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Is distance quantised?
By Neil Morrison (P1462) on Thursday, February 3, 2000 - 08:52 pm:

Hi everybody,

This is more of a quantum theory thing, but I want to know if you can say that distance is quantised. Charge is obviously quantised; any charge is equal to a whole number of electrons. Therefore energy is charged (?) because E=QV. And E=Fd

You can possibly say that force is quantised, because mass is (whole number of particles) and F=ma. So if F and E are q.ed, is d quantised?

If it is, this might have something to do with electron transitions between energy levels. They sort of zap between them.

Neil M

By Dan Goodman (Dfmg2) on Thursday, February 3, 2000 - 09:05 pm:

I don't think distance is quantised in quantum theory. The position operator of a quantum state has a continuum of eigenfunctions, so position is not quantised when observed. Unfortunately, the relations you give above don't hold in quantum theory, so arguments about them cannot be used to prove that distance is quantised. Energy is quantised, this is where the transitions between energy levels with electrons comes about. Is any of that comprehensible to you, I'm not sure what you know about quantum theory? I could go into more detail if you'd like.

By Neil Morrison (P1462) on Friday, February 4, 2000 - 09:31 pm:

Yes I knew that 'convential' (ie wrong) mechanics did not apply, but I thought there would still be a way of showing this. Charge, hence Energy and hence mass are obviously quantised, but from the Einstein mass ratio formulas (or length ratios) I thought distance might be. Perhaps it is just ratios of distances that are.

Thanks anyway

Neil

By Sean Hartnoll (Sah40) on Saturday, February 5, 2000 - 01:36 pm:

You can't conclude that one quantity is quantised just because in classical mechanics it depends on other quantities that are quantised. As Dan said, in Quantum Mechanics physical quantities are related to each other in a very different way.

The basic idea is that each quantity (i.e. momentum, position, energy...) is associated with an operator (you can think of these as infinite dimensional matrices). These operators then have eigenvalues which are the values that the quantity is allowed to take. Often the values are discrete, in which case the quantity is quantised, but some operators have continuous eigenvalues. Position and momentum can both take any value in principle (although the uncertainty principle means we can't measure both at once).

In fact, in some circumstances the energy is also not quantised. This happens in scattering, when a particle is fired at a potential, such as an electron being fired at a nucleus, and is deflected. In these circumstances the range of values the energy of the particle can take is continuous.

Finally, the concept of "force" isn't really used at all in Quantum Mechanics. All you have are potentials that are included as part of the energy.

Hope this helps,

Sean

By Anton Ilderton (Abi20) on Thursday, February 10, 2000 - 12:41 pm:

Actually, there are some emerging theories which suggest that space may well be `quantised'. Below the `Plank Length' no-one really knows what's going on because of Heisenberg's Uncertainty Principle, but discrete as opposed to continuous space may be the answer.

Anton.

By Neil Morrison (P1462) on Friday, February 11, 2000 - 07:29 pm:

But don't planks come in different lengths?

By Andrew Rogers (Adr26) on Saturday, February 12, 2000 - 12:35 am:

If so, we have another factor to take into account that could make things quite complex, as it says in the Good Book:

"Take the plank out of your own i before you try and take the spec out your neighbour's"


(I'm sorry, I just want to state that not all mathematicians have quite this bad a sense of humour ;))


Andrew R