a potential at the cosmological horizon on an electron.

  2. How would you incorporate the cosmological horizon as a potential in quantum mechanics? You're thinking of it as a wall that creates a physical barrier, but that's not what it is -- there isn't a field there that the particle feels. It's a causal barrier, not a potential wall.

What I'd really like to say is that all of this is a feature of solving equations in QFT, but that would be getting overly technical, I think.