What paper(s) or theory(s) describe or prove that the elementary particles that we have determined today cannot be made up of smaller more fundamental particles?
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$\begingroup$ +1 Nice question, but the title is a bit uninformative. I made a suggestion (but feel free to pick your own) $\endgroup$– Tobias KienzlerCommented Mar 21, 2011 at 9:05
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$\begingroup$ Many papers proceed from an idea of particle being point-like, and what can be even smaller? ;-) $\endgroup$– Vladimir KalitvianskiCommented Mar 21, 2011 at 9:31
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5$\begingroup$ I don't think there can be such a proof, ever. The reason is that there is no (experimental) distinction between "very tiny" and point-like. That's why we still often treat atoms as non-composite when dealing with them at larger scales (or even forget there are any atoms altogether...). $\endgroup$– MarekCommented Mar 21, 2011 at 9:53
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1$\begingroup$ it may very well be that there is no limit to the true levels of substructure of elementary particles. However, what is becoming clearer, and what I believe, is that for explaining natural phenomena it is not the irreducible properties of elementary particles that matter as much as the emergent properties of aggregates of many such particles interacting in many-body systems. $\endgroup$– user346Commented Mar 27, 2011 at 6:36
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$\begingroup$ Also the question of whether there exists an irreducible description - in the reductionist sense - of matter becomes unclear in light of the mutable nature of particles as revealed by phenomena such as bosonization (fermionization) and fractionalization which are found in lower-dimensional condensed matter systems. $\endgroup$– user346Commented Mar 27, 2011 at 6:37
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3 Answers
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One of the questions under investigation in the data being gathered at LHC is the search for compositeness of quarks and leptons. They gave limits for quark compositeness from the data of 2010.
So the answer is, it is an open question under investigation, though not popular with the theorists.
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There is no such theory. We treat the elementary particles as elementary simply because we have never seen any evidence of them having a substructure.
I suppose someone might have published a paper claiming that they must be fundamental (after all, there are a lot of papers out there), but the vast majority of physicists do not take such claims seriously.
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This answer, though somewhat dated, comes with the best credentials: "The question is still open experimentally, but theory and experiment are pointing more than ever before to the possibility that we have discovered the 'ultimate constituents'." — National Research Council (U.S.), Elementary-Particle Physics Panel (1998), Elementary-Particle Physics, National Academy Press, Washington, D.C., p. 23.
But are the "ultimate constituents" pointlike entities, or are they formless?
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$\begingroup$ The question was if the present particles are fundamental or composite. It depends on your definition of formless. If they are described mathematically by some spatial probability functions, they have a mathematical form. At the moment the objective of theorists, most of them string theorists, is to define this mathematical form. $\endgroup$– anna vCommented Mar 27, 2011 at 4:55
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$\begingroup$ Isn't "formless" self-explantory? Either a fundamental particle has a form (and then this can only be the form of a geometrical point, unless extra dimensions are introduced) or it lacks a form. My point (pardon the pun) is that nothing in the formalism of contemporary physics refers to the form of an object that lacks components or internal structure. When we call a particle pointlike, what we are really saying is that it lacks internal structure. The claim that in addition to that it has a pointlike form would be, in Pauli's felicitous phrase, not even wrong. $\endgroup$– KoantumCommented Mar 27, 2011 at 7:18
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$\begingroup$ It also seems to me that your antecedent "If they are described mathematically by some spatial probability functions" is wrong. What is described by spatial probability functions is the (relative) positions of particles rather than their forms — unless you want to define the form of a composite object as the totality of its internal relative positions, in which case a fundamental particle, lacking internal relative positions, would be formless as a matter of course. $\endgroup$– KoantumCommented Mar 27, 2011 at 7:22