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What is the size of a point? Or, what is a particle?

  1. Aug 9, 2009 #1
    This quote is by Naty1 from another thread. I wanted to expand on it, but it would have been off-topic.
    "They" refers to strings. I have always wondered about this. Is it true that the troublesome infinities which lead to the need for renormalization and such are the result of particles being infinitesimally small?

    The reason I'm asking this is that apparently the Standard Model requires that elementary particles be infinitesimally small points. Does this mean literally infinitesimal? Sometimes I see the term "point" and other times "point-like" which seems to leave some room for some size. I just cannot philosophically wrap my mind around any "thing" (even if the "thing" is just a field disturbance) that has absolutely no dimension at all, and it also seems to lead to all kinds of quantum confusion at planck lengths. It's easier for me to accept 11 dimensions that that...

    I think that that is one of the big reasons that, for me, a non physicist, String Theory is so appealing at least on a qualitative level, because it allows a particle as having some finite size, about a planck length, which also renders the sub-planck quantum stuff irrelevant. I understand that the SM is spectacularly successful, but I don't quite understand why this requirement is so important (probably because I don't understand the math). Is this requirement strictly a mathematical necessity to make the formaulae work, or is it reasonable to accept the idea of infinity or infinitely small as being physically real?
     
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  3. Aug 9, 2009 #2
    Infinitesimal size is not a requirement for SM. It just presumes they are really teeny weeny. Also, effects we normally think of as "surface" effects (cross sections, for example) don't abruptly start at any certain radius, but gradually increase the closer you get. I doubt the concept of "hard surface" has meaning for a particle.
     
  4. Aug 9, 2009 #3

    dx

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    The idea of points is difficult to avoid. It may seem unnatural to have particles which are points, but even if we replace them with extended entities like strings, they are still points in a different space: configuration space. Any continuum theory seems to force us to use points in a fundamental way. Of course it remains to be seen whether quantum spacetime will turn out to be a continuum or not.
     
    Last edited: Aug 9, 2009
  5. Aug 9, 2009 #4
    It's true that the mathematics in the standard model represents particles as points and that leads to infinities. The particles themselves, in the "real world", don't seem to have any trouble following the actual laws of nature, which don't exhibit such infinites, and so it would appear we do not have the "final" model quite yet.

    String theory also seems to avoid such infinites via characteristics other than one dimensional extension as well: T dualities. As the radius R of a small circular dimension in one theory is decreased it interchanges with another theory with radiuus 1/R...hence further decreasing the dimension in one theory causes an increase in another theory!! R can't get to arbitrarily small dimensions!

    This is similar to dual string coupling constants which reflect the strength of string interactions, the likelihood that a string will split into two for example. A strong coupling constant in one theory reflects a weak constant in another. Strange as this may seem (and it sounds suspiciously like a form of Heinsenberg uncertainty to me, although I have never read that) it means that by varying string coupling constants and dimensional sizes you can move from one string theory to another...this is important because only approximate calculation techniques are available and as either approaches some limits, the approximate methods become less and less accurate.
     
  6. Aug 9, 2009 #5
    Interesting replies. The above quote exactly summarizes what has always been difficult for me. I think I just have a conceptual problem with the idea of a continuum of space and time). For some reason, the idea of a quantum space/time actually makes more intuitive sense to me than a continuum. I don't know why because both are hard to imagine, but it has to be one or the other in the absence of alternatives (are there any?). A continuum seems to lead inevitably to physical reality or existence of infinite and infinitesimal objects, space, time, ad infinitum (no pun intended) and that is what I can't get past. Naty1's reference to T dualities is another example of this problem. No infinities for me, please.

    Ron
     
  7. Aug 9, 2009 #6

    apeiron

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    You are asking metaphysical level questions - about the reality behind the models. And here is another way to think about the answer.

    Paradoxes arise if you treat either dichotomous extreme - continuum or point - as needing to "exist". Instead, treat them both as limits. So pointiness is the limit that bounds us in one direction. The continuum would be the limit that bounds us in the other direction.

    In this metaphysical interpretation of the models you can see that reality is neither perfectly pointy at the local limit, nor perfectly continuous at the global limit either. The modelling takes a shortcut by assuming reality can be represented in terms of limit entities. But reality itself exists only asymptotically close to either of its bounding extremes.
     
  8. Aug 9, 2009 #7
    This is a good answer and I understand the concept. You are right, these kinds of questions are metaphysical, but I believe, fair. Would it be fair to say that questions of this nature are the result of asking more of physics than physicists can provide at this time? Some of us can't help but try to link the models with physical reality because, after all, that is the ultimate goal presumably.

    Believe me, these questions and comments are not meant to be critical; I understand the magnitude of the problems and admire the brilliance of people who have gotten us this far and are continuing.

    Ron
     
  9. Aug 9, 2009 #8

    apeiron

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    Meta-physics is a good thing in my book. Other people may chose to look at it as a dirty word or a failed method, but that is foolish. It is a way of seeing where we are trying to get to with out modelling, while not having to burden our models with extraneous baggage. You could say it is like the difference between preparing for the game and actually playing the game.

    Models are the stripped-down-as-possible theories where you chuck out everything unnecessary for the sake of efficiency. This makes them "unreal" - but again in a good way.

    A famous example would be Newton and his "action at a distance". It was his breakthrough to make the "unreal" modelling assumption that gravity could act across empty space without any need of a material connection.

    Contrast this with Descartes getting caught up in corpuscular theories, jostling particles and celestial eddies to swirl the heavenly bodies about. But even Newton did not believe so stark a model could be true - or at least he struggled. Hypotheses non fingo, he said.

    So good science is about knowing when to step back and contemplate at a metaphysical level - where we are trying to find guidance by imagining what could be "real".

    Then we capture such truths in minimal models, models so stripped down of baggage that they can come to seem paradoxical and unreal in what they are assuming.

    The map is not the territory as they say. The models are our maps. Metaphysics is trying to see the territory.
     
  10. Aug 9, 2009 #9
    @apeiron: Thank you very much for your perspective. When one considers the contributions over the history of the physical sciences, it is certainly clear that despite the fact that no theory has been complete or completely correct, many, such as the important ones you mentioned, have been extraordinarily successful considering their purpose, and directly influenced subsequent successful theories. I believe that Einstein was directly inspired by the works of Maxwell, Planck and others, for example, and strived to improve. I believe we are probably getting closer.

    Perhaps, at least as these cutting edge physical sciences are concerned, models such as GR, QM, the QFT's and maybe Strings and other Quantum Gravity models will always be approximations by necessity, due to inherent limitations of the math. I can live with that.

    Ron
     
  11. Aug 10, 2009 #10
    No. There is inevitable quantum-mechanical smearing. Quantum-mechanical smearing (charge "cloud" in an atom, for example) is quite different from classical one - it is a set of points of different measurements rather than a classical multi-charge density. On average such a "cloud" has a center with which we usually identify the "point-like" particle (electron) position (see atomic orbitals at http://sevencolors.org/images/photo/hydrogen_density_plots.jpg ).

    Apart from this, the real electron is always in interaction with the quantized electromagnetic field, so it is not really free and "point-like" but smeared quantum-mechanically, even in a "free" (non bound) state. The corresponding physics was first described by T. Welton in 1948 (Phys. Rev. V. 74, pp. 1157-1167). It is given in many QED textbooks as a qualitative explanation to more exact QED calculations.
     
    Last edited: Aug 10, 2009
  12. Aug 10, 2009 #11
    Why is that? Mathematically, there is no difficulty at all working with dimensionless points. What harm is done if they have no length? It's no worse than the fact that strings span no area.

    Ignore the uncertainty principle until you measure. As far as we can tell, there's nothing to prevent the world from acting perfectly deterministic up until the point where we shoot it full of energy to take a measurement.

    Whenever you ask if something is "real", you have opened a can of nonsense. Reality is what you make of it. If invisible angels beating their wings gives you the correct motions for the planets, they might as well be reality.
     
  13. Aug 10, 2009 #12
    I am certainly aware that the use of the term "reality" is problematic because it quickly has philosophical and therefore controversial implications. However, I defend it's use because usually it is used as a general descriptor of what is going on in the world/universe. If the study of the physical world is not about that, then what is is about? I see describing "reality" as the ultimate goal of any scientific research. But then this admittedly is the perspective of a non-physicist who is looking to the scientific community to find the "truth" (is this another way saying "reality"?) So the whole point (sorry, again - no pun intended) of my query is, and I am asking respectfully: Is this, the pursuit of "reality", a reasonable ultimate goal? I know it's asking a lot and maybe it is un-"realistic" but shouldn't be an un-"reasonable" one in my mind.
     
    Last edited: Aug 10, 2009
  14. Aug 10, 2009 #13

    ZapperZ

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    Unless this discussion is based on physics rather than philosophical ramblings, it will not stay in this forum and will be moved to the Philosophy forum. It is your choice and your decision in which direction this should go. Does the philosophy form needs ANOTHER thread on "what is real?" that hasn't been discussed ad nauseum already?

    Zz.
     
  15. Aug 10, 2009 #14
    I don't think that is really true at all... are you arguing for local realism? That idea has been pretty discredited experimentally. Superposition of states is a very real phenomenon, and is what leads to things like entanglement and quantum teleportation. To the best of our knowledge it is epistemologically correct to say a system can exist in a superposition of observable states. It goes much deeper than uncertainty.

    But he didn't seem to be talking about uncertainty, but a philosophical uneasiness with accepting the physical reality of the infinite(ssimal). Mathematicians have been worrying about this one for a while, I'd look into what they have to say about it. As of yet we don't have any experimental evidence for accepting the extended string as a better approximation of reality than the point particle.

    For the purposes of this discussion can we agree that whatever our best, experimentally confirmed model uses can be called "reality"
     
  16. Aug 11, 2009 #15
    Hi ZZ

    Has any truly great discovery in physics ever come about without a decent balance between philosophy and calculation/measurement ? Apart from Dirac, can you name a founder of Quantum Mechanics that did not use philosophy as much as measurement ? And even Dirac saw some kind of philosophical beauty in mathematics!

    In a forum whose sole topic is reaching beyond the limits of our current understanding, when our science has become so advanced in regions so mysterious to the common man, I'd suggest that no progress is actually possible without reconsidering our basic epistemological and philosophical (even ontological) basis of investigation.

    As such I'd humbly request that you be more patient with people that meander into philosophy on this board. There are indeed many crazy people on the internet that don't progress anything anywhere, and its good to have bulldogs Dirac to police them away. But I love discussions like those in this thread and think many others do too. Please be gentle with your moderation.

    Regards

    Simon
     
  17. Aug 11, 2009 #16

    ZapperZ

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    Your post is the poster child on why this thread is heading towards the Philosophy forum. If you want to discuss the beauty and utility of philosophy, then open another thread. Your post is seriously off topic.

    Zz.
     
  18. Aug 12, 2009 #17

    Vanadium 50

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    Zz, I am going to disagree. This isn't philosophy. This is not a carefully reasoned ontological argument. It's a demand that nature behave in a manner that some prefer. It's not science, and it's not philosophy. The philosophy section shouldn't be filled with random musings - that's not philosophy.
     
  19. Aug 12, 2009 #18

    ZapperZ

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    I disagree. This IS science, and certainly, this IS a physics question. But it shouldn't be an argument based on a matter of tastes. That's why this thread hasn't been moved to the philosophy forum. There have been posts in here that are very much based on physics, and those I certainly encourage. It is why this thread is still where it is.

    However, there have been insertions based not on physics, but rather what I termed as "personal preferences" not based on physics, but some ideology. When we do that, then this discussion has deteriorated into an argument on one's favorite color. That is no longer physics, and that is what I'm urging all participants not to get into. We have had way too many of that in the Philosophy forum and we don't need another one.

    Zz.
     
  20. Aug 12, 2009 #19
    Tac-Tics posts:
    yes there is a problem: Both general relativity and quantum theory have problems with infinites. In nature, we have yet to encounter anything measureable that has an infinite value. Yet in both thoeries, we encounter predictions of physically sensible quantities becoming infinites.

    GR has problems with infinites inside black holes where the density of matter and the strength of the gravitational field become infinite. Infinites appear in quantum theory whenever you try to descibe fields because every point has a value and there are an infinite number of points in a classical field.

    So we have good reason to conclude that neither theory is quite correct.
     
    Last edited: Aug 13, 2009
  21. Aug 12, 2009 #20

    ZapperZ

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    That isn't quite right. First order phase transition, by definition, has a discontinuity in a state variable. This clearly implies that the rate of change at such a phase transition is infinite.

    The van Hove singularity is very common in your semiconductor.

    The density of states of a superconductor right at the energy gap edge is infinite.

    The spectral function of a quasiparticle in an ordinary metal, which is the imaginary part of the single-particle Green's function, is essentially a delta function. This gets you the ordinary metallic behavior that gives you all the Drude model that we know and love.

    Etc... etc.

    We have no issues with dealing with an infinite value. A whole branch of mathematics is built around dealing with poles like this.

    Zz.
     
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