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Measuring Quantum Superpositions

(Or, “It Is Only the Theory Which Decides What Can Be Observed.”)

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Non-Reflexive Logics, Non-Individuals, and the Philosophy of Quantum Mechanics

Part of the book series: Synthese Library ((SYLI,volume 476))

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Abstract

In this work we attempt to confront the orthodox widespread claim, present in the philosophical and foundational debates about Quantum Mechanics (QM), that ‘superpositions are never actually observed in the lab’. In order to do so, we begin by providing a critical analysis of the famous measurement problem which, we will argue, was originated as a consequence of the strict application of the empirical-positivist requirements to subsume the quantum formalism under their specific understanding of a physical ‘theory’. In particular, the ad hoc introduction of the projection postulate (or measurement rule) can be understood as the necessity of imposing a naive empiricist standpoint which presupposes that observations are self evident givens of “common sense” experience independent of metaphysical (or conceptual) presuppositions yet necessarily represented in binary terms. We then turn our attention to two “non-collapse” interpretations of QM—namely, modal and many worlds—which even though deny that the “collapse” is a real physical process retain anyhow the projection rule as a necessary axiom of the theory itself. In contraposition, following Einstein’s claim that “it is only the theory which decides what can be observed”, we propose a return to the realist representational understanding of physical theories in which ‘observation’ is not a “self evident” given of experience but something that can be only understood in the context of a theoretical (formal-conceptual) scheme. It is from this standpoint that we discuss a new non-classical conceptual representation which allows us to understand quantum phenomena in an intuitive (anschaulicht) manner. Leaving behind the projection postulate, we discuss the general physical conditions for measuring and observing quantum superpositions in the lab.

The highest would be: to realize that everything factual is already theory.

Goethe

Fellow Independent Researcher of the Consejo Nacional de Investigaciones Científicas y Técnicas.

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Notes

  1. 1.

    As Lee Smolin (2007, p. 312) would describe the post-war instrumentalist view of physics recalling his own experience as a student: “When I learned physics in the 1970s, it was almost as if we were being taught to look down on people who thought about foundational problems. When we asked about the foundational issues in quantum theory, we were told that no one fully understood them but that concern with them was no longer part of science. The job was to take quantum mechanics as given and apply it to new problems. The spirit was pragmatic; ‘Shut up and calculate’ was the mantra. People who couldn’t let go of their misgivings over the meaning of quantum theory were regarded as losers who couldn’t do the work.”

  2. 2.

    In this respect, it is interesting to notice that matrix mechanics was developed by Heisenberg replacing Bohr’s correspondence principle and the problem of classical trajectories by Mach’s observability principle.

  3. 3.

    As Deutsch (2004, p. 312) remarks: “[…] empiricism did begin to be taken literally, and so began to have increasingly harmful effects. For instance, the doctrine of positivism, developed during the nineteenth century, tried to eliminate from scientific theories everything that had not been ‘derived from observation’. Now, since nothing is ever derived from observation, what the positivists tried to eliminate depended entirely on their own whims and intuitions.” Regarding the Danish physicist, Deutsch (2004, p. 308) makes the point that: “The physicist Niels Bohr (another of the pioneers of quantum theory) then developed an ‘interpretation’ of the theory which later became known as the ‘Copenhagen interpretation’. It said that quantum theory, including the rule of thumb, was a complete description of reality. Bohr excused the various contradictions and gaps by using a combination of instrumentalism and studied ambiguity. He denied the ‘possibility of speaking of phenomena as existing objectively’—but said that only the outcomes of observations should count as phenomena. He also said that, although observation has no access to ‘the real essence of phenomena’, it does reveal relationships between them, and that, in addition, quantum theory blurs the distinction between observer and observed. As for what would happen if one observer performed a quantum-level observation on another, he avoided the issue.”

  4. 4.

    Given a quantum system represented by a superposition of more than one term, \(\sum c_i | \alpha _i \rangle \), when in contact with an apparatus ready to measure, |R0〉, QM predicts that system and apparatus will become “entangled” in such a way that the final ‘system + apparatus’ will be described by \(\sum c_i | \alpha _i \rangle |R_i \rangle \). Thus, as a consequence of the quantum evolution, the pointers have also become—like the original quantum system—a superposition of pointers \(\sum c_i |R_i \rangle \). This is why the measurement problem can be stated as a problem only in the case the original quantum state is described by a superposition of more than one term.

  5. 5.

    Technically speaking, the distinction between empirical terms (i.e., the empirically “given”) and theoretical terms (i.e., their translation into simple statements) comprised this new understanding of theories.

  6. 6.

    It is important to remark that the meaning of ‘metaphysics’ in the positivist context was understood as an ungrounded discourse about the un-observable.

  7. 7.

    “In the US, which after the Second World War became the central stage of research in physics in the West, the discussions about the interpretation of quantum mechanics had never been very popular. A common academic policy was to gather theoreticians and experimentalists to gather in order to favour experiments and concrete applications, rather than abstract speculations. This practical attitude was further increased by the impressive development of physics between the 1930s and the 1950s, driven on the one hand by the need to apply the new quantum theory to a wide range of atomic and subatomic phenomena, and on the other hand by the pursuit of military goals. As pointed out by Kaiser, ‘the pedagogical requirements entailed by the sudden exponential growth in graduate student numbers during the cold war reinforced a particular instrumentalist approach to physics’.” (Osnaghi et al., 2009, pp. 2–3)

  8. 8.

    What seems very paradoxical with respect to the present Oxfordian account of Everett’s ideas—mainly due to Deutsch, Wallace and Saunders—is the complete elimination of Everett’s positivist standpoint regarding observability, prediction and anti-metaphysical commitments (Sect. 13.3.1). Jefferey Babrret, who studied Everett’s original texts and was responsible for the edition of his complete works (Everett, 2012), has repeatedly remarked that Everett’s ideas have nothing to do with the present Oxfordian misuse of his name. In fact, it is very easy to see that Everett’s Relative State interpretation of QM is much closer to QBism or Rovelli’s Relational Interpretation than to the MWI.

  9. 9.

    See Everett (2012, 364–366) for scans of Everett’s comments.

  10. 10.

    In this respect, it is very interesting to notice that we could think of the “branching process” as the mirror image of the “collapse process”—none of which is addressed nor explained by QM. While the collapse turns the superposition into only one if its terms, the branching goes from one single measurement into a superposition of parallel worlds.

  11. 11.

    In recent interviews the many worlds followers have been confronted to some of these questions. Wallace’s (2017) answer is that: “It is hard to define exactly because this branching process is not precise, but to put a number out of the air \(10^{10^{100}}\), so 10 to the number of particles in the Universe.” We might point out that the acknowledgment that “the branching process is not precise” in an interpretation which attempts to describe “literally” the quantum formalism seems, to say the least, very unsatisfactory. Another question which immediately pops up is how did Wallace compute the number, \(10^{10^{100}}\)?

  12. 12.

    This point is recognized explicitly by Dieks himself in many occasions. See, for example: Dieks (1989, p. 1407).

  13. 13.

    In fact, this linguistic duality had been already proposed by van Fraassen who distinguishes between dynamical states and value states. What van Fraassen does not do, is to provide a realist interpretation of such a distinct naming.

  14. 14.

    This argument was first used by Bohr who argued in 1927 that “quantum jumps” could not be represented. As recalled by Heisenberg (1971, p. 74), Bohr’s reply to Schrödinger’s criticisms related exclusively to the limits imposed by QM: “What you say is absolutely correct. But it does not prove that there are no quantum jumps. It only proves that we cannot imagine them, that the representational concepts with which we describe events in daily life and experiments in classical physics are inadequate when it comes to describing quantum jumps. Nor should we be surprised to find it so, seeing that the processes involved are not the objects of direct experience.” As Bohr (1935, p. 701) would argue: “The impossibility of a closer analysis of the reactions between the particle and the measuring instrument is indeed no peculiarity of the experimental procedure described, but is rather an essential property of any arrangement suited to the study of the phenomena of the type concerned, where we have to do with a feature of [quantum] individuality completely foreign to classical physics.” For a more detailed analysis see de Ronde (2023a).

  15. 15.

    For a critical analysis of the role of observation in physical theories see Deutsch (2004), Maudlin (2019).

  16. 16.

    As Heisenberg begun his foundational paper of 1925: “The present paper seeks to establish a basis for theoretical quantum mechanics founded exclusively upon relationships between quantities which in principle are observable. It was this same principle which was also kernel for Einstein’s development of special relativity and his criticism of the notion of simultaneity.”

  17. 17.

    As explained by Asher Peres See Peres (1993, p. 66): “The simplest observables are those for which all the coefficients ar are either 0 or 1. These observables correspond to tests which ask yes-no questions (yes = 1, no = 0).”

  18. 18.

    It might be remarked that we consider the idea that such theoretical representations provide a description of reality-as-it is not only naïve but also extremely misleading for a proper understanding of the realist quest (de Ronde, 2016b).

  19. 19.

    As proposed in de Ronde (2016a) there is a natural extension of what can be considered to a Generalized Element of Physical Reality: If we can predict in any way (i.e., both probabilistically or with certainty) the value of a physical quantity, then there exists an element of reality corresponding to that quantity.

  20. 20.

    It is important to stress that the potential mode of existence to which we refer is completely independent of the actual realm and should not be understood in teleological hylomorphic terms as referring to the future actualization of measurement outcomes (de Ronde, 2017).

  21. 21.

    Gerard t’ Hooft (2001) has argued that: “Working with long chains of arguments linking theories to experiment, we must be able to rely on logical precision when and where experimental checks cannot be provided.” Following the same line of reasoning Steven Weinberg (2003) has gone even further claiming that: “I think 100 years from now this particular period will be remembered as a heroic age when theorists cut themselves temporarily free from their experimental underpinnings and tried and succeeded through pure theoretical reasoning to develop a unified theory of all the phenomena of nature.” More recently, Richard Dawid has also argued in favor of considering non-empirical arguments in order to justify mathematical theories (Dawid, 2013).

  22. 22.

    As discussed in detail in de Ronde and Massri (2022), an Actual State of Affairs (ASA) can be defined as a closed system considered in terms of a set of actual (definite valued) properties which can be thought as a map from the set of properties to the {0,  1}. Specifically, an ASA is a function \(\Psi : \mathcal {G}\rightarrow \{0,1\}\) from the set of properties to {0,  1} satisfying certain compatibility conditions. We say that the property \(P\in \mathcal {G}\) is true if Ψ(P) = 1 and \(P\in \mathcal {G}\) is false if Ψ(P) = 0. The evolution of an ASA is formalized by the fact that the morphism f satisfies Φf =  Ψ.

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Acknowledgements

This work was partially supported by the following grants: the Project PIO CONICET-UNAJ (15520150100008CO) “Quantum Superpositions in Quantum Information Processing”, UNAJ INVESTIGA 80020170100058UJ.

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de Ronde, C. (2023). Measuring Quantum Superpositions. In: Arenhart, J.R.B., Arroyo, R.W. (eds) Non-Reflexive Logics, Non-Individuals, and the Philosophy of Quantum Mechanics. Synthese Library, vol 476. Springer, Cham. https://doi.org/10.1007/978-3-031-31840-5_13

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