What’s Wrong with Einstein’s 1927 Hidden-Variable Interpretation of Quantum Mechanics?

Einsteins unpublished 1927 deterministic trajectory interpretation of quantum mechanics is critically examined, in particular with regard to the reason given by Einstein for rejecting his theory. It is shown that the aspect Einstein found objectionable—the mutual dependence of the motions of particles when the (many-body) wavefunction factorises—is a generic attribute of his theory but that this feature may be removed by modifying Einsteins method in either of two ways: using a suggestion of Grommer or, in a physically important special case, using a simpler technique. It is emphasized though that the presence or absence of the interdependence property does not determine the acceptability of a trajectory theory. It is shown that there are other grounds for rejecting Einsteins theory (and the two modified theories), to do with its domain of applicability and compatibility with empirical predictions. That Einsteins reason for rejection is not a priori grounds for discarding a trajectory theory is demonstrated by reference to an alternative deterministic trajectory theory that displays similar particle interdependence yet is compatible with quantum predictions.PACS: 03.65.Bz.Essay written in memory of J.T. Cushing.     

On Essential Incompleteness of Hertz’s Experiments on Propagation of Electromagnetic Interactions

The historical background of the 19th century electromagnetic theory is revisited from the standpoint of the opposition between alternative approaches in respect to the problem of interactions. The 19th century electrodynamics became the battle-field of a paramount importance to test existing conceptions of interactions. Hertzs experiments were designed to bring a solid experimental evidence in favor of one of them. The modern scientific method applied to analyze Hertzs experimental approach as well as the analysis of his laboratory notes, dairy and private letters show that Hertzs crucial experiments cannot be considered as conclusive at many points as it is generally implied. We found that alternative Helmholtzs electrodynamics did not contradict any of Hertzs experimental observations of transverse components as Maxwells theory predicted. Moreover, as we now know from recently published Hertzs dairy and private notes, his first experimental results indicated clearly on infinite rate of propagation. Nevertheless, Hertzs experiments provided no further explicit information on non-local longitudinal components which were such an essential feature of Helmholtzs theory. Necessary and sufficient conditions for a decisive choice on the adequate account of electromagnetic interactions are discussed from the position of modern scientific method.     

Ritz,Einstein, and the Emission Hypothesis

Just as Albert Einsteins special theory of relativity was gaining acceptance around 1908, the young Swiss physicist Walter Ritz advanced a competing though preliminary emission theory that sought to explain the phenomena of electrodynamics on the assumption that the speed of light depends on the motion of its source. I survey Ritzs unfinished work in this area and review the reasons why Einstein and other physicists rejected Ritzs and other emission theories. Since Ritzs emission theory attracted renewed attention in the 1960s, I discuss how the earlier observational evidence was misconstrued as telling against it more conclusively than actually was the case. Finally, I contrast the role played by evidence against Ritzs theory with other factors that led to the early rejection of his approach.     

Faux-boolean algebras,classical probability,and determinism

It is possible to define, for any quantum system, an algebra of definite-valued events—those events that are definitely occurrent or non-occurrent. It is shown that two different sets of constraints on the algebra of definite-valued events are each equivalent to the definition of that set as a certain pseudo-Boolean algebra.     

Robert Hooke’s Seminal Contribution to Orbital Dynamics

During the second half of the seventeenth century, the outstanding problem in astronomy was to understand the physical basis for Keplers laws describing the observed orbital motion of a planet around the Sun. In the middle 1660s,Robert Hooke (1635–1703) proposed that a planets motion is determined by compounding its tangential velocity with the change in radial velocity impressed by the gravitational attraction of the Sun, and he described his physical concept to Isaac Newton (1642–1726) in correspondence in 1679. Newton denied having heard of Hookes novel concept of orbital motion, but shortly after their correspondence he implemented it by a geometric construction from which he deduced the physical origin of Keplers area law,which later became Proposition I, Book I, of his Principia in 1687.Three years earlier, Newton had deposited a preliminary draft of it, his De Motu Corporum in Gyrum (On the Motion of Bodies), at the Royal Society of London, which Hooke apparently was able to examine a few months later, because shortly there-after he applied Newtons construction in a novel way to obtain the path of a body under the action of an attractive central force that varies linearly with the distance from its center of motion (Hookes law). I show that Hookes construction corresponds to Newtons for his proof of Keplers area law in his De Motu. Hookes understanding of planetary motion was based on his observations with mechanical analogs. I repeated two of his experiments and demonstrated the accuracy of his observations.My results thus cast new light on the significance of Hookes contributions to the development of orbital dynamics, which in the past have either been neglected or misunderstood.Michael Nauenberg is Professor Emeritus of Physics at the University of California, Santa Cruz. His primary research has been in theoretical physics, but he also has written several articles and coedited a book on the historical development of dynamics by Huygens, Newton, and Hooke.     

Niels Bohr’s Generalization of Classical Mechanics

We clarify Bohrs interpretation of quantum mechanics by demonstrating the central role played by his thesis that quantum theory is a rational generalization of classical mechanics. This thesis is essential for an adequate understanding of his insistence on the indispensability of classical concepts, his account of how the quantum formalism gets its meaning, and his belief that hidden variable interpretations are impossible.     

A Conversation with Frank Press

Geophysicist Frank Press was director of Caltechs Seismological Laboratory from 1957 to 1965. In this interview, he recalls his work with Maurice Ewing at Columbias Lamont Geological Observatory; his directorship of Caltechs Seismological Laboratory and colleagues Charles Richter, Beno Gutenberg, and Hugo Benioff; his work on the free oscillations of the earth; and his part in establishing the worldwide network of seismographs for the detection of nuclear weapons testing.     

The Reality in Bohmian Quantum Mechanics or Can You Kill with an Empty Wave Bullet?

Several situations, in which an empty wave causes an observable effect, are reviewed. They include an experiment showing surrealistic trajectories proposed by Englert et al. and protective measurement of the density of the quantum state. Conditions for observable effects due to empty waves are derived. The possibility (in spite of the existence of these examples) of minimalistic interpretation of Bohmian quantum mechanics in which only Bohmian positions supervene on our experience is discussed.     

Nordström,Ehrenfest, and the Role of Dimensionality in Physics

In the summer of 1916, Finnish physicist Gunnar Nordström (1881–1923) arrived in Leiden to carry out research with Paul Ehrenfest (1880–1933), Hendrik A. Lorentzs successor in the chair of theoretical physics. Nordström had recently published the first five-dimensional unified model of the universe, a theory that went virtually unnoticed by the physics community. Ehrenfests personal journals reveal that Nordströms visit coincided with a flowering of Ehrenfests own interest in dimensionality, which resulted in his well-known paper on the connection between the fundamental laws of physics and the three-dimensionality of space. I examine Nordströms and Ehrenfests collaboration and explore the relationship between their ideas and the Kaluza-Klein model of five-dimensional unification.Paul Halpern is Professor of Physics at the University of the Sciences in Philadelphia. He received a Guggenheim Fellowship in 2002 to study the history of dimensionality in science.     

К теории коэрцитивно й силы и кривой намагничивания

. , , . .     

Chiral Charged Fermions,One-Dimensional Quantum Field Theory and Vertex Algebras

We give an explicit L ²-representation of chiral charged fermions using the Hardy–Lebesgue octant decomposition. In the pure case such a representation has already been used by M. Sato in holonomic field theory. We study both pure and mixed cases. In the compact case, we rigorously define unsmeared chiral charged fermion operators inside the unit circle. Using chiral fermions, we orient our findings towards a functional analytic study of vertex algebras as one-dimensional quantum field theory.     

‘In’ and ‘out’ vertex operators in a class of UV-finite nonlinear σ-models

In and out scalar vertex operators are constructed perturbatively in a class of recently discovered UV finite nonlinear -models describing the string evolution in gravitational plane wave backgrounds. They exhibit peculiar singularities in the target space related to the focusing phenomena in such backgrounds well known from the classical and quantum gravity theories. The computation is performed up to three loops of the usual perturbation expansion and to all loops of the weak field limit. An argument is given that the vertex operator singularities should persist, even when summing up the all perturbation expansions.     

Why do clocks tick?

Drawing on recent developments in the matrix model approach to string theory and the causal set program for quantum gravity we address the question of the origin of time as one aspect of the phase transition from a topological quantum field theory to a quantum theory of gravity. We construct a model with two phases which can be interpreted as containing clocks which either do not tick or tick exactly once. This demonstrates that while a theory based on causal sets may appear to have inherent notions of time and causality, the existence of a phase transition means, that as Saint Augustine wrote in hisConfessions, the time, if such we may call it, when there was no time was not time at all.Received an Honorable Mention in the 1992 Gravity Research Foundation Essay Contest—Ed.     

On the relation between weak and strong invariance of differential equations

Some concepts of Lie algebra cohomology are used to systematize the search for differential equations invariant under a given Lie groupG. In particular, it is shown that if a strongly invariant equation exists, then all weakly invariant equations differ from it only by an arbitrary multiplicative factor. If no strongly invariant equation exists, then cohomology theory can be used to simplify the search for weakly invariant equations.     

A note on a paper by Atkin and Bastin

The paper A Homological Foundation for Scale Problems in Physics (Atkin & Bastin, 1970) is criticised on account of several inconsistencies in the argument. Possible applications of the general ideas used are then discussed in the context of a quantum logic type of framework.     

A formulation of linearised gravity

The formulation of linearised gravity in terms of the electric and magnetic gravitational fields is extended to take into account the presence of matter. The modes of radiation, the equations of motion and the potential in the static case are given. The relevant components of the superenergy tensor are calculated and a quantity named the superforce is introduced.     

On the origin of Kaluza’s idea of unification and its relation to earlier work by Thirring

We argue that the starting point of Kaluzas idea of unifying electrodynamics and gravity was the analogy between gravitation and electromagnetism which was pointed out by Einstein and Thirring. It seems that Kaluzas attention was turned to this point by the three papers on the Lense–Thirring effect and the analogy between gravitation and electromagnetism which were published a short time before Kaluzas paper was submitted. We provide here also an English translation of the third of these papers (Phys. Zeits. 19: 204, 1918).     

The Strange Story of the Concept which Inaugurated Modern Theoretical Physics

The strange Story of the Concept which inaugurated Modern Theoretical Physics is the title of a lecture which I delivered on the invitation of Professor Franco Selleri at the University of Bari about 20 years ago. Since Professor Selleri himself has written several interesting papers on this concept and since the centennial of the birth of modern theoretical physics will be celebrated soon, I found it appropriate to dedicate this essay, containing so far unpublished critical and historical comments on this concept, to Professor Selleri on the occasion of his 70th birthday. It should be emphasized that the critical comments in this essay are not intended to question the validity of the theory initiated by this concept, a theory which in the realm of its applicability is daily corroborated by numerous experiments in high-energy laboratories all over the world. Although these critical remarks refer almost exclusively to the first publication of this theory, a publication which has been hailed as the most important paper written in the 20th century, they discuss profound problems of general importance for the study of the foundations of physics.     

The ground state of the Bose gas

The mathematical formalism describing the Bose gas at zero temperature is analysed with the aid of methods that have recently been successful in relativistic quantum field theory. First the spectrum conditions for an infinitely extended system are given and the algebra of observables and the algebra of field operators are defined. General properties of states over these algebras are discussed and theorems are given which connect the linked cluster property, translation invariance and the purity of the states. It is proved that pure states over the algebra of observables have the property of factorisable off-diagonal long range order. The class of quasi free states is defined and of these states those which are translation invariant and possess the linked cluster property are analysed. It is shown that this class of states contains a subclass of pure states of the Bogoliubov type and a subclass of states which are mixtures of non-translationally invariant pure states. The applications of these quasi free states to the interacting Bose gas are summarized.