2016 International Workshop on Quantum Observers

Measurements as External Constraints

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    Ken Wharton

    When two systems are in spatial contact, it’s natural for the bigger system to constrain the smaller system, not vice-versa. For instance, consider classical statistical mechanics. When one system has an overwhelming number of possible internal states, it will act like a thermal reservoir for smaller systems in contact with it, constraining the entirety of the smaller system. From this statistical perspective, any macroscopic device-system should act as a strong external constraint on any microscopic quantum-system. (On a microscale both systems will be correlated via the interaction, so each system “knows” something about the other — this is the unproblematic “informational” aspect of measurement. The asymmetry lies not in the correlations, but the constraints: the larger system forces the smaller system into a special, even unlikely, configuration — this is the “invasive” aspect of measurement.) Such a conclusion is in general agreement with observations: measured quantum systems seem constrained to a small subset of their generic possibility space.

    But even though this statistical logic is clear for spatially-adjacent systems, our intuition suddenly changes when it comes to systems that span a region of spacetime. The question of which system is “bigger” is now assumed to be trumped by temporal order. For quantum measurement, this is a typical context: a small quantum system is spatiotemporally adjacent to a large macroscopic device, but the small system is typically earlier, and the device is typically later. No longer it is assumed that the large device constrains the small system; in fact, it is almost always assumed that the large device can have no affect on the system — at least, not at spacetime locations before the interface. But without a constraint that extends at least somewhat into the quantum system, one encounters the usual discontinuities and problems concerning quantum measurement.

    This curious trumping of temporal order over statistical logic is a result of framing our physical models in terms of the “Newtonian Schema”, the standard dynamical framework more fully defined in the attached paper. In this widely-assumed schema, past states generate future states via dynamical rules (either deterministic or stochastic), such that the setting of a measurement device can only constrain the future. But while the quantum measurement problem is almost always analyzed from this perspective, many physicists do not realize that the Newtonian Schema is merely an assumption — an assumption to which there is a clear alternative.

    This alternative is the Lagrangian Schema, also discussed in the attached paper. In any Lagrangian- or action-based framework, entire spacetime regions are analyzed “all at once”, not in sequential spacelike slices. In this framework one imposes boundary constraints not only at the beginning, but also at the end. (In general, on a closed hypersurface around the region in question.) From such a perspective, it is far more natural to think of a (large) future measurement apparatus as constraining a (small) prior quantum system; in fact, such a constraint is already present in the mathematics of such approaches, but typically viewed as a mathematical trick rather than a true external constraint.

    Granted, the most familiar Lagrangian framework is when one exactly extremizes the action. This leads to classical physics, arguably equivalent to a Newtonian Schema governed by Euler-Lagrange dynamics. But quantum theory has proven to us that the classical action is *not* generally extremized. More generally, the Lagrangian Schema has variants which cannot be mapped onto dynamical processes at all, and in those variants the logic which leads to the primacy of temporal order is suspect.

    The attached paper explains in detail how statistical considerations still apply in Lagrangian-Schema models, even in the complete absence of dynamical rules. In the examples, it is the external observer-chosen future settings that naturally constrain the allowable states of prior quantum systems. This is strongly counter-intuitive to those thinking in a Newtonian-Schema-mindset, but tellingly, this approach leads to precisely the type of counter-intuitive phenomena that are already evident from quantum experiments.

    This perspective also clarifies which types of interactions should be treated as external measurement constraints: those with a much greater number of degrees of freedom than the system being measured. (As applied to a familiar thought experiment, opening a box and “looking” at a cat should not in any way be treated as a measurement of the cat; the massive cat would constrain its nearby electromagnetic field far more than vice-versa.) The statistical perspective allows for nested constraints (large systems can be constrained by still larger systems) but does not lead to an infinite-regress of measurements. The obvious ultimate constraint would simply be cosmological boundary conditions (the closest, dominant one being the Big Bang).

    Beyond helping us to better understand quantum phenomena, framing measurements in the Lagrangian Schema permits a new perspective on how external observers might meaningfully influence quantum systems — a live alternative that is typically overlooked. If an observer’s free decisions, made external to some quantum system, can constrain the entirety of that system (even at times before the decision is made!), then observers have a much greater influence than is typically considered possible. By taking this potential influence into account, we might be less likely to insist on forcing quantum theory to conform with our innate Newtonian Schema intuitions, opening up new perspectives and opportunities.

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