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Why No Decoherence?

  1. Apr 16, 2009 #1
    I'm hoping that someone has the patience to help a poor ignorant layman understand... and be warned that I am mathematically impotent. My struggle is in wrapping my mind around the concept of decoherence driven quantum collapse. As I understand it, the interaction between particles causes a quasi-measurement that "collapses" the quantum state of those particles (and all other entangled entities). If that is accurate, why does the photon strike in the double slit experiment not produce decoherence in the quantum state? Why the interference pattern?
     
  2. jcsd
  3. Apr 16, 2009 #2
    Suppose you have some experimental setup in which the photon interacts strongly with an object in the interference experiment, e.g. the photon bounces off a mirror if it mves through one of the two slits.


    Decoherence destroying the interference pattern will then occur if the state of the mirror would be affected by the photon to such an extent that you could, in principle, examine the mirror and tell that the photon had bounced off the mirror and hence tell which path the photon has taken.


    If the photon bounces off the mirror elastically then the momentum of the photon changes so, the mirror must absorb some momentum. So, it seems that the "which path information" does exist. But this is not true. The mirror (and rest of the world if themirror is fixed to the ground) doesn't have a precisely defined momentum. The mirror has a very precisely defined position and that causes the momentum of the mirror to be undetermined to some extent due to the Uncertainty relation.


    Clearly, if position of the mirror were not determined to witin a wavelength of the light, you wouldn't be able to see an interference pattern. If the position of the nirror is determined to within a fraction of the wavelength of the light, then you can show that the uncertainty of the mometum is necessarily larger than the momentum of the photon.


    So, the collision of the photon with the mirror causes the wavefunction of the mirror as a function of momentum to shift a bit, but this shift is much smaller than the width of the momentum distribution. This means that the mometum of the mirror gives you almost no information about the path the photon took and the inteference pattern will be almost unaffected.


    Now, the reason why macroscopic objects have a well defined position is explained by decoherence. So, in a way, decoherence in the macroworld explains why the photon does not decohere and why we can observe interference phenomena.
     
  4. Apr 16, 2009 #3

    Fredrik

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    If you or anyone else have more information about this, I'd be interested. Why does the environment "measure" the position of everything, rather than some other observable, like momentum?
     
  5. Apr 16, 2009 #4
    I think the observable that is "seemingly" measured depends on the type of interaction.

    Environment -- Coherent state encompasses a large number of phenomena.

    If you have a up spin-impurity ( a large quasi-classical particle) that interacts with a down-spin electron, environment measures the momentum of the spin because by checking the spin of your impurity after the interaction, you could conclude that the initial state (momentum) of the electron.

    I can think of other examples, like the interaction of a large contact with a one-level molecule, etc...
     
  6. Apr 16, 2009 #5
  7. Apr 16, 2009 #6
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  8. Apr 17, 2009 #7

    vanesch

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    I think that the simple answer to that is that most interactions are mainly dependent on distance (think, say, Coulomb interaction) ; that is, the interaction hamiltonian can be diagonalized in the position basis. That is not universally so, and in fact, most of the time it is not the position basis in which one decoheres, but in a kind of coherent state basis of "position and momentum" coherent states.
     
  9. Apr 17, 2009 #8
     
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