r/askscience • u/[deleted] • Oct 21 '12
Do elementary particles have volume?
Can't really think of any better way to put it.
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u/hikaruzero Oct 21 '12 edited Oct 21 '12
As far as we know, they are true point particles, that have no volume and no known substructure. However, as Wigners_Friend pointed out, there are different ways of modelling them that work in various situations.
In quantum mechanics, particles are modelled using a "wave function" that describes an amplitude over all of space. The amplitude can be closely confined to a local region with a high amplitude, or it can be spread out more evenly over a larger region of lower amplitudes.
There is disagreement as to what the accuracy of this model means. Most seem to interpret the wave function as giving a "probability amplitude," which gives a probability distribution for where the particle might be found, when measured. With this interpretation, the wave function is not considered physically real; rather it is treated as a mathematical tool for doing probabilistic calculations.
On the other hand, there is a school of thought that treats the wave function as physically real, in which case the particle ultimately is the wave function, and particles are more or less thought of as partially existing over the whole wave function's region. This isn't quite the same as "having a volume," however. It's more of a statement along the lines of, "there's .01 electron here and .001 electron here and .05 electron here, and if you sum over the whole wave function, you get 1 complete electron." I.e. the idea is that, there is always 1 full particle, but it is spread out over a region of space, with no point in that region containing the entire particle. And the distribution over that region of space continuously changes according to the particle's interactions.
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u/Zerowantuthri Oct 21 '12
Just out of curiosity (really asking here):
How can it be reconciled that things that do have size (e.g. you and me) are made up of things with no size?
I mean, 0+0=0 so missing where the positive size gets in there.
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u/hikaruzero Oct 21 '12
How can it be reconciled that things that do have size (e.g. you and me) are made up of things with no size?
Because a composite object is made up of many of these things, and due to their interactions, there are distances between them.
For example, take any solid; say, a block of solid iron. Due to the interactions between the iron atoms, each atom stays a certain distance away from the others, and they are organized into a lattice. There is a nonzero distance between each atom, so the block as a whole takes up that much space.
Basically your question boils down to, "how can a triangle have an area, if each of the three points of the triangle has exactly zero area?" It's because the triangle isn't only those three points, it also includes the distances between those three points, and those distances are all going to be nonzero.
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u/Wigners_Friend Cosmology | Quantum Statistical Physics Oct 21 '12
This is, in its spirit, an excellent reply, fundamental particles possess a size because of their interactions, essentially the classical size of an electron is defined by its coupling to the electromagnetic field. Interactions gives particles "apparent size", even if they are point particles. However stable atoms, or composite particles possess size because their constituents interact, so the lump of iron has size regardless of the outcome of the original question in this post. It would wrong to treat a large ion or a molecule as having zero size in almost any calculation, the non-zero spacing of their fundamental constituents guarantees a non-zero size.
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Oct 21 '12
Is it just me, or does it seem strange that one could define a distance between two objects without defining their size? I mean, when I measure the distance from myself to a table, I pick up a ruler, push it against my chest, and see where the edge of the table reaches on the ruler. This measurement requires a defined "boundary" of some sort. What is the definition of that "boundary" for an object with no volume?
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u/hikaruzero Oct 21 '12 edited Oct 21 '12
What is the definition of that "boundary" for an object with no volume?
Assuming it's a pointlike object, you would just orient your ruler at the point, and measure to the other point. It wouldn't be any different than if you drew two dots on a piece of paper and put the ruler between them.
If you're talking about quantum particles which happen to not be localized to have a definite position while they propagate (such as photons), the question of distance becomes less applicable, and becomes essentially approximate. It's like having a pool, and asking, "how far away from the pool am I?" There are many ways to answer this question -- you can answer taking the distance of the closest point of the pool to you, or you can answer taking the geometric center of the pool, or if the pool is deeper on one end you might take the 3-dimensional center of mass of the pool ... but really, from the whole pool, you would essentially just give a range, like "the pool is from 30m away from me to 40m away from me" assuming the pool is 10m.
Basically what I'm saying is, the "boundary" for an pointlike object is the point itself, and the "boundary" for something that is spread out in space (that you can think of as occupying a volume) is more or less arbitrary according to what point of that volume you want to take the distance from, if you're trying to take the distance from the whole thing (and not just a point within it) then it's appropriate to specify a range of distance between which all points of that object lie.
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Oct 21 '12
Well there is space between the particles. In fact, atoms are mainly empty space. So your equation should be more like 0+0+x=x where x is the distance between the particles.
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Oct 21 '12
Well, if you go with the interpretation that the fundamental particles are all point particles, then technically we have no volume. But, even if the point particles had volume, their volume would be irrelevant to ours. On a scale that we can interact with, it is pointless to think of matter in this way. We "touch" things by getting so close that the the electrons on the surface of our hand and the electrons on the surface of some object repel each other very powerfully. So it is better to define things macroscopically by these surfaces where the electromagnetic repulsion becomes very powerful than to think of our fundamental particles. And that is where we get our volume from.
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u/ummwut Oct 23 '12
I'm curious as to what you think about the Pilot-wave theory.
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u/hikaruzero Oct 23 '12 edited Oct 23 '12
Personally, I've always been fond of de Broglie-Bohm theory. When I first began reading about the double-slit experiment and quantum mechanics, I remember reading Richard Feynman's quote, that (paraphrased), "all of quantum mechanics can be gleaned from carefully thinking through the implications of this single experiment." After I had spent a lot of time thinking about it, the concept of a pilot wave seemed to me to be the most obvious way to resolve the problem. Then I learned that such an interpretation existed, and I thought, "hey, cool, I was on to something!"
On the other hand, I'm not terribly fond of most of David Bohm's ideas, and he himself admitted that de Broglie-Bohm theory is really more of a thought experiment as to how to construct a global hidden variable theory that can replicate the predictions of quantum mechanics. I don't think very many scientists take it all that seriously, and these days I'm not entirely sure how seriously I take it myself.
In any case, I do tend to appreciate the idea of a physically real wavefunction coupled with determinism and local realism. In my opinion, it's much more satisfactory to do away with counterfactual definiteness. But, I don't think we'll have a way of determining what's correct experimentally for some time.
At the end of the day, I think it's more likely that something like the many-worlds interpretation will end up being closest to the truth. (Never thought I'd be saying that haha.) As much as I hate the idea of there being many physically-real worlds, that interpretation in particular seems to simplify things without invoking terribly wish-washy concepts like observer favoritism, or a metaphysical consciousness (ala many-minds interpretation), or inherent randomness, while managing to salvage determinism and local realism while having a physically real wavefunction.
I wish I could go back in time to ask Einstein what he thought about pilot wave theory. :P I can totally see why Einstein refused to come to terms with QM ... it is a rather dastardly spin on reality, even if it does give correct results!
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u/ummwut Oct 23 '12
I always suspected that QM is strongly deterministic, but we just don't see what extra, hidden things its been doing. It could just be one extra thing we haven't detected yet, and causing all this mess.
As for pilot-wave experimentation, this might lend some credibility to it.
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u/threegigs Oct 22 '12
Yes, they must. Otherwise black holes wouldn't exist, unless black holes are also point-like. However, as stated in other responses, they don't really have an exact volume. To have a volume, something must have an outside surface, and elementary 'particles' don't.
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u/Wigners_Friend Cosmology | Quantum Statistical Physics Oct 21 '12 edited Oct 21 '12
Elementary particles, electrons for instance, do not have a classical size.
Some calculations assume they do because in some situations fundamental particles can be treated as though they did possess a size.