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Q: non-local effects & 4th spatial dimension

  1. Mar 11, 2004 #1
    i've been reading Brian Greene's latest book and have enjoyed his excellent analogies and metaphors for understanding quantum mechanics (among other things).

    IANAP, but one thing that comes to mind as a theory is that the concept of particles that are non-local having an effect on each other is perhaps explainable if you expand the definition of spacetime to include a 4th spatial dimension.

    in other words, it appears, in the spacetime recognizesd, that there are two particles that are separated by "space". is it possible that they are only separate in the 3d spatial model we are familiar with, but that in a 4th spatial dimension they share a locality?

    if i am way off here, please accept my apologies.
     
  2. jcsd
  3. Mar 11, 2004 #2
    Your proposal is not that far-fetched since the predominating structures at the planck scale are wormholes which could connect you with SOME (unknown) point in the universe. The problem is that in the 4 dimensions that we know exist you can only connect any location with at most one other location in such a fashion and for any two particles at any point in space to communicate with each other you need trillions of trillions of dimensions folding the universe in on itself trillions of times. For this to be the case these dimensions must be extended and not the ultra small curled up ones as proposed in string theory. If they were extended then theyre existence would have been common knowledge, so I think we can safely lay that prospect to rest.

    However inconceivable by me it might still be possible in just 4 dimensions by virtue of some quantum quackery and manipulation of the ironically sole certainty in our world, which is uncertainty.

    I hope that was all sufficiently confusing.
     
    Last edited: Mar 11, 2004
  4. Mar 11, 2004 #3

    Janitor

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    I like that, Palpatine

    There is nothing certain but uncertainty itself.
     
  5. Mar 12, 2004 #4
    In many variants of quantum gravity (other than string theory) spacetime is not the underlying reality, but emerges from a low-energy limit of some more fundamental structure.

    Suppose such a structure has the form of a graph, where nodes on the graph are linked by edges if they are causally connected. Non-local effects might be explained by postulating that nodes that are linked by edges do not have to correspond to spacetime points that are close together in the low energy limit.

    Some ideas along these lines have been proposed by Lee Smolin and Fotini Markopoulou-Kalamara
    (Quanum theory from quantum gravity)
     
  6. Mar 12, 2004 #5

    LURCH

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    Not a bad bit of reasoning, Underworld. The presence of an additional spatial demension would indeed expalin "spooky behavior", but ti brings up some problems of its own. Why does the condition we call entanglement (in which a single object has ywo locations ni 3d space or two objects share a common locality in hyperspace) only occur under special conditions? That is, if it is possible for a single object to have more than one location in 3 spacial dimensions, or for two seperate objects to have a common hyperdimensional location, why isn't it observed all the time? How does a beam splitter cause this condition?

    An idea I had some time ago regarding entanglement speculated that the information gets from one particle to the other through some routs other than normal space. Said signal, not travelling through any space, would also not travel through any time to arrive at its new location. And now I find myself wondering; what method of testing could determine the difference between that model and the one you have proposed? I can think of no observable difference between them.

    Certainly got some new stuff to think about now!
     
  7. Mar 13, 2004 #6
    entanglement is possible only in systems where some quantity is conserved, isn't it? like, in the singlet state, total spin in the z directoion is conserved.
     
  8. Mar 14, 2004 #7
    It depends on exactly what you mean by 'entanglement'. In quantum information theory, an operational approach is usually taken. For example, we might say that a state is entangled if it is possible by local operations and classical communication to convert it to a state which can be used to teleport a qubit.

    Clearly, this definition depends on what 'local operations' are allowed. For example, if the total spin in the z-direction is strictly conserved, then we are not able to do operations that change this quantity. This is an example of a 'superselection rule', which is a restriction on the allowed operations arising from symmetries of the system under consideration.

    Other examples of superselction rules are those that are induced by the symmetries of identical particles and photon-number conservation in linear optics. These rules can make states that look entangled actually be unentangled in the operational sense. For example, under photon number conservation the state

    |0>|1> + |1>|0>

    is not entangled, where the order of the Kets labels an optical mode and the numbers in the kets indicate the number of photons in that mode. This is because teleportation requires measuring in a basis that includes states like |00> + |11>, which would violate photon number conservation.

    Similarly, with fermionic statistics, the state |01> - |10> is not entangled since one cannot change the antisymmetric character of the state.

    In these examples, conserved quantities actually reduce the amount of entanglement in the state. One would need to find a way to break the superselection rules in order to regard the state as being entangled. In the photon number case, introducing a nonlinear interaction would do the trick and in the fermion case, the particles need to have some other label (such as well-localized position wavefunctions) that distinguises them.

    Of course, there is still a sense in which the above examples can be regarded as entangled and which definition of entanglement you choose depends on the sort of application you have in mind.
     
  9. Mar 15, 2004 #8

    TeV

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    Re: Re: Q: non-local effects & 4th spatial dimension

    I seem to remember that certain Austrian Physicist demonstrated experimentaly few years ago how laws of quantuum physics can be used to send signal at faster than light velocities.He used a probability of photon tunneling effect of laser beam passing through the ~10 cm (?) space distance with obstacles between receiver and the beam source .
    There was lot of smoke about that experiment on the internet and discussion of it(but I'm too lazy now to search for on-line refference on it ).The experiment does not vioalate relativity postulate (since photon does not propagate uniformily) but is demonstration of quantuum tunelling effect at work at macrodistances.
     
  10. Mar 15, 2004 #9
    Faster than light.

    Let's get one thing clear: If this were true then it definitely WOULD violate relativity.

    The controversy surrounds the definition of exactly what we mean by sending a signal faster than light. To illustrate, consider the following example:

    Suppose we represent one bit of information, 0 or 1, by two different gaussian wavepackets with the same mean but different variances. Now, each of these wavepackets extends over the whole of space, albeit with an exponentially decreasing aplitude. However, the amplitudes of the wavepackets representing 0 and 1 are different at every spatial location, so in a sense the information about whether the signal is 0 or 1 is already available at the detector before the experiment has even begun. This is essentially how these experiments can be reconciled with relativity. The peak of the wavefunction is transferred superluminally, but the information was already available at the location it moved to - it has simply been amplified.

    Now, the controversy begins if we imagine that we have some machine that will do one of two things depending on whether it receives a 0 signal or a 1 signal. Suppose the machine has a minimum amplitude of signal that it can detect. Then, the signal does appear to travel superluminally from the point of view of the machine. The effect which causes the machine to act really does arrive before it possibly could have if it travelled at the speed of light.

    From my point of view, I think we need to do a thorough information theoretic analysis to resolve this issue.
     
  11. Mar 16, 2004 #10

    TeV

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    Re: Faster than light.

    Frankly speaking it doesn't.There was a lot of controversy when Gunther Nimtz published his results.
    That would include lots of craps like sites of building time machines to the proposals that special relativity should be completely abandoned (you can find that on the internet associated with Nimtz' experiment along the line ).
    Conditions in the experiment are far from being "uniform wave propagating *" + there is a high probability that single photon does not exhibit a quantuum tunneling barrier jump.However,some photons do that** and and if the dense sequence of photons is used in the beam ,under enhancing conditions, information between two points in space separated by the barrier can be transmited with probability which isn't smallish any more.Theoretical treating of such more or less uncertain information isn't a trival problem at all.And puzzling lows of QM and various interpretations of it reread their ugly heads again .It would carry me away to debate on this more so I will stop here.I think It should suffice to say that it's been proven recently that the experiment ala Nimtz doesn't violate causality.
    ________
    * One assumption of special relativity is uniform wave propagation through the isotropic space.No mention of quantuum tunnelings.Besides ,General relativity violate postulate of constancy of the speed of light,but on the grounds of other causes:Presence of gravitation.
    **QM can't specify an origin of new photon which reappears on the oposite side of the barrier after the tunneling.The incident wave packet generaly speaking splits "instantly" into two once the collision takes place (propagating in opposite directions) and in general is only partially transmitted.
     
  12. Mar 16, 2004 #11
    If the experiment does not violate causality then there must be some sense in which no signal travels faster than light, although perhaps not in the manner I suggested in my previous post. It seems to be a matter of defining carefully what we mean by transmitting information and this is non-trivial for real physical systems. I don't think it has to do with the interpretation of QM, since I think it should be possible to come up with an operational definition that we can all agree on.

    I would be interested if you could send me some references to the debate on this issue. I have been addressing similar questions for experiments with photons propagating through non-linear crystals, which can appear to travel faster than light in some circumstances.
     
  13. Mar 16, 2004 #12

    TeV

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    You can find a lot of internet data and references dealing FTL tunneling experiments.But be careful: consider only per-reviewed sources ,papers published in recognized sci. journals, and avoid crackpot links.
    My apology for my previous post.I seem to be forgetting,and I shouldn't.It is a fascinating stuff.
    Nimtz dealed with microwaves in waveguides FTL signal tunneling exps while Chiao's group on Berkeley actually experimented/experiments with superluminal tunneling effects of laser beam passing barrier of cool cesium gas filled chamber.
    The latter is even more stricking for my taste.
    Nimtz on his experiment:
    http://members.fortunecity.com/celfers/nimtz-paper.html

    Site with more links including Berkeley group work:
    http://www.aei-potsdam.mpg.de/~mpoessel/Physik/FTL/tunnelingftl.html
     
  14. Mar 16, 2004 #13
    entanglement

    Since the wave function is referred to by some mathematicians as a "vector in configuration space", it begs the question whether we are running up against the limitations of space-time. Perhaps a kind of Hilbert space is a real thing, just not located in space-time. Perhaps space-time is a part of this Hilbert space. Laws of relativity in space-time would not apply outide said space, and faster than light or action at a distance phenomena are real. Why do we accept some math operators as part of the "real world", but do not accept math in general as being "real" as opposed to just a trick that gives correct answers? Perhaps what appears in space-time (real physical world) are just parts of an abstract existence we do not fully understand. The orthodox interpretation would still hold true because without knowledge of the abstractness lying beneath space-time, we really can't say what a particle does between measurements. We have not yet acquired the physics of the non-physical.
     
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