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Gravitation and Decoherence : New Scientist Article

  1. Jun 17, 2015 #1
    It says here that time dilation due to gravity can cause decoherence:

    http://www.newscientist.com/article...ce-us-to-do-quantum-experiments-in-space.html

    But.. wouldn't the effect of time dilation be more like a modification of the expected unitary evolution, so that there will be a slow change in the probabilities of different measurement results (compared with the zero-g case) ?
     
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  3. Jun 17, 2015 #2
    I doubt there is any way to make any predictions about an entangled pair once they decohere. It doesn't really make logical sense to me, that you could have a pair of "twins" who age at different rates in different environments, but retain some time skewed correlation?

    I do wonder if there is a way to do a double slit across a gravitational gradient, would it smear the interference pattern or eliminate it?
     
    Last edited: Jun 17, 2015
  4. Jun 17, 2015 #3
    It sounds like the ideas of Roger Penrose about objective collapse of the wave function due to gravity.
     
  5. Jun 17, 2015 #4
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  6. Jun 17, 2015 #5
    I asked Caslav this question yesterday morning:
    Last night before going to bed I checked my emails, he responded:
    So on the physorg.com article "They calculated that once the small building blocks form larger, composite objects - such as molecules and eventually larger structures like microbes or dust particles -, the time dilation on Earth can cause a suppression of their quantum behavior. The tiny building blocks jitter ever so slightly, even as they form larger objects. And this jitter is affected by time dilation: it is slowed down on the ground and speeds up at higher altitudes. The researchers have shown that this effect destroys the quantum superposition and, thus, forces larger objects to behave as we expect in everyday life."
    is wrong - quantum superposition is still present.
     
  7. Jun 17, 2015 #6
    I read part of the paper.

    Yes, the effect is just a modification of the unitary evolution. The idea seems to be this: Suppose at time ##t = 0## you have an atom in a superposition of two energy eigenstates.

    [tex]|\psi(0)\rangle = \frac{1}{\sqrt 2} |E_1\rangle + \frac{1}{\sqrt 2} |E_2\rangle[/tex]

    After a time ##t## the unitary evolution of the state takes the atom to the following state

    [tex]|\psi(t)\rangle = \frac{1}{\sqrt 2} e^{-iE_1 t/\hbar}|E_1\rangle + \frac{1}{\sqrt 2} e^{-iE_1 t/\hbar}|E_2\rangle[/tex]

    Now suppose the atom is not only in a superposition of energies but also in a superposition of heights above the ground. Say the initial state is

    [tex]|\psi(0)\rangle = \frac{1}{2} |h_1\rangle (|E_1\rangle + |E_2\rangle) + \frac{1}{2} |h_2\rangle (|E_1\rangle + |E_2\rangle)[/tex]

    In a given time interval, the component at height ##h_1## will experience a different elapsed proper time from the component at height ##h_2## because of gravitational time dilation. Let's say the elapsed proper time at ##h_1## is ##t_1##, while the elapsed proper time at ##h_2## is ##t_2##. So the state will evolve to

    [tex]\frac{1}{2} |h_1\rangle (e^{-iE_1 t_1/\hbar} |E_1\rangle + e^{-iE_2 t_1/\hbar} |E_2\rangle) + \frac{1}{2} |h_2\rangle (e^{-iE_1 t_2/\hbar} |E_1\rangle + e^{-iE_2 t_2/\hbar} |E_2\rangle)[/tex]

    (Actually I haven't included the effect of the gravitational potential energy term in the Hamiltonian, but we can actually ignore that for our current purpose). Now we look at the relative phase between the ##E_1## and ##E_2## components of the state. For the ##h_1## part of the wave function this relative phase is ##(E_1 - E_2)t_1/\hbar##. For the ##h_2## part of the wave function this relative phase is ##(E_1 - E_2)t_2/\hbar##. The relative phases are different because of the different elapsed proper times. This is the effect pointed out by the article.

    For a system with more internal degrees of freedom, these slight phase differences will eventually make the ##h_1## component internal state completely orthogonal to the ##h_2## component of the internal state. Once this happens the ##h_1## component can no longer interfere with the ##h_2## component. So we can say that the time dilation is producing decoherence.

    If the object has no internal degrees of freedom, the interference pattern will be unaffected.

    If the object has internal degrees of freedom but it is in an eigenstate of the internal energy, the interference pattern will be unaffected.

    The effect discussed here only operates when the object is in a superposition of different values of the internal energy. In this case, yes, the interference pattern will be degraded if the two interfering paths experience different amounts of time dilation. The amount of degradation depends on the amount of time dilation, on the number of internal degrees of freedom, and on the uncertainty of the internal energy.
     
    Last edited: Jun 17, 2015
  8. Jun 17, 2015 #7
    It is mentioned, in the pre-print article -- http://arxiv.org/abs/1311.1095 --
    "We also stress that the time-dilation-induced decoherence is entirely within the framework of quantum mechanics and classical general relativity. This is in stark contrast to hypothetical models where gravity leads to spontaneous collapse of the wave function and that require a breakdown of unitarity [2, 3] ..."
    [2] Penrose, R. On Gravity's role in Quantum State Reduction. Gen. Relat. Gravit. 28, 581-600 (1996).
    [3] Diosi, L. Models for universal reduction of macroscopic quantum uctuations. Phys. Rev. A 40, 1165-1174 (1989)
     
  9. Jun 17, 2015 #8
    Looking at it as an interferometer whose arms are subject to a differential time dilation,

    (1) Is it possible that this process will periodically bring the object back through the initial state? At least in certain situations?

    (2) If we let the arms of the interferometer cross over in the middle, so that paths A and B have the same overall "gravitational experience", will the decoherence go away? If so, this is perhaps a sort of "weak" decoherence removal setup, that is sometimes given the dubious distinction of quantum-eraserhood... what say?
     
  10. Jun 17, 2015 #9
    Sure. The time for this to happen is probably exponential in the number of internal degrees of freedom.

    Yes, this "decoherence" is easily reversible if you even out the time dilation between the two legs.
     
  11. Jun 17, 2015 #10
    So from the viewpoint of MWI, "No new worlds were created in the making of this experiment" ...
     
  12. Jun 17, 2015 #11
    Did you read the email exchange between myself and Caslav? https://www.physicsforums.com/threa...ce-new-scientist-article.819441/#post-5144084 -- I would most certainly say new worlds would be created in the experiment proposed by the article.

    Unless of course you are referring to a different experiment, which you might want to clarify.
     
  13. Jun 17, 2015 #12

    bhobba

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    Why would you think that?

    In MW each part of a mixed state after decoherence is a separate world.

    If gravity decoheres its no different to anything else doing it.

    Thanks
    Bill
     
  14. Jun 17, 2015 #13
    OK, that was just an imprecise attempt to sum it up in a tag line o_O

    New worlds were created when the superposed entity reached the first fork in the interferometer -- agreed.
    But are more worlds created with the gravity gradient, compared with the zero-g case ?
     
  15. Jun 17, 2015 #14

    bhobba

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    They are created whenever decoherence occurs.

    Thanks
    Bill
     
    Last edited: Jun 17, 2015
  16. Jun 17, 2015 #15
    From these replies (which seemed to confirm my own, naive and unreliable, take on it), I gathered that we have to qualify this decoherence with a pair of big quotes around it.
    Maybe it hinges on whether one agrees to call this "decoherence" in the same sense as entanglement with a complicated "ancilla", as opposed to a complicated but smooth/gradual smearing process. A weak electrical potential acting near one path through the apparatus would perhaps produce an analogous effect.

    An alternative view could be that a thing with complex internal degrees of freedom can become its own ancilla, and the gravity gradient helps this process along.
     
    Last edited: Jun 17, 2015
  17. Jun 17, 2015 #16

    zonde

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    It's strange to call orthogonal phase a decoherence. There is no interaction with environment and you can easily reverse the process (and I mean really easily, just let the effect last for twice the time and phase goes to opposite instead of orthogonal).
     
  18. Jun 17, 2015 #17

    bhobba

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    It transforms it to a mixed state - its decoherence.

    Thanks
    Bill
     
  19. Jun 18, 2015 #18
    So this wouldn't affect photons because they only have a fixed internal energy?
     
  20. Jun 18, 2015 #19
    I feel as if we (humans) are close to the point where we can say we finally understand QM.
     
  21. Jun 18, 2015 #20
    Yes, for the simple example I gave above, you can just wait longer and the "decoherence" is reversed. But if the internal state is more complicated the decoherence will not spontaneously reverse unless you wait an exponentially long time. (Though as I said above you can reverse the decoherence by evening out the relative time dilation between the two components of the wave function.)

    In the case where there are many internal degrees of freedom, I think it really is quite similar to the usual model of decoherence due to interaction between system and environment. Here we can think of the position degree of freedom as the "system" and the internal state as the "environment."

    Right, a double-slit experiment with photons will still work fine even if time dilation is significant.
     
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