End of complementarity? Was Einstein right after all?…

Whereas the wavefunction is usually interpreted statistically, and it reflects our inability to know the quantum particle’s state prior to the act of measurement, a quite new paper interprets it, instead, without any respect to observation or measurement. This is the popular account and now to the more serious one…

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In philosophy we usually make a distinction between two views: the view that something corresponds directly to reality, observation-independent: refers to what is there, what is “physically real”, and independent of anything we say, believe, or know about the system.

In this case, quantum states represent knowledge about an underlying reality, real objects, real properties of quantum systems.

If we consider Schrodinger’s cat gedankenexperiment, then from the above point of view, Schrödinger’s cat in superposition of two states is a monster inside a box: both alive and dead cat at the same time. How come then when we open the box and observe (and measure) the both alive and dead cat at same time, we only see alive cat or dead cat? The orthodox interpretation of quantum mechanics invokes the collapse of the wave function whereby the act of observing the cat causes it to turn into alive-cat or dead-cat state. If the quantum state is a real physical state, then collapse is a mysterious physical process, whose precise time of occurrence is not well-defined. Accordingly, people who hold this view are generally led to alternative interpretations that eliminate the collapse, such as Everett’s relative state formulation of quantum mechanics, many-worlds theory.

The “state of knowledge” view, observation-dependent: refers to experimenter’s knowledge or information about some aspect of reality; what we think, know, or believe what is reality. We presuppose tools of observation and measurement.

In this case, the quantum state does not represent knowledge about some underlying reality, but rather it only represents knowledge about the consequences of measurements that we might make on the system; states that undergo a discontinuous change in the light of measurement results; it does not imply the existence of any real physical process.

From this point of view (anti-realist or neo-Copenhagen point of view), collapse of the wavefunction need be no more mysterious than the instantaneous Bayesian updating of a probability distribution upon obtaining new information: Hence Schrodinger’s cat is also not at all mysterious. When we consider superposition of states, both alive and dead cat at the same time, we mean that it has a fifty percent probability of being alive and a fifty percent probability of being dead (what is the likelihood of the cat being dead or alive). The process depends for its action on observations, measurements, and the knowledge of the observer. The collapse of the wave function corresponds to us observing and finding out whether the cat is dead or alive.

Erhard Scheibe introduced the notions of epistemic and ontic states of a system. The Ontic state of the system is the system just the way it is, it is empirically inaccessible. It refers to individual systems without any respect to their observation or measurement. On the other hand, the epistemic state of the system depends on observation and measurement; it refers to the knowledge that can be obtained about an ontic state.

As commonly understood, Bohr was advocating epistemic physics while Einstein was considering ontic physics. And indeed Jaynes wrote that the two physicists were not discussing the same physics: “needless to say, we consider all of Einstein’s reasoning and conclusions correct on his level; but on the other hand we think that Bohr was equally correct on his level, in saying that the act of measurement might perturb the system being measured, placing a limitation on the information we can acquire and therefore on the predictions we are able to make. There is nothing that one could object to in this conjecture, although the burden of proof is on the person who makes it”. Hence, the famous Bohr-Einstein debate was never actually resolved in favor of Bohr – although common thinking even among physicists and philosophers of science is that it was.

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The million-dollar question is: What does a quantum state represent? What is the quantum state? Is the quantum wavefunction an ontic state or an epistemic state? Using the terminology of Harrigan and Spekkens, let us ask: is it possible to construct a ψ-ontic model? A ψ-ontic hidden variable model is a quantum state which is ontic, but we construct some underlying ontic hidden variable states theory. Hidden variable theories are always ontic states theories.

Or else, is it possible to construct a ψ-epistemic model? A ψ-epistemic hidden variable model is a quantum state which is epistemic, but there is some underlying ontic hidden state, so that quantum mechanics is the statistical theory of this ontic state.

In a paper entitled, “The Quantum State Cannot be Interpreted Statistically” by Matt Pusey, Jon Barrett and Terry Rudolph (henceforth known as PBR), PBR answer the above question in the negative, ruling out ψ-epistemic theories, and attempting to provide a ψ-ontic view of the quantum state.

PBR present a no-go theorem which is formulated for an ontic hidden variable theory: any model in which a quantum state represents mere information about an underlying physical state of the system must make predictions which contradict those of quantum theory.

In the terminology of Harrigan and Spekkens, the PBR theorem says that ψ-epistemic models cannot reproduce the predictions of quantum theory.

The PBR theorem holds only for Systems that are prepared independently, have independent physical states (independent preparations). A system has an ontic hidden state λ. A quantum state ψ describes an experimenter’s information which corresponds to a distribution of ontic hidden states λ. PBR show that when distinct quantum states ψ correspond to disjoint probability distributions of ontic hidden variables (i.e., what PBR call independent preparations, they do not have values of ontic hidden variables in common), these quantum states ψ are ontic and they are not mere information. And if the states of a quantum system do not correspond to ontic disjoint probability distributions (the distributions of the values of ontic hidden values overlap), the quantum wavefunctions are said to be epistemic.

The PBR theorem is in the same spirit as Bell’s no-go theorem, which states that no local theory can reproduce the predictions of quantum theory. Bell’s theorem was formulated for ontic hidden variable theory as well. Bell’s theorem shows that a ψ-epistemic hidden variable theory which is local is forbidden in quantum mechanics, i.e, any ψ-epistemic hidden variable theory must be non-local in order to reproduce the quantum statistics of entanglement (EPR).

PBR ended their paper by saying: “For these reasons and others, many will continue to view the quantum state as representing information [epistemic]. One approach is to take this to be information about possible measurement outcomes [epistemic], and not about the objective state of a system [ontic]”; i.e., one approach is not to take this as a ψ-epistemic model. Hence, why not follow a ψ-ontic model?

Einstein would finally not emerge victorious. Although the PBR theorem favors “Einstein” who believes that quantum physics is not ontic complete, it does not rule “Bohr” who believes in quantum physics that is epistemic complete (Wavefunctions are epistemic, but there is no underlying ontic hidden variable states theory). Indeed PBR are aware of this possibility.

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It seems that the PBR theorem does not end the century-old debate about the ontology of quantum states. It does not prove, with mathematical certitude, that the ontic interpretation is right and the epistemic one is wrong.

Read my paper on the PBR theorem and Einstein.

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Another no-go theorem, Kochen–Specker (KS) theorem: non-contextual (does not depend on the context of the measurement) deterministic hidden variable theories are incompatible with quantum mechanics.

Kochen, Simon B., and Ernst .P. Specker, “On the problem of hidden variables in quantum mechanics”, Journal of Mathematics and Mechanics 17, 1967, pp. 59–87.

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