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Connection between path, particle and space

  1. Jan 2, 2005 #1

    I wonder if there is a connection between that path integral formulation of QM, the nature of particles as extended objects, and spacetime. Dynamical Triangulation trys to construct the classical 4D world as a quantum superposition of various kinds of spacetime. Could it be that the path integral formulation of QM is correct only because classical spacetime is a quantum mechanical superposition of various kinds of spacetime? You have every kind of path because you have every kind of spacetime? It seems to me that the connection between paths and spacetime itself is the particles. Somehow particle mediate between the QM of paths and the QM of spacetime. This might indicate that particle are features of spacetime such as boundary holes or genus holes. Then particles themselves might be a quantum mechanical supperposition of various kinds of boundaries or various kinds of genus holes. Any thoughts on this?
  2. jcsd
  3. Jan 2, 2005 #2
    I'm not quite sure what you're saying Mike but its kind of like the way I see things. We see something we call a wave because, in terms of youngs experiment, it spreads across both slits. But if the actual 'phenomena' of the particle is its 'expression', made by the mathematicians into a probability function, is in fact based in another dimension (or dimensions) that ARE NOT SPACE-TIME, then why on earth would it not pass through both slits ?

    I rekon Eintein was almost prophetic (purely due to intelligence rather than anything spiritual) in his understanding of the increasing loss of the broad horizon of science. Nowdays any significant new discovery leads to a new theory rather than a better understanding of the current one. Then everyone is surprised by the fact they don't all fit together.
  4. Jan 2, 2005 #3
    I guess I'm thinking in terms of what happens when you strink the distance of the path in the path integral to shorter and shorter distances. You start to wonder about the nature of spacetime itself that would allow a quantum mechanical superposition between two almost infinitesimal points. It sounds like there must be something in the nature of spacetime itself that would give rise to path integrals, or at least a connection between the path integral, the particle that is travelling the paths, and the space it travels through. It seems to suggest to me that if there is a superposition of one, then there is probably a superposition involved with the others, with spacetime and with the particle. The question is does the nature of the path integral in QM and QFT imply a specific nature to spacetime itself?

    It seems particles must have emerged from some properities of spacetime so that spacetime developed first before particles existed. For we can describe spacetime without particles, but we cannot describe particles without resorting to a reliance on an underlying spacetime. The only thing I can think of that are stable structures of spacetime are boundaires or genus holes. Waves would tend to dissipate in all directions. Or do you know of how some combination of waves perhaps of differing dimension can form a stable structure? Some have suggested the quantization of spacetime itself. But I don't know how you have information travel through disconnected regions. If everything is rigid, then there is instantaneous transfer of information. If everything is not rigid, then you're back to waves in smoothly connected regions.
  5. Jan 2, 2005 #4
    What do you mean by "disconnected regions" , or "rigid" ? Maybe you don't understand the scale of what I'm suggesting. I've been trying to find an analogy to explain this but I can't find anything that stands its ground. So instead of an accurate analogy, lets take a swimmer in a pool doing the crawl (freestyle for those who watch the olympics). Now consider that the view you have is just below their bodies, so all you see is the action between the elbow and half way up to the shoulder.

    Ahh that doesn't even start to explain what I mean in terms of your "disconneted".

    I'll start again :)

    Lets take a hologram. Part of a 'beam' reflects off an object and the other part does not. You are left with a two dimensional intereference pattern. Yet you can cut that image up at any time, and you will know about all the regions that are now disconnected. These apparently disconnected regions where imprinted in an instant. Do you see why dimensions are relevant here in terms of your question ?

    Space-time is relativity. How exactly do you describe space-time without particles ? My impression is the opposite. Space-time is described too much by particles, and not enough about what gives rise to the medium itself.
  6. Jan 3, 2005 #5
    Disconnected mean not continuous. For space this would mean that there is some distance between regions of space. But since that does not make any sense to have space between space, I don't think it exists.

    Rigid would mean regions which cannot warp. It would be like ice cubes stacked together. If nothing gives in an elastic way, then any movement in one cube is instantly transfered to every other.
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