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Completely real? A critical note on the claims by Colbeck and Renner

Ronnie Hermens

Published Jul 4, 2019• 5 citations
OpenAlex

Abstract

In a series of papers Colbeck and Renner claim to have shown that the quantum state provides a complete description for the prediction of future measurement outcomes. In this paper I argue that thus far no solid satisfactory proof has been presented to support this claim. Building on the earlier work of Leifer, Landsman and Leegwater, I present and prove two results that only partially support this claim. I then discuss the arguments by Colbeck, Renner and Leegwater concerning how these results are to generalize to the full claim. This argument turns out to hinge on the implicit use of an assumption concerning the way unitary evolution is to be represented in any possible completion of quantum mechanics. I argue that this assumption is unsatisfactory and that possible attempts to validate it based on measurement theory also do not succeed.

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Completely real? A critical note on the claims by Colbeck and Renner

Ronnie Hermens

In a series of papers Colbeck and Renner (2011, 2015a, 2015b) claim to have shown that the quantum state provides a complete description for the prediction of future measurement outcomes. In this paper I argue that thus far no solid satisfactory proof has been presented to support this claim. Building on the earlier work of Leifer (2014), Landsman (2015) and Leegwater (2016), I present and prove two results that only partially support this claim. I then discuss the arguments by Colbeck, Renner and Leegwater concerning how these results are to generalize to the full claim. This argument turns out to hinge on the implicit use of an assumption concerning the way unitary evolution is to be represented in any possible completion of quantum mechanics. I argue that this assumption is unsatisfactory and that possible attempts to validate it based on measurement theory also do not succeed.

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Completely Real? A Critical Note on the Theorems by Colbeck and Renner

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In a series of papers Colbeck and Renner (2011, 2015a,b) claim to have shown that the quantum state provides a complete description for the prediction of future measurement outcomes. In this paper I argue that thus far no solid satisfactory proof has been presented to support this claim. Building on the earlier work of Landsman (2015) and Leegwater (2016) I highlight the implicit use of an assumption concerning the way unitary evolution is to be represented in any possible completion of quantum mechanics. I show that the assumption is quite crucial to the proof of the claim and argue that it is unwarranted. I further discuss a possible validation for a restricted version of this assumption that is based on considerations of measurement processes. I argue that also this restricted version is unsatisfactory.

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Restoring physical realism

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Problem- Many attempts have been made, starting from Quantum mechanics (QM), to prove the non-viability of hidden-variable (HV) solutions, and to justify the unnaturalness of QM explanations over physical realism. In particular, Colbeck & Renner (C&R) (2011) claimed to prove that no extension of quantum theory can exist with better predictive power than quantum mechanics itself. This implies that QM is an ideal theory, and that physical realism should be abandoned. Purpose- This paper critiques this proof. Approach- Logical considerations are used to examine the premises in the proof. Findings- The C&R proof is show to be capable of entirely the opposite interpretation that its authors intended, namely that a new deeper physics may exist based on physical realism, but that it will definitely not be quantum theory or even an extension thereof. Also, the proof is falsified by presenting a viable theory of internal structures (hidden-variable solution) with demonstrably better ontological explanatory power than QM. Implications- QM is interpreted as an approximate stochastic representation of a deeper dynamic behaviour at the finer scale. Originality- This work predicts that physical realism still applies, and that hidden-variable solutions still have vitality as the way forward for fundamental physics.

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On the completeness of quantum mechanics and the interpretation of the state vector

Gian Carlo Ghirardi, Raffaele Romano

Recently, it has been argued that quantum mechanics is complete, and that quantum states vectors are necessarily in one-to-one correspondence with the elements of reality, under the assumptions that quantum theory is correct and that measurement settings can be freely chosen. In this work, we argue that the adopted form of the free choice assumption is stronger than needed. In our perspective, there are hidden assumptions underlying these results, which limit their range of validity. We support our argument by a model for the bipartite two-level system, reproducing quantum mechanics, in which the free will assumption is respected, and different quantum states can be connected to the same state of reality.

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In a series of papers Colbeck and Renner claim to have shown that the quantum state provides a complete description for the prediction of future measurement outcomes. In this paper I argue that thus far no solid satisfactory proof has been presented to support this claim. Building on the earlier work of Leifer, Landsman and Leegwater, I present and prove two results that only partially support this claim. I then discuss the arguments by Colbeck, Renner and Leegwater concerning how these results are to generalize to the full claim. This argument turns out to hinge on the implicit use of an assumption concerning the way unitary evolution is to be represented in any possible completion of quantum mechanics. I argue that this assumption is unsatisfactory and that possible attempts to validate it based on measurement theory also do not succeed.
In a series of papers Colbeck and Renner (2011, 2015a, 2015b) claim to have shown that the quantum state provides a complete description for the prediction of future measurement outcomes. In this paper I argue that thus far no solid satisfactory proof has been presented to support this claim. Building on the earlier work of Leifer (2014), Landsman (2015) and Leegwater (2016), I present and prove two results that only partially support this claim. I then discuss the arguments by Colbeck, Renner and Leegwater concerning how these results are to generalize to the full claim. This argument turns out to hinge on the implicit use of an assumption concerning the way unitary evolution is to be represented in any possible completion of quantum mechanics. I argue that this assumption is unsatisfactory and that possible attempts to validate it based on measurement theory also do not succeed.
In a series of papers Colbeck and Renner (2011, 2015a,b) claim to have shown that the quantum state provides a complete description for the prediction of future measurement outcomes. In this paper I argue that thus far no solid satisfactory proof has been presented to support this claim. Building on the earlier work of Landsman (2015) and Leegwater (2016) I highlight the implicit use of an assumption concerning the way unitary evolution is to be represented in any possible completion of quantum mechanics. I show that the assumption is quite crucial to the proof of the claim and argue that it is unwarranted. I further discuss a possible validation for a restricted version of this assumption that is based on considerations of measurement processes. I argue that also this restricted version is unsatisfactory.
In three papers, Colbeck and Renner [Nat. Commun. 2, 411 (2011); Phys. Rev. Lett. 108, 150402 (2012); e-print arXiv:1208.4123] argued that “no alternative theory compatible with quantum theory and satisfying the freedom of choice assumption can give improved predictions.” We give a more precise version of the formulation and proof of this remarkable claim. Our proof broadly follows theirs, which relies on physically well motivated axioms, but to fill in some crucial details, certain technical assumptions have had to be added, whose physical status seems somewhat obscure.
It was argued [1] that there can be no extension of quantum mechanics with improved predictive power on a measurement freely chosen, independently of any event that is not in its future light cone. The assumption of measurement choice was criticized [2] to be too strong to be physically necessary and extensions of quantum mechanics were shown [3] to be possible under a more relaxed measurement assumption. Here I point out an error in the criticism and observe that the actual mistake of the no-go theorem lies in an unwarranted assumption implicitly made in the proof of [1]. Hence, quantum mechanics is guaranteed to have the maximal predictive power only in situations of complete certainty and complete uncertainty about measurement outcomes. I then show that the measurement assumption can be further relaxed without affecting the conclusion on the predictive power of quantum mechanics versus alternative theories. I further study the optimal predicative improvement over quantum mechanics of local spin measurements on a pair of entangled qubits by any alternative theory and conjecture a strict upper bound.
Problem- Many attempts have been made, starting from Quantum mechanics (QM), to prove the non-viability of hidden-variable (HV) solutions, and to justify the unnaturalness of QM explanations over physical realism. In particular, Colbeck & Renner (C&R) (2011) claimed to prove that no extension of quantum theory can exist with better predictive power than quantum mechanics itself. This implies that QM is an ideal theory, and that physical realism should be abandoned. Purpose- This paper critiques this proof. Approach- Logical considerations are used to examine the premises in the proof. Findings- The C&R proof is show to be capable of entirely the opposite interpretation that its authors intended, namely that a new deeper physics may exist based on physical realism, but that it will definitely not be quantum theory or even an extension thereof. Also, the proof is falsified by presenting a viable theory of internal structures (hidden-variable solution) with demonstrably better ontological explanatory power than QM. Implications- QM is interpreted as an approximate stochastic representation of a deeper dynamic behaviour at the finer scale. Originality- This work predicts that physical realism still applies, and that hidden-variable solutions still have vitality as the way forward for fundamental physics.
Recently, it has been argued that quantum mechanics is complete, and that quantum states vectors are necessarily in one-to-one correspondence with the elements of reality, under the assumptions that quantum theory is correct and that measurement settings can be freely chosen. In this work, we argue that the adopted form of the free choice assumption is stronger than needed. In our perspective, there are hidden assumptions underlying these results, which limit their range of validity. We support our argument by a model for the bipartite two-level system, reproducing quantum mechanics, in which the free will assumption is respected, and different quantum states can be connected to the same state of reality.