How isolated must a system be for it's wave function to be considered not collapsed?

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Solution 1

''How isolated must a system be for it's wave function to be considered not collapsed?''

Experimentally, a system whose collapse is observable must be so small that one can prepare it in a well-defined pure state. If this is not the case, one can only speculate about what happened, leaving much room to imagination.

This means that even when the carrier of the system is fairly big, the wave function collapsed models only extremely few degrees of freedom, and the real system considered is the one with these few degrees of freedom, not the bigger one.

For example, arXiv:1103.4081 discusses superposition and collapse of macroscopic objects. But prepared in a superposition is only a single degree of freedom, the distance; all other degrees of freedom are either uncontrolled (and hence presumably in a mixed state) or eliminated by extreme cooling. Thus the system measured is in effect a single quantum oscillator.

Now a typical quantum oscillator decoheres rapidly unless isolated, and a quantum oscillator of some size is hard to isolate. The experimental art consists in maintaining a superposition of two distances by isolating this particular degree of freedom from the environment. This isolation must be almost perfect, as otherwise decoherence effects responsible for the collapse set in extremely rapidly. (No special observer is needed. The environment does the observing by itself.)

''why most physicists [...] reject objective collapse.''

The main reason is that they want to maintain the simplicity of the traditional quantum mechanical foundations that are based on the assumption that the dynamics of quantum states is exactly linear, which seems to suffice for all applications. Objective collapse theories would require a tiny nonlinear modification of the basic laws, and spoil simplicity for (so far) uncheckable philosophy.

Note that ''no objective collapse'' doean't mean that collapse isn't observable (it is observed routinely), but only that the collapse is not due to decoherence (the approximation in which the collapse is derivable in terms of generally believed assumptions from statistical mechanics - needed already in classical physics) but to objective deviations from the Schroedinger equation. The latter has no observable basis, and hence is rejected by most physicists.

Solution 2

The minute you make the box able to change the surroundings, it ceases to be just a box; and becomes a measuring device.

How this happens can be easily visualised. Lets take an ideal geiger counter-atom setup in a similar box. It is wired outside to a display. Now, for obvious reasons, the atom wavefunction will be immediately collapsed. It will not slowly evolve. This is because you can observe the system using the display. We cannot argue that the geiger counter's wavefunction itself will be affected.

A more stark way of formulating your problem is by attaching the counter to a hammer. If, within the first xyz seconds, there is a decay, the hammer wil strike the box lid; opening it. If you are outside, and the box does not open in xyz secs, you will know that there were no decays, and will have collapsed the wavefunction WITHOUT opening the box. Here, the counter did not become a measuring device by affecting the surrounding; it did so by its ability to affect the surroundings.

Your box is again a measurement device, with the ability to affect the surroundings. Same thing happens, it immediately collapses the wavefunction.

Now to your original question: Anything that can affect the surroundings in a measurable way on the basis of whatever property is being measured counts as a measuring device for that property in the surroundings.

Now heres where everything goes crazy: I've specifically kept the weasel words 'in a measurable way' as QM observations are a fuzzy and conttoverersial topic. May be only conscious beings can make an observation. Maybe only beings who know the implication of their measurement can collapse the wavefunction (so a random person who sees the lever shift but doesn't know what the shift signifies won't collapse it). In the latter case, stuff like 'negligible effects' also create an issue, as the experimenter can't conscously register them and segregate them from 'noise', even though they might feel it.. For example, your geiger counter can emit a photon depending on the results. An experimenter can see the photon with his eyes (our sight is a photon phenomenon),but not register it. Im assuming that the experimenter doesn't have photon detectors.

From there onwards, it gets more philosophical. Which is IMHO why physicists have gone 'shut up and calculate' as @JohnRennie mentioned.

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Updated on August 01, 2022

Comments

  • AdamRedwine
    AdamRedwine 6 days

    As an undergrad I was often confused over people's bafflement with Schodinger's cat thought experiment. It seemed obvious to me that the term "observation" referred to the Geiger counter, not the person opening the box. Over time, I have come to realize that the Copenhagen interpretation actually is ambiguous and that "observer" cannot be so easily defined. Nonetheless, an objective collapse theory (which is what I was unknowingly assuming) still seems to me the simplest explanation of wave collapse phenomena.

    I have read some of the objections cited in the Wikipedia article linked above, but it is still unclear to me why most physicists adopt the Copenhagen interpretation and reject objective collapse. For example, in this question on hidden observers, there was some discussion about the mechanism of wave collapse. It was suggested that perhaps the gravitational pull of a hidden observer would collapse the wave function. In response, it was pointed out that the gravitational pull would be negligible at the scales involved.

    Okay, then imagine the following:

    A hermetically sealed (i.e. isolated) box is balanced on a fulcrum. Inside the box is a radioactive isotope, a Geiger counter, and a trigger mechanism connected to a spring loaded with a mass on one side of the box. If the Geiger counter detects a decay, the trigger releases the spring and the mass shifts to the other side of the box. The shift in mass would, under observable conditions tilt the box on the fulcrum.

    According to the interpretation of Schrodinger's cat that I often hear (the cat is in a superposition) it seems that the box should slowly tilt over as the wave function of the system evolves with the half-life of the isotope. I can't imagine that anyone thinks this is a realistic expectation.

    I can see that people might object and say "But the contents of the box are interacting gravitationally with the outside system and observer so it is not really isolated!" Well, what of it? The same is true of the cat even if the interaction is less dramatic.

    The question, then, is: How isolated must a system be for it's wave function to be considered not collapsed?

    • AdamRedwine
      AdamRedwine over 10 years
      Also, I find it odd that an appeal to parsimony is cited as one of the objections to objective collapse. It seems to me that defining and incorporating the necessity of an "observer" in every system is less parsimonious.
    • dmckee --- ex-moderator kitten
      dmckee --- ex-moderator kitten over 10 years
      To first order I think this is a "question [which] will likely solicit opinion, debate, arguments, polling, or extended discussion.", and I considering closing it on that basis, but I would like to hear opposing views.
    • dmckee --- ex-moderator kitten
      dmckee --- ex-moderator kitten over 10 years
      Nor is it clear to me that the introductory text books which cite The Copenhagen Interpretation actually care about the alleged role of a observer beyond getting to explain the cat-in-a-box gedanken experiment. // irrelevant off the ball suggestion: the short story "Schödinger's Cat Lady" by Marjorie James, which was read for EscapePod.org and is therefore available under a CC license
    • John Rennie
      John Rennie over 10 years
      Speaking as an outsider, the impression I get is that most physicists are in the "shut up and calculate" camp. The foundations of QM articles that I see seem to come from a small section of the community.
    • AdamRedwine
      AdamRedwine over 10 years
      @dmckee: I think you're right about the commentary... I'll try to revise it sometime today, but if it gets closed, I understand.
    • kartsa
      kartsa over 10 years
      Slowly downwards evolving wave function of a box interacting gravitationally with wave function of the earth is not a problem. There is interaction, but there is no information exchange type of interaction.
    • Admin
      Admin almost 9 years
      Collapsed/uncollapsed is the wrong distinction; collapse is unobservable even in principle, and is only present in some interpretations of QM, not others. Coherent/decoherent would be a better distinction. Related: physics.stackexchange.com/questions/59426/…
  • Ron Maimon
    Ron Maimon over 10 years
    I didn't downvote, but D-wave Systems is not a very reliable source, they have a financial stake in their system working, and it is difficult to imagine that they surmounted the difficulties others have no clue how to surmount.
  • AdamRedwine
    AdamRedwine over 10 years
    I think that's the clearest explaination I've heard. Thanks.