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arXiv:1603.09463

$ψ$-Epistemic Models, Einsteinian Intuitions, and No-Gos. A Critical Study of Recent Developments on the Quantum State

Florian J. Boge

Published Mar 31, 2016• 0 citations
arXivHTMLPDF

Abstract

Quantum mechanics notoriously faces the measurement problem, the problem that if read thoroughly, it implies the nonexistence of definite outcomes in measurement procedures. A plausible reaction to this and to related problems is to regard a system's quantum state $|ψ\rangle$ merely as an indication of our lack of knowledge about the system, i.e., to interpret it epistemically. However, there are radically different ways to spell out such an epistemic view of the quantum state. We here investigate recent developments in the branch that introduces hidden variables $λ$ in addition to the quantum state $|ψ\rangle$ and has its roots in Einstein's views. In particular, we confront purported achievements of a concrete model that has been considered to serve as evidence for an epistemic view of the envisioned kind, as well as specific no-go results and their import. It will be argued that while an epistemic account of the particular kind is not straightforwardly ruled out by the no-go results, they demonstrate that the evidential character of the model(s) discussed rests on a rather shaky foundation, and that they make some achievements widely recognized in the literature appear worthy of doubt.

DOI
10.48550/arxiv.1603.09463

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ψψψ-Epistemic Models, Einsteinian Intuitions, and No-Gos. A Critical Study of Recent Developments on the Quantum State
Quantum mechanics notoriously faces the measurement problem, the problem that if read thoroughly, it implies the nonexistence of definite outcomes in measurement procedures. A plausible reaction to this and to related problems is to regard a system's quantum state ∣ψ⟩|ψ\rangle∣ψ⟩ merely as an indication of our lack of knowledge about the system, i.e., to interpret it epistemically. However, there are radically different ways to spell out such an epistemic view of the quantum state. We here investigate recent developments in the branch that introduces hidden variables λλλ in addition to the quantum state ∣ψ⟩|ψ\rangle∣ψ⟩ and has its roots in Einstein's views. In particular, we confront purported achievements of a concrete model that has been considered to serve as evidence for an epistemic view of the envisioned kind, as well as specific no-go results and their import. It will be argued that while an epistemic account of the particular kind is not straightforwardly ruled out by the no-go results, they demonstrate that the evidential character of the model(s) discussed rests on a rather shaky foundation, and that they make some achievements widely recognized in the literature appear worthy of doubt.
Quantum mechanics notoriously faces the measurement problem, the problem that if read thoroughly, it implies the nonexistence of definite outcomes in measurement procedures. A plausible reaction to this and to related problems is to regard a system’s quantum state |ψ> merely as an indication of our lack of knowledge about the system, i.e., to interpret it epistemically. However, there are radically different ways to spell out such an epistemic view of the quantum state. We here investigate new developments in the branch that introduces hidden variables λ in addition to the quantum state |ψ> and has its roots in Einstein’s views. In particular, we confront purported achievements of the view in the light of recent no-go results. It will be demonstrated that, despite the debatability of the premises of such results, they force the hidden variable theorist to make ad hoc moves which undermine the very conceptual basis of his own approach.
Since the famous debates of Einstein & Bohr, physicists have argued about the nature of the quantum state. Is it best thought of as describing the-way-things-are out there in the world, or merely as a description of our knowledge of such things? In more recent years, this has been termed the ψ-epistemic/ψ-ontic debate, and that distinction has been given a mathematical definition within the ontological models formalism. This formalism is a framework for describing a large class of interpretations of quantum mechanics. Here we show that consideration of sequential measurements, and the fact that the quantum state changes during measurements, has been a neglected topic in this area as it places nontrivial restrictions on the structure of ψ-epistemic ontological models. \n \nWe do this by finding a general restriction on the structure of ψ-epistemic models, although not one that is strong enough to rule them out categorically. We then apply this restriction to all of the known examples of ψ-epistemic ontological models and show that they can’t represent sequential measurements. We also present a new version of the ontological models formalism, based on hidden Markov models, which we develop briefly and describe how it may be useful for either proving a no-go theorem (i.e. ‘ψ-epistemic models can’t exist’) or for learning more about the structure of ψ-epistemic models and how to construct them.
The quantum state ψ is a mathematical object used to determine the probabilities of different outcomes when measuring a physical system. Its fundamental nature has been the subject of discussions since the inception of quantum theory. Is it ontic, that is, does it correspond to a real property of the physical system? Or is it epistemic, that is, does it merely represent our knowledge about the system? Assuming a natural continuity assumption and a weak separability assumption, we show here that epistemic interpretations of the quantum state are in contradiction with quantum theory. Our argument is different from the recent proof of Pusey, Barrett, and Rudolph and it already yields a nontrivial constraint on ψ-epistemic models using a single copy of the system in question.
A quantum state, via the Born Rule, assigns probabilities to the different possible values of observables of a quantum system. It is only in virtue of these probabilities — or, alternatively, expectation values — that quantum mechanics is empirically testable. Since assigning a state to a system means assigning probabilities to the values of observables, it may seem natural to read Peierls’ claim that the state ‘represents our knowledge of the system’ (Peierls [1991], p. 19) as a shorthand for saying that the state represents our knowledge of these probabilities. The latter view is sometimes even straightforwardly identified with the epistemic conception of states, for example by Marchildon, who claims that ‘[i]n the epistemic view [of quantum states], the state vector (or wave function or density matrix) does not represent the objective state of a microscopic system […], but rather our knowledge of the probabilities of outcomes of future measurements’ (Marchildon [2004], p. 1454). However, according to an argument due to Fuchs and endorsed by Timpson, 31 the idea that quantum states represent our knowledge about quantum probabilities should not be regarded as the core claim of the epistemic conception of quantum states, simply because, as they argue, this idea is in fact incompatible with the latter. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
ψ -epistemic interpretations of quantum theory maintain that quantum states only represent incomplete information about the physical states of the world. A major motivation for this view is the promise to provide a reasonable account of state update under measurement by asserting that it is simply a natural feature of updating incomplete statistical information. Here we demonstrate that all known ψ -epistemic ontological models of quantum theory in dimension d≥3 , including those designed to evade the conclusion of the PBR theorem, cannot represent state update correctly. Conversely, interpretations for which the wavefunction is real evade such restrictions despite remaining subject to long-standing criticism regarding physical discontinuity, indeterminism and the ambiguity of the Heisenberg cut. This revives the possibility of a no-go theorem with no additional assumptions, and demonstrates that what is usually thought of as a strength of epistemic interpretations may in fact be a weakness.
Ψ-epistemic models of quantum mechanics imply that the quantum state does not correspond to physical reality, but instead reflects the observer's knowledge of the underlying quantum system. The epistemic view of the quantum state has the potential to shed light on several foundational problems of quantum theory and has attracted considerable attention in the literature. On the other hand, the Pusey-Barrett-Rudolph theorem demonstrated that broad classes of ψ-epistemic models must lead to predictions that deviate from those of quantum mechanics. Although the original theorem involved entangled joint measurements on composite systems, alternative no-go theorems involving measurements on single quantum systems were developed shortly thereafter. Experimental investigations of the deviations predicted by ψ-epistemic models from quantum mechanics are still ongoing. So far, such tests have been performed within the framework of non-relativistic quantum mechanics and predominantly rely on quantum information based measurement procedures. In this work, we show that ψ-epistemic models can give rise to deviations from standard quantum field-theoretic predictions through modifications of polarized scattering cross sections and decay widths. Our results do not require a relativistic formulation of ontological models or of the Harrigan-Spekkens criterion; the essential assumption is merely that measurements implemented through relativistic processes can still be represented within the ontological framework by well-defined response functions and probabilities. The present work constitutes a proof-of-principle study demonstrating that particle physics tests of the ontological status of the quantum state are possible and that ψ-epistemic models may exhibit experimentally distinguishable signatures in particle phenomenology.