Quantum measurements as weighted symmetry breaking processes: the hidden measurement perspective

The purpose of the present note is twofold. Firstly, we highlight the similarities between the ontologies of Kastner's possibilist transactional interpretation (PTI) of quantum mechanics - an extension of Cramer's transactional interpretation - and the authors' hidden-measurement interpretation (HMI). Secondly, we observe that although a weighted symmetry breaking (WSB) process was proposed in the PTI, to explain the actualization of incipient transactions, no specific mechanism was actually provided to explain why the weights of such symmetry breaking are precisely those given by the Born rule. In other terms, PTI, similarly to decoherence theory, doesn't explain a quantum measurement in a complete way, but just the transition from a pure state to a fully reduced density matrix state. On the other hand, the recently derived extended Bloch representation (EBR) - a specific implementation the HMI - precisely provides such missing piece of explanation, i.e., a qualitative description of the WSB as a process of actualization of hidden measurement-interactions and, more importantly, a quantitative prediction of the values of the associated weights that is compatible with the Born rule of probabilistic assignment. Therefore, from the PTI viewpoint, the EBR provide the missing link for a complete description of a quantum measurement. However, EBR is in a sense more general than PTI, as it does not rely on the specific notion of transaction, and therefore remains compatible with other physical mechanisms that could be at the origin of the measurement-interactions. [http://arxiv.org/pdf/1601.05222v1.pdf]

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Avatar of Massimiliano Sassoli de Bianchi

3 Responses

  1. Ruth Kastner
    Ruth Kastner at | |

    The author is entitled of course to present his own preferred deterministic model of measurement. But the paper goes too far in its characterization of another interpretation’s account of measurement as ‘incomplete’ based on the author’s own particular (optional) metaphysical preference. Nature may not in fact behave in the deterministic way that his model proposes. Thus, an indeterministic model such as TI cannot be fairly characterized as missing something deterministic if Nature is not in fact deterministic.

    Similarly, the author seems to have expectations for a derivation of the Born Rule that misconstrues the Rule as applying to a measurement process that leads deterministically to one outcome. But that is not what it is. The Born Rule is no more and no less than a rule for obtaining the probability of each outcome as a square of the probability amplitude for that outcome; as noted in the Stanford Encyclopedia of Philosophy, it is a “definition of the probabilities for measurement results.” (http://plato.stanford.edu/entries/qt-nvd/)
    The author seems to be confusing the Born Rule with the second stage of von Neumann’s “Process 1,” in which the density operator manifesting the Born Rule (as weights of a sum of projection operators) collapses to a single projection operator. But that is not a part of the Rule.

    To derive something means to trace the origin of that thing from a source (e.g., Merriam-Webster). The Transactional Interpretation obtains the quantities appearing in the Born Rule from a specific theoretical source--the direct action theory of fields. The weights of outcomes (that latter represented by projection operators) derived from the direct-action theory are the absolute squares of the Schrödinger probability amplitude. That is a derivation of the Born Rule. To say that it is not is to say that Schrödinger failed to ‘derive’ that his wave equation was an equation for a probability amplitude, which is to confuse physics with mathematics. All physical theories must have physical correlates, and those are a matter of empirical correspondence, not mathematical deduction.

    Thus the author’s allegation that TI is incomplete is just a statement that it does not satisfy an optional metaphysical preference for a deterministic account that the author apparently does not recognize as optional. If the wave function is a probability amplitude (the square root of a probability), then an interpretation showing that each outcome is associated with the square of the probability amplitude is to show that that outcome is characterized by that probability—which is the entire content of the Born Rule. That is, TI clearly derives von Neumann’s “Process 1,” but the author apparently does not recognize von Neumann’s Process 1 transition as an expression of the Born Rule—at variance with all precedent in the peer-reviewed literature on this topic, as far as I know.

    If the author wants to insist that TI does not derive the Born Rule in the sense that the square of the wave function corresponds to a probability, then he must also criticize Schrödinger for not ‘deriving’ that his equation was an equation for a probability amplitude. As noted above, the wave function has as its basic physical correlate a probability amplitude. That is not subject to mathematical derivation from any more basic principle, unless additional assumptions are imposed that might not even be correct, such as an epistemic interpretation of quantum probability--which is what the author appears to be assuming without recognizing it.

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