2017 International Workshop: Collapse of the Wave Function

Three arguments for the reality of wave-function collapse

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    Shan Gao
    Shan Gao

    Quantum mechanics is an extremely successful physical theory due to its accurate empirical predictions. The core of the theory is the Schrodinger equation and the Born rule. The Schrodinger equation is linear and it governs the time evolution of the wave function assigned to a physical system. The Born rule says that the result of a measurement on a physical system is definite but generally random, and the probability is given by the modulus squared of the wave function of the system. However, when assuming the wave function of a physical system is a complete description of the system, the linear Schrodinger equation is apparently incompatible with the Born rule, in particular the appearance of definite results of measurements. This leads to the measurement problem. Maudlin (1995) gave a precise formulation of the problem in terms of the incompatibility.
    Correspondingly, the three approaches to avoiding the incompatibility lead to the three main solutions to the measurement problem: Everett’s theory, Bohm’s theory and collapse theories.

    It is widely thought that these theories can indeed solve the measurement problem, although each of them still has some other problems. Then, which solution is the right one? Although there have been many analyses of this issue, the investigation seems still not thorough and complete.
    In my view, there are still three possible ways to examine these competing solutions before experiments can finally test them.

    The first way is to analyze the link between the physical state and the measurement result, and in particular, whether the link satisfies certain principles or restrictions.
    In Everett’s theory, Bohm’s theory and collapse theories, the measurement results are represented by different physical states. Then, which physical state represents the measurement result? There are at least two restrictions. The first one is the Born rule; the measurement result represented by a certain physical state should be consistent with the Born rule. This is not so obvious as usually think, and as I have argued, Bohm’s theory seems to be problematic (a more recent version) in this aspect.

    The second restriction concerns the psychophysical connection. It has been realized that the measurement problem is essentially the determinate-experience problem (Barrett, 1999). In the final analysis, the problem is to explain how the linear dynamics can be compatible with the existence of definite experiences of conscious observers. This requires that the physical state representing the measurement result should be also the physical state on which the mental state of an observer supervenes. The restriction is then the form of psychophysical connection required by a quantum theory should satisfy the principle of psychophysical supervenience. As I have argued, it seems that Everett’s theory fails to satisfy this restriction.

    The second way to examine the solutions to the measurement problem is to analyze whether they are consistent with the meaning of the wave function. The conventional research program is to first find a solution to the measurement problem, such as Bohm’s theory or Everett’s theory or collapse theories, and then try to make sense of the wave function in the solution. By such an approach, the meaning of the wave function will have no implications for solving the measurement problem. However, this approach is arguably problematic.
    The reason is that the meaning of the wave function (in the Schrodinger equation) is independent of how to solve the measurement problem, while the solution to the measurement problem relies on the meaning of the wave function. For example, if assuming the operationalist psi-epistemic view, then the measurement problem will be dissolved.

    There are two issues here. The first one concerns the nature of the wave function, and the second one concerns
    the ontology behind the wave function. Is the wave function ontic, directly representing a state of reality, or epistemic, merely representing a state of (incomplete) knowledge, or something else? If the wave function is not ontic, then what, if any, is the underlying state of reality? If the wave function is indeed ontic, then exactly what physical state does it represent? As I have argued in Gao (2017), even when assuming the psi-ontic view, the ontological meaning of the wave function also has implications for solving the measurement problem. In particular, it seems that Bohm’s and Everett’s theories can hardly be consistent with the suggested ontological interpretation of the wave function, while the suggested ontology behind the wave function may not only support the reality of the collapse of the wave function, but also provide more resources for formulating a collapse theory.

    In my view, the underlying ontology and the psychophysical connection are the two extremes that should be understood fully in the first place when trying to solve the measurement problem; the underlying ontology is at the lowest quantum level, and the psychophysical connection is at the highest classical level. It is very likely that once we have found the underlying ontology and the psychophysical connection, we will know which solution of the measurement problem is in the right direction. Certainly, we still need to understand the dynamics bridging the quantum and classical worlds.

    Finally, the third way to examine the solutions to the measurement problem is to analyze whether they are consistent with the principles in other fields of fundamental physics. A very speculative analysis is here.

    • This topic was modified 3 months, 4 weeks ago by editor editor.
    • This topic was modified 3 months, 4 weeks ago by editor editor.
    Avatar of Robert Griffiths
    Robert Griffiths

    5 June 2017

    Dear Shan,

    First me suggest you take a look at my contribution to this workshop under the heading of “Wavefunction Collapse Not Needed”, as then some of the following comments will make more sense. In particular, note the representation of physical properties by means of Hilbert subspaces or the corresponding projectors. This idea goes back to von Neumann, and has the virtue that it works both at the microscopic and the macroscopic level. Thus ‘the pointer points at 5′ corresponds to an enormously large Hilbert subspace. Measurement outcomes (pointer positions) are best described using such subspaces.

    Next, your say that

    ” …the linear Schrodinger equation is apparently incompatible with the Born rule, in particular the appearance of definite results of measurements.”

    The source of this difficulty, in my opinion, is that you are using the linear Schrodinger equation to generate what I call the ‘uniwave’, what others call ‘THE wavefunction’. It encompasses the whole universe and develops unitarily in time. Born taught us to use solutions to the Schrodinger equation (i.e., unitary time development) in order to calculate probabilities, not to describe physical reality, and if you follow Born (along with some clarifications he was not aware of) many of your troubles will disappear, though some new ones will crop up. Naturally I consider my own solution satisfactory, and am disappointed that you dismissed it in a single footnote in your book dealing with quantum ontology.

    Returning to the uniwave |W(t)>. The corresponding rank-1 projector |W(t)><W(t)| will (in general) not commute with the projector corresponding to a measurement outcome (pointer position), and this is the incompatibility you referred to. Nor does it commute with other things one might wish to express in quantum terms, such as “my coffee cup is on top of my desk”. A lof of your problems will be solved if you simply get rid of the uniwave, in which case, of course, you won’t have to collapse it. Lest I sound as if I am trying to undermine this entire Workshop, I hasten to add that I believe there is a quite legitimate use for wavefunction collapse as a convenient, though not essential, calculational tool; used in this capacity the wavefunction is what I call a “pre-probability”, and it is epistemic, not ontic. (Quantum ontology, in my opinion, should be based on Hilbert subspaces.)

    Bob Griffiths

    Shan Gao
    Shan Gao

    Dear Bob,

    Thanks for your comments! I am sorry for not discussing your ideas in detail in my book. The reason is that I have not studied your CH solution very deeply, and I cannot give my own opinions on it. I will try to study your solution in the near future.


    Avatar of Ilja Schmelzer
    Ilja Schmelzer

    Dear Shan,

    I would object to your claim (paper) about a problem of dBB with the Born rule. The point is that it is not the relative positions of the Bohm particles which matters, but their absolute positions.

    Of course, what humans perceive as a measurement result would have to be, in principle, relative. But simply including the positions of particles of the Sun, or Andromeda if you like, which can be considered not to be influenced at all from the measurement, would make absolute positions formally relative too. But we don’t even need this to see that QT is not a relativistic theory, but one with absolute space. So, simply having different absolute positions is sufficient to make a difference.

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