In 1964 John Bell demonstrated that quantum theory does not always agree with our classical intuitions about what should happen in the laboratory. Bell's uncanny skill as a translator of the classical commitments voiced by EPR into the language of mathematics is remarkable, all the more so given that he was equally at home in the world of quantum theory. In this chapter, we shift our attention to the latter perspective. We start by reviewing some of the key experiments that shed light on the quantum prediction. We then consider in some detail the singular feature that distinguishes quantum theory from all other previous physical theories, namely, its use of the principle of superposition. Finally, we reexamine polarization, this time from the quantum perspective, for the sake of constructing the quantum prediction for Bell-type experiments. The concepts introduced here form the core of the vocabulary employed in the next chapter, which treats various philosophical interpretations of quantum entanglement. In particular, this chapter's discussion of photon polarization prepares the way for the next chapter's discussion of quantum theory's so-called “measurement problem.”
In 1964 John Bell demonstrated that quantum theory does not always agree with our classical intuitions about what should happen in the laboratory. Bell's uncanny skill as a translator of the classical commitments voiced by EPR into the language of mathematics is remarkable, all the more so given that he was equally at home in the world of quantum theory. In this chapter, we shift our attention to the latter perspective. We start by reviewing some of the key experiments that shed light on the quantum prediction. We then consider in some detail the singular feature that distinguishes quantum theory from all other previous physical theories, namely, its use of the principle of superposition. Finally, we reexamine polarization, this time from the quantum perspective, for the sake of constructing the quantum prediction for Bell-type experiments. The concepts introduced here form the core of the vocabulary employed in the next chapter, which treats various philosophical interpretations of quantum entanglement. In particular, this chapter's discussion of photon polarization prepares the way for the next chapter's discussion of quantum theory's so-called “measurement problem.”
This chapter introduces core quantum mechanics concepts, focusing on Heisenberg's uncertainty principle and Schrödinger's equation, which describe quantum particles' wave–particle duality and probabilistic nature. The uncertainty principle and Schrödinger's equation are fundamental postulates validated by experiments, with the latter governing quantum behavior. The chapter explores wave functions, superposition, and entanglement, using light polarization to contrast classical and quantum interpretations, demonstrating that single photons exhibit probabilistic outcomes when interacting with polarizers. Additionally, it discusses polarizers and polarizing beam splitters, analyzing light propagation through these components using the law of Malus and comparing classical and quantum interpretations. The chapter concludes by highlighting the implications of these findings on photon polarization and measurement, providing a foundation for understanding quantum technologies.
Various interpretations of quantum mechanics, favored (or neglected) by John Bell in the context of his nonlocality theorem, are compared and discussed. Varenna 1970 I met John Bell for the first time at the Varenna conference of 1970 [1]. I had been invited on the suggestion of Eugene P. Wigner, who had already helped me to publish my first paper on the concept that was later called decoherence – to appear in the first issue of Foundations of Physics a few months after the conference [2]. This concept arose from my conviction, based on many applications of quantum mechanics to composite systems under various conditions, that Schrödinger's wave function in configuration space, or more generally the superposition principle, is universally valid and applicable. In particular, stable narrow wavepackets can represent classical configurations, while their superpositions define novel individual properties – such as “momentum,” defined as a plane wave superposition of different positions. Superpositions of macroscopically different properties, on the other hand, are regularly irreversibly “dislocalized” (distributed over many degrees of freedom) by means of interactions described by the Schrödinger equation. The corresponding disappearance of certain local superpositions (“decoherence”) seems to explain the phenomenon of a classical world as well as the apparent occurrence of quantum jumps or stochastic “events” – see Sect. 20.4 or [3] for a historical overview of the conceptual development of quantum theory. So I had never felt any motivation to think of “hidden variables” or any other physics behind the successful wave function. Therefore, I was very surprised on my arrival in Varenna to hear everybody discuss Bell's inequality. It had been published a few years before the conference, but I had either not noticed it or not regarded it as particularly remarkable until then. As this inequality demonstrates that the predictions of quantum theory would require any conceivable reality possibly underlying the nonlocal wave function to be nonlocal itself, I simply found my conviction that the latter describes individual reality confirmed. For example, I had often discussed the conservation of total spin or angular momentum in an individual decay process, which requires nonlocal entanglement between the fragments at any distance in a form that was later called a “Bell state”.
From the point of view of classical theory and our everyday experience, quantum phenomena are surprising and the concepts of quantum mechanics are incomprehensible. Since the beginning of quantum theory scientists questioned its very basic concepts, such as locality, reality, and complementarity, and proposed gedankenexperiments , or thought experiments, to probe its foundations. In the light of new optical technology we have been able to realize some of these experiments. This chapter will focus on three of them: (1) EPR-Bohm-Bell correlation and Bell’s inequality; (2) Scully’s quantum eraser; (3) Popper’s experiment. The results of these experiments are very interesting. On one hand, the experimental observations confirm the predictions of EPR-Bell, Scully, and Popper. On the other hand, the calculations from quantum theory perfectly agree with the experimental data. Moreover, apparently, the experimental observations do not lead to any “violations” of the principles of quantum mechanics. One important conclusion we may draw from these optical tests is that all the observations are the results of multi-photon interference: a group of photons interferes with the group itself at distance. The nonlocal multi-photon interference phenomena may never be understood in classical theory, however, it is legitimate in quantum mechanics. The superposition principle of quantum theory supports the superposition of multi-photon amplitudes, whether the photons are entangled or randomly grouped and despite the distances between these individual photodetection events. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Quantum theory is considered as the most successful scientific theory of all time. The realization of a controversy between quantum mechanics and reasonable assumptions was pointed out by Einstein, Boris Podolsky and Nathan Rosen (EPR) in 1935. It was John Stewart Bell, an Irish physicist, established what the quantum theory can tell us about the nature of the world. Bell formulated certain inequalities based on the arguments of EPR. They should be valid for any theory satisfying the notions of reality and locality. The striking news is that the Bell's inequality is violated by quantum mechanics but the experimental results agree with the predictions of quantum theory. This chapter presents the Schrodinger cat paradox and Bohm's version of EPR paradox. It gives a brief sketch of Bell's inequality and the quantum mechanical examples violating it. Most of the experiments were based on correlations between the polarizations of pairs of photons. Correlated photons can be produced in many ways.
The previous chapter surveyed part of the rich variety of physical phenomena that can be understood using the ideas of quantum physics. Now that we are beginning the task of looking more deeply into the subject we shall find it useful to concentrate on examples that are comparatively simple to understand but which still illustrate the fundamental principles and highlight the basic conceptual problems. Some years ago most writers discussing such topics would probably have turned to the example of a ‘particle’ passing through a two-slit apparatus (as in Figure 1.2), whose wave properties are revealed in the interference pattern. Much of the discussion would have been in terms of wave–particle duality and the problems involved in position and momentum measurements, as in the discussion of the uncertainty principle in the last chapter. However, there are essentially an infinite number of places where the particle can be and an infinite number of possible values of its momentum, and this complicates the discussion considerably. We can illustrate all the points of principle we want to discuss by considering situations where a measurement has only a small number of possible outcomes. One such quantity relating to the physics of light beams and photons is known as polarisation . In the next section we discuss it in the context of the classical wave theory of light, and the rest of the chapter extends the concept to situations where the photon nature of light is important.
How it all began In 1935, a decade after the invention of quantum theory by Heisenberg (1925) and Schrödinger (1926), three papers appeared, setting the stage for a new concept, quantum entanglement. The previous decade had already seen momentous discussions on the meaning of the new theory, for example by Niels Bohr (see his contribution to Albert Einstein: Philosopher-Scientist in Further reading); but these new papers opened up the gates for a new, very deep philosophical debate about the nature of reality, about the role of knowledge, and about their relation. Since the 1970s, it has become possible for experimenters to observe entanglement directly in the laboratory and thus test the counter-intuitive predictions of quantum mechanics whose confirmation today is beyond reasonable doubt. Since the 1990s, the conceptual and experimental developments have led to new concepts in information technology, including such topics as quantum cryptography, quantum teleportation, and quantum computation, in which entanglement plays a key role. In the first of the three papers, Einstein, Podolsky, and Rosen (EPR) realized that, if two particles had interacted in their past, their properties will remain connected in the future in a novel way, namely, observation on one determines the quantum state of the other, no matter how far away. Their conclusion was that quantum mechanics is incomplete and they expressed their belief that a more complete theory may be found. Niels Bohr replied that the two systems may never be considered independent of each other, and observation on one changes the possible predictions on the other. Finally, Erwin Schrödinger, in the paper which also proposed his famous cat paradox, coined the term “entanglement” (in German Verschränkung ) for the new situation and he called it “not one, but the essential trait of the new theory, the one which forces a complete departure from all classical concepts.”