In a quantum world, there are nonlocal correlations with no common cause, where a direct causal influence between the correlated events can be excluded. Moreover, these correlated events are separately intrinsically random. In the contemporary quantum information literature, correlations are studied abstractly in “Boxworld.” A “box” is an imaginary device, with input and output ports on each side, defined by a particular correlation between inputs and outputs, without any specification of an internal mechanism that could produce the correlation. Bananaworld is Boxworld, with bananas and peelings and tastes instead of boxes with inputs and outputs. The idea is to get at what is puzzling about quantum correlations by considering the extent to which Alice and Bob, limited to certain resources, could simulate various correlations in Bananaworld. This introductory chapter introduces these ideas, beginning with a brief exposition of the birth of quantum mechanics in Heisenberg’s 1925 breakthrough paper. The chapter concludes with a self-contained introduction to special relativity.
In a quantum world, there are nonlocal correlations with no common cause, where a direct causal influence between the correlated events can be excluded. Moreover, these correlated events are separately intrinsically random. In the contemporary quantum information literature, correlations are studied abstractly in “Boxworld.” A “box” is an imaginary device, with input and output ports on each side, defined by a particular correlation between inputs and outputs, without any specification of an internal mechanism that could produce the correlation. Bananaworld is Boxworld, with bananas and peelings and tastes instead of boxes with inputs and outputs. The idea is to get at what is puzzling about quantum correlations by considering the extent to which Alice and Bob, limited to certain resources, could simulate various correlations in Bananaworld. This introductory chapter introduces these ideas, beginning with a brief exposition of the birth of quantum mechanics in Heisenberg’s 1925 breakthrough paper. The chapter concludes with a self-contained introduction to special relativity.
Abstract Chapter 1 points out that the mystery of entanglement has led Physics Nobel Laureates to claim “nobody understands quantum mechanics.” The Chapter goes on to introduce: the EPR and EPR–Bell paradoxes, various attempts to resolve them, our proposed resolution whereby the relativity principle (no preferred reference frame, NPRF) justifies the Planck postulate (NPRF + h) exactly like the relativity principle justifies the light postulate (NPRF + c), the Planck postulate as a result of Information Invariance & Continuity from quantum information theory, the importance of the relativity principle, subjective versus objective spacetime models of reality, spacelike and timelike relations in spacetime, and four experiments leading to our Poincaré symmetric ontology.
Chapter 1 begins by introducing the quantum world as part of the physical world, not in opposition to or separate from the classical world. It then introduces the basic tools needed to work with quantum mechanics, and describes the scope and purpose of this textbook. It discusses how despite its successes, current quantum mechanics lacks adequate explanations for important observed atomic properties, suggesting an incompleteness of the theory. After a brief overview of its main interpretative issues , the chapter concludes with an introduction of the vacuum or zero-point field as the physical element that restores causality and serves to complete the quantum picture by providing a causal explanation of characteristic quantum phenomena.
Unlike special relativity, quantum mechanics was not the inspired product of one mind. It developed, in fits and starts, over a period of 25 years (1900–1925), and many cooks stirred the broth. Even now, a century later, quantum mechanics raises profound conceptual questions. Every competent physicist can “do” quantum mechanics, and the predictions it makes are in spectacularly good agreement with experimental results; there can be little doubt that quantum mechanics is “right.” On the other hand, as Richard Feynman once remarked, “nobody understands quantum mechanics.” I'll tell the story in two parts. First the history (how the essential pieces of the puzzle were assembled), and then the implications (what the finished picture has to say about our world). Photons Like relativity, quantum mechanics began with the study of light. In both cases, this historical association is misleading. Relativity, really, has nothing to do with light – to be sure, it involves that magic speed limit, c , and of course the most familiar thing that travels at speed c is light. So light is a convenient vehicle for introducing the subject. But it is perfectly possible to imagine a universe in which there is no such thing as light, and yet relativity might still be valid. Quantum mechanics, too, starts with light – in this case the “quantum” of light (the photon). But, as it turns out, this is just one rather specialized example of much more general principles – in fact, a rather bad example, because photons are by their nature relativistic (they travel at the speed of light), and it would be more natural to begin with the quantum mechanics of slow-moving objects, in analogy with Newtonian mechanics.
This chapter discusses a Bananaworld version of a correlation analyzed by Einstein, Podolsky, and Rosen in a 1935 argument for the incompleteness of quantum mechanics. This correlation can be simulated by Alice and Bob with a shared random local resource, which is equivalent to showing that the correlation has a common cause explanation. A superquantum correlation proposed by Popescu and Rohrlich can’t be perfectly simulated with local resources, but a quantum simulation with entangled quantum states can do better than the optimal simulation with local resources (up to a quantum limit called the “Tsirelson bound”). So there is no common cause explanation of the correlation of a pair of Popescu–Rohrlich bananas. Since the correlated events can be arbitrarily far apart, there is no direct causal explanation either, because information would have to be transmitted faster than light between the correlated events. This is a version of Bell’s theorem.
This is intended to be a serious paper, in spite of the title. The idea is that quantum mechanics is about probabilistic correlations, i.e., about the structure of information, since a theory of information is essentially a theory of probabilistic correlations. To make this clear, it suffices to consider measurements of two binary-valued observables, x with outcomes a = 0 or 1, performed by Alice in a region A, and y with outcomes b = 0 or 1 performed by Bob in a separated region B --or, to emphasize the banality of the phenomena, two ways of peeling a banana, resulting in one of two tastes. The imagined bananas of Bananaworld are non-standard, with operational or phenomenal probabilistic correlations for peelings and tastes that lie outside the polytope of local correlations. The 'no go' theorems tell us that we can't shoe-horn these correlations into a classical correlation polytope, which has the structure of a simplex, by supposing that something has been left out of the story, without giving up fundamental principles that define what we mean by a physical system. The nonclassical features of quantum mechanics, including the irreducible information loss on measurement, are shown to be generic features of correlations that lie outside the local correlation polytope. As far as the conceptual problems are concerned, we might as well talk about bananas.