In this critical notice we argue against William Craig's recent attempt to reconcile presentism (roughly, the view that only the present is real) with relativity theory. Craig's defense of his position boils down to endorsing a ‘neo-Lorentzian interpretation’ of special relativity. We contend that his reconstruction of Lorentz's theory and its historical development is fatally flawed and that his arguments for reviving this theory fail on many counts. 1 Rival theories of time 2 Relativity and the present 3 Special relativity: (...) one theory, three interpretations 4 Theories of principle and constructive theories 5 The relativity interpretation: explanatorily deficient? 6 The relativity interpretation: ontologically fragmented? 7 The space-time interpretation: does God need a preferred frame of reference? 8 The neo-Lorentzian interpretation: at what price? 9 The neo-Lorentzian interpretation: with what payoff? 10 Why we should prefer the space-time interpretation over the neo-Lorentzian interpretation 11 What about general relativity? 12 Squaring the tenseless space-time interpretation with our tensed experience. (shrink)

In his book, Physical Relativity, Harvey Brown challenges the orthodox view that special relativity is preferable to those parts of Lorentz's classical ether theory it replaced because it revealed various phenomena that were given a dynamical explanation in Lorentz's theory to be purely kinematical. I want to defend this orthodoxy. The phenomena most commonly discussed in this context in the philosophical literature are length contraction and time dilation. I consider three other phenomena of this kind that played a role in (...) the early reception of special relativity in the physics literature: the Fresnel drag effect in the Fizeau experiment, the velocity dependence of electron mass in beta-ray deflection experiments by Kaufmann and others, and the delicately balanced torques on a moving charged capacitor in the Trouton-Noble experiment. I offer historical sketches of how Lorentz's dynamical explanations of these phenomena came to be replaced by their now standard kinematical explanations. I then take up the philosophical challenge posed by the work of Harvey Brown and Oliver Pooley and clarify how those kinematical explanations work. (shrink)

In his book, Physical Relativity, Harvey Brown challenges the orthodox view that special relativity is preferable to those parts of Lorentz's classical ether theory it replaced because it revealed various phenomena that were given a dynamical explanation in Lorentz's theory to be purely kinematical. I want to defend this orthodoxy. The phenomena most commonly discussed in this context in the philosophical literature are length contraction and time dilation. I consider three other phenomena of this kind that played a role in (...) the early reception of special relativity in the physics literature: the Fresnel drag effect in the Fizeau experiment, the velocity dependence of electron mass in beta-ray deflection experiments by Kaufmann and others, and the delicately balanced torques on a moving charged capacitor in the Trouton-Noble experiment. I offer historical sketches of how Lorentz's dynamical explanations of these phenomena came to be replaced by their now standard kinematical explanations. I then take up the philosophical challenge posed by the work of Harvey Brown and Oliver Pooley and clarify how those kinematical explanations work. (shrink)

This paper takes as its point of departure two striking incongruities between scientiªc practice and trends in modern history and philosophy of science. (1) Many modern historians of science are so preoccupied with local scientiªc practices that they fail to recognize important non-local elements. (2) Many modern philosophers of science make a sharp distinction between explanation and evidence, whereas in scientiªc practice explanatory power is routinely used as evidence for scientiªc claims. I draw attention to one speciªc way in..

The relationship between Albert Einstein’s special theory of relativity and Hendrik A. Lorentz’s ether theory is best understood in terms of competing interpretations of Lorentz invariance. In the 1890s, Lorentz proved and exploited the Lorentz invariance of Maxwell’s equations, the laws governing electromagnetic fields in the ether, with what he called the theorem of corresponding states. To account for the negative results of attempts to detect the earth’s motion through the ether, Lorentz, in effect, had to assume that the laws (...) governing the matter interacting with the fields are Lorentz invariant as well. This additional assumption can be seen as a generalization of the well-known contraction hypothesis. In Lorentz’s theory, it remained an unexplained coincidence that both the laws governing fields and the laws governing matter should be Lorentz invariant. In special relativity, by contrast, the Lorentz invariance of all physical laws directly reflects the Minkowski space-time structure posited by the theory. One can use this observation to produce a common-cause argument to show that the relativistic interpretation of Lorentz invariance is preferable to Lorentz’s interpretation. (shrink)

Readers of this volume will notice that it contains only a few papers on general relativity. This is because most papers documenting the genesis and early development of general relativity were not published in Annalen der Physik . After Einstein took up his new prestigious position at the Prussian Academy of Sciences in the spring of 1914, the Sitzungsberichte of the Berlin academy almost by default became the main outlet for his scientific production. Two of the more important papers on (...) general relativity, however, did find their way into the pages of the Annalen [35,41]. Although I shall discuss both papers in this essay, the main focus will be on [35], the first systematic exposition of general relativity, submitted in March 1916 and published in May of that year. (shrink)

In publications in 1914 and 1918, Einstein claimed that his new theory of gravity in some sense relativizes the rotation of a body with respect to the distant stars and the acceleration of the traveler with respect to the stay-at-home in the twin paradox. What he showed was that phenomena seen as inertial effects in a space-time coordinate system in which the non-accelerating body is at rest can be seen as a combination of inertial and gravitational effects in a space-time (...) coordinate system in which the accelerating body is at rest. Two different relativity principles play a role in these accounts: the relativity of non-uniform motion, in the weak sense that the laws of physics are the same in the two space-time coordinate systems involved; what Einstein in 1920 called the relativity of the gravitational field, the notion that there is a unified inertio-gravitational field that splits differently into inertial and gravitational components in different coordinate systems. I provide a detailed reconstruction of Einstein's rather sketchy accounts of the twins and the bucket and examine the role of these two relativity principles. I argue that we can hold on to but that is either false or trivial. (shrink)

In 1909, Einstein derived a formula for the mean square energy fluctuation in blackbody radiation. This formula is the sum of a wave term and a particle term. In a key contribution to the 1926 Dreim¨.

In October 1924, The Physical Review, a relatively minor journal at the time, published a remarkable two-part paper by John H. Van Vleck, working in virtual isolation at the University of Minnesota. Van Vleck used Bohr's correspondence principle and Einstein's quantum theory of radiation to find quantum formulae for the emission, absorption, and dispersion of radiation. The paper is similar but in many ways superior to the well-known paper by Kramers and Heisenberg published the following year that is widely credited (...) to have led directly to Heisenberg's Umdeutung paper. As such, it clearly shows how strongly the discovery of matrix mechanics depended on earlier work on the application of the correspondence principle to the interaction of matter and radiation. (shrink)

“Special relativity killed the classical dream of using the energy-momentumvelocity relations as a means of probing the dynamical origins of [the mass of the electron]. The relations are purely kinematical” (Pais, 1982, 159). This perceptive comment comes from a section on the pre-relativistic notion of electromagnetic mass in ‘Subtle is the Lord . . . ’, Abraham Pais’ highly acclaimed biography of Albert Einstein. ‘Kinematical’ in this context means ‘independent of the details of the dynamics’. In this paper we examine (...) the classical dream referred to by Pais from the vantage point of relativistic continuum mechanics. (shrink)

In publications in 1914 and 1918, Einstein claimed that his new theory of gravity somehow relativizes the rotation of a body with respect to the distant stars and the acceleration of the traveler with respect to the stay-at-home in the twin paradox. What he showed was that phenomena seen as inertial effects in a space-time coordinate system in which the non-accelerating body is at rest can be seen as a combination of inertial and gravitational effects in a space-time coordinate system (...) in which the accelerating body is at rest. Two different relativity principles play a role in these accounts: the relativity of non-uniform motion, in the weak sense that the laws of physics are the same in the two space-time coordinate systems involved; what Einstein in 1920 called the relativity of the gravitational field, the notion that there is a unified inertio-gravitational field that splits differently into inertial and gravitational components in different coordinate systems. I provide a detailed reconstruction of Einstein's rather sketchy accounts of the twins and the bucket and examine the role of these two relativity principles. I argue that we can hold on to but that is either false or trivial. (shrink)

There is a striking difference between the methodology of the young Einstein and that of the old. I argue that Einstein’s switch in the late 1910s from a moderate empiricism to an extreme rationalism should at least in part be understood against the background of his crushing personal and political experiences during the war years in Berlin. As a result of these experiences, Einstein started to put into practice what, drawing on Schopenhauer, he had preached for years, namely to use (...) science as his means of escaping from “the merely personal.” Whatever the exact sources of Einstein’s about-face, the older man has left us with a highly misleading picture of how the younger man achieved the successes that we still celebrate today. This has had a harmful influence on theoretical physics. If the young Einstein’s successes are any guide as to how successful theoretical physics is done, close adherence to general features of the empirical data is much more and mathematical elegance is much less important than the old Einstein wanted us to believe. (shrink)

In this critical notice we argue against William Craig’s recent attempt to reconcile presentism (roughly, the view that only the present is real) with relativity theory. Craig’s defense of his position boils down to endorsing a ‘neo-Lorentzian interpretation’ of special relativity. We contend that his reconstruction of Lorentz’s theory and its historical development is fatally flawed and that his arguments for reviving this theory fail on many counts.

. This paper takes as its point of departure two striking incongruities between scientific practice and trends in modern history and philosophy of science. Many modern historians of science are so preoccupied with local scientific practices that they fail to recognize important non-local elements. Many modern philosophers of science make a sharp distinction between explanation and evidence, whereas in scientific practice explanatory power is routinely used as evidence for scientific claims. I draw attention to one specific way in.

This volume is the first systematic presentation of the work of Albert Einstein, comprising fourteen essays by leading historians and philosophers of science that introduce readers to his work. Following an introduction that places Einstein's work in the context of his life and times, the book opens with essays on the papers of Einstein's 'miracle year', 1905, covering Brownian motion, light quanta, and special relativity, as well as his contributions to early quantum theory and the opposition to his light quantum (...) hypothesis. Further essays relate Einstein's path to the general theory of relativity and the beginnings of two fields it spawned, relativistic cosmology and gravitational waves. Essays on Einstein's later years examine his unified field theory program and his critique of quantum mechanics. The closing essays explore the relation between Einstein's work and twentieth-century philosophy, as well as his political writings. (shrink)

In early 1927, Pascual Jordan published his version of what came to be known as the Dirac-Jordan statistical transformation theory. Later that year and partly in response to Jordan, John von Neumann published the modern Hilbert space formalism of quantum mechanics. Central to both formalisms are expressions for conditional probabilities of finding some value for one quantity given the value of another. Beyond that Jordan and von Neumann had very different views about the appropriate formulation of problems in the new (...) theory. For Jordan, unable to let go of the analogy to classical mechanics, the solution of such problems required the identification of sets of canonically conjugate variables, i.e., p’s and q’s. Jordan ran into serious difficulties when he tried to extend his approach from quantities with fully continuous spectra to those with wholly or partly discrete spectra. For von Neumann, not constrained by the analogy to classical physics and aware of the daunting mathematical difficulties facing the approach of Jordan ), the solution of a problem in the new quantum mechanics required only the identification of a maximal set of commuting operators with simultaneous eigenstates. He had no need for p’s and q’s. Related to their disagreement about the appropriate general formalism for the new theory, Jordan and von Neumann stated the characteristic new rules for probabilities in quantum mechanics somewhat differently. Jordan was the first to state those rules in full generality, von Neumann rephrased them and then sought to derive them from more basic considerations. In this paper we reconstruct the central arguments of these 1927 papers by Jordan and von Neumann and of a paper on Jordan’s approach by Hilbert, von Neumann, and Nordheim. We highlight those elements in these papers that bring out the gradual loosening of the ties between the new quantum formalism and classical mechanics. (shrink)

In October 1924, The Physical Review, a relatively minor journal at the time, published a remarkable two-part paper by John H. Van Vleck, working in virtual isolation at the University of Minnesota. Using Bohr’s correspondence principle and Einstein’s quantum theory of radiation along with advanced techniques from classical mechanics, Van Vleck showed that quantum formulae for emission, absorption, and dispersion of radiation merge with their classical counterparts in the limit of high quantum numbers. For modern readers Van Vleck’s paper is (...) much easier to follow than the famous paper by Kramers and Heisenberg on dispersion theory, which covers similar terrain and is widely credited to have led directly to Heisenberg’s Umdeutung paper. This makes Van Vleck’s paper extremely valuable for the reconstruction of the genesis of matrix mechanics. It also makes it tempting to ask why Van Vleck did not take the next step and develop matrix mechanics himself. (shrink)

This is the second installment of a two-part paper on developments in quantum dispersion theory leading up to Heisenberg’s Umdeutung paper. In telling this story, we have taken a 1924 paper by John H. Van Vleck in The Physical Review as our main guide. In this second part we present the detailed derivations on which our narrative in the first part rests. The central result that we derive is the Kramers dispersion formula, which played a key role in the thinking (...) that led to Heisenberg’s Umdeutung paper. We derive classical formulae for the dispersion, emission, and absorption of radiation and use Bohr’s correspondence principle to construct their quantum counterparts both for the special case of a charged harmonic oscillator (Sect. 5) and for arbitrary non-degenerate multiply-periodic systems (Sect. 6). We then rederive these results in modern quantum mechanics (Sect. 7). (shrink)

If through rotation of a hollow sphere one produces a Coriolis field inside of it, then a centrifugal field is produced [...] that is not the same as the one that would occur in a rotating rigid system with the same Coriolis field. One can therefore not think of rotational forces as produced by the rotation of the fixed stars ….

This is the chapter on general relativity for the Cambridge Companion to Einstein which I am co-editing with Christoph Lehner.

1.1. The two postulates of special relativity and the tension between them. When Einstein first presented what came to be known as special relativity, he based the theory on two postulates or principles, called the “relativity postulate” or “relativity principle” and the “light postulate.” Both postulates are supported by a wealth of experimental evidence. The combination of the two, however, appears to lead to contradictions. To avoid such contradictions, Einstein argued, we need to change some of our fundamental ideas about (...) space and time. Einstein formulated the relativity postulate as follows: “The same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good” (Einstein 1905r, 891). Such frames of reference are called inertial frames and an observer at rest in one of them is called an inertial observer. A few examples will suffice to understand both the concept of an inertial frame and the meaning of the relativity postulate. First consider a plane which starts out sitting on the tarmac, proceeds to fly through clear skies, and eventually hits turbulence. All the while a passenger is nursing a cup of coffee. Sipping coffee without spilling is easy during the smooth portion of the flight. This is because the laws governing the behavior of the coffee in the frame of reference of the plane flying at constant velocity are the same as in the frame of reference of the airport.1 In fact, these same laws hold in any frame moving uniformly (i.e., with constant velocity) with respect to the frame of the airport. Drinking coffee without spilling when the plane ride gets bumpy is much harder. The laws for the coffee in noninertial frames, such as the frame of a plane encountering turbulence, are more complicated than in inertial frames. As a second example consider a cruise ship that sets out from its port of origin, sails smoothly on a calm sea, and eventually is caught in a storm. All the while two passengers engage in a drawn-out tennis match on the ship’s upper deck.. (shrink)

In this critical notice we argue against William Craig's recent attempt to reconcile presentism (roughly, the view that only the present is real) with relativity theory. Craig's defense of his position boils down to endorsing a 'neo-Lorentzian interpretation' of special relativity. We contend that his reconstruction of Lorentz's theory and its historical development is fatally flawed and that his arguments for reviving this theory fail on many counts.

I defend the widely held view challenged by Harvey Brown in his recent book that special relativity is preferable to those parts of Lorentz’s electron theory it replaced because various phenomena that special relativity reveals to be of purely kinematical origin were given a dynamical explanation in Lorentz’s theory. The phenomena most commonly discussed in this context in the philosophical literature are length contraction and time dilation. I consider three other such phenomena that played a role in the early reception (...) of special relativity in the physics community: the Fresnel drag effect in the Fizeau experiment, the velocity dependence of electron mass in the -ray deflection.. (shrink)

A brief review (~8K words) of the history and philosophy of special and general relativity for a Dictionary of the History of Ideas.

Scientists working on the wave theory of light in the 19 th century took it for granted that there had to be a medium for the propagation of light waves. This medium was called the luminiferous [= “light carrying”] ether. One of the central questions about this medium concerned its state of motion. There were two options: (1) The ether is completely undisturbed by matter moving through it (stationary or immobile ether); (2) Matter drags along the ether in its vicinity (...) and/or in its interior (dragged-along ether). Stellar aberration provided the main argument for the first option (even though a special dragging effect in the case of transparent matter had to be built into the theory to account for refraction). Polarization provided the main argument for the second option. These two options and the arguments pro and con will be explained in more detail below. (shrink)

With the discovery that the universe is expanding at an accelerating rate, Einstein’s cosmological constant, which he once supposedly called his biggest blunder, is making a remarkable comeback. Einstein’s introduction of this constant had little to do with cosmology. It was part of yet another failed attempt to eliminate absolute space from physics. It took the Dutch astronomer Willem de Sitter only a few days to blow the idea out of the water. It took Einstein over a year to concede (...) the point. In the process Einstein and De Sitter produced the first two models of relativistic cosmology, the Einstein cylinder universe and the De Sitter hyperboloid universe. (shrink)

A substantial part of my reconstruction can aheady be found, in a very condensed form, in the annotauon for the relevant pages of the Einstein-Besso manuscript in Einstein CP4: doc. 14, pp. [41— 42]. The letter to Freundlich and other correspondence from the period 1915 — 1917 that I drew on for this paper appear in Einstein CPS. I wrote this paper in the context of a larger project of the Maxplanck-Institut flir Wissenschaflsgeschichte which aims at giving the most detailed (...) reconstruction yet of Einstein's path to general relativity. My paper does not necessarily reflect the views of the other members of the group working on this project. See Renn tk Sauer 1996 for a preliminary report on the gmup's findings. (shrink)

This paper is part II of a trilogy on the transition from classical particle mechanics to relativistic continuum mechanics that one of the authors is working on. The first part, on the Trouton experiment, was published in the Stachel festschrift (Janssen 2003). This paper focuses on the Lorentz-Poincaré electron, and, in particular, on the "Poincaré pressure" or "Poincaré stresses" introduced to stabilize the electron. It covers both the original argument by Poincaré (1906) and a modern relativistic argument for adding (...) a negative pressure term to the system's energy-momentum tensor inspired by the work of Laue (1911a, b). It highlights the importance of a paper by Lorentz (1899) in this context and of the "electromagnetic mechanics" of Abraham (1903). (shrink)

Einstein’s 1905 paper on special relativity suggests that relativistic mechanics is simply a matter of adjusting Newton’s to make it Lorentz invariant. Einstein, for instance.

In 1907, Einstein set out to fully relativize all motion, no matter whether uniform or accelerated. After five failed attempts between 1907 and 1918, he finally threw in the towel around 1920, setting himself a new goal. For the rest of his life he searched for a classical field theory unifying gravity and electromagnetism. As he struggled to relativize motion, Einstein had to readjust both his approach and his objectives at almost every step along the way; he got himself hopelessly (...) confused at times; he fooled himself with fallacious arguments and sloppy calculations; and he committed what he later allegedly called the biggest blunder of his career: he introduced the cosmological constant. There is a very uplifting moral to this somber tale. Although Einstein never reached his original destination, the harvest of his thirteen-year odyssey is quite impressive. First of all, what is left of absolute motion in general relativity is far more palatable than absolute motion in special relativity or Newtonian theory. And general relativity does seem to eliminate absolute space. More importantly, from a modern physics point of view, Einstein produced a spectacular new theory of gravity based on what he called the equivalence principle. This principle says that inertial and gravitational effects are due to one and the same structure, the inertio-gravitational field, which in Einstein’s theory is represented by a metric tensor field. In addition to laying the foundations of this theory, Einstein, among other things, launched relativistic cosmology, suggested the possibility of gravitational waves, gave the first sensible definition of a space-time singularity, and caught on to the intimate connection between general covariance and energy-momentum conservation, an example of the general connection between symmetries and conservation laws of Noether’s theorems. These results more than make up for the—at least by the standards of modern philosophy of science—rather opportunistic way in which they were obtained.. (shrink)

In the course of his work on optics and electrodynamics in systems moving through the ether, the 19th-century medium for light waves and electric and magnetic fields, Lorentz discovered and exploited the invariance of the free-field Maxwell equations under what Poincaré later proposed to call Lorentz transformations. To account for the negative results of optical experiments aimed at detecting the earth’s motion through the ether, Lorentz, in effect, assumed that the laws governing matter interacting with light waves are Lorentz invariant (...) as well. Like Lorentz, Einstein first encountered the Lorentz transformations in electrodynamics. Unlike Lorentz, for whom the transformation merely provided convenient mathematical substitutions, but like Poincaré, Einstein recognized that the Lorentz-transformed quantities are the measured quantities for the moving observer. More importantly, Einstein recognized that the Lorentz invariance of all physical laws had nothing to do with electrodynamics per se, but reflected the kinematics in a new relativistic space-time, to be named after Minkowski who worked out its geometry a few years later. (shrink)

This paper will serve as the editorial note on Einstein's 1916 review article on general relativity in a planned volume with all of Einstein's papers in Annalen der Physik. It summarizes much of my other work on history of general relativity and draws heavily on the annotation of Einstein's writings and correspondence on general relativity for Vols. 4, 7, and 8 of the Einstein edition.

Inspired by the Monty Hall Problem and a popular simple solution to it, we present a number of game-show puzzles that are analogous to the notorious Sleeping Beauty Problem (and variations on it), but much easier to solve. We replace the awakenings of Sleeping Beauty by contestants on a game show, like Monty Hall’s, and increase the number of awakenings/contestants in the same way that the number of doors in the Monty Hall Problem is increased to make it easier to (...) see what the solution to the problem is. We show that these game-show proxies for the Sleeping Beauty Problem and variations on it can be solved through simple applications of Bayes’s theorem. This means that we will phrase our analysis in terms of credences or degrees of belief. We will also rephrase our analysis, however, in terms of relative frequencies. Overall, our paper is intended to showcase, in a simple yet non-trivial example, the efficacy of a tried-and-true strategy for addressing problems in philosophy of science, i.e., develop a simple model for the problem and vary its parameters. Given that the Sleeping Beauty Problem, much more so than the Monty Hall Problem, challenges the intuitions about probabilities of many when they first encounter it, the application of this strategy to this conundrum, we believe, is pedagogically useful. (shrink)

Scientists working on the wave theory of light in the 19th century took it for granted that there had to be a medium for the propagation of light waves. This medium was called the luminiferous [= “light carrying”] ether. One of the central questions about this medium concerned its state of motion. There were two options: (1) The ether is completely undisturbed by matter moving through it (stationary or immobile ether); (2) Matter drags along the ether in its vicinity and/or (...) in its interior (dragged-along ether). Stellar aberration provided the main argument for the first option (even though a special dragging effect in the case of transparent matter had to be built into the theory to account for refraction). Polarization provided the main argument for the second option. These two options and the arguments pro and con will be explained in more detail below. (shrink)

The recently published Vol. 8 of Einstein’s Collected Papers brings together for the first time all extant letters and postcards documenting the famous debate of 1916–18 between Einstein and the Leyden astronomer Willem de Sitter (1872–1934), over, as they referred to it, the relativity of inertia. It was in the course of this debate that the first two relativistic cosmological models were proposed: the “Einstein cylinder world,” filled with a uniform static mass distribution; and the completely empty “De Sitter hyperboloid (...) world” (a name introduced in.. (shrink)

In the Fall of 1900, Frederick T. Trouton started work on an ingenious experiment in his laboratory at Trinity College in Dublin. The purpose of the experiment was to detect the earth’s presumed motion through the ether, the 19th century medium thought to carry light waves and electric and magnetic fields. The experiment was unusual in that, unlike most of these so-called ether drift experiments, it was not an experiment in optics. Trouton tried to detect ether drift by charging and (...) discharging a capacitor in a torsion pendulum at its resonance frequency, which he hoped would set the system oscillating. (shrink)

I relate the story of how matrix mechanics grew out of the treatment of optical dispersion in the old quantum theory, paying special attention to the contributions of the American theoretical physicists John H. Van Vleck and John C. Slater. Van Vleck shares the credit with Max Born for being the first to publish a full derivation of the crucial Kramers dispersion formula using Bohr’s correspondence principle. Slater was one of the architects of the short-lived but influential Bohr-Kramers-Slater (BKS) theory (...) that helped popularize the so-called Ersatz- or virtual oscillators central both to the treatment of dispersion in the old quantum theory and to the transition to matrix mechanics. (shrink)

We discuss the early career of John H. Van Vleck, one of the earliest American quantum theorists who shared the 1977 Nobel prize with his student Philip W. Anderson and Sir Nevill Mott. In particular, we follow Van Vleck's trajectory from his 1926 Bulletin for the National Research Council on the old quantum theory to his 1932 book, The Theory of Electric and Magnetic Susceptibilities. We highlight the continuity of formalism and technique in the transition from dealing with spectra in (...) the old quantum theory to dealing with susceptibilities in the new quantum mechanics. Our main focus is on the checkered history of a numerical factor in the so-called Langevin-Debye formula for the electric susceptibility of gases. Classical theory predicts, under very general conditions, that this factor is equal to 1/3. The old quantum theory predicted values up to 14 times higher. Van Vleck showed that quantum mechanics does away with this "wonderful nonsense" and restores the classical value 1/3 under equally general conditions. The Langevin-Debye formula thus provides an instructive example of a Kuhn loss in one paradigm shift that was regained in the next. In accordance with the expectation of Thomas S. Kuhn that textbooks tend to sweep Kuhn losses under the rug, Van Vleck did not mention this particular Kuhn loss anywhere in his 1926 NRC Bulletin. Contrary to Kuhn's expectations, however, he put the regained Kuhn loss in susceptibility theory to good pedagogical use in his 1932 book. Kuhn claimed that textbooks must suppress, truncate, and/or distort the prehistory of their subject matter if they are to inculcate the exemplars of the new paradigm in their readers. This claim is not borne out in this case. We argue that it is ultimately because of the continuity of formalism and technique that we draw attention to that Van Vleck could achieve his pedagogical objectives in his 1932 book even though he devoted about a third of it to the treatment of susceptibilities in classical theory and the old quantum theory in a way that matches the historical record reasonably well. (shrink)

On savait que c’était l’entité la plus complexe de l’univers connu. Mais le feu d’artifice de découvertes récentes dépasse l’entendement et fait exploser tous les schémas. Votre cerveau est (beaucoup) plus fabuleux que vous le croyez. Il est : totalement élastique, même âgé, handicapé, voire amputé de plusieurs lobes, le système nerveux central peut se reconstituer et repartir à l’assaut des connaissances et de l’action sur le monde ; totalement social, un cerveau n’existe jamais seul, mais toujours en résonance avec (...) d’autres. Mieux : nous sommes neuronalement constitués pour entrer en empathie avec autrui et aller à son secours. Ce livre aborde ces questions passionnantes avec cinq spécialistes. (shrink)

Hardy and Unruh constructed a family of non-maximally entangled states of pairs of particles giving rise to correlations that cannot be accounted for with a local hidden-variable theory. Rather than pointing to violations of some Bell inequality, however, they pointed to apparent clashes with the basic rules of logic. Specifically, they constructed these states and the associated measurement settings in such a way that the outcomes satisfy some conditionals but not an additional one entailed by them. Quantum mechanics avoids the (...) broken ‘if …then …’ arrows in such Hardy–Unruh chains, as we call them, because it cannot simultaneously assign truth values to all conditionals involved. Measurements to determine the truth value of some preclude measurements to determine the truth value of others. Hardy–Unruh chains thus nicely illustrate quantum contextuality: which variables do and do not obtain definite values depends on what measurements we decide to perform. Using a framework inspired by Bub and Pitowsky and developed in our book Understanding Quantum Raffles (co-authored with Michael E. Cuffaro), we construct and analyze Hardy–Unruh chains in terms of fictitious bananas mimicking the behavior of spin-1/2 particles. (shrink)

We use Bub's (2016) correlation arrays and Pitowksy's (1989b) correlation polytopes to analyze an experimental setup due to Mermin (1981) for measurements on the singlet state of a pair of spin-12 particles. The class of correlations allowed by quantum mechanics in this setup is represented by an elliptope inscribed in a non-signaling cube. The class of correlations allowed by local hidden-variable theories is represented by a tetrahedron inscribed in this elliptope. We extend this analysis to pairs of particles of arbitrary (...) spin. The class of correlations allowed by quantum mechanics is still represented by the elliptope; the subclass of those allowed by local hidden-variable theories by polyhedra with increasing numbers of vertices and facets that get closer and closer to the elliptope. We use these results to advocate for an interpretation of quantum mechanics like Bub's. Probabilities and expectation values are primary in this interpretation. They are determined by inner products of vectors in Hilbert space. Such vectors do not themselves represent what is real in the quantum world. They encode families of probability distributions over values of different sets of observables. As in classical theory, these values ultimately represent what is real in the quantum world. Hilbert space puts constraints on possible combinations of such values, just as Minkowski space-time puts constraints on possible spatio-temporal constellations of events. Illustrating how generic such constraints are, the equation for the elliptope derived in this paper is a general constraint on correlation coefficients that can be found in older literature on statistics and probability theory. Yule (1896) already stated the constraint. De Finetti (1937) already gave it a geometrical interpretation. (shrink)

This book offers a thorough technical elaboration and philosophical defense of an objectivist informational interpretation of quantum mechanics according to which its novel content is located in its kinematical framework, that is, in how the theory describes systems independently of the specifics of their dynamics. -/- It will be of interest to researchers and students in the philosophy of physics and in theoretical physics with an interest in the foundations of quantum mechanics. Additionally, parts of the book may be used (...) as the basis for courses introducing non-physics majors to quantum mechanics, or for self-study by those outside of the university with an interest in quantum mechanics. (shrink)