Feynman’s Proof of Maxwell Equations: in?the?Context?of Quantum Gravity

Many of us are familiar with Feynman’s “proof” of 1948, as revealed by Dyson, which demonstrates that Maxwell equations of electromagnetism are a consequence of Newton’s laws of motion of classical mechanics and the commutation relations of coordinate and momentum of quantum mechanics. It was Feynman’s purpose to explore the universality of dynamics of particles while making the fewest assumptions. We re-examine this formulation in the context of quantum gravity and show how Feynman’s derivation can be extended to include quantum gravity.     

On a possibility to find experimental evidence for the many-worlds interpretation of quantum mechanics

The many-worlds interpretation of quantum mechanics predicts the formation of distinct parallel worlds as a result, of a quantum mechanical measurement. Communication among these parallel worlds would experimentally rule out alternatives to this interpretation. A possible procedure for “interworld” exchange of information and energy, using only state of the art quantum optical equipement, is described. A single ion is isolated from its environment in an ion trap. Then a quantum mechanical measurement with two discrete outcomes is performed on another system, resulting in the formation of two parallel worlds. Depending on the outcome of this measurement the ion is excited from only one of the parallel worlds before the ion decoheres through its interaction with the environment. A detection of this excitation in the other parallel world is direct evidence for the many-worlds interpretation. This method could have important practical applications in physics and beyond.     

Planck’s Constant in the Light of Quantum Logic

The goal of quantum logic is the “bottom-top” reconstruction of quantum mechanics. Starting from a weak quantum ontology, a long sequence of arguments leads to quantum logic, to an orthomodular lattice, and to the classical Hilbert spaces. However, this abstract theory does not yet contain Planck’s constant ℏ. We argue, that ℏ can be obtained, if the empty theory is applied to real entities and extended by concepts that are usually considered as classical notions. Introducing the concepts of localizability and homogeneity we define objects by symmetry groups and systems of imprimitivity. For elementary systems, the irreducible representations of the Galileo group are projective and determined only up to a parameter z, which is given by z=m/ℏ, where m is the mass of the particle and ℏ Planck’s constant. We show that ℏ has a meaning within quantum mechanics, irrespective of use the of classical concepts in our derivation.     

An Introduction to Many Worlds in Quantum Computation

The interpretation of quantum mechanics is an area of increasing interest to many working physicists. In particular, interest has come from those involved in quantum computing and information theory, as there has always been a strong foundational element in this field. This paper introduces one interpretation of quantum mechanics, a modern ‘many-worlds’ theory, from the perspective of quantum computation. Reasons for seeking to interpret quantum mechanics are discussed, then the specific ‘neo-Everettian’ theory is introduced and its claim as the best available interpretation defended. The main objections to the interpretation, including the so-called “problem of probability” are shown to fail. The local nature of the interpretation is demonstrated, and the implications of this both for the interpretation and for quantum mechanics more generally are discussed. Finally, the consequences of the theory for quantum computation are investigated, and common objections to using many worlds to describe quantum computing are answered. We find that using this particular many-worlds theory as a physical foundation for quantum computation gives several distinct advantages over other interpretations, and over not interpreting quantum theory at all.     

Towards a Resolution of Dilemma: Nonlocality or Nonobjectivity?

This paper discusses a possible resolution of the nonobjectivity-nonlocality dilemma in quantum mechanics in the light of experimental tests of the Bell inequality for two entangled photons and a Bell-like inequality for a single neutron. My conclusion is that these experiments show that quantum mechanics is nonobjective: that is, the values of physical observables cannot be assigned to a system before measurement. Bell’s assumption of nonlocality has to be rejected as having no direct experimental confirmation, at least thus far. I also consider the relationships between nonobjectivity and contextuality. Specifically, I analyze the impact of the Kochen-Specker theorem on the problem of contextuality of quantum observables. I argue that, just as von Neumann’s “no-go” theorem, the Kochen-Specker theorem is based on assumptions that do not correspond to the real physical situation. Finally, I present a theory of measurement based on a classical, purely wave model (pre-quantum classical statistical field theory), a model that reproduces quantum probabilities. In this model continuous fields are transformed into discrete clicks of detectors. While this model is classical, it is nonobjective. In this case, nonobjectivity is the result of the dependence of experimental outcomes on the context of measurement, in accordance with Bohr’s view.     

Rovelli’s World

Carlo Rovelli’s inspiring “Relational Quantum Mechanics” serves several aims at once: it provides a new vision of what the world of quantum mechanics is like, and it offers a program to derive the theory’s formalism from a set of simple postulates pertaining to information processing. I propose here to concentrate entirely on the former, to explore the world of quantum mechanics as Rovelli depicts it. It is a fascinating world in part because of Rovelli’s reliance on the information-theory approach to the foundations of quantum mechanics, and in part because its presentation involves taking sides on a fundamental divide within philosophy itself.     

Identical Quantum Particles and Weak Discernibility

Saunders has recently claimed that “identical quantum particles” with an anti-symmetric state (fermions) are weakly discernible objects, just like irreflexively related ordinary objects in situations with perfect symmetry (Black’s spheres, for example). Weakly discernible objects have all their qualitative properties in common but nevertheless differ from each other by virtue of (a generalized version of) Leibniz’s principle, since they stand in relations an entity cannot have to itself. This notion of weak discernibility has been criticized as question begging, but we defend and accept it for classical cases likes Black’s spheres. We argue, however, that the quantum mechanical case is different. Here the application of the notion of weak discernibility indeed is question begging and in conflict with standard interpretational ideas. We conclude that the introduction of the conceptual resource of weak discernibility does not change the interpretational status quo in quantum mechanics.     

Relational Interpretation of the Wave Function and a Possible Way Around Bell’s Theorem

The famous “spooky action at a distance” in the EPR-scenario is shown to be a local interaction, once entanglement is interpreted as a kind of “nearest neighbor” relation among quantum systems. Furthermore, the wave function itself is interpreted as encoding the “nearest neighbor” relations between a quantum system and spatial points. This interpretation becomes natural, if we view space and distance in terms of relations among spatial points. Therefore, “position” becomes a purely relational concept. This relational picture leads to a new perspective onto the quantum mechanical formalism, where many of the “weird” aspects, like the particle-wave duality, the non-locality of entanglement, or the “mystery” of the double-slit experiment, disappear. Furthermore, this picture circumvents the restrictions set by Bell’s inequalities, i.e., a possible (realistic) hidden variable theory based on these concepts can be local and at the same time reproduce the results of quantum mechanics. PACS: 03.65.Ud, 04.60.Nc     

Explaining the Unobserved—Why Quantum Mechanics Ain’t Only About Information

A remarkable theorem by Clifton et al [Found Phys. 33(11), 1561–1591 (2003)] (CBH) characterizes quantum theory in terms of information-theoretic principles. According to Bub [Stud. Hist. Phil. Mod. Phys. 35 B, 241–266 (2004); Found. Phys. 35(4), 541–560 (2005)] the philosophical significance of the theorem is that quantum theory should be regarded as a “principle” theory about (quantum) information rather than a “constructive” theory about the dynamics of quantum systems. Here we criticize Bub’s principle approach arguing that if the mathematical formalism of quantum mechanics remains intact then there is no escape route from solving the measurement problem by constructive theories. We further propose a (Wigner-type) thought experiment that we argue demonstrates that quantum mechanics on the information-theoretic approach is incomplete.     

Can the Past Be Changed?

The paper shows that the past, history in a non-technical sense, can be changed in quantum mechanics. The first part of the paper reviews Deutsch's analysis in his paper of 1991. It is demonstrated that Deutsch assumes the existence of a multiplicity of essentially classical worlds. Such a multiplicity of worlds would allow the past to be changed in classical mechanics. It is argued that the existence of multiple classical worlds is not required by quantum mechanics. It is then shown that it is possible to change the past in conventional quantum mechanics even without the assumption of a multiplicity of worlds.     

Quantum Analogues of Hardy’s Nonlocality Paradox

Hardy’s nonlocality is a “nonlocality proof without inequalities”: it exemplifies that quantum correlations can be qualitatively stronger than classical correlations. This paper introduces variants of Hardy’s nonlocality in the CHSH scenario which are realized by the PR-box, but not by quantum correlations. Hence this new kind of Hardy-type nonlocality is a proof without inequalities showing that superquantum correlations can be qualitatively stronger than quantum correlations.     

Double-slit experiment and Bogoliubov’s causality principle

In the Bogoliubov approach the causality principle is the basic constructive element of quantum field theory. At the same time, this principle has obvious classical interpretation. On the other hand, it is well-known Feynman statement that the double-slit experiment is “impossible, absolutely impossible to explain in classical way, and has in it the heart of quantum mechanics. We describe how taking into account of infrared singularities allows to give quite evident interpretation to double-slit experiment. And this interpretation agrees with the Bogoliubov’s causality principle.     

Nonlocality Without Nonlocality

Bell’s theorem is purported to demonstrate the impossibility of a local “hidden variable” theory underpinning quantum mechanics. It relies on the well-known assumption of ‘locality’, and also on a little-examined assumption called ‘statistical independence’ (SI). Violations of this assumption have variously been thought to suggest “backward causation”, a “conspiracy” on the part of nature, or the denial of “free will”. It will be shown here that these are spurious worries, and that denial of SI simply implies nonlocal correlation between spacelike degrees of freedom. Lorentz-invariant theories in which SI does not hold are easily constructed: two are exhibited here. It is conjectured, on this basis, that quantum-mechanical phenomena may be modeled by a local theory after all. This paper is dedicated to the memory of John A. Wheeler.     

Time-delay of classical and quantum scattering processes: a conceptual overview and a general definition

We present a step by step introduction to the notion of time-delay in classical and quantum mechanics, with the aim of clarifying its foundation at a conceptual level. In doing so, we motivate the introduction of the concepts of “fuzzy” and “free-flight” sojourn times that we use to provide the most general possible definition for the quantum time-delay, valid for simple and multichannel scattering systems, with or without conditions on the observation of the scattering particle, and for incoming wave packets whose energy can be smeared out or sharply peaked (fixed energy). We conclude our conceptual analysis by presenting what we think is the right interpretation of the concepts of sojourn and delay times in quantum mechanics, explaining why, in ultimate analysis, they should not be called “times.”     

A New Book of Numbers: On the Precise Definition of Quantum Variables and the Relationships between Mathematics and Physics in Quantum Theory

Following Asher Peres’s observation that, as in classical physics, in quantum theory, too, a given physical object considered “has a precise position and a precise momentum,” this article examines the question of the definition of quantum variables, and then the new type (as against classical physics) of relationships between mathematics and physics in quantum theory. The article argues that the possibility of the precise definition and determination of quantum variables depends on the particular nature of these relationships.