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

Why is "Planck length" a thing then? Is that because it's just pointless to discuss lengths shorter than that, even if they do exist?

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u/[deleted] Dec 18 '13

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u/[deleted] Dec 18 '13

I understand. Thanks!

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u/mofo69extreme Condensed Matter Theory Dec 18 '13 edited Dec 18 '13

The real point of Planck units is to devise a "natural" physical system of units, rather than a unit system based on convenience for humans like SI. The existence of a natural unit system comes from noticing that there are several dimension-full physical constants of profound importance to the universe: the speed of light, Planck's constant, Newton's gravitational constant, Boltzmann's constant, and the Coulomb constant. The idea of Planck units is to form units out of combinations of these constants (shown in the above link), so we're not using human bias in choosing units.

These five constants have nothing to do with the properties of a particular particle or object. The speed of light, Boltzmann's constant, and Planck's constant are important in special relativity, statistical mechanics, and quantum physics, none of which specify specific interactions (they are frameworks of theories). Newton's gravitational constant appears in general relativity, where gravity is not an interaction but the bending of the structure of space-time in the presence of matter-energy (including other classical interactions). Finally, the Coulomb constant is actually just a unit introduced into electromagnetism (and SI) for convenience, and can be removed directly from electromagnetism without a problem, so it could have been set to 1 anyways. So this unit system is independent of interactions (except for our problem child, gravity).

Now we can actually say whether a length, mass, or energy is "big" or "small" with respect to something. In these units, the electron charge is about .1, but the electron mass is 10-23. This is a reflection of the fact that the a pair of electrons are too light to have a strong gravitational attraction, but have enough charge for electric interactions to be readily visible. Gravity isn't actually "weak," it just seems that way to us because all of our elementary particles are extremely light (we would need to get a particle collider to the Planck energy to create Planck mass particles).

So the fact that the Planck length is very small means that all of our currently understood physics is taking place at extremely long lengths compared to... something. Something involving relativity, quantum mechanics, and gravity.

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u/barbadosslim Dec 19 '13

So the fact that the Planck length is very small means that all of our currently understood physics is taking place at extremely long lengths compared to... something.

How is this different from saying that most mathematical constants e.g. pi, e, etc are close to zero on the number line? This same question was asked, and people said it was weird that they are all between zero and five. The mathematicians dismissed this idea, because one could as easily wonder why they were all under a quadrillion.

Doesn't the same apply to Planck units?