Quantum Theory and Philosophy

Discussion in 'Physics & Math' started by Human001, Sep 24, 2010.

  1. Green Destiny Banned Banned

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    I'd agree with that.


    But as far as most threads go here in this place, I honestly don't find this one any more speculative than some of the others...

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  3. Neverfly Banned Banned

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    The thread is not what is speculative.
    The topic is.

    Other threads on much less speculative topics may be more speculative than necessary, but I cannot vouch for that.
     
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  5. BWE1 Rulers are for measuring. Registered Senior Member

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    Has quantum decoherence been named yet? If you can read physics, this serves as a reasonable overview I found a while back.
    http://aps.arxiv.org/PS_cache/quant-ph/pdf/0312/0312059v4.pdf
     
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  7. Pandaemoni Valued Senior Member

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    One can believe that, but strictly speaking, that itself is a metaphysical interpretation of the science underlying decoherence, and not a scientifically provable truth. Believing it does eliminate certain philosophical problems (and I happen to believe you are right myself), but that belief is a philosophical, not scientific, position and not universally accepted.

    What can be said in accordance with the scientific theory and uncontroversially, is that quantum decoherence causes an apparent, not an actual collapse of the wave function, hence the paper cited by BWE1 above.

    The paper is an interesting survey of the issue in its relation to decoherence, thanks for it.
     
  8. Green Destiny Banned Banned

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    There must be an indestinguishability problem here.

    In other words, if experimentation cannot reduce decoherence as not being effect which mirrors that of the collapse, then truely we have no model to destinguish the two as being seperate phenomenons.
     
  9. Green Destiny Banned Banned

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    Somewhere along the line, I believe someone has treated decoherence as something inherently different to the collapse effect - when really, it's something dressed in already familiar phenom.
     
  10. przyk squishy Valued Senior Member

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    It's where the state of a quantum system becomes entangled with the state of its environment, in such a way that you can't attribute a pure state vector to it any more. For example, suppose you have an atom and two of its atomic states are \(| 1 \rangle\) and \(| 2 \rangle\), and suppose that if the atom is in state \(| 1 \rangle\) it'll cause the environment to evolve from its initial state \(| i \rangle\) to some state \(| a \rangle\), while if the atom is in state \(| 2 \rangle\) the environment will respond by evolving into state \(| b \rangle\). Then if the atom is initially in the superposition \(\alpha \, | 1 \rangle \,+\, \beta \, | 2 \rangle\), the evolution of the combined system and environment is
    \( \Bigl[ \alpha \, | 1 \rangle \,+\, \beta \, | 2 \rangle \Bigr] \, | i \rangle \,\mapsto\, \alpha \, | 1 \rangle | a \rangle \,+\, \beta \, | 2 \rangle | b \rangle \;. \)​
    If you just look at the atom in isolation, you can't attribute a final state vector to it because it's entangled with its environment. The best you can do is describe its final state with a density matrix. For example, if \(| a \rangle\) and \(| b \rangle\) are orthogonal then the atom's final state is
    \( \hat{\rho}_{\mathrm{atm}} \,=\, | \alpha |^{2} \, | 1 \rangle \langle 1 | \,+\, | \beta |^{2} \, | 2 \rangle \langle 2 | \;. \)​
    If you're just looking at the atom, you see it evolve from a quantum superposition of states into a statistical superposition of states. Once that happens, all the interesting effects associated with QM disappear. Decoherence is one of the main difficulties in building a large working quantum computer for instance.

    No, though it is related to apparent wave function collapse in some interpretations of QM which attempt to address the measurement problem. It involves treating the observer as part of the environment. The idea is that a "measurement" is an interaction that results in an "observer" evolving into a state that's entangled with the state of the system they're measuring. For example, if you "observed" Shroedinger's cat, it means you interacted with it in such a way that the global system consisting of you and the cat evolved as
    \( \frac{1}{\sqrt{2}} \Bigl[ | \mathrm{dead} \rangle \,+\, | \mathrm{alive} \rangle \Bigr] \, | \mathrm{don't\ know} \rangle \,\mapsto\, \frac{1}{\sqrt{2}} \Bigl[ | \mathrm{dead} \rangle | \mathrm{know\ it's\ dead} \rangle \,+\, | \mathrm{alive} \rangle | \mathrm{know\ it's\ alive} \rangle\Bigr] \;. \)​
    From the perspective of each of the final states you take (configurations of your brain corresponding to knowledge of a dead or a living cat) in the superposition, the cat appears to have collapsed into the corresponding "dead" and "alive" states.
     
  11. Neverfly Banned Banned

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    Concise and to the point.

    This post succinctly sums up the nature of our Model of Reality -- Mathematics-- and the issues that can be raised when that model meets reality. I've rarely seen it expressed this neatly.
     
  12. RJBeery Natural Philosopher Valued Senior Member

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    przyk: I've never made the distinction between "decoherence" and "wave function collapse" before. To me it sounds like what you're suggesting is that decoherence is subjective, possibly bringing the decohering agent(s) into the wave function propagation, while wave function collapse is absolute. Is that what you're saying?
     
  13. Neverfly Banned Banned

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    I lack the understanding on this topic that przyk has and am by no means answering for him. But I am sitting here bored, as I have been for the last several days... So I'm going to give it a shot anyway.

    First off, I haven't the foggiest on what you are asking here.

    Wave Function collapse, to my understanding, simply means that a wave function collapses when the state of something is determined.
    To use the oft used example of the [dead/alive] cat-in-a-box...
    If the state of the cat is to be determined as living, the wave function collapses down to [alive].
    And this is why I don't understand what you're asking. Because wave function collapse, in quantum mechanics, cannot be absolute...
    But if you're talking about a specific case in which wave function collapse occurs, in repeated experiments, then you could call it absolute.
     
  14. arfa brane call me arf Valued Senior Member

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    To understand "collapse" you need to understand entanglement, as pryzk states.
    Really it's about measurement. The measurement entangles the wavefunction with the environment--IOW measurement "is" the environment; measuring quantum states implies their entanglement with some device, which is also the quantum-classical correlator.

    You get a classical result, but only because the measurement has many more degrees of freedom than the quantum state. Coherent states are the result of superposition, or roughly stated, the alignment of the phase of abstract waves within some corrective "quantum distance". Decoherence is when the phase-factor disappears, because the states are separable.

    None of this really tries to explain what a wavefunction "is", but it's a general outline of how the quantum state is "defined" by the measurement paradigm, since measurement looks like a kind of boundary for the wavefunction.
     
    Last edited: Sep 27, 2010
  15. Green Destiny Banned Banned

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    Well yes, Pryzk is correct. I said I wan't going to contribute anymore, but I put a lot of work into this thread explaining decoherence.

    Pryzk explanation is actually very easy to picture in nature. Particles condense, their wave functions collapse, attrubutes for particles are defined, and is itself a solution to wave particle duality problem or ''measurement problem'' of quantum physics.

    A body for instance, like you or me, are in fact a collection of entangled particles. Our wave functions are so small, we cannot see them, they have been deflated by their environments, and because these particles are defining each other particles attributes in their vicinities, they are said to be in a state of entanglement. This is why, the cat is alive, not truely dead. But after a certain threashold, this can only be seen in macroscopic bodies. On much smaller scales particle can be quantum entangled, but equally have a wave function that spread vast over spacetime.

    It must be noted however, that entanglement and the wave function are not requisites of each other - they are only requisites when taking into account a large collaction of particles.
     
  16. BWE1 Rulers are for measuring. Registered Senior Member

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    You're welcome. And this is a good post. Thanks.

    Well, I recommend reading that paper. Some of it is challenging but that's the price of doing business in physics n stuff.

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    I only discovered recently (a year maybe?) that decoherence is often cited as the standard interpretation of state vector collapse. I don't have my head around the application of density matrices well enough to offer any useful perspective on the issue but that paper does explain the decoherence concept pretty well.
     
  17. Green Destiny Banned Banned

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    Sorry, yes. I will read the paper.

    Many here have caught me up on other things, if you haven't noticed

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  18. przyk squishy Valued Senior Member

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    Actually if anything I'm saying the opposite: decoherence is an "absolute" process (it actually occurs in nature) while wave function collapse is subjective (Everett originally called his interpretation the "relative state formulation" of quantum mechanics). It's also worth pointing out that decoherence in general doesn't have to have anything to do with measurement. A nice graphical example is seen in Rabi oscillations: this is an experiment in which you illuminate an atom with a laser at a resonance frequency, causing it to oscillate periodically between its ground state and an excited state. If you measure the state of the atom after a certain time interval and plot the average result for different time intervals, the result typically looks something like this:

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    (source). If the atom were perfectly isolated, you'd see the oscillation pattern continue for arbitrarily long laser pulses, but in practice the atom isn't perfectly isolated: it's coupled to the electromagnetic field and can interact with neighbouring atoms. Through these interactions, information about the atom's quantum state gets encoded in the environment, and once this happens the atom itself isn't in a pure quantum state any more. In a sense, the phase information in the atomic state leaks out to the environment, and if you ignore the environment (eg. because your experiment doesn't involve it directly) and look at the atom in isolation, it's state decays from a quantum superposition to one that resembles a statistical superposition. The atomic state is still undetermined, but interference effects disappear, which in this case shows up as a damping of the oscillation pattern.
     
  19. quadraphonics Bloodthirsty Barbarian Valued Senior Member

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    How on Earth has this thread reached into 3 pages without a single link to the Bohm Interpretation?
     
  20. RJBeery Natural Philosopher Valued Senior Member

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    przyk: fascinating, let me digest
     
  21. prometheus viva voce! Registered Senior Member

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    Because the Bohm interpretation is ruled out by Bell's inequalities?
     
  22. RJBeery Natural Philosopher Valued Senior Member

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    Why do you say that? I'm afraid you are mistaken prometheus.
     
  23. Neverfly Banned Banned

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    If so, can you outline how?
     

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