Are Quantum Probabilities Merely Epistemic?

(Wissenschaftstheorie, Englisch)

n Quantum Mechanics (QM), the state of an isolated system is described by a state function (or state vector) |ψ>. This state function describes the system as being in a superposition of different definite states with respect to a certain class of observable properties. From this state function one can derive the probability of measuring each definite value of the system for a given observable in a respective measurement procedure. Standard interpretations of QM consider these state functions to be complete descriptions of a system's state. Hence on this kind of an account, under certain circumstances the system has no definite value for any of its observables.

From its very beginnings, QM has been subject to considerable doubt and criticism (famously also by Albert Einstein; cf. Einstein Podolski and Rosen 1935), and attempts have been made to interpret its astonishing features (such as superposition) as mere reflections of incomplete knowledge. One such approach to QM, often simply referred to as the statistical interpretation, is quite widespread throughout modern textbooks (cf. Grifftiths 1995). But more recently, approaches from Quantum Information Theory also attempt to give credence to the epistemic view of quantum states. One particular examlple is the Spekkens toy model approach, which presents a model of incomplete knowledge and then gives a numer of analogies to QM (cf. Spekkens 2007; Harrigan and Spekkens 2010).

However, three powerful arguments exist that weaken this approach: the famous theorem by John Bell (1964), the (not much less famous) Kochen-Specker Theorem (1967), and the recently developed argument by Pusey, Barrett, and Rudolph (PBR Argument) (2012). Bell's Theorem shows that any interpretation of QM which attempts to explain its odd features in terms of hidden variables (and hence in terms of incomplete knowledge) has to be non-local; i.e.: there has to be a special kind of connection between certain types of quantum systems (entangled quantum systems) which enables them to communicate at a speed faster than the speed of light. This, however, leads to a conflict with the special theory of relativity which does not permitt such communication. The Kochen-Specker Theorem shows that any such interpretation has to be contextual, i.e., the outcome of measuring a certain observable will in some cases depend on which other observables it is measured with. Finally, the PBR Argument suggests that if quantum states would be a reflection of incomplete knowledge, there should be the possibility of overlaps in the probability distributions corresponding to two distinct quantum states |ψ(0)> and |ψ(1)>. This assumption can be shown to lead to a contradiction with the predictions of quantum mechanics.

It is crucial to note that bell's theorem (or, more precisely, its key ingredient, the violation of Bell-type inequalities) has been tested experimentally.

Furthermore, PBR offer a suggestion of how to test for the implications of their theorem as well.

I will argue that those three arguments suffice to render the epistemic approach to quantum states futile, as the virtue of such an approach lies in explaining the counter-intuitive features of QM away. Since this cannot be done, QM must be taken to reveal something important and profound about the foundations of the physical world. This in turn suggests that the philosophic implications of QM should be taken seriously and a clear interpretation of quantum states must be of key interest to philosophers of science and ontologists.

References

1 Bell, J. S. 1964. ''On the Einstein Podolsky Rosen Paradox'', Physics 1 (3), 195200.

2 Einstein, A., Podolski B. and Rosen, N. 1935. ''Can quantum-mechanica description of physical reality be considered complete?'', Physical Review 47, 777-780.

3 Griffith, David J. 1995. Introduction to Quantum Mechanics. New Jersey: Prentice Hall.

4 Harrigan, N. and Spekkens, R. 2010. ''Einstein, incompleteness and the epistemic view of quantum states'', Foundations of Physics 40, 125-157.

5 Kochen, S. and Specker, E. 1967. ''The Problem of Hidden Variables in Quantum Mechanics'', Journal of Mathematics and Mechanics 17, 59-87.

6 Pusey, M.F., Barrett, J., and Rudolph, T. 2012. ''On the reality of the quantum state'', Nature 8, 475-478.

7 Spekkens, R. 2007. ''Evidence for the epistemic view of quantum states: A toy theory'', Phys. Rev. A 75, 032110.

Chair: Christine Schurz

Zeit: 17:30-18:00, 12. September 2013 (Donnerstag)

Ort: HS 105

Florian Boge

(Universität zu Köln, Deutschland)

Florian Boge is a PhD student in Philosophy and an undergraduate student in Physics at the University of Cologne. He finished his M.A. study in Philosophy in 2012 with a thesis on trope ontology an similarity relations. He has since taught several undergraduate classes on epistemology, ontology and the philosophy of science at the University of Düsseldorf. He ist currently working on the philosophic questions raised by quantum mechanics. His main interest is in the relation between quantum mechanics and the question of reality.

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Letzte Aktualisierung: 2013-02-14.