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Disregarding String Theory, which says that electrons and quarks are 1-dimensional, why are electrons and quarks 0-dimensional?

The way I look at it is that they have mass, and if we were the same size as an up quark and looked at another up quark, it would look like a 3-dimensional object. So why do we say particles are 0-dimensional as opposed to 3-dimensional?

I hope I'm correcting in saying they are regarded as 0-dimensional, the reason I think it is because of this quote from Wikipedia:

String theory posits that the electrons and quarks within an atom are not 0-dimensional objects, but rather 1-dimensional...

ODP
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    Why do you visualize an up quark as two dimensional? Because of the drawing "up"? Visualize it as a point. In addition, if we could be that size we would not be able to localize it by sight because both it and we would be jiggling around according to the probabilistic nature of our wave functions. – anna v Apr 23 '12 at 04:40
  • @anna v, I meant 3-dimensional, I must have been thinking of the second dimension at the time of writing. I've edited – ODP Apr 23 '12 at 15:31

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I think the best answer to your question is simply "because that's all we can see when we do experiments."

That is, no matter how hard anyone tries or how much energy they toss into the processes, electrons and quarks show no signs of any appendages, surfaces, hair-like structures, bumps, volume, whatever. When you model them mathematically as points, the math works -- and when you don't, you start getting problems and mismatches.

Protons and neutrons in sharp contrast show every sign of having volume, and emphatically are no more point-like (zero dimensional) than atoms, although their volumes are hugely smaller (grain of sand compared to a large football stadium).

String theory postulates, well, stringy structure, but has no experimental evidence for it, and does not expect any direct evidence. The energy levels are too high to be accessible to any conceivable direct-detection experiment.

Terry Bollinger
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