Quantum thought experiment

Discussion in 'Physics & Math' started by arfa brane, Aug 4, 2015.

  1. krash661 [MK6] transitioning scifi to reality Valued Senior Member

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    travels as a wave, reacts as a particle.
     
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  3. Fednis48 Registered Senior Member

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    This is arguably true, but you should be very careful drawing any conclusions from it, because it's an extreme oversimplification of concepts from the very subtle field of measurement theory. In the same way a single slit at location X measures a particle's location to be at X, double slits at X and Y measure the particle's location to be X or Y. But note that this is still just a two-outcome measurement: the particle is either at (X OR Y), or it is at NOT(X OR Y). If the former, the measurement device makes no distinction between X and Y, and the particle comes out in a coherent superposition of the two locations. This is distinct from, say, an output measurement with two screens, where one screen or the other lights up independently. Such screens are performing a three-outcome measurement, where X and Y are two distinct outcomes. In this case, coherence between X and Y is not preserved, and no subsequent interference can occur. That's the difference between "preparation" and "measurement", insofar as there is one.

    Also, I'm with Q-Reeus in wondering where you're going with all this. Everything you've said so far is true, if a bit oddly worded at times. Are you getting to a more controversial point eventually, or are we just talking out the fundamentals of measurement theory?
     
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  5. arfa brane call me arf Valued Senior Member

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    There are no conclusions. It's what happens, and I disagree that it's an extreme oversimplification.

    The position of particles is measured by the slits, one slit or two slits. One should be very careful about how these are different situations, but that's all they are.
    Whether the slits "do" any measuring, or whether the particles are "measuring the slits", isn't really all that relevant. What is relevant is how the underlying Hilbert space "behaves".

    Nobody really knows why the space is one of complex probability amplitudes or why a classical measurement is the square of such an amplitude, I would argue (I'm probably not the only one).
     
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  7. brucep Valued Senior Member

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    Nothing controversial about wanting to understand quantum physics. Seems like an industry. I really tend to enjoy arfa brane' posts. He doesn 't appear to be studying physics in a formal setting. Something I'm familiar with. The best discussion [that I could understand, ha,ha] about the double slit experiment was in Feynman's QED.
     
  8. Q-reeus Banned Valued Senior Member

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    By chance I found the article very selectively quoted from in #20: http://arxiv.org/pdf/quant-ph/0703126 (always a good idea to provide the source when quoting)
    So they choose to call interaction with a slit or even slits plural 'measurement' as well as preparation. I'm familiar with the usual definition of measurement in QM as that which leaves a permanent record in a macroscopic measuring device - e.g. the dots on the screen as per Wikipedia gifs in #1. These days decoherence via environment is also considered a type of measurement process in that initial superposition(s) is destroyed thus 'wave-function collapse' occurs. Anyway there is no record generated at the stage of particle-slit(s) interaction/preparation - and no 'wave-function collapse'. Still, interesting to know such is considered measurement by some.
    Fednis48's elaboration on some of the subtleties involved in measurement theory was quite helpful. And all this gets us where on the path to what?
     
  9. Q-reeus Banned Valued Senior Member

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    From #25: "Anyway there is no record generated at the stage of particle-slit(s) interaction/preparation - and no 'wave-function collapse'."
    OK since any transmitted particle is forced to assume at some stage a particular position eigenstate in the case of an ideal single slit setup, it can be said 'collapse' has occurred. But to say that is a measurement rather than preparation doesn't sit well with me.
     
  10. arfa brane call me arf Valued Senior Member

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    I rationalise the (non)distinction between preparation and measurement by calling preparation a quantum measurement, and collapse of the wavefunction a classical measurement.
    Somehow it doesn't seem to resolve much, so I also usually don't make any distinction, everything still works out. If you remove the screen, what happens? The screen is another device that we say is where the wavefunction collapses; isn't it just a projection of the Hilbert space?

    We rationalise that classical measurement exists because we have memory; "the slits don't record anything" . . .

    You could argue that there is no classicality, conscious observers don't see any collapse but are also doing quantum measurements. You could ignore the metaphysics and just calculate.
     
    Last edited: Aug 7, 2015
  11. krash661 [MK6] transitioning scifi to reality Valued Senior Member

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    • Please don't bait other members, since this can lead to a flame war.
    in my irrelevant opinion, you should just ignore " q-reeus " . you're far advanced.
     
  12. arfa brane call me arf Valued Senior Member

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    It seems that a classical measurement has to be something that is a record, a static picture. The quantum states have to be projected "from" the quantum domain, the Hilbert space of abstract vectors, "to" a domain that is no longer changing--the evolution of states comes to a halt, the wavefunction has collapsed we say.

    But all we do is put a screen in the way and read off the eigenvalues. Does a projection of an eigenstate to an eigenvalue (a classical measurement) really change anything? Or is it simply a necessary condition so that we have something we can store in a memory? That is to say, the notion of "wavefunction collapse" is something conscious observers project onto states?

    Maybe I've been reading too much of Penrose's ideas.
     
  13. quantum_wave Contemplating the "as yet" unknown Valued Senior Member

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    You are correct about that from what I have read. When you think about the energy that causes a molecule in an emulsion to turn dark, the energy doesnt stop there. It is consereved and changes the energy surrounding the molecule and continues on in new superpositions/entanglements until it is again measured in some way.
     
  14. arfa brane call me arf Valued Senior Member

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    And so, the measurement "problem" is that the projection of states into a patten of static dots represents a memory.

    We have to imagine that we can use this to project everything backwards in time to the quantum measurements, outgoing mixed states in a beam that are absorbed by an electron sink.
    The memory (static image) implies this, but quantum mechanics doesn't allow it--there is no time-symmetry, we require the notion so we can explain cause and effect. We invent another notion of collapse of wavefunctions into probable values.
     
  15. quantum_wave Contemplating the "as yet" unknown Valued Senior Member

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    If you phrase it like that, yes the static dots are a "memory" of the events of the decoherence of the wave-particle; the wave-particle being a single electron for each dot, in the context of your thread. That said, as you implied in the previous post, that event is an observation or measurement, but not the final resting place of the particle's energy. The energy is disbursed outwardly from the dot.
    True, we can contemplate the process backwards through the apparatus.
    True, but since the postulates of QM are the same for every interpretation of them, having observables and measurements resulting from the sequence of events lends itself to those kinds of notions. Conceiving of the process backwards in time is part of determining your preferred interpretation of QM.
     
  16. arfa brane call me arf Valued Senior Member

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    That's an interesting thing to say. How do you contemplate a process like that without being able to reverse the direction of time?
     
  17. Fednis48 Registered Senior Member

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    I think the following nicely illustrates how far we can go treating quantum measurement collapse as just an interpretational/perceptional thing, and why doing so eventually breaks down.

    Consider a very simple experiment, in which we send a photon through a beamsplitter. The photon is in a superposition of two states: travelling down path 1, and travelling down path 2. Now say we have photodetectors at the ends of the paths. When the photon gets to the end of one path or another, it interacts with the photodetector and produces a current. If we're interested in a practical application, we would probably say this is when the photon is measured. But we don't have to - we can say the system is still in a superposition, but now the photodetectors are entangled with the photons. To put it a little more formally, the two states are now [photon is on path 1 and photodetector 1 has a current] and [photon is on path 2 and photodetector 2 has a current]. The Hamiltonian describing the full photon+photodetector system is extremely complicated, so the quantum phase between the two states will transform in a similarly complicated way, and it will effectively become randomized before long. Even if we had a way to bring the two states back together and interfere them, the random phase would prevent us from seeing fringes or other signatures of coherence. This is why we can get away with calling the event a measurement; as arfa brane mentioned, modern theories often treat any such phase-randomizing interaction with the environment as a measurement.

    To reiterate, the two states now in superposition have essentially zero chance of interfering again at a later time. But quantum mechanics is linear, so each state can continue its normal time-evolution without regard to the other. The current in the photodetectors becomes entangled with the hard drive of the computer monitoring them, which in turn becomes entangled with its monitor, and then with the photons bouncing off the monitor... on and on until each state involves a highly-entangled mess of particles all over the room. But still, there's no reason we can't keep treating it as a quantum superposition. Now say someone looks at the computer monitor. The photons from it become entangled with the molecules in her retina, and from there with the state of her brain. Notwithstanding all the other degrees of freedom in play, the researcher's brain is now in a quantum superposition of having observed outcome 1 and having observed outcome 2. Now, in terms of predicting the results of experiments, there's still nothing wrong with this picture. But in terms of everyday experience, it's clearly absurd. We don't experience superpositions of brain states; we experience one state at a time, and which one we experience seems to be a random selection from all the states available at the time. So what it boils down to is this: somewhere between the clearly quantum pre-environmental-interaction state and our brains, the wavefunction collapses. According to hidden variable interpretations, the "collapse" is there from the very beginning, and we only think the state is ever in a superposition because we don't understand all the hidden variables. According to the many worlds interpretation, our brains actually do go into a quantum superposition, but our conscious minds somehow pick one state out of the superposition to experience. I'm sure there are a lot of other proposed resolutions. But it's far from a settled question, and there's definitely something deeper going on than just human perception of quantum superposition.
     
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  18. arfa brane call me arf Valued Senior Member

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    Well, perhaps even more absurd is that a thousand double slits and screens can collect random patterns, then stop. If the patterns aren't put in the same frame, is there a recording of an interference pattern?

    Yes, each random pattern and the (mathematical) union of random patterns is a record, but no, there is no interference pattern if they stay separated, or if some computer doesn't scan all the images or enough of them to halt when it sees a pattern. When does classical information exist, then?
     
  19. Q-reeus Banned Valued Senior Member

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    In the ideal case all the energy is absorbed and locked up fapp permanently within that chemical/physical change. If 'the energy' just bounces off and goes elsewhere, no permanent change has occurred, just a reversing of a reversible process, hence no measurement in the usual sense.
     
  20. Q-reeus Banned Valued Senior Member

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    Err..think that was me, in #25.
    Yes, that it's very much bound up with interpretations is something I forgot to mention but put nicely there. Even within interpretations there can be divergence - e.g. Bohr/Heisenberg within Copenhagen interpretation, as explained in that article linked to in #19.
     
  21. arfa brane call me arf Valued Senior Member

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    Anyone who looks at quantum mechanics, not necessarily by enrolling in a course at say, a university, encounters the interpretations of it.

    Why is QM a theory that has several interpretations? Why do we need them? Maybe we don't.
     
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  22. brucep Valued Senior Member

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    Several is an understatement. The interpretations are considered a pedagogical tool for helping students understand how the theory works. They all recover the same predictions as the mother theory. Or they're not an interpretation.
    The following is three posts from Mr_Homm. Who is a Professor of physics and mathematics at UW. This is something you might find interesting.

    Mr_Homm's treatise on the Copenhagen interpretation and Heisenberg's uncertainty principle. The thread was 'A simple question'. Scroll down to the date and time I list for the Mr_Homm posts.

    This was the first installment: Mr_Homm, Jan. 23, 2008 05:41 AM

    http://www.physforum.com/index.php?showtopic=19663&st=0

    This was the second installment: Mr_Homm, Jan. 26, 2008 06:22 AM

    http://www.physforum.com/index.php?showtopic=19663&st=15

    Final installment: Mr_Homm Jan. 30, 2008 06:15 AM

    http://www.physforum.com/index.php?showtopic=19663&st=30

    Even though I think Mr_Homm might think I'm silly I consider his three posts on the Uncertainty Principle and the Copenhagen Interpretation the most informative I've read on QM. It really works for me since much of the discussion is about the Hilbert Space and choice of coordinates. I messed up it's mr_homm not the way I wrote with capitals.
     
    Last edited: Aug 9, 2015
  23. quantum_wave Contemplating the "as yet" unknown Valued Senior Member

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    I was referring to the case where the absorbed energy of the electron into the molecule changes that molecule permanently fapp, and yields the observation of a black dot, and was not referring to the case of a non-measurement were the energy bounces off. My statement was made from the perspective that some physicists hold that particles are standing waves. Standing wave particles would be composed of inflowing and out flowing wave energy, and so the energy absorbed would be inlowing, and there would be a corresponding out flowing component, even while the molecule and the particles that make it up continue to dispaly the change from a white to a black dot. Given that perspective, the energy absorbed is rapidly disbursed as out flowing wave energy, while the standing wave particle has a continued stable presence.
     

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