The Klein-Gordon Equation in Machian Model

The non-local Machian model is regarded as an alternative theory of gravitation which states that all particles in the Universe as a ‘gravitationally entangled’ statistical ensemble. It is shown that the Klein-Gordon equation can be derived within this Machian model of the universe. The crucial point of the derivation is the activity of the Machian energy background field which causing a fluctuation about the average momentum of a particle, the non-locality problem in quantum theory is addressed in this framework.     

An intuitive form of non-localism for quantum mechanics

The two-slit interference experiment provides a vivid demonstration of quantum mechanics. It is clear that one can describe the effects using standard probability theory if one makes a non-localism assumption. But many scientists dismiss non-localism as implying “action-at-a-distance”. This paper shows that it is possible to construct a non-local model which does not assume “action-at-a-distance”.     

Entanglement Between Degrees of Freedom in?a?Single-Particle System Revealed in Neutron Interferometry

Initially Einstein, Podolsky, and Rosen (EPR) and later Bell shed light on the non-local properties exhibited by subsystems in quantum mechanics. Separately, Kochen and Specker analyzed sets of measurements of compatible observables and found that a consistent coexistence of these results is impossible, i.e., quantum indefiniteness of measurement results. As a consequence, quantum contextuality, a more general concept compared to non-locality, leads to striking phenomena predicted by quantum theory. Here, we report neutron interferometric experiments which investigate entangled states in a single-particle system: entanglement is, in this case, achieved not between particles, but between degrees of freedom i.e., between spin, path, and energy degrees of freedom. Appropriate combinations of the spin analysis and the position of the phase shifter in the interferometer allow an experimental verification of the violation of a Bell-like inequality. In addition, state tomography, tomographic analysis of the density matrix of a quantum system, and Kochen-Specker-like phenomena are presented to characterize neutrons’ entangled states and their peculiarity. Furthermore, a coherent energy manipulation scheme is accomplished with a radio-frequency (RF) spin-flipper. This scheme allows the (total) energy degree of freedom to be entangled: the remarkable behavior of a triply entangled GHZ-like state is demonstrated.     

Apparatus independence in proofs of non-locality

In standard proofs of non-locality in quantum mechanics assumptions regarding the statistical independence of the states of the measuring apparatuses are made. Recently, proofs by A. Elby [1], and by R. Clifton, M. Redhead, and J. Butterfield [2,3] have been put forward in which it is claimed that such assumptions are not needed. In this paper I argue that Elby's proof and the first proof of Clifton, Redhead, and Butterfield are fallacious, and that their second proof, though valid, does make assumptions regarding the statistical independence of apparatus states. I further argue that any valid proof must make assumptions regarding the probabilities of apparatus states.     

Experimental Evidence for a Dynamical Non-locality Induced Effect in Quantum Interference Using Weak Values

The quantum theoretical concepts of modular momentum and dynamical non-locality, which were introduced four decades ago, have recently been used to explain single particle quantum interference phenomena. Although the non-local exchange of modular momentum associated with such phenomena cannot be directly observed, it has been suggested that effects induced by this exchange can be measured experimentally using weak measurements of pre- and post-selected ensembles of particles. This paper reports on such an optical experiment that yielded measured weak values that were consistent with the theoretical prediction of an effect induced by a non-local exchange of modular momentum.     

About a “Nonlocal” Local Model Considered by L. Vervoort,and the Necessity to Distinguish Locality from Einstein Locality

L. Vervoort claims to have found a model which “can violate the Bell inequality and reproduce the quantum statistics, even if it is based on local dynamics only”. This claim is false. The proposed model contains global elements. The physics behind the model is local, but would not allow the explanation of violations of Bell inequalities for space-like separated events, if superluminal causal influences are forbidden. To use it for this purpose, one has to introduce a preferred frame where information can be send faster than light. As a cause of the misunderstanding we identify the unfortunate convention to use “local” as a synonym for Einstein-local, so that theories which are local in every physically relevant sense have to be named “non-local”, and argue that this convention should be abandoned.     

Bits,time, carriers,and matter

The formal structure of quantum information theory is based on the well-founded concepts and postulates of quantum mechanics. In the present contribution, I am inverting the usual approach presented in textbooks by beginning with the use of bit states as basic and fundamental units of information and establish a dynamical map for them. The condition of reversibility, imposed on an ordered sequence of actions operating on a bit state, introduces, by necessity, the unitarity property of actions. I also verify that the uniformity of time, as a parameter for ordering events, is due to the admission of a composition law for the actions. In the limit of infinitesimal intervals between actions, a reversible and linear equation arises for the dynamical changes in time of a qubit (superposition of bit states). The admission that a bit of information is stored or carried by a massive particle necessarily leads to the Schrödinger–Pauli equation (SPE); the bit is associated to a spin 1/2. Within this approach, I verify that the particle dynamical equation becomes “enslaved” by the spin dynamics. In other words, the bit (or spin) precedes in status the particle dynamical evolution, being at the root of the quantum character of the standard Schr¨odinger equation, even when spin and spatial degrees of freedom are uncoupled.     

High degree of entanglement and nonlocality of a two-photon state generated at 532 nm

In the last years the attention of the scientific community on the generation of entangled states has constantly increased both for their importance in the foundation of quantum mechanics and for their application in the quantum computation and communication field. To these aims high quality of generated states is required. A standard procedure to produce entangled photons pairs is spontaneous down conversion process in nonlinear crystals. In this paper we report preparation of quantum entangled states using CW laser at 266 nm pumping the standard Kwiat’s source. We have been able to generate the full set of Bell’s states with very high purity, fidelity and Concurrence which have been estimated using standard tomography procedure. To proof the high degree of achieved entanglement, we performed a non-locality test obtaining a high violation of the CHSH inequality.     

Hidden Yangians in 2D massive current algebras

We define non-local conserved currents in massive current algebras in two dimensions. Our approach is algebraic and non-perturbative. The non-local currents give a quantum field realization of the Yangians. We show how the noncocommutativity of the Yangians is related to the non-locality of the currents. We discuss the implications of the existence of non-local conserved charges on theS-matrices.Laboratoire de la Direction des sciences de la matière du Commissariat à l'énergie atomique     

Quantum Gravity If Non-Locality Is Fundamental

I take non-locality to be the Michelson–Morley experiment of the early 21st century, assume its universal validity, and try to derive its consequences. Spacetime, with its locality, cannot be fundamental, but must somehow be emergent from entangled coherent quantum variables and their behaviors. There are, then, two immediate consequences: (i). if we start with non-locality, we need not explain non-locality. We must instead explain an emergence of locality and spacetime. (ii). There can be no emergence of spacetime without matter. These propositions flatly contradict General Relativity, which is foundationally local, can be formulated without matter, and in which there is no “emergence” of spacetime. If these be true, then quantum gravity cannot be a minor alteration of General Relativity but must demand its deep reformulation. This will almost inevitably lead to: matter not only curves spacetime, but “creates” spacetime. We will see independent grounds for the assertion that matter both curves and creates spacetime that may invite a new union of quantum gravity and General Relativity. This quantum creation of spacetime consists of: (i) fully non-local entangled coherent quantum variables. (ii) The onset of locality via decoherence. (iii) A metric in Hilbert space among entangled quantum variables by the sub-additive von Neumann entropy between pairs of variables. (iv) Mapping from metric distances in Hilbert space to metric distances in classical spacetime by episodic actualization events. (v) Discrete spacetime is the relations among these discrete actualization events. (vi) “Now” is the shared moment of actualization of one among the entangled variables when the amplitudes of the remaining entangled variables change instantaneously. (vii) The discrete, successive, episodic, irreversible actualization events constitute a quantum arrow of time. (viii) The arrow of time history of these events is recorded in the very structure of the spacetime constructed. (ix) Actual Time is a succession of two or more actual events. The theory inevitably yields a UV cutoff of a new type. The cutoff is a phase transition between continuous spacetime before the transition and discontinuous spacetime beyond the phase transition. This quantum creation of spacetime modifies General Relativity and may account for Dark Energy, Dark Matter, and the possible elimination of the singularities of General Relativity. Relations to Causal Set Theory, faithful Lorentzian manifolds, and past and future light cones joined at “Actual Now” are discussed. Possible observational and experimental tests based on: (i). the existence of Sub- Planckian photons, (ii). knee and ankle discontinuities in the high-energy gamma ray spectrum, and (iii). possible experiments to detect a creation of spacetime in the Casimir system are discussed. A quantum actualization enhancement of repulsive Casimir effect would be anti-gravitational and of possible practical use. The ideas and concepts discussed here are not yet a theory, but at most the start of a framework that may be useful.     

Testing for non-locally correlated particle motions in the hydrogen atom

We report on an experiment to test for a separate proton spectrum for hydrogen. The null results is in direct violation with the predictions of local hidden variable theories, and supports either non-local quantum potential theories or an “orthodox” (Copenhagen) interpretation of quantum mechanics, where the reality of particles is not conserved.     

Time-Symmetric Quantization in Spacetimes with Event Horizons

The standard quantization formalism in spacetimes with event horizons implies a non-unitary evolution of quantum states, as initial pure states may evolve into thermal states. This phenomenon is behind the famous black hole information loss paradox which provoked long-standing debates on the compatibility of quantum mechanics and gravity. In this paper we demonstrate that within an alternative time-symmetric quantization formalism thermal radiation is absent and states evolve unitarily in spacetimes with event horizons. We also discuss the theoretical consistency of the proposed formalism. We explicitly demonstrate that the theory preserves the microcausality condition and suggest a “reinterpretation postulate” to resolve other apparent pathologies associated with negative energy states. Accordingly as there is a consistent alternative, we argue that choosing to use time-asymmetric quantization is a necessary condition for the black hole information loss paradox.     

Modular variables in quantum theory

The non-local aspects of interaction between quantum systems are investigated. These aspects are particularly conspicuous in quantum phenomena without a classical analog, such as the quantum effects of electromagnetic potentials. The study of the potential effect leads to the introduction of a new type of dynamical variable, the modular variable, which brings out the physical features of quantum mechanical non-locality.The material contained in this article is based on work done in the period 1965–67. This work was supported in part by O.A.R. Air Force Cambridge Research Laboratories, Bedford, Mass., U.S.A., under Contracts No. AF 19(629)-5143 and AF 19(628)-5833.     

Critical layer singularities and complex eigenvalues in some differential equations of mathematical physics

Singular differential equations are a common feature of many problems in mathematical physics. It is often the case that systems with a similar mathematical structure can arise in many different contexts. In this article, mathematically related problems are drawn from areas as diverse as hydrodynamics (with applications to oceanography and meteorology), magnetohydrodynamics and plasma physics (with applications to astrophysics and geophysics, especially solar physics, ionospheric and magnetospheric physics; also nuclear fusion devices), acoustics, electromagnetics, quantum mechanics and nuclear physics. One major unifying feature common to the problems discussed here is the existence of complex eigenvalues, often associated with so-called “classical self-adjoint” equations. No real contradiction is involved here, but the resulting wave functions are often referred to variously as “radioactive states”, “damped resonances”, “leaky waves”, “non-modal solutions” , “singular modes”, “virtual modes”, or “improper eigenfunctions”. In the hydrodynamics of shear flows, such modes are associated with the existence of “critical layers” at which a singularity occurs in the governing (ordinary) differential equation. Similar, but usually more general singular layers are known to occur in equations arising in many of the above-mentioned contexts, and it is the purpose of this review to identify the nature of these singular layers and complex eigenvalues, and the relationships that exist between the different context in which they are found, and in particular to emphasize the occurrence of and interpretation of complex eigenvalues in quantum mechanics. Thus the “exponential catastrophe” is a clearly identified and recurring theme throughout this article by virtue of the similarities that exist between the classical and quantum system discussed here. The examples quoted from quantum mechanics are simple in form, and found in many standard texts, but the virtue of including them here is twofold: the results are easy to understand and relate to the more complicated “classical” systems, and they provide a valuable didactic and pedagogic tool for those readers whose background in quantum mechanics is limited. It is also hoped that this article will be of interest to readers who wish to become more acquainted with some aspects of hydrodynamics and magnetohydrodynamics.     

The Conway-Kochen Argument and Relativistic GRW Models

In a recent paper, Conway and Kochen proposed what is now known as the “Free Will theorem” which, among other things, should prove the impossibility of combining GRW models with special relativity, i.e., of formulating relativistically invariant models of spontaneous wavefunction collapse. Since their argument basically amounts to a non-locality proof for any theory aiming at reproducing quantum correlations, and since it was clear since very a long time that any relativistic collapse model must be non-local in some way, we discuss why the theorem of Conway and Kochen does not affect the program of formulating relativistic GRW models.     

The Uncertainty Relation for Quantum Propositions

Logical propositions with the fuzzy modality “Probably” are shown to obey an uncertainty principle very similar to that of Quantum Optics. In the case of such propositions, the partial truth values are in fact probabilities. The corresponding assertions in the metalanguage, have complex assertion degrees which can be interpreted as probability amplitudes. In the logical case, the uncertainty relation is about the assertion degree, which plays the role of the phase, and the total number of atomic propositions, which plays the role of the number of modes. In analogy with coherent states in quantum physics, we define “quantum coherent propositions” those which minimize the above logical uncertainty relation. Finally, we show that there is only one kind of compound quantum-coherent propositions: the “cat state” propositions.     

Spin and statistics of quantum kinks

Apart from some brief and inconclusive remarks concerning the problem of spin and statistics of quantum kinks in space-time dimension D > 2, we give a detailed discussion of the D = 2 situation. Our main results is that two-dimensional quantum kinks are statistical “schizons”; they exist in the same Hilbert space either as bosons or as fermions. In those cases where one can introduce local kink-sector generating operators as in the sine-Gordon model, the Bose and Fermi fields are strictly local fields, which are relatively non-local with respect to each other.