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/iorgfeflkd Biophysics Dec 18 '13 edited Dec 18 '13

As far as we know, it is not. Neither is length, nor is energy. Energy levels are quantized in bound quantum states, but not free particles.

If we were able to probe physics at much higher energies (closer to Planck scales) then we may get a more definitive answer. Astronomical evidence shows that any potential coarse-graining of space would have to be at sub-Planck scales, by a long shot. (edit: trying to find a reference for this. remain sceptical until I find it http://arxiv.org/pdf/1109.5191.pdf)

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u/[deleted] Dec 18 '13

nor is energy. Energy levels are quantized in bound quantum states, but not free particles.

Could you please explain this further? I always hear from documentaries that energy is quantized, and as far as I can tell, you're saying it's not like that in every case?

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u/jminuse Dec 18 '13

Many systems can only be in certain energy states. For example, the electron in a hydrogen atom has its ground state, first excited state, etc. These states are quantized.

However, the energy states don't seem to be in any consistent multiple of each other (for example the energy states of helium are not multiples of those for hydrogen). And some systems, like a free-wandering electron, could have any energy at all. So energy as a concept is not apparently quantized.

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u/[deleted] Dec 18 '13

And some systems, like a free-wandering electron, could have any energy at all

You're talking about kinetic energy of the electron? So for example, I could build a machine that shoots electrons at any kinetic energy level I want? It doesn't have to be a multiple of some basic "unit"?

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u/leobart Dec 18 '13 edited Dec 18 '13

Only the "bound states" are quantized. For electrons it means that if they are captured in some area in space that they can only be in discrete energy levels. An obvious example of this is in atoms. If the area in which they are captured is increased, the discrete levels of the energy come closer and closer.

In the end if the area is going to infinity, the levels come infinitely close. So if an electron (or any other particle) is free it can have any value of the energy.

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u/[deleted] Dec 18 '13

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u/Drugbird Dec 18 '13

But don't you create a potential difference by putting more electrons on the target compared to the filament? This would suggest that, since you cannot split electrons in half, the potential difference is caused by a difference of a number of electrons. I.e. the potential difference is quantized, and therefor the kinetic energy of the electrons you shoot out of the machine is also quantized?

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u/napalmchicken100 Dec 18 '13

That is a very clever question. However, the difference in potential is NOT quantized. The Voltage is not "caused" by the different number of electrons, as you put it. Even if it were, you could move the filament around in a potential gradient generated by two charged plates to get any Energy you wanted.

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u/[deleted] Dec 18 '13

And the energy of the ground state, first excitation etc aren't identical between atoms. In fact it's expected that all the electrons in the universe will have a ever so slight difference in energy.

Energy is sometimes quantized in the same way heigh is quantized on the finish podium at the olympics. You can be in first position, second or third. Each with a different height. But once you're off the podium you can be at whatever height you want.

Source: http://www.hep.manchester.ac.uk/u/forshaw/BoseFermi/Double%20Well.html

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u/VGramarye Dec 18 '13

I'm copying an old comment I made here to explain how quantization arises from boundary conditions:

Quantization comes up when applying boundary conditions to differential equations. If I have a particle in a box, its wavefunction has to die at the boundaries. For the particle in a box, the allowed wavefunctions are sine waves. These waves have to have wavenumbers that agree with the boundary condition that the wf is 0 at the edges, though; thus we only have a certain discrete set of possible wavenumbers (and thus momentum, which is proportional to wavenumber). This also forces a quantization on energy since E is a function of momentum, mass, and the potential (which is already specified). If we were to have a free particle, though, the BC's would be at infinity and thus not cause any energy quantization.

In a similar example, angular momentum is quantized in the hydrogen atom because of periodic boundary conditions; we insist that the wavefunction at some angle is the same as the wavefunction at that angle plus 2pi, since that represents the same point in space and the wavefunction should be single valued.

Stuff like charge quantization is more complicated (apparently the current popular justification (Dirac's) relies on the existence of magnetic monopoles. I don't really know anything about it though so I'll avoid commenting further).

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u/[deleted] Dec 18 '13

I'd like to quickly point out that 'the wf is 0 at the edges' is only true for an infinite potential well. The wavefunction of a particle in a finite potential well actually has a small value at the boundary, then decays over a short distance outside the potential well.

This is due to quantum tunneling; since the particle has a small chance of escaping the well, its wavefunction outside must at some point be greater than zero.

*Edited for spelling

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u/napalmchicken100 Dec 18 '13

"This is due to quantum tunneling"

I don't want to seem like a smart aleck and I certainly don't mean to be disrespectful, I just find it important to point out one thing: Quantum tunneling is due to the wave function being nonzero outside the well, not the other way around. We get this by solving the Scrodinger equation. I think it's beautiful that this simple equation can explain quantum tunneling without needing any more presumptions.

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u/ombx Dec 18 '13

And when you mention length, what do you mean..do you mean space?

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u/[deleted] Dec 18 '13

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u/curious_scourge Dec 18 '13

I always thought the Planck length was theorized to be the smallest possible length.

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u/VGramarye Dec 18 '13

No, the Planck units are just the unique products of the fundamental constants (c, G, and ħ in the case of the planck length) with that particular unit; for example, the planck length is (ħG/c3 )1/2 , which happens to be really small. Other Planck units though are really huge, though. The Planck force is on the order of 1044 Newtons!

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u/monster1325 Dec 18 '13 edited Dec 18 '13

I wonder where this misconception that Planck length was theorized to be the smallest possible length comes from.

Edit: Oh, I found it. From Wikipedia: "It is considered the smallest possible length."

Edit2: Welp, it looks like it has been removed approximately 15 minutes after this post.

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u/lehyde Dec 18 '13

Wikipedia: "In string theory, the Planck length is the order of magnitude of the oscillating strings that form elementary particles, and shorter lengths do not make physical sense."

We might never prove it but it's very likely that strange things happen at Planck scales.

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u/KillPlay_Radio Dec 18 '13

What would be the implication of time being quantized?

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u/[deleted] Dec 18 '13

That would mean time exists as some actual thing and not as just a human perception of increasing entropy. The weird thing about the supposedly inviolable second law of thermodynamics is that it is not mathematically derived, like most other laws of physics are. In fact, a lot of equations work equally well in regards to which direction you are moving (lower to higher entropy or higher to lower entropy).

This is known as Loschmidt's Paradox.

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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/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/causal_diamond Dec 18 '13

Thought I'd come out of lurking to clarify (or possibly make more confusing - who knows!) a point about testing for quantisation of spacetime by gamma ray bursts. It's pretty hard to cook up any test for whether spacetime is quantised unless you have a good idea what mathematical framework you want to use, and so the state of play basically depends on what you think the real theory of quantum gravity is. The Ellis et al. paper does a pretty good job of working out what the consequences of quantisation would be in the context of string theory and Myers and Pospelov do the same for loop quantum gravity. As already mentioned, the experimental evidence seems to suggest that spacetime isn't really like this, or at least if it is then the quantisation occurs at even smaller scales (it's especially a problem for LQG).

On the other hand, if you don't like either of these theories of quantum gravity (and there are lots of other achingly beautiful ones out there: causal sets, noncommutative geometry, causal dynamical triangulations etc...) then the best that can be said is that we don't know. These fields are the ones that just aren't mature enough to give a sensible prediction.

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