In the previous chapter we have introduced the distinction between locality and non-locality. In this chapter we shall explore non- locality, one of the most amazing aspects of quantum mechanics. We shall discover that it consists in non-local correlations without transmission of signals. Along the way we will formulate and prove three important theorems as well as introduce the phenomenon of entanglement swapping that reveal unequivocally quantum non- locality.
In the previous chapter we have introduced the distinction between locality and non-locality. In this chapter we shall explore non- locality, one of the most amazing aspects of quantum mechanics. We shall discover that it consists in non-local correlations without transmission of signals. Along the way we will formulate and prove three important theorems as well as introduce the phenomenon of entanglement swapping that reveal unequivocally quantum non- locality.
This chapter focuses the concepts of entanglement and non-locality. Quantum mechanics has yet another mystery—one that occurs as a consequence of superposition states involving two or more particles or two or more beams of photons. This is referred to as entanglement, also known as non-separability. The existence of entangled states is allowed, and even mandated, by quantum mechanics, and this leads us into yet another mystery: non-locality. It demonstrates how subatomic particles can be put into entangled states which reveal strange correlation effects—the effects being the essence of entanglement. It discusses the EPR argument, from the 1935 paper by Einstein, Boris Podolsky, and Nathan Rosen; the polarization states of photons; Bell's theorem; and the Hardy–Jordan argument.
In classical mechanics, two (or more) systems that do not interact – that do not exert any kind of force on each other – are completely separated (see Sec. 1.1), i.e. experiments performed locally on one of them cannot in any way influence experiments performed locally on the other. Quantum mechanics, on the other hand, admits that there can be a form of interdependence even in absence of physical interaction. This type of correlation goes under the name of entanglement (see Def. 5.1: p. 183). We already know that entanglement means non-factorizability of the state vector describing a system with at least two different degrees of freedom. In this chapter, we shall see that this may be the case also for systems that are very far away (space-like distant) from each other and we shall learn many interesting consequences of this state of affairs. Recent developments show that one may entangle even particles that have never interacted with each other. The starting point of the following analysis is necessarily represented by the pioneering paper of Einstein, Podolsky, and Rosen, who inaugurated an incredible series of theoretical and experimental investigations right up to the present day that have confirmed the predictions of quantum mechanics. The “irony” of this history is that Einstein, Podolsky, and Rosen, EPR for short, aimed to present a definitive proof of the inconsistency of quantum mechanics relative to classical physical theory. In fact, they initiated one of the most prolific fields of modern science.
For Abner Shimony. Your influence on me goes well beyond physics. Knowing you and being close to you is one of the greatest privileges and pleasures in my life. Introduction Quantum mechanics is, without any doubt, a tremendously successful theory: it started by explaining black-body radiation and the photoelectric effect, it explained the spectra of atoms, and then went on to explain chemical bonds, the structure of atoms and of the atomic nucleus, the properties of crystals and the elementary particles, and a myriad of other phenomena. Yet it is safe to say that we still lack a deep understanding of quantum mechanics – surprising and even puzzling new effects continue to be discovered with regularity. That we are surprised and puzzled is the best sign that we still don't understand; however, the veil over the mysteries of quantum mechanics is starting to lift a little. One of the strangest things microscopic particles do is to follow non-local dynamics and to yield non-local correlations. That particles follow non-local equations of motion was discovered by Aharonov and Bohm, while non-local correlations – which are the subject of this chapter – were discovered by John Bell and first cast in a form that has physical meaning, i.e., that can be experimentally tested, by Clauser, Horne, Shimony, and Holt. When they were discovered, both phenomena seemed to be quite exotic and at the fringe of quantum mechanics. By now we understand that they are some of the most important aspects of quantummechanical behavior.
Abstract In the strange new world of quantum physics we have consistently uncovered aspects of physical reality at odds with our everyday sense of this reality. But no previous discovery has posed more challenges to our usual understanding of the “way things are” than the amazing new fact of nature known as nonlocality. This new fact of nature was revealed in a series of experiments testing predictions made in a theorem developed by theoretical physicist John Bell in response to a number of questions raised by Albert Einstein and two younger colleagues in 1936. Although Bell’s now famous theorem led to the discovery that physical reality is non-local, this was not his primary motive for developing the theorem, and he was quite disappointed by the results of experiments testing the theorem.
We now have under our belts several interpretations of quantum mechanics, each requiring, or anyhow advocating, some understanding of quantum probabilities. In the next two chapters, I will consider some connections among various interpretations of quantum probabilities and non-locality. I do so in the context of the well-known EPR–Bohm experiment, though it is worth emphasizing at the start that non-locality is very likely the rule rather than the exception for quantum-mechanical systems. Entanglement of systems occurs not only in the confines of a laboratory, but also in the course of quite typical interactions among quantum-mechanical systems. Nonetheless, the EPR-Bohm experiment shines a bright light on the phenomenon of non-locality, and is therefore the most useful context in which to explore the relation between probability and non-locality. In this chapter, I consider models of the EPR–Bohm experiment that deliver probabilities for the various outcomes given the initial state of the pair of particles. In the next chapter, I consider fully dynamical models, i.e., ones that provide a dynamics for the complete state of the pair of particles as well as probabilities for various outcomes based on these complete states. The EPR–Bohm experiment The EPR–Bohm experiment is well known, but some observations about it are important for later.
Thus far I have been primarily concerned with how an interpretation of quantum mechanics might, or might not, be local. This question is traditionally not sharply distinguished from the question of whether quantum mechanics is consistent with the theory of relativity. However, the two questions are indeed quite distinct, and should be recognized as such explicitly. The theory of relativity What does relativity require? As a first approximation, we may make the distinction by noting that the requirements of the theory of relativity are themselves unclear. Minimally, relativity seems to require that there be no way to distinguish one reference frame from another – i.e., that there be no experimental procedure that can determine which of two inertial observers is ‘really’ moving, or more generally that there be no way to discover an observer's absolute velocity. Most authors are willing to find in (special) relativity a stronger requirement: namely, Lorentz-invariance. They say that relativity requires that in fact there is no such thing as absolute velocity. This requirement goes beyond the minimum – it might be that there is an absolute rest frame (so that absolute velocities are given by motion relative to this frame) while there is no way to find it. (As I will discuss in chapter 9, exactly this situation occurs in Bohm's theory.)