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I know that per current knowledge there are layers of size of physical entities going from elementary particles to molecules (and from molecules to molecular structures such as bricks or organism cells and further into a tools, buildings, machines and organism bodies).

I understand that the notion between human scientists is that the "size" or "scale" of elementary particles (whatever these will be) is finite;
that is: Elementary particles are the smallest physical entities in this universe and there can't be anything smaller than them in this universe.

Is there a theory according to which infinity for how small physical entities can be, is real?

I am not talking about a theory theorizing even more and smaller elementary particles than accepted, but rather a theory that its theoreticians are "irreverent" to suggest that there is no such thing as "elementary" particle by the sense that one could always go down in the "scale" of size.
One could be further irreverent to derive from such theory that because time passes faster in micro than in macro, entire universes could exist and might appear to an observing organism as a "particle" with a lifespan of way less than a millisecond.

Also, of course the opposite question (Can there be maximal size of physical entities?) is dependent on if the cosmos is finite or infinite, but the current question doesn't seem to me such.

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    $\begingroup$ It’s actually not quite right to say that elementary particles have a finite size. We can assign “sizes” to them (Compton wavelength, de-Broglie wavelength, etc.), but the notion of physical “size” of elementary particles is not a well-defined notion. $\endgroup$
    – Bob Knighton
    Commented Nov 21, 2019 at 9:38
  • $\begingroup$ @BobKnighton I believe you're right as far as GR and QM are concerned, but the relativistic ECSK theory, worked out by the mathematician Cartan through conversations with Einstein in the late 1920's and later elaborated by Sciama and Kibble, assigns a spatial extent to fermions which, in our locality, is greater than the Planck length. It's been used, in such theories as Nikodem J. Poplawski's "Cosmology with torsion", to posit an inflationary multiverse with an infinitesimal geodesic (described roughly at arxiv.org/pdf/1104.0160.pdf) that allows eternality to the past. $\endgroup$
    – Edouard
    Commented Dec 24, 2019 at 5:20

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In philosophy there are discussions about mereological gunk: wholes whose parts all have further proper parts. That is, there are no eventual indivisible "simples". Whether gunk can exist or not is debated.

Physics, dealing with things that at least in principle can be observed, has not cared as much about whether there are gunky objects or not. There are also simples that in a sense have indefinitely small spatial parts like fields, where one can zoom in on a small region endlessly and speak about the value of the field there - but it is still just an aspect of the basic field.

I have never seen anybody suggest a theory with an infinite hierarchy of partons making up larger particles, but presumably it could be theoretically constructed. I suspect the infinite degrees of freedom do cause trouble since they affect the larger-scale statistics.

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  • $\begingroup$ The Wikipedia page on 'gunk' seems incredibly confused, in the light of modern (post-1890) physics. Have philosophers reconciled 'gunks' and 'simples' with what we know today? $\endgroup$
    – knzhou
    Commented Nov 21, 2019 at 19:09
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    $\begingroup$ There are philosophers of physics who care a lot about actual physics. Mereology is a branch of metaphysics and hence cares more about what must be true for any possible world than what happens to be true in this world. $\endgroup$
    – Anders Sandberg
    Commented Nov 22, 2019 at 1:42
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Is there a theory according to which infinity for how small physical entities can be, is real?

You have to define what the definition of "small" is . If you means size, the standard model of particle physics has elementary particles as point particles, no size at all, so they fulfill already the "smallnes".

If you mean if their invariant mass can be very small, already the photon the gluon and maybe the graviton have zero mass in the mainstream models.

am not talking about a theory theorizing even more elementary particles than accepted, but rather a theory that its theoreticians are "irreverent" to suggest that there is no such thing as "elementary" particle by the sense that one could always go down in the "scale" of size.

The existing standard model has elementary particles with zero dimensions.

There are theories where what are considered as elementary particles now are modeled as complexes , made up by another layer of particles, and it is those that have really the zero dimensions, but there is no experimental verification of these hypotheses.

There is the theory of strings, which says that the elementary string is the real "particle" and the particles in the standard model table are vibrations on a string, but this is a different level of complexity.

String theory is the theoretical framework in physics in which the point-like particles of particle physics are replaced by one-dimensional objects called strings

So, it is not a simple size matter.

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