The Planck scale might or might not be the "smallest" scale. Wikipedia gives the Planck scale as:[math]\ell_P=\sqrt{\frac{\hbar G}{c^3}}\approx 1.6\times 10^{-35}\ \mathrm{meters,}[/math]but this is just what you get when you look for the simplest way to construct something that has units of length using some of the dimensioned constants in QM+gravity, it's not in itself part of any theory. An actual theory might reference the Planck length multiplied by any dimensionless constant whatsoever (for example, e-137.035999=.306テ--10-59 would be nicely small, where 137.035999 is the inverse fine structure constant, which is dimensionless, but of course any such number depends on details of how a theory works).

If a specific theory, even something much more accurate and much more beautiful than the Standard model smashed with general relativity, says there is nothing smaller than the Planck length, that is a theoretical statement that might be supported by experiments for a few centuries or a few millions of years, but we can never be certain that some future experiments won't demonstrate that in fact there is a much smaller scale. Even if in fact there is no smaller scale, we can't be certain there is no smaller scale. One can have theories, this is not a counsel of despair, but nonetheless one has to be cautious of hubris, IMO, albeit that also includes that one shouldn't be too attached to lengths in a 3- or 4-dimensional geometry as necessarily absolutely important, perhaps something else altogether yet to be imagined is the measure of what it's really at.

In philosophy of science this argument, more-or-less, is called "the pessimistic (meta)induction" (at the link, reasons are given that hope to limit the consequences of the argument for scientific realism, but see also Structural Realism for a different response, or one can be an optimistic anti-realist[The theory might not be real, or it might be, but so what, we can still do stuff, we can even spray stuff even if it's only theoretically real]).

Hi Colinn

It is a beautiful explaination. But it is more complex. When I speak about the volumes ,I speak about a kind of gravitational primordial fractal. In logic this serie is finite and correlated with primes. This serie is also probably the same for the two series, the finte quantum serie and the cosm serie finite also. Now take my two equation E=m(b)c²+m(nb)l² and mlsoV=cosntant this second has a problem of equivalence with the 3 motions of quantum and cosm 3D spheres. So what I say is simple when you consider a decreasing of volumes from this cenytral singularity,the central cosm BH the biggest volume the number 1. Now about this BB,I must say that I prefer a gravitational spherical expansion? That impkies that I consider a gravitational aether with l tending to infinity due to this central volume See that this aether ,these particles of gravitation are not relativistic nor baryonic, the dark matter probably. Now you can see easily why I see a fractal of volumes. You can see easily alos that our standard model is encircled by this gravitation, cold.The zero absolute is fascinating.We have so a serie of quantum BHs with these volumes farer than nuclear forces and we have also particles encoded weaker than electromagnetic forces and photons;You can see that the gravity encircles this standard model at all scales, quant and cosm. Now see that all quantum central BHs these quantum singulaties, these biggest spherical volumes turn around this central cosm singularity.They turn so they are these spheres. I work actually about the creation of spherical geometrical spherical algebras. I search to encircle this gravitation and this infinite entropical potential and its codes and informations.

Hope that helps :)

Hi Peter,

Nice to see you around again:). You have always been so kind to comment on my idea, so please could you do it one more time, it should take you 5-10 minutes. In the latest FQXI contest I presented a very brief paper that shows the results of my simulations that predict the electron mass and proton size actually already exists in standard physics! Moreover, my simulation( which already produce many QM results) produce Newtons gravity law( at large distance) with a very simple constraint.

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Thanks

Adel Sadeq

    I'm sorry, Adel, that I do not have anything at all constructive to say about your essay. As little as I often think the mathematics I use makes too little contact with what physicists are accustomed to using, I fear you have the same problem even more severely. I do not see that you make any contact with quantum field theory at all, for example, which I think you have to if you care what physicists think, at least to persuade them why you don't have to make any contact with, say, the Standard Model of Particle Physics and the experiments that are understood to support it.

    Hi Peter,

    Thanks for your most informative post and for the references, which I've looked up. They and you have opened my eyes in that I no longer regard the set of Planck units as always fixing the "smallest possible" measure of anything, e.g. "Most Planck units are fantastically small and thus are unrelated to "macroscopic" phenomena (or fantastically large, as in the case of Planck temperature). Energy of 1 EP, on the other hand, is definitely macroscopic, approximately equaling the energy stored in an automobile gas tank (57.2 L of gasoline at 34.2 MJ/L of chemical energy)." Learning about Entity Realism was fun ... I got a lovely mental picture of all those electrons and positrons speeding towards that superconducting metal sphere at Stanford!

    Thank you, Colin, the Stanford Encyclopedia of Philosophy is a worthwhile place to learn about how philosophers of physics think -- not always sensibly, because philosophers, but it's almost always at least not obvious why an idea is nonsense. The SEP often doesn't obscure ideas by using technical words quite as badly as does the philosophy literature proper.

    Indeed, the whole concept of a smallest scale is tendentious. One has the Javelin argument that the universe is infinite in extent and the turtles-all-the-way-down argument, which one can turn to anything that rests or relies on anotherthing. So, I suppose, one could have a microscopes-all-the-way-down argument, or one could just talk of fractals, which in broad summary is apparently Steve Dufourny's approach, though there is an infinite diversity of possible fractal structure). Such arguments are not definitive: the Wikipedia page is very keen to deflate the javelin argument by mentioning that the universe might be a closed space, like a sphere, but the javelin argument also fails if the javelin we use keeps breaking (because temperature or whatever) so we have to keep replacing each javelin with successive different kinds of javelin, if we can, or if we cease being able to detect the javelin from where we are, so that perhaps the javelin does or does not exist (and, mutatis mutandis, microscopes for javelins); so perhaps the world is fractal, but perhaps it is not. I think the question, however, is how much of life rests on whether it's all the way out or inwards or not? For me the answer is that it is not at all, even though knowledge and skills still seem precious things.

    Ian Hacking's idea that spraying electrons makes them really real (or something like that) has had a profound effect on how people think about electrons, but we do not know whether there will be such a thing in some future theory. There will be an account, more-or-less, of how what an electron used to be thought to be is related to the structure of the future theory (just as quantization is an account, more-or-less, of how classical is related to quantum), but electrons may eventually be thought to be no more helpful as an idea than was phlogiston, even though we will very likely continue to use quantum mechanics as a practical mathematics just as we still use Newtonian mechanics. That's the pessimistic metainduction applied to the specific case of the electron, so it could be wrong, and anyway it's OK to use at least the idea of an electron field until we have something else to use (again, this is not a counsel of despair, it's a counsel against hubris). Against thinking in terms of electrons too much, try my YouTube video, Quantum Mechanics: Event Thinking, because, after all, too much Particle Thinking is a bugbear of mine.

    Colin, I forgot to discuss the Planck energy scale that you mention, EP. I suggest that we should take EP to be no more significant than the other Planck scales unless it is put in the context of a specific theory, wherein it will have specific measurable consequences for some experiments, almost none for others. In a specific theory, the Planck energy scale times some arbitrarily small or large dimensionless constant may be the energy scale at which measurable effects occur.

    Hi Peter,Adel, Colin,

    You know when I speak about spheres I insist, about their 3D SPHERICAL VOLUMES.Whe I speak about a fractal, I see a serie of volumes from the main central. The planck scale is like a bridge for me ,like is the bridge between the matter baryonic and not baryonic simply. Like a BH also ,it is the same logic.

    Infinity is a relative concept like the finite groups and series.The planck scale is not infinite in its serie of particles, nor in energy, that said we go towards a paradoxal entire entropy more we go towards our singularities, the main centyral codes which are gravitational and not baryonic in logic.

    The infinity like the numbers, the groups, ...the number of 3D sphers must be ranked in fact like all. A fractal for me is a serie from a singularity in my model of quantum and cosm 3D spheres inside an evolutive 3D sphere in spherisation optimisation of matter energy on a irreversible entropical arrow of time. They turn so they are these 3D spheres baryonic and not baryonic.The infinity is a very complex thing needing a relative interpretation.Eternity,infinity, time ,physicality, energy, matter, evolution,encodings.....all this is an incredible mechanic after all and we know so few, the planck scale at 10^-35m is like a bridge between these two matters baryonic and not baryonic.

    Best Regards

    Hi Peter ,

    Thank you for your comment.

    While I do agree that I need to make a better presentation with jazzed up mathematics (which I will one day), however I do think I have made important connection with QM/QFT. Notice I said important and not good, because you and me (and other researchers) only try to show important points in the beginning and once those are accepted then further development can proceed.

    Beside the clean and coherent build up of the physics, I have made the connection with the electron/proton mass ratio with the proton size, that is a hell lot more than what the "standard model" can dream of. As you know the SM contains many unstable particles and the proton construction look like a shack in a slump:) and all permeating Higgs with utter mismatch with known CC, and so on.

    Thanks again.

    P.S. the interaction problem which you are working with will be the next step in exploring my model which I hope it will show the origin of the problem by automatically providing the solution which it should IF my model is fundamental. BTW, what is you latest.

    Kind of you to ask, Adel. You can see a few comments above a YouTube link to how I find it most congenial to think about quantum mechanics; that's four months old. My latest is that I'm continuing to try to fix the approach in arXiv:1507.08299. I've added my most recent version to this comment as an attachment, so I'll say to look at that, not at the arXiv version.

    I see this as an approach to doing interacting QFT mathematically correctly, but Appendix C, almost the very end, contains the killer sentence, "there is no immediately obvious construction that implements the U(1) and other gauge symmetries that have been so effective when using Lagrangian and other dynamical methods." I don't know how to fix this, or at least I don't know how to gloss it so a journal editor/referee would perhaps accept the paper.

    Even if I could fix it, I see the paper as an approach to QFT, not as a final solution, particularly for its suggestions by example as to which of the Wightman/Haag-Kastler axioms I think it might be good to weaken so that there would be non-trivial interacting models.Attachment #1: MP.pdf

    IMO you are on the right track with dodecahedra. And we may ask what provides the pressure inside the "bubbles" and what is the membrane between "cells" of the foam? I suggest a unit of charge in each cell and dynamic membranes formed by surrounding units of charge. Maximum packing density of elements would be "close packing" for solid round static bits of charge. But for charged dynamic particles density is greater than "close packing." This "shape" may be described as a distorted dodecahedra. This maximum in the packing density prescribes the background temperature of the cosmos! And it varies with direction! Can you see the dodecahedral structure in the cosmic microwave background (CMB)? Yes. And the maximum density of the "vacuum charge" distorted dodecahedra-- is less symmetrical than one may at first assume. It has a natural twist.

    Hello,

    It is beautiful extrapolation with strings and the primordial fractal considering this dodecahedre. I consider presonally the 3d SPHERES but I see convergences with these works. The relevance was about the fact to conside this 1D primordial field and the building by this infinite entropy if I can say. We see a kind of luminiferous aether in this reasoning connected with our main central codes, mathematical or physical.It is relevant but that does not explain this quantum gravitation.Because I beleive humbly that we must consider an other logic not baryonic nor relativistic. But it is just my opionin of coure?The photons are not relally the main primordial quantum of E.Best

    Thank you for the link to Event Thinking, Peter. I watched that but have put dipping into the SEP on hold for a while! Event and Particle Thinking must come together from time to time, I guess, e.g. your experimental set-up may be recording the event of a particle emerging from the QV?

    Using Particle Thinking for a moment, is there a separate class of Field Thinking, or are P's and F's too closely related to be split apart?

    I believe quantum mechanics teaches that some?all? particles exist as fields until they are observed. Probability fields ... probably ... but are they also energy fields? In which case, the QV must be like a kind of great, all-purpose "field reservoir" of energy.

    "Ya wanna see a photon, OK, I'll collapse this bit of the QV into one. Sorry, didja say ya wanna see a proton? OK, I'll carve you off a bigger piece of the QV and let you have one."

    Is this how it all works?

      Personally, I now try to think mostly in terms of fields. Quantum fields are quite different from classical random fields, because of measurement incompatibility, "quantum" doesn't just go away when one thinks in terms of fields, but I find the difference to be subtly less than between QM and classical particle mechanics. What I think can be said about QM: Event Thinking is that it's rather different from most other empiricist interpretations of QM just because of really trying hard to avoid particle talk. Not many other people are as anti-particle as I am, however, so I have to try to speak both languages.

      Also with my curmudgeonly hat on, I've come to think that "energy" is overrated as an organizing principal, at least in QM, because conserved energy is a global observable. Not many other people ...

      Although I backslide all too often, I prefer to try to think about ways to describe what happens rather than to think too much that I understand "how it all works". It is what it is, it does what it does, we can engineer some parts of it, which is useful.

      Thank you for your comment, albeit I have to apologize for talking too much at a tangent to its concerns.

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