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Atoms were once thought to be indivisible (i.e. have no substructure) until it was discovered that they are made of protons and neutrons. Protons and neutrons in turn are made of quarks, and that's where current knowledge ends.

I had always assumed that it must only be a matter of time until the particles that quarks and other elementary particles are made of are found, but recently I ran into a physicist at a party who to my great surprise told me that scientists aren't looking very hard for such particles because there is a theoretical justification to strongly believe that yes, this time we really have reached the bottom of the ladder and the reason we have not discovered any constituents of elementary particles is that they have none.

Unfortunately, our conversation was interrupted at this point and I didn't see the guy again afterward. Needless to say, I'm now burning with curiosity for the "theoretical justification" that will make me believe science indeed has closed that chapter. Can anyone here enlighten me?

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    $\begingroup$ Because it is really awkward to call them "elementary-as-far-as-we-know-and-we've-looked-really-hard particles" which is what the word actually means when used by physicists. $\endgroup$ Sep 27 '14 at 16:02
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    $\begingroup$ In science we don't "believe" anything. Before we decide to change our mind about something, we need evidence, though. There is, at the current time, no evidence that elementary particles like the photon or the electron are not elementary. The very day we will generate that evidence experimentally, we will start correcting the textbooks. I have no idea what your physicist friend may have meant by "theoretical justification". There is no such thing in science and I suspect that you may have misunderstood what he was trying to say. Parties are not the place to explain high energy physics. $\endgroup$
    – CuriousOne
    Sep 27 '14 at 16:14
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    $\begingroup$ That physicists are not looking hard for non-trivial properties of elementary particles that may be related to internal structure is total nonsense, by the way. See e.g. adsabs.harvard.edu/abs/2011Natur.473..493H about new limits on the electric dipole moment of the electron. $\endgroup$
    – CuriousOne
    Sep 27 '14 at 16:28
  • $\begingroup$ Related: physics.stackexchange.com/q/39590/2451 , physics.stackexchange.com/q/41676/2451 and links therein. $\endgroup$
    – Qmechanic
    Sep 27 '14 at 16:31
  • $\begingroup$ @CuriousOne Note that an electric dipole moment, like a magnetic dipole moment, may be an intrinsic property of a particle without any internal structure; the small-or-missing EDMs of particles with lots of nonzero $CP$-even quantum numbers is part of the evidence that $CP$ is mostly a good symmetry in the standard model. $\endgroup$
    – rob
    Sep 27 '14 at 16:39
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At the moment the grand majority of data in particle physics is modeled extremely well by the standard model which also has been able to predict new phenomena. The most recent success is the discovery of the Higgs meson at the LHC at CERN. The particles in the table are called elementary, because they are enough to explain the complexity we observe in matter and its behavior.

standard model particles

The Standard Model of elementary particles, with the three generations of matter, gauge bosons in the fourth column, and the Higgs boson in the fifth.

Any new theory of particle physics will have to show that it can embed the standard model in its structure. From the current theories, whose direction goes towards a unifying model of all four forces, i.e. including quantization of gravity, the dominant proposal is a string theory based model. In string theory, all the particles in the table above are no longer fundamental to the theory, but are excitations of a string. What becomes elementary is a string, and interactions happen between strings etc. etc.

It is a different way of formulating what "elementary" means, and what a level of "elementariness" ( not really levels of an onion or a matriuska doll series) means, but it stops the particles in the table above of being fundamental.

At the moment there is no experimental proof that string theory is the correct theory to use in modelling a theory of everything, other than that it can accomodate the standard model.

There exist at times proposals for theories in the series of levels you are envisaging, for example the preon theory, but no experimental evidence has been found to confirm it. There exist experiments looking for compositeness of quarks and leptons and giving limits, for example this one for the top quark compositeness and this one from the CMS experiment at LHC :

Within the context of a quark and lepton compositeness model with a left-left isoscalar contact interaction, 95\% CL lower limits are set on Λ, the energy scale parameter for the contact interaction. .

In conclusion, physics is not about beliefs, but about observations and mathematical models that fit these observations and predict new ones to test the model. At the moment there is no reason to change the level of "elementariness" as far as the data is concerned and experimentalists are open to the possibility .

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    $\begingroup$ There is a theory that uses only two elementary particles (less there can´t be) and that´s the rishon theory of Haïm Harari. Rishons have an electric charge of 1/3 (the T-rishon) or 0 (the V-rishon), and by combining them you can construct all the known particles. It could also explain why a chargeless Z-particle can decay in three photons: it consists of three T-rishons and three anti T-rishons. In this model the weak force is a residue force. And for example, an up quark is a TTV combination. You can find out for yourself how the other quarks and leptons are made up. $\endgroup$ May 6 '16 at 4:51
  • $\begingroup$ Maybe at the moment there is no evidence for composite quarks and leptons, but that can be because the energies aren´t reached yet where the compositeness shows up. In any case, the rishon theory looks much more economic and elegant. $\endgroup$ May 6 '16 at 4:56
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    $\begingroup$ @descheleschilder as one can see here people are still trying to define the necessary conditions so that a rishon based model can explain the data ( about page 13), uwaterloo.ca/phys13news/sites/ca.phys13news/files/uploads/files/… . At the moment mainstream theory moves towards quantization of gravity and unification of forces. Rishons and derivative theories are at the stage that the quark model was in 1964 . Quarks were confirmed as experimental entities by their jets in the 1980s. The rishons, due to the much higher binding energies needed for $\endgroup$
    – anna v
    May 6 '16 at 5:43
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    $\begingroup$ electrons to appear in our measurements as point particles, will need much higher energy experiments than provided even at LHC. Maybe the linear collider, if built, might show structure in electrons and positrons. Or maybe 50 years hence. The theory is not forgotten, it is just not worked on much because it is an alternative that cannot be checked by data. $\endgroup$
    – anna v
    May 6 '16 at 5:45
  • $\begingroup$ @DescheleSchilder it also has anti-rishons so 4 elementary particles. $\endgroup$
    – user253751
    Sep 23 '20 at 12:49
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There is a model that uses only two elementary particles (less there can´t be) and that´s the Rishon Model made up mainly by Haïm Harari (there are other preon models but I think this model is the most elegant one).
Rishons have an electric charge of 1/3 (the T-rishon) or 0 (the V-rishon), and by combining them you can construct all the known particles. It could also explain why a chargeless Z-particle can decay in three photons: it consists of three T-rishons and three anti-T-rishons. In this model, the weak force is a residue force. And for example, an up quark is a combination of three T-rishons and one V-rishons. You can find out for yourself how the other quarks and leptons are made up.

So in this model only four truly elementary particles are needed to make up all quarks and lepton. More economical it can't get! The force-carrying particles (the photon, the gluon, the hyper gluon, and maybe the graviton) are not accounted for in the Rishon Model. They are just there.

Of course, the theory has its flaws but doesn't every theory (model) has flaws?

To answer your question:
You shouldn't believe that elementary particles are indeed elementary. You can ask yourself if the rishons are made up of other, more fundamental particles but that can't be the case.
If you consider elementary particles as non-point-particles (as I do, but in a non-string-theoretical way), you can ask yourself, what's the material the non-point structure is made of.

I hope this answer gives you some enlightenment.

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