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Are elementary particles large or small

  1. Jun 30, 2009 #1
    Following is a summary from Chapter 20 of Leonard Susskind's 2008 book THE BLACK HOLE WAR: I'd appreciate any further insights, especially on interpreting what Susskind says about String theory as it was vague for me. These are not exact quotes.

    Elementary particles are usually imagined to be very small objects. Quantum Field Theory(QFT) and string theory share the property that that things appear to change as the resolution of experiments increases. Elementary particles appear so small because we can only see the portion revealed by low resolution (low energy) investigations. Experiments do not seem to be able to reveal the outlying high frequency vibrating structures.

    QFT at higher and higher resolution would reveal further internal structure, a reduction in a blurred image via finer resolution detail would reveal ever more detail from atoms, to a nucleus, to protons and neutrons, to quarks, etc. Things inside of things describes QFT.

    String theory in contrast reveals an increasing amount of structure; the complex structure grows and occupies more space as we see higher frequency quantum jitters. Most of the quantum jitters are too fast to observe currently.

    Analogies: As a small particle approaches a black hole, the particle appears perfectly normal to an accompanying free falling observer. Eventually its pulled apart by gravitational forces as it gets closer to the singularity. But to an external observer, the particle is smashed apart and spread it over the stretched horizon#. It’s content is reflected in the information of the stretched horizon and any resolution is dependent on possible long wave Hawking radiation that would be emitted.

    #The stretched horizon is a thin layer of hot microscopic degrees of freedom a planck length outside the event horizon...

    My own comment:
    Seems like the Schrodinger wave equation, de Broglie wave- particle duality, and maybe Feynman sum over paths also hint at a large (extended) size for what we often experimentally observe as “small” particles. If there isn’t an as yet undiscovered unifying theory underlying all of this, it sure seems like an awful lot of circumstantial evidence exists for one.
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  3. Jun 30, 2009 #2


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    Hi Naty, I am trying to remember who said this, could it have been Feynman?
    They said that an electron could easily be as big as the Empire State Building, because it has a conductive steel frame. An electron is a field which, in a conductor, can be as big as the conductor.

    So you don't even have to talk about black holes :biggrin: Perhaps I have this slightly wrong and someone will correct me on this but I think that was the general idea of what they were saying---and they used the example of the Empire State building.

    Hopefully you will get a more satisfactory answer, but at the moment I think that the correct answer to your question "Are elementary particles large or small" would be "No."

    That is, they are neither large nor small. Some of them anyway.
    Of course there's the Compton wavelength, which is useful in certain contexts and which is the reciprocal of the mass. The more massive the field is the shorter is its Compton and the less massive it is, the longer its Compton is.
    Last edited: Jun 30, 2009
  4. Jun 30, 2009 #3
    Remarkable example from Marcus!

    Let us see a Hydorgen atom: the electron localization size is about a0 - the Bohr radius, the proton localization size in Hydrogen is about (me/Mp)a0 which is larger than the proper proton size [1].

    If you look at a Hydrogen atom in an excited (metastable) state with an~a0n2, the proton localization size is even larger: (me/Mp)an, so none of elementary particles gets point-like in the limit n→∞; on the contrary. So there is no reason to think of elementary particles as of point-like entity.

    A "free" electron is physically in permanent interaction with the quantized EMF, so it is smeared quantum mechanically, just like any bound charge [2]. So the electron and the quantize EMF form a compound system in fact (I call it an electronium). The charge smearing size depends on external field too. For a free electronium it is infinity, for a bound electronium in Hydrogen atom, the effect of quantum EMF fluctuations reduces tremendously - to about Compton length so the main smearing comes now from the bound state in the external (Coulomb) field (~a0 at least).

    The same statement is valid for the other "elementary" particles - they are not "free" and therefore are not point-like. The point-like image is the inclusive (illusory) one (see the inclusive cross section derivation in my publications).


    [1] Vladimir Kalitvianski, Atom as a "dressed" nucleus, Central European Journal of Physics, V. 7, N. 1. pp. 1-11 (2009), available in arXiv:0806.2635.

    [2] Vladimir Kalitvianski, Reformulation instead of Renormalizations, arxiv:0811.4416.
    Last edited: Jul 1, 2009
  5. Jun 30, 2009 #4
    Your comments reminded me of the "T duality" in string theory: string theory views a shrinking radius R as 1/R keeping the overall properties of a formulation unchanged. Maybe that's what Susskind had in mind with his very brief comments.

    Bob for short:
    Your smeared quantum comment is another concept which relates closely to the above ideas....as in changing the shape of the quantum probability functions ....


    Anyone have any similar insights regarding Feynmans path intergral approach? I don't know much about it, but if one has to sum all paths, an infinity of possible trajectories, that also seems to imply a widely dispersed "particle".

    I just stumbled across this: (wikipedia)

    which makes me think I should have referred to wavefunction collapse and superposition rather than the Schrodinger equation in my original comments....
  6. Jun 30, 2009 #5
    The probability amplitude (the wave function) obeys a wave equation, it exists everywhere, so the paths should cover all available space.

    The probability (as well as the probability amplitude=wave function) belongs to an ensemble of measurements. Each particular measurement is a point in the whole event space. There is no wave function collapse in a separate measurement as there is no probability collapse.

  7. Jul 1, 2009 #6


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    I'm not sure I got the question but one IMO interesting reflection that relates large and small and connects that to the QM collapse issues is that if you instead of thinking of the state vector, as a property of the system, or even a realist-sense relation, instead thinks of it as a evolved emergent relation of between the observer and it's environment, then clearly it takes a massive/complex observer to resolve finestructure in the environment.

    So informationwise - finestructure would have to correspond to a complex context. Now wether that's spatially large or just dense is another story, but I think the point is the complexity.

    Picture what information capacity is needed to encode the details of the microstructure of matter?

    If you think of the unitary evolution as the self-evolution required by the consistenty of the information, then the collapse is simply an information update to this evolution. I guess I never understood why so many people don't like that interpretation.

    This would also relat to the sum over states, since if you consider the wavefunction to be an emergent relation between observer, observed and more or less a property of the observer, then a finite observer has no infinite paths to sum over. It is always bounded.

    People kep talking about summing over an infinity of states, without considering wether there is a physical basis to this. The objection to the continuum is analogous. This means that the complexity bound of the observer is kind of "dual" to a minimum resolution in finestructure - IOW it takes an infinitely large and massve observer, to relate to the arbitrary resolution of a continuum all the way down through the planck scale. This as an argument against that, independent of the "it turns into a black hole argument".

  8. Jul 5, 2009 #7


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    Rather than thinking of the path integral formalism as a sum over all configurations (which could include paths in space as well as paths in configuration space), I think of it as a measure of the symmetry contained in the kernel of the action (that part of the action independent of the integration variable). This kernel is the fundamental description of the click distribution in question, i.e., for which you are computing the transition amplitude (which I call the symmetry amplitude). In this view, the integration variable (field) is not “real” (has no ontic status), i.e., it is merely a calculational device. What are real are the detector clicks and the goal of particle physics is to classify “sets of clicks,” i.e., trajectories, which are characterized by variables called mass, charge, spin, etc. In this interpretation of the transition/symmetry amplitude, these variables are not the properties of a “click-causing object” (particle) moving through the detector, but rather characterize the distribution of a set of detector clicks as a whole. In particle physics experiments these sets are easily identified through space as a function of time so it’s safe to assume the existence of a trans-temporal object moving through the detector to cause them. In other situations, it may be strained at best to explain click distributions via particles, e.g., EPR-Bell phenomena. Obviously, this view of the path integral formalism also answers your original question, i.e., the particles aren't large or small, they just "aren't."
    Last edited: Jul 5, 2009
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