It is my aim to compare the conceptual and historical paths that led Bohr and Schrödinger to develop their positions with regard to the phenomenon of entanglement. For this purpose, the concept of holism and non-separability in relation to the views of Bohr and Schrödinger will be crucial for reconstructing their standpoints. The idea will be upheld that the concept of non-separability underlies the phenomenon of entanglement. Furthermore, I shall place emphasis on the divergences between Bohr and Schrödinger in spite of their shared holistic world view.
It is my aim to compare the conceptual and historical paths that led Bohr and Schrödinger to develop their positions with regard to the phenomenon of entanglement. For this purpose, the concept of holism and non-separability in relation to the views of Bohr and Schrödinger will be crucial for reconstructing their standpoints. The idea will be upheld that the concept of non-separability underlies the phenomenon of entanglement. Furthermore, I shall place emphasis on the divergences between Bohr and Schrödinger in spite of their shared holistic world view.
Idea of quantum entanglement is discussed in the context of debate about the Einstein-Podolsky-Rosen thought experiment and some theoretical studies of quantum systems. It is noted that Schrödinger invented this idea in 1935 in order to fix some features of the quantum-mechanical description of two systems with temporary interaction. However, he did not grasp essence of these features really. In view of the concepts of mixture and statistical operator proposed by von Neumann and adopted by Schrödinger in 1936, it is argued that the idea of entanglement and related terminology are not necessary in quantum mechanics. One can use this idea and terms "entanglement" etc. as "visual" surrogates for the "mixture – statistical operator" pair. Deeper comparative analysis of several theoretical works by Schrödinger, von Neumann, and Landau showed that the modeling of non-trivial complex quantum systems as quasi-classical aggregates has been gradually overcome. Instead, wholeness of such quantum systems was actually recognized step by step. Thus, wholeness is immanent not only to quantum phenomena, as Niels Bohr had argued, but also to the quantum systems themselves, objectively. The pair "mixture – statistical operator" and especially the pair "mixed state – density matrix" similar to it appear to be adequate tools to comprehend and describe wholeness of diverse quantum reality. It is insisted, it is advisable to understand the surrogate idea of entanglement and relevant terminology in the same sense. In mature quantum paradigm, they are possible but not necessary theoretical tools to grasp wholeness of reality. Respectively, acceptable understanding of quantum entanglement must be based on recognition of quantum wholeness. Philosophically speaking, the idea of entanglement is understandable and conditionally acceptable in the view of contemporary rational holism, or holistic rationality. The clarified understanding of quantum entanglement, as well as Bohr's substantiation of wholeness of quantum phenomena, demonstrates irreducibility of the Universe to any quasi-classical aggregate. Moreover, all this supports the view of the Universe as real wholeness, which rational holism intends to grasp. It is concluded, further development and regular implementation of rational holism have the undoubted potential for revolutionary replacement of the hitherto widespread worldview in the spirit of Democritus and pure analytical methodology of knowledge.
Genesis of concept of quantum entanglement is explored in context of the controversy regarding the Einstein-Podolsky-Rosen thought experiment and, more broadly, the debate about the completeness of quantum mechanics. Taking into account the concepts of mixture and statistical operator, which were introduced by von Neumann and borrowed by Schrödinger, it is argued that the concept of entanglement is not necessary in quantum physics. The in-depth comparative analysis of some Schrödinger’s, von Neumann’s, and Landau’s theoretical works concludes that presentation of a complex quantum system as a quasi-mechanical aggregate was gradually being overcome. Its objective wholeness was being substantiated. Therefore, wholeness is inherent not only to quantum phenomena, but also to quantum systems themselves. Complete explanation of the Einstein-Podolsky-Rosen thought experiment requires consideration of both these appearances of the quantum wholeness. Therefore, main result of the long-term discussion of the EPR thought experiment is the exhaustive recognition of wholeness of quantum reality. Study of "the rise and fall" of the quantum entanglement concept, as well as Bohr's substantiation of the concept of wholeness of phenomenon, confirm irreducibility of the Universe to a set of Democritus' atoms and their combinations, aggregates. Moreover, all these enrich picture of the Universe as an undivided wholeness, which is revolutionary replacement for the still popular worldview in the spirit of Democritus. Analysis of contemporary use of the concept of entanglement finds out that, on the one hand, it grasps undividedness, wholeness of complex quantum systems of various kinds and, thus, is an instrument of rational holism. However, on the other hand, the concept of entanglement was call into life within the framework of imagining quantum systems as quasi-classical aggregates. Until now, this results in a shallow everyday-descriptive understanding of it, in principally limited attempts to model or think holistic systems as a set of separate objects, albeit in any entangled states.
Concept of quantum entanglement, its role in physics, philosophy, and in updating general worldview are studied in this article. It is pointed out that Schrodinger introduced this concept and some derivatives from it into description of physical reality in the 1935 article in the context of discussion around the Einstein-Podolsky-Rosen thought experiment, but in the related 1936 publication he did not use them. Taking into account the concepts of a mixture and statistical operator, which were introduced by von Neumann and borrowed by Schrödinger, it is shown that the concept of entanglement is not necessary in quantum mechanics unconditionally. At a certain moment of development of the complex quantum systems theory, this concept and its derivatives served as not very successful substitutes for the concepts of a mixture, situation of a mixture. Comparative analysis of some Schrödinger’s, von Neumann’s, and Landau’s theoretical works concludes that imagination of a complex quantum system as a quasi-mechanical aggregate was gradually being overcome; its objective wholeness was being substantiated instead. Therefore, wholeness is inherent not only to quantum phenomena, but also to quantum systems by itself, objectively. By the essence, just the attempt to think this circumstance had brought into life the concept of quantum entanglement. The concept of a mixture and its substitutes – the concepts of entangled state, entanglement, etc. – have not only the scientific but some metaphysical meaning as well: they prove the possibility of rational thinking of wholeness, the reasonableness and effectiveness of rational holism. Therefore, the metaphysics of quantum entanglement in its correct understanding is a manifestation of the rational holism metaphysics. Complete explanation of the Einstein-Podolsky-Rosen thought experiment requires consideration of both these appearances of the quantum wholeness. One can say the essential result of long-term discussion of the EPR experiment is the exhaustive recognition of the quantum reality wholeness. A row of generalizations achieved by A. Alexandrov, I. Tsekhmistro, and D.Bohm are considered. Together with the completed study of the concept of quantum entanglement or Bohr's substantiation of the concept of undivided quantum phenomenon, they support irreducibility of physical reality, the Universe in general to any set of Democritian atoms and their countless combinations, aggregates. All this enriches and improves the understanding of the Universe as a real wholeness. Perhaps, this understanding will be newest substitution for the hitherto popular worldview in the spirit of Democritus.
From its seemingly non-intuitive and puzzling nature, most evident in numerous EPR-like gedanken experiments to its almost ubiquitous presence in quantum technologies, entanglement is at the heart of modern quantum physics. First introduced by Erwin Schrödinger nearly a century ago, entanglement has remained one of the most fascinating ideas that came out of quantum mechanics. Here, we attempt to explain what makes entanglement fundamentally different from any classical phenomenon. To this end, we start with a historical overview of entanglement and discuss several hidden variables models that were conceived to provide a classical explanation and demystify quantum entanglement. We discuss some inequalities and bounds that are violated by quantum states thereby falsifying the existence of some of the classical hidden variables theories. We also discuss some exciting manifestations of entanglement, such as N00N states and the non-separable single particle states. We conclude by discussing some contemporary results regarding quantum correlations and present a future outlook for the research of quantum entanglement.
Expository paper providing a historical survey of the gradual transformation of the "philosophical discussions" between Bohr, Einstein and Schrödinger on foundational issues in quantum mechanics into a quantitative prediction of a new quantum effect, its experimental verification and its proposed (and loudly advertised) applications. The basic idea of the 1935 paper of Einstein-Podolsky-Rosen (EPR) was reformulated by David Bohm for a finite dimensional spin system. This allowed John Bell to derive his inequalities that separate the prediction of quantum entanglement from its possible classical interpretation. We reproduce here their later (1971) version, reviewing on the way the generalization (and mathematical derivation) of Heisenberg's uncertainty relations (due to Weyl and Schrödinger) needed for the passage from EPR to Bell. We also provide an improved derivation of the quantum theoretic violation of Bell's inequalities. Soon after the experimental confirmation of the quantum entanglement (culminating with the work of Alain Aspect) it was Feynman who made public the idea of a quantum computer based on the observed effect.