Abstract Developments since Einstein are summarized. Our systems of units and their relationship to the speed of light. Light propagation in vacuum—what stuff is an electric field made of? Quantum field theory ideas. The Casimir force and energy. Olbers’ paradox and the cosmic horizon. Effect of gravity on speed of light. Schemes for messaging at speeds greater than that of light. The Einstein–Rosen–Podolsky paper of 1935 and its interpretation in simple terms. The reality of the quantum world. Hidden variable theories and Bell’s theorem. Interpretation of many-body quantum wavefunctions—Bohm, Born, Schrӧdinger, Heisenberg, de Broglie, their lives and contributions to physics. The Copenhagen interpretation of quantum mechanics and others. The measurement problem and collapse of the wavefunction. Entangled states. The unreasonable effectiveness of mathematics in the natural sciences.
Abstract Developments since Einstein are summarized. Our systems of units and their relationship to the speed of light. Light propagation in vacuum—what stuff is an electric field made of? Quantum field theory ideas. The Casimir force and energy. Olbers’ paradox and the cosmic horizon. Effect of gravity on speed of light. Schemes for messaging at speeds greater than that of light. The Einstein–Rosen–Podolsky paper of 1935 and its interpretation in simple terms. The reality of the quantum world. Hidden variable theories and Bell’s theorem. Interpretation of many-body quantum wavefunctions—Bohm, Born, Schrӧdinger, Heisenberg, de Broglie, their lives and contributions to physics. The Copenhagen interpretation of quantum mechanics and others. The measurement problem and collapse of the wavefunction. Entangled states. The unreasonable effectiveness of mathematics in the natural sciences.
Quantum mechanics is our most successful physical theory. It predicts the behavior of atoms, molecules, and light to ten decimal places. No experiment has ever contradicted it. It also contains a crack at its foundation. The theory’s central equation—the Schrodinger equation—describes a smooth, continuous, perfectly predictable evolution of the quantum state. But whenever anyone performs a measurement, they get a single, definite result. Which result they get appears to be random. The transition from smooth evolution to random outcome is called the “collapse of the wavefunction,” and after nearly a century of analysis, there is no agreed-upon explanation for what causes it, when it occurs, or whether it occurs at all. This is the measurement problem. The measurement problem is not a minor puzzle at the margins of the theory. It is a failure to explain the most basic operation in science: looking at the result of an experiment. Around it cluster other puzzles. Light behaves like a wave in some experiments and like a particle in others—two contradictory descriptions. Two particles that have interacted remain correlated across arbitrary distances, as though communicating faster than light. The probabilities that govern measurement outcomes appear as a postulate—the Born rule—inserted by hand with no deeper justification. And the theory offers no unified picture of reality: quantum mechanics, general relativity, and the standard model of particle physics speak incompatible mathematical languages. A century of effort has produced many interpretations of quantum mechanics. Copenhagen. Many-worlds. De Broglie-Bohm. Objective collapse. Quantum Bayesianism. None has achieved consensus. The measurement problem remains. This document proposes that the source of these puzzles is not quantum mechanics itself. It is a single, invisible assumption made at the very beginning of the theory in 1900—an assumption so deeply embedded that nobody noticed they were making it. Change that assumption, and the puzzles do not get solved. They dissolve. They stop being puzzles. They become predictable consequences of geometry.
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.
Preface to the 2nd edition. Preface. Acknowledgements. Reality in the quantum world: The quantum revolutions External reality The potential barrier and the breakdown of determinism The experimental challenge to reality Summary of chapter one. Quantum theory: The description of a particle in quantum theory The wavefunction The potential barrier according to quantum mechanics Interference Other applications of quantum theory Summary of chapter two. Quantum theory and external reality: Review of the problem The ensemble interpretation of quantum mechanics The wavefunction as a measure of our knowledge The wavefunction as part of external reality Measurement in quantum theory Interference and macroscopic objects Can quantum mechanics be changed so that it will reduce wavefunctions? Summary of chapter three. Consciousness: The relevance of conscious observers: What is a conscious observer? Does wavefunction reduction require conscious observers? God as the conscious observer The many-worlds interpretation Summary of chapter four. Hidden variables and non-locality: Review of hidden-variable theories The pilot wave The Einstein-Podolsky-Rosen thought experiment Bell's theorem Experimental verification of the non-local predictions of quantum theory Can signals travel faster than light Summary of chapter five. The mysteries of the quantum world: Where are we now? Quantum theory and relativity Where do we go next? Early history and the Copenhagen interpretation A bibliography and some recent opinions A final plea for reality A last look at the wavefunction Conclusions. Recent developments: Models with explicit collapse The Bohm model Many worlds Time and quantum theory A peculiarly quantum measurement Locality. Appendices. Index.
Preface. In defense of dogma: why there cannot be a relativistic quantum mechanics of (localizable) particles D.B. Malament. Just how radical is hyperplane dependence? G. Fleming. Is there superluminal causation in relativistic quantum field theory? M. Redei. EPR, relativity, and the GHZ experiment C. Pagonis, et al. Hidden quantum non-locality N.D. Mermin. Royer's measurements - the rise and fall of (yet another) signalling scheme I. Pitowsky. Tails of Schrodinger's cat D.Z. Albert, B. Loewer. Wavefunction collapse models with nonwhite noise P. Pearle. The emergence of classical properties from quantum mechanics L.E. Ballentine. Relativism S. Saunders. Wave and particle concepts in quantum field theory P. Teller. The conceptual relation between standard quantum mechanics and quantum field theory D. Robinson. What measurement problem? J.T. Cushing. Bovine metaphysics: remarks on the significance of the gravitational phase effect in quantum mechanics H.R. Brown. Exotic (quixotic?) applications of Bohm theory R. Weingard. Complementarity and the orthodox (Dirac-von Neumann) interpretation of quantum mechanics J. Bub. Logical reflections on the Kochen-Specker theorem J.L. Bell. Construction of quantum mechanics via commutative operations S. Kochen.
This article surveys a selection of key conceptual and interpretational developments in quantum mechanics, tracing the theory from its foundational postulates to contemporary discussions of measurement, nonlocality, and the emergence of classicality. Beginning with the structure of Hilbert space and the postulates governing state evolution and measurement, the epistemic stance of the Copenhagen interpretation and its modern reformulations are examined. The Einstein-Podolsky-Rosen argument, Bell's theorem, and Hardy's paradox are then discussed as probes of locality and realism, alongside the deterministic but explicitly nonlocal de Broglie-Bohm theory. The measurement problem and the implications of contextuality are analyzed in relation to objective collapse models, which introduce new physical dynamics to account for definite outcomes. Finally, the role of decoherence in the suppression of interference and the emergence of classical behavior is explored, together with the interpretational frameworks of many-worlds and consistent histories. This material aims to provide a coherent introductory overview of how several of the most prominent interpretations address the central concern of what quantum mechanics tells us about the nature of physical reality.
This article surveys a selection of key conceptual and interpretational developments in quantum mechanics, tracing the theory from its foundational postulates to contemporary discussions of measurement, nonlocality, and the emergence of classicality. Beginning with the structure of Hilbert space and the postulates governing state evolution and measurement, the epistemic stance of the Copenhagen interpretation and its modern reformulations are examined. The Einstein–Podolsky–Rosen argument, Bell’s theorem, and Hardy’s paradox are then discussed as probes of locality and realism, alongside the deterministic but explicitly nonlocal de Broglie–Bohm theory. The measurement problem and the implications of contextuality are analyzed in relation to objective collapse models, which introduce new physical dynamics to account for definite outcomes. Finally, the role of decoherence in the suppression of interference and the emergence of classical behavior is explored, together with the interpretational frameworks of many-worlds and consistent histories. This material aims to provide a coherent introductory overview of how several of the most prominent interpretations address the central concern of what quantum mechanics tells us about the nature of physical reality.