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Essence of Particles

  1. Jun 1, 2004 #1
    As I understand it Strings are preferred as a discription of particles because the various vibrational modes can be (or is hoped to be) correlated to the various masses and charges, etc. But I am beginning to wonder if strings are a natural choice to describe particles. Why not higher dimensional objects like surfaces? These can have vibrational modes as well, right? I can certainly visualize how a 3D field can converge on a 2D object; it just stops there. But I'm not sure how a 3D field would converge on a 1D object. It would seem as though one of the dimensions of 3D would have to shrink to zero to fit on a string. Wouldn't that give the same troubles as 3D converging to a point? I would think that if something (particle) actually "exists" inside at least 3D, then you'd have to bump into it no matter which way you approach it. If it exists for all observers, then there can be no possible observer that could not preceive it. But with a 1D string, with no width, it cannot be precieved when viewed on its side. So I think this means that particle must have a 2D surface.

    Any thoughts? Thanks.
     
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  3. Jun 1, 2004 #2
    This?:According to Brian Hatfield's book, Quantum Field Theory of Point Particles And Strings, page 481, "...string theory will find an application any time a problem can be formulated as a sum over random surfaces... The sum over all world-sheets is a sum over random surfaces, hence any sum over surfaces can be interpreted as the propagation of some string." This is what we are dealing with here.

    So the question is, if the fundamental particles of matter are really strings that sweep out more (sample) space with time, what characteristic values can particles have, how are these values calculated, and what interactions can exist between particles?

    Below I show a number of different ways a string might propagate as it sweeps out more space with time. Every possible interaction must start with strings sweeping out more space and end with strings sweeping out more space, for that is how we have defined events growing with time. Fig 6 shows no interaction at all as a string moves through the dimension of time.

    And this:But why do we perceive only 3 dimensions? Whatever dimensionality the manifold of reality has, a region of this sample space is described by a hypersurface that is itself a manifold of one dimension less then the original space. In 3-D a region is described by a surface that is a manifold of 2 dimensions. So in a 4 dimensional space, a hypersurface would be a 3 dimensional manifold. In an n-dimensional space, a region would be described by an (n-1) hypersurface.
     
  4. Jun 1, 2004 #3
    Where did you get that wonderful quote? :wink: However, this doesn't prove that particles are (closed) strings. It only states that some growing events in a probability space might also use the methods of string theory. So I'm left wondering if higher dimensional objects have been ruled out for the matter we are commonly used to.
     
  5. Jun 1, 2004 #4
    The reason why I posted the above, I have seen your recent postings about the nature of Dimesional classification is evident in your questions, especially the Particle Field one's :smile:

    To measure is to guage?..then you need Two Locations, with dual identities, thus, the HUP only occurs because objects and detectors are connected, but not at the same location. To measure 'Wholes', you must be seperate and detached from the object being measured, thus no exact measure can actually occur by default! think about it, all 3-Dimensional objects are connected, some are more connected than others, for instance the Proton for instance?

    Now interestingly, one can ask this, Can a Particle and its corresponding Wave, occupy the same locations in QM?.. YES! this is the Duality, according to QED a 3-D particle can have a corresponfing 2-D wavefunction! :rolleyes:
     
  6. Jun 1, 2004 #5
    A particle in those settings is considered to be a point particle singularity of the Standard Model; it has no dimension at all. So of course it fits in 3D as well as 2D models. But if particles are regions of missing space, as it were, we can't know anything about what is inside. All we can know is what is happening on the surface. But it is hard to visualize how 1D strings would interact in 3D space. They have no width whatsoever; so it would seem that it would be practically improbable that they would ever actuall touch in order to become one string. Remember, there can be no force to draw one string to the other, for all forces are strings; so they would have to interact by the shere luck of their trajectories, right?
     
  7. Jun 2, 2004 #6
    OK, now that I mention it. How can the point particles of the Standard Model possibly interact when they have no dimensions at all? It is easy to understand deflections when each point particle has an electric field which acts at a distance on other particles. But if you replace the force field with particles/bosons, then there is no more field, and you would only have to rely on the probability that particle trajectories would intersect. And this would of course be a probablity of zero for particles with no dimension.

    I know somewhere that the interfering wave functions comes into play. But this is not suppose to deny the particle view either. Is there any clear explanation? Thanks.
     
  8. Jun 2, 2004 #7

    selfAdjoint

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    Well, the particles (fermions) have charge, they have energy, they disturb the quantum vacuum, they are "dressed" in clouds of virtual particles, and pretty soon a virtual boson is "exchanged"; voila!

    There's a lot of trouble (which they get out of) with the interactive vacuum in quantum field theory. Once a particle passes by, there's always a smear of unabsense in it which makes it seemingly impossible to isolate anything.
     
  9. Jun 3, 2004 #8
    "clouds of virtual particles". Yes, but wouldn't there have to be an infinite number of these virtual particles before it would even be remotely possible for trajectories to intersect? Maybe that's what you mean. And I think that might work for me. But wouldn't that mean we would have to calculate ALL the higher order Feynman diagrams before we could know the probability of any particle interaction? If you left out the highest order Feynman diagram of the perturbation expansion, then wouldn't that mean that you would then have extra room for a dimensionless particle to escape through?
     
  10. Jun 3, 2004 #9

    selfAdjoint

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    Concerning infinite numbers of virtual particles, look up infrared catastrophe in QED. An electron can emit and reabsorb one photon of a small energy, or two of half that energy, or four of a quarter that energy or... and there is no lower limit on the energy. Quite apart from the usual high energy problems, this infintite emissions with a finite energy is something the field theorists have to deal with.
     
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