The smallest probed length scale to date is around $\Delta x \approx 10^{-18} m$ (see here).

If we compare this to the Planck scale of $\Delta x \approx 10^{-35} m$ we are left with almost 20 orders of magnitude to bridge.

I am wondering about the following: emergence. The size of a quark is roughly a factor of $10^3$ below the size of a proton (as John Rennie points out in the comments, the quark size is zero within measurement uncertainty). And the size of a proton is roughly a factor of $10^4-10^5$ below the size of the hydrogen atom. And this pattern continues.

Based on this observation, is it reasonable to expect another hierarchy of phenomena on the journey from $\Delta x \approx 10^{-18} m$ down to $\Delta x \approx 10^{-35} m$ and how do current theories address this? How do current attempts of a unifying theory try to close this gap?

EDIT: Since this might be too broad, let me try to narrow it down on string theory. What does string theory say about the orders of magnitude between the Planck scale in the currently observable scale?

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    $\begingroup$ Quarks don't have a size. $10^{-18}$m is the smallest size probed, not the size of a quark. As far as we know quarks are fundamental and don't have a size. $\endgroup$ Nov 30, 2018 at 9:22
  • $\begingroup$ So quarks do not have a size w.r.t. the length scales we are able to probe $\endgroup$ Nov 30, 2018 at 9:43
  • $\begingroup$ In string theory I guess quarks are excitations of the string. So the "quark size" is somewhere on the Planck length. But do we have a good reason to believe so? Or might there just be another hierarchy of entities, i.e., the possibility that the quark is not fundamental. It seems to me that we need a very good argument in order to bridge 20 order of magnitude $\endgroup$ Nov 30, 2018 at 9:48
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    $\begingroup$ If you're asking whether there is new physics between the LHC energy and the Planck energy the answer is ... no-one knows. All we can say is that no evidence (no $5\sigma$ evidence) of anything beyond the Standard Model has ever been found. $\endgroup$ Nov 30, 2018 at 10:02
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    $\begingroup$ Are you asking if there's anything between quarks and the Planck scale? If so, that's an extremely broad question, it's essentially the entire field of 'beyond the Standard Model' physics. There are thousands if not tens of thousands of papers on this subject. $\endgroup$
    – knzhou
    Nov 30, 2018 at 10:36

1 Answer 1


I will let someone else answer this properly. But briefly: the existence of different characteristic phenomena at different scales - different length scales, or equivalently, different energy scales - is one of the basic ways that particle physicists organize their thinking, about known phenomena and about possible phenomena. The different known scales can generally be associated with particular quantities - particle masses, coupling constants - which are just free parameters in field theory, but which in string theory should derive from geometric properties like brane volumes and interbrane distances.

In field theory, one speaks of "effective field theories" which are only valid over a certain range of energies. There is a highly developed understanding of the relationship between EFTs at different scales, due for example to Kenneth Wilson's work on renormalization. String theory is much less understood, but there are some striking insights already, such as the correlation between energy scale and depth in an extra holographic dimension (in AdS/CFT), or the new constraints on EFTs coming out of Vafa's "swampland conjectures" (the landscape is the possible physics you can get from string theory, the swampland is all those field theories which cannot be obtained from strings).

We have a well-established theory, the standard model, which appears to be valid at least up to the highest energies the LHC could measure. (Higher energies equals smaller scales.) It was once widely believed that there must be new particles at those energies - something in addition to the Higgs boson, such as supersymmetry - because of a kind of extreme sensitivity of the Higgs boson mass to any extra physics. This sensitivity could be minimized if extra physics happened at scales close to the standard model, and in a symmetrical way.

But nothing like that has been seen, and meanwhile the Higgs mass was successfully predicted by Shaposhnikov and Wetterich, using an unorthodox framework (asymptotic safety) in which there is no new physics between standard model scales and the Planck scale. Also, some other conventional and well-motivated ideas for new physics at intermediate scales, like "grand unification", have failed to show up.

One could therefore argue that the evidence now slightly favors the existence of no new structure - a "desert" - between here and the Planck scale. But this is not a conventional view, and the majority of theories still introduce something new... The possibilities are very broad and difficult to summarize; as @knzhou implied, this encompasses thousands of speculations made since the 1970s, when the standard model came together.


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