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On The Origin Of Correlations

Valerio Scarani

Published Jan 5, 2006• 0 citations
Publisher

Abstract

Abstract In Chapter 2, we saw that indistinguishability deriving from cars in relation to the knowledge of a pedestrian does not lead to any surprising modification in the properties of those cars. Indistinguishability in everyday life is linked to the ignorance of the observer, which can be overcome, while indistinguishability at the particle level cannot be removed without leading to qualitative change of the physical properties. The arguments in Chapter 2, as well as the failure of the ‘Heisenberg mechanism’ discussed in Chapter 4, have taught us that quantum indistinguishability is not a kind of insurmountable ignorance. Quantum indistinguishability is therefore a new idea – to affirm that two paths for a car are indistinguishable is not the same as affirming that two alternatives for a particle are indistinguishable. We are going to see that it is possible to argue in a similar way on the subject of correlations – in the quantum world, the notion of correlations appears in a new, unexpected light.

DOI
10.1093/oso/9780198570479.003.0007

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Abstract In Chapter 2, we saw that indistinguishability deriving from cars in relation to the knowledge of a pedestrian does not lead to any surprising modification in the properties of those cars. Indistinguishability in everyday life is linked to the ignorance of the observer, which can be overcome, while indistinguishability at the particle level cannot be removed without leading to qualitative change of the physical properties. The arguments in Chapter 2, as well as the failure of the ‘Heisenberg mechanism’ discussed in Chapter 4, have taught us that quantum indistinguishability is not a kind of insurmountable ignorance. Quantum indistinguishability is therefore a new idea – to affirm that two paths for a car are indistinguishable is not the same as affirming that two alternatives for a particle are indistinguishable. We are going to see that it is possible to argue in a similar way on the subject of correlations – in the quantum world, the notion of correlations appears in a new, unexpected light.
Abstract During the lectures to the students in Fribourg, as with other people foreign to the world of physics, I have stated that my audience was driven to raise the same questions as the physicists: can we accept randomness in physical phenomena? Is interference determined by the mechanisms, and correlations at a distance by an exchange of information? In the presence of non-separability of physical properties, can we still talk about distinct entities? We feel the need to interpret quantum phenomena because we are not at ease with the indistinguishability principle and with some of its consequences. The unease comes from the fact that this principle, which appears to be omnipresent in the microscopic world, is unknown in everyday life and even seems to contradict our normal perceptions – the reader must recall the game with the sets of cars in Chapter 2. Seen from this point of view, the interpretations can be divided into three broad categories:
Abstract According to classical physics particles are basic building blocks of the world. These classical particles are distinguishable objects, individuated by unique combinations of physical properties. By contrast, in quantum mechanics the received view is that particles of the same kind (“identical particles”) are physically indistinguishable from each other and lack identity. This doctrine rests on the quantum mechanical (anti)symmetrization postulates together with the “factorist” assumption that each single particle is represented in exactly one factor space of the tensor product Hilbert space of a many-particle system. Even though standard in theoretical physics and the philosophy of physics, the assumption of factorism and the ensuing indistinguishability of particles are problematic. Particle indistinguishability is irreconcilable with the everyday meaning of “particle”, and also with how this term is used in the practice of physics. Moreover, it is a consequence of the standard view that identical quantum particles remain indistinguishable even in the classical limit, which makes a smooth transition to the classical particle concept impossible. Lubberdink (1998; 2009) and Dieks and Lubberdink (2011) have proposed an alternative conception of quantum particles that does not rely on factorism and avoids these difficulties. We further explain and discuss this alternative framework here. One of its key consequences is that particles in quantum theory are not fundamental but emergent; another that once they have emerged, quantum particles are always physically distinguishable and thus possess a physically grounded identity.
In this chapter, we study the properties of quantum entanglement, and more generally the way correlations can appear in quantum mechanics. Quantum entanglement is an important notion that we have already discussed, for instance in the context of the Von Neumann chain or of the Schrödinger cat, but here we give more details on its properties. In classical physics, the notion of correlation is well known. It hinges on the calculation of probabilities and on linear averages over a number of possibilities. A distribution gives the probability of having the first system in a some given state and the second in another state. If this distribution is not a product, the two systems are correlated. If it is a product, they are uncorrelated; measuring the properties of one system does not bring any information on the other. This is in particular the case if the state of each of the two systems is perfectly defined (which also defines the state of the whole system perfectly well). The notion of correlation between sub-systems therefore stems from the multiplicity of possible states of the whole system; fluctuations of this state are necessary to give its full meaning to the classical notion of correlation. In quantum mechanics, the situation is different: as we have seen (in particular in Chapter 4), even a physical system that is perfectly defined by a given state vector already contains fluctuations.
It is widely accepted that the papers by Bose in 1924 and by Einstein in 1924-1925 definitely opened the path to the quantum concept of ‘indistinguishability’. Since then, distinction in physics between ‘identity’ and ‘indistinguishability’ of particles has come to be required. However, even before the rise of quantum physics, Maxwell, Boltzmann and Gibbs, among others, had to tackle the difficulties and paradoxes that appear when counting identical particles. Later, after Sackur’s and Tetrode’s first quantum derivation of the canonical partition function of an ideal gas, much confusion arose around its dependence on the number of molecules in the system. Many other physicists, such as Planck, Lorentz or Schrodinger took part in those debates. In 1921, Ehrenfest and Trkal devoted a whole paper to this subject. Clearly, in the days before Bose’s seminal work, embroiling and misunderstanding were commonplace. In considering the emergence of the distinction between ‘identical’ and ‘indistinguishable’ particles, we will go through the so-called statistical route to quantum mechanics. The first developments in statistical mechanics became immediately confused and entangled with the irruption of quantum physics. In the first quarter of the twentieth century the mutual influence between both disciplines was profuse. We will pay special attention to the story of the so-called ‘Gibbs Paradox.’ We will argue that what is now often known by this name in some textbooks of statistical mechanics did not exist as such in those foundational days.
Nowadays, no one should doubt that quantum entanglement is (at least, one of) the \ncharacteristic traits of quantum mechanics. Furthermore, quantum information science \nis strongly influenced by the advantages provided by quantum entanglement, as the \nlatter can be regarded as a genuine resource for an efficient (better-than-classical) \nprocessing of information in certain computational tasks. The very basic notion of \ncorrelation is fundamental for the conceptualization of the physical communicational \nproblem and, as a consequence, for the notion of information itself. Thus, the question \nabout the nature of quantum information is close (and unavoidably linked) to the \nquestion about the nature of quantum correlations.
The rapidly increasing interest in the quantum properties of living matter stimulates a discussion of the fundamental properties of life as well as quantum mechanics. In this discussion often concepts are used that originate in philosophy and ask for a philosophical analysis. In the present work the classic philosophical tradition based on Aristotle and Aquinas is employed which surprisingly is able to shed light on important aspects. Especially one could mention the high degree of unity in living objects and the occurrence of thorough qualitative changes. The latter are outside the scope of classical physics where changes are restricted to geometrical rearrangement of microscopic particles. A challenging approach is used in the philosophical analysis as the empirical evidence is not taken from everyday life but from 20th century science (quantum mechanics) and recent results in the field of quantum biology. In the discussion it is argued that quantum entanglement is possibly related to the occurrence of life. Finally it is recommended that scientists and philosophers should be open for dialogue that could enrich both. Scientists could redirect their investigation, as paradigm shifts like the one originating from philosophical evaluation of quantum mechanics give new insight about the relation between the whole en the parts. Whereas philosophers could use scientific results as a consistency check for their philosophical framework for understanding reality.