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Contexts, Systems and Modalities: A New Ontology for Quantum Mechanics

Abstract

In this article we present a possible way to make usual quantum mechanics fully compatible with physical realism, defined as the statement that the goal of physics is to study entities of the natural world, existing independently from any particular observer’s perception, and obeying universal and intelligible rules. Rather than elaborating on the quantum formalism itself, we propose a new quantum ontology, where physical properties are attributed jointly to the system, and to the context in which it is embedded. In combination with a quantization principle, this non-classical definition of physical reality sheds new light on counter-intuitive features of quantum mechanics such as the origin of probabilities, non-locality, and the quantum-classical boundary.

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Notes

  1. 1.

    Some philosophical background is given in the Appendix.

  2. 2.

    This is clearly an idealized view of classical mechanics, ignoring e.g. chaotic systems, but what matters is that classical mechanics do behave generically in such a way.

  3. 3.

    Classically one could do the same experiment with a polarized light wave, and also get different results according to the ordering of the polarizers. However the interpretation is completely different: the classical polarization has an orientation in space, which can be determined by carrying out more measurements, whereas the photon can only give a probabilistic yes/no answer.

  4. 4.

    With respect to the usual QM formalism, a modality corresponds to a pure state. We adopt here the usual view that statistical mixtures correspond to an extra layer of classical probabilities, added over a truly quantum structure provided by pure states: we are interested here in establishing this structure. We note also that certainty and repeatability is associated with projective measurements. On the other hand, generalized measurements (such as POVM’s) may be very useful tools, but they don’t provide fully predictable and repeatable results, and therefore they are not relevant for our present purpose.

  5. 5.

    In practice our definitions can be restricted to some sub-ensemble of contexts, relevant for some degrees of freedom of the complete physical system. What actually matters is that the transformations within the relevant set of contexts have the mathematical structure of a continuous group, see Sect. 4.

  6. 6.

    For continuous systems, see remark in Sect. 7. The full consideration of infinite dimension deserves more discussion, and is postponed to another article [15].

  7. 7.

    This principle is reminiscent of other approaches which bound the information extractable from a quantum system [22, 26]. However, in the realist perspective we chose, quantization has not a purely informational character, but characterizes reality itself.

  8. 8.

    Here the modality is defined as previously, i.e. as a set of values that can be predicted with certainty, but there is initially no physical contact between the context and the system. Moreover, the specific property of the context needed to define the modality, e.g. the polarizer’s orientation, can be classically broadcasted, so that the relevant context can be reproduced in another place. But checking the predicted results does require the actual measurement to be done, i.e. the context and the system to be at the same place.

  9. 9.

    This calculation was initially done in Chapter VI of [14], which considers the ensemble made of I (quantum system) + II (ancilla) + III (observer’s device), and shows that for a properly designed system-ancilla interaction (in modern terms, it should be a QND interaction [18]), the same result is obtained by applying the measurement between I and II, or between II and III. Such an approach fully agrees with CSM, and is very far from a “many worlds” point of view [24].

  10. 10.

    Though contexts play a central role in our construction, let us emphasize that it is “noncontextual” in the sense associated with Gleason’s theorem: this just means that the same modality can be found in different contexts. As an example, consider a system of two spin 1/2 particles \(\mathbf {S}_1\) and \(\mathbf {S}_2\), and define \(\mathbf {S} = \mathbf {S}_1 + \mathbf {S}_2\). Using standard notations for coupled and uncoupled basis, the \(|m_1=1/2, m_2=1/2 \rangle \) modality in the context \(\{S_{z1},S_{z2} \}\) is the same as the \(|S=1, m_S=1 \rangle \) modality in the context \(\{\mathbf {S}^2, S_{z} \}\), though other modalities in the same two contexts are different.

  11. 11.

    We emphasize that this ultimate physical reality remains within the physical world, so it is not “noumenal” in a Kantian sense.

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Acknowledgments

The authors thank Nayla Farouki for essential contributions, especially in the Appendix, and Francois Dubois, Franck Laloë, Maxime Richard, Augustin Baas, Cyril Branciard for many useful discussions.

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Correspondence to Alexia Auffèves.

Appendix: Some Philosophical Remarks on the Nature of Physical Reality

Appendix: Some Philosophical Remarks on the Nature of Physical Reality

In the present approach, the weight of philosophy is larger than in many other interpretations of QM. However we are still doing physics, not philosophy, and for clarity we present in this Appendix some elementary philosophical considerations, spelling out the conceptual shifts introduced by the CSM ontology.

From a philosophical point of view, let us emphasize again that we adopt the point of view of physical realism, telling that the purpose of physics is to study entities of the natural world, existing independently from any particular observer’s perception, and obeying universal and intelligible rules. Therefore philosophical issues like the separation between subject vs object are definitely out of our scope: we are interested in defining “objects” consistent with QM, and we claim this can be done – though not in a naive classical sense.

Here we want to discuss an objection which can be made to CSM, and could also be made to Bohr’s answer to EPR: in ordering to keep the above arguments consistent, the context seems to acquire a special status, evading the quantum description of reality which is being built. This objection can be answered relatively easily, but this requires a distinction between two notions of reality, that occur frequently in the history of philosophy.

The first kind of reality is the “ultimate physical reality”, constituted by all the objects in nature which are, from a scientific point of view, made of particles, waves and all their combinations, giving rise to macroscopic objects. There is no need to be very specific about what this reality is made of, but it must have a major property: it does exist—i.e. it is external to our thinking—even if we cannot know much about it, because it is too complicated. It is also a global reality, because no part of it should play a particular roleFootnote 11.

The second kind of reality is “empirical reality”, this is the reality of the phenomena that are amenable to scientific knowledge. Empirical reality has two main properties: it is real, it does exist independently of the “observer”, because it is obviously included in the ultimate physical reality; and it can be known, which means that it can be perceived and apprehended by observers, as knowledge must (also obviously) pertain to perceiving and thinking agents. Scientific knowledge of empirical reality is thus a synthesis of facts—what is really going on, in some subset of the ultimate physical reality, and concepts, elaborated through the observation and formalization of what is going on. It is precisely this synthesis that produces understanding about the physical world, what we sometimes call the “aha!” effect.

This distinction between realities is probably as old as philosophy, but physicists often ignore it, and think that physics can address directly the ultimate physical reality, by defining, attributing and measuring properties that belong unconditionally to the objects under study. Unfortunately, this way of thinking leads to a dead end as far as QM is concerned.

Actually, physics always deals with empirical reality, not with ultimate physical reality. Its duty is to describe phenomena with mathematical tools, which will allow one to predict the values of measurable physical quantities. These measurements and their mathematical formalization take place in a framework where phenomena can occur and eventually be described and measured. In practice, this framework is the classical macroscopic world, and though this appears only as a practical requirement, it can hardly be escaped, due to the very nature of empirical reality. Let us emphasize that this statement does not restrict physics only to what can be perceived. All along its history, physics has elaborated concepts that take an ontological value, such as atoms, and it is perfectly entitled to do so, because empirical reality is grounded on ultimate physical reality. Atoms are a very good example of such a progress: in the 19th century, they were introduced as abstract hypothetical entities with a strong explanatory power, then they were identified, and now they can easily be visualized and manipulated at the individual level. More generally, physical concepts such as photon, electron, charge, mass, energy, fields... are also entities required for describing the empirical reality in a synthetic way, referring again to the above mentioned synthesis of what is going on—the facts out there—and of its observation and formalization through physical, conceptual and mathematical tools that belong to science.

Fig. 3
figure3

Graphical representations of various ontologies discussed in the text. The CSM ontology is a much better basis for physical realism than the usual quantum ontology

Now we can consider again the difference between classical and quantum mechanics (see Fig. 3). In both, one deals with empirical reality grounded on ultimate physical reality, but in classical physics, one can easily get the delusion that knowing the state of the system is knowing directly the ultimate reality. In quantum mechanics, this is clearly wrong, because empirical reality must be mediated by a classical context, and the latter cannot be ignored. The context is part of the ultimate physical reality, and its own details in terms of particle, fields etc. certainly “exist”. However, they are not relevant as far as the definition of a (CSM) modality is concerned: here the context is required as a necessary practical condition allowing the physicist to make measurements on the system, which is a physically-grounded but abstract concept, like the atoms are. The context’s role is to reveal a phenomenon, the modality, which must be accessible to the observer, in ordering for knowledge to take place.

Given all that, a modality in CSM is essentially a phenomenon - a matter of fact—which involves a context (as a practical requirement) and a system (as a physically-grounded concept), and which provides measurement results, that can be known and reproduced with certainty. One should notice that most experiments do not give access to the full modality (pure quantum state), because of experimental imperfections: some properties may not be measured properly; experimental devices may add some noise, etc. However, the essential point is that, according to QM, modalities (i.e., pure quantum states) do exist as real phenomena, and the whole theory is based on that. In addition, the modality as a phenomenon is objective, i.e. it can occur anywhere, and requires no role for belief or for any agent’s crucial presence. Though observation is part of scientific knowledge as a human endeavor, it is not required for the phenomenal existence of a modality.

It should be clear also that the “cut” or “split” [10] is a requirement at the level of empirical reality, in ordering to specify the observed phenomenon, but at the level of ultimate physical reality, it does not imply that the macroscopic world is different in nature from the microscopic one. It rather means that in QM, macroscopic properties are required to describe phenomena, because the context cannot be ignored, due to the combination of the CSM and quantization postulates introduced above. Therefore for empirical consistency, the quantum system with its either mutually exclusive or incompatible modalities has to connect somewhere to the macroscopic world, where quantization does not show up at first sight.

As a conclusion, a lot of trouble in QM results from a confusion between ultimate physical reality and empirical reality, associated with the classical delusion of addressing directly the ultimate reality. But this is no more possible in quantum mechanics, due to the empirical frontier imposed by the quantization postulate. Again, quantum mechanics can describe anything, but one should be very careful with attempts at using it to describe everything.

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Auffèves, A., Grangier, P. Contexts, Systems and Modalities: A New Ontology for Quantum Mechanics. Found Phys 46, 121–137 (2016). https://doi.org/10.1007/s10701-015-9952-z

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Keywords

  • Quantum ontology
  • Non-locality
  • Probabilities in quantum mechanics
  • Quantization
  • Born’s rule
  • Contextual objectivity