Hidden Variables with Nonlocal Time

To relax the apparent tension between nonlocal hidden variables and relativity, we propose that the observable proper time is not the same quantity as the usual proper-time parameter appearing in local relativistic equations. Instead, the two proper times are related by a nonlocal rescaling parameter proportional to |ψ|², so that they coincide in the classical limit. In this way particle trajectories may obey local relativistic equations of motion in a manner consistent with the appearance of nonlocal quantum correlations. To illustrate the main idea, we first present two simple toy models of local particle trajectories with nonlocal time, which reproduce some nonlocal quantum phenomena. After that, we present a realistic theory with a capacity to reproduce all predictions of quantum theory.     

Information,physics, and computation

This paper presents several observations on the connections between information, physics, and computation. In particular, the computing power of quantum computers is examined. Quantum theory is characterized by superimposed states and nonlocal interactions. It is argued that recently studied quantum computers, which are based on local interactions, cannot simulate quantum physics.     

Transport properties of strongly correlated electrons in quantum dots studied with a simple circuit model

Numerical calculations are shown to reproduce the main results of recent experiments involving nonlocal spin control in quantum dots [Craig, Science 304, 565 (2004).]. In particular, the experimentally reported zero-bias-peak splitting is clearly observed in our studies. To understand these results, a simple "circuit model" is introduced and shown to qualitatively describe the experiments. The main idea is that the splitting originates in a Fano antiresonance, which is caused by having one quantum dot side connected in relation to the current's path. This scenario provides an explanation of the results of Craig et al. that is an alternative to the RKKY proposal, also addressed here.     

Hidden variable models for quantum theory cannot have any local part

It was shown by Bell that no local hidden variable model is compatible with quantum mechanics. If, instead, one permits the hidden variables to be entirely nonlocal, then any quantum mechanical predictions can be recovered. In this Letter, we consider general hidden variable models which can have both local and nonlocal parts. We show the existence of (experimentally verifiable) quantum correlations that are incompatible with any hidden variable model having a nontrivial local part, such as the model proposed by Leggett.     

A Locally Deterministic,Detector-Based Model of Quantum Measurement

This paper describes a simple, causally deterministic model of quantum measurement based on an amplitude threshold detection scheme. Surprisingly, it is found to reproduce many phenomena normally thought to be uniquely quantum in nature. To model an \(N\) -dimensional pure state, the model uses \(N\) complex random variables given by a scaled version of the wave vector with additive complex noise. Measurements are defined by threshold crossings of the individual components, conditioned on single-component threshold crossings. The resulting detection probabilities match or approximate those predicted by quantum mechanics according to the Born rule. Nevertheless, quantum phenomena such as entanglement, contextuality, and violations of Bell’s inequality under local measurements are all shown to be exhibited by the model, thereby demonstrating that such phenomena are not without classical analogs.     

Nonlinear Theory of Quantum Brownian Motion

A nonlinear theory of quantum Brownian motion in classical environment is developed based on a thermodynamically enhanced nonlinear Schrödinger equation. The latter is transformed via the Madelung transformation into a nonlinear quantum Smoluchowski-like equation, which is proven to reproduce key results from the quantum and classical physics. The application of the theory to a free quantum Brownian particle results in a nonlinear dependence of the position dispersion on time, being quantum generalization of the Einstein law of Brownian motion. It is shown that the time of decoherence from quantum to classical diffusion is proportional to the square of the thermal de Broglie wavelength divided by the classical Einstein diffusion constant.     

What does low energy physics tell us about the zero momentum gluon propagator

The connection between QCD, a nonlocal Nambu–Jona-Lasinio type model and the Landau gauge gluon propagator is explored. This two point function is parameterized by a functional form which is compatible with Dyson–Schwinger and lattice QCD results. Demanding the nonlocal model to reproduce the experimental values for the pion mass, the pion decay constant, Γ_π→γγ${\Gamma }_{\pi \to \gamma \gamma }$ and the light quark condensate we conclude that low energy physics does not distinguish between the so-called decoupling and scaling solutions of the Dyson–Schwinger equations. This result means that, provided that the model parameters are chosen appropriately, one is free to choose any of the above scenarios. Furthermore, the nonlocal Nambu–Jona-Lasinio quark model considered here is chiral invariant and satisfies the GMOR relation at the 1% level of precision.     

An explicit schrödinger picture for aharonov’s modular-variable concept

We propose to address in a natural manner the modular-variable concept explicitly in a Schrödinger picture. The idea of modular variables was introduced in 1969 by Aharonov, Pendleton, and Petersen to explain certain nonlocal properties of quantum mechanics. Our approach to this subject is based on Schwinger’s finite quantum kinematics and its continuous limit.     

Phase structure of a 3D nonlocal U(1) gauge theory: deconfinement by gapless matter fields

In this paper, we study a 3D compact U(1) lattice gauge theory with a variety of nonlocal interactions that simulates the effects of gapless/gapful matter fields. We restrict the nonlocal interactions among gauge variables only to those along the temporal direction and adjust their coupling constants optimally to simulate the isotropic nonlocal couplings of the original model. This theory is quite important to investigate the phase structures of QED₃ and strongly-correlated electron systems like the 2D quantum spin models, the fractional quantum Hall effect, the $t\text{–}J$ model of high-temperature superconductivity. We perform numerical studies of this theory to find that, for a certain class of power-decaying couplings, there appears a second-order phase transition to the deconfinement phase as the gauge coupling constant is decreased. On the other hand, for the exponentially-decaying coupling, there are no signals for second-order phase transition. These results indicate the possibility that introduction of sufficient number of massless matter fields destabilizes the permanent confinement in the 3D compact U(1) pure gauge theory due to instantons.     

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.     

A Smooth Path between the Classical Realm and the Quantum Realm

A simple example of classical physics may be defined as classical variables, p and q, and quantum physics may be defined as quantum operators, P and Q. The classical world of p&q, as it is currently understood, is truly disconnected from the quantum world, as it is currently understood. The process of quantization, for which there are several procedures, aims to promote a classical issue into a related quantum issue. In order to retain their physical connection, it becomes critical as to how to promote specific classical variables to associated specific quantum variables. This paper, which also serves as a review paper, leads the reader toward specific, but natural, procedures that promise to ensure that the classical and quantum choices are guaranteed a proper physical connection. Moreover, parallel procedures for fields, and even gravity, that connect classical and quantum physical regimes, will be introduced.     

Quantum nonlocality and beyond: limits from nonlocal computation

We address the problem of "nonlocal computation," in which separated parties must compute a function without any individual learning anything about the inputs. Surprisingly, entanglement provides no benefit over local classical strategies for such tasks, yet stronger nonlocal correlations allow perfect success. This provides intriguing insights into the limits of quantum information processing, the nature of quantum nonlocality, and the differences between quantum and stronger-than-quantum nonlocal correlations.     

Quantization in the large

A model theory is constructed that exhibits quantization on a cosmic scale. A holistic rationale for the theory is discussed. The theory incorporates a fundamental length, of cosmic size, and preserves the weak, geometrical equivalence principle. The momentum operator is an integral, nonlocal, naturally contravariant operator, in contrast to the usual quantum case. In the limit of high quantum numbers the theory reduces to classical physics, giving rise to a world which is quantized both on the microscopic and cosmic scale, each of which passes over to the usual macroscopic, continuous, classical, world in the highn limit. The theory is applied to two experimental situations, absorption lines in high-z quasars and elliptical rings around normal galaxies, with suggestive but not definitive results.     

Unifying model for several classes of two-dimensional phase transition

A relatively simple and physically transparent model based on quantum percolation and dephasing is employed to construct a global phase diagram which encodes and unifies the critical physics of the quantum Hall, "two-dimensional metal-insulator," classical percolation and, to some extent, superconductor-insulator transitions. Using real-space renormalization group techniques, crossover functions between critical points are calculated. The critical behavior around each fixed point is analyzed and some experimentally relevant puzzles are addressed.     

Symmetries, Quantum Geometry, and the Fundamental Interactions

A generalized Noether's theorem and the operational determination of a physical geometry in quantum physics are used to motivate a quantum geometry consisting of relations between quantum states that are defined by a universal group. Making these relations dynamical implies the nonlocal effect of the fundamental interactions on the wave function, as in the Aharonov–Bohm effect and its generalizations to non-Abelian gauge fields and gravity. The usual space–time geometry is obtained as the classical limit of this quantum geometry using the quantum-state space metric.     

In Appreciation¶The Depth and Breadth of John Bell's Physics

This essay surveys the work of John Stewart Bell, one of the great physicists of the twentieth century. Section 1 is a brief biography, tracing his career from working-class origins and undergraduate training in Belfast, Northern Ireland, to research in accelerator and nuclear physics in the British national laboratories at Harwell and Malvern, to his profound research on elementary particle physics as a member of the Theory Group at CERN and his equally profound "hobby" of investigating the foundations of quantum mechanics. Section 2 concerns this hobby, which began in his discontent with Bohr's and Heisenberg's analyses of the measurement process. He was attracted to the program of hidden variables interpretations, but he revolutionized the foundations of quantum mechanics by a powerful negative result: that no hidden variables theory that is "local" (in a clear and well-motivated sense) can agree with all the correlations predicted by quantum mechanics regarding well-separated systems. He further deepened the foundations of quantum mechanics by penetrating conceptual analyses of results concerning measurement theory of von Neumann, de Broglie and Bohm, Gleason, Jauch and Piron, Everett, and Ghirardi-Rimini-Weber. Bell's work in particle theory (Section 3) began with a proof of the CPT theorem in his doctoral dissertation, followed by investigations of the phenomenology of CP-violating experiments. At CERN Bell investigated the commutation relations in current algebras from various standpoints. The failure of current algebra combined with partially conserved current algebra to permit the experimentally observed decay of the neutral pi-meson into two photons stimulated the discovery by Bell and Jackiw of anomalous or quantal symmetry breaking, which has numerous implications for elementary particle phenomena. Other late investigations of Bell on elementary particle physics were bound states in quantum chromodynamics (in collaboration with Bertlmann) and estimates for the anomalous magnetic moment of the muon (in collaboration with de Rafael). Section 4 concerns accelerations, starting at Harwell with the algebra of strong focusing and the stability of orbits in linear accelerators and synchrotrons. At CERN he continued to contribute to accelerator physics, and with his wife Mary Bell he wrote on electron cooling and Beamstrahlung. A spectacular late achievement in accelerator physics was the demonstration (in collaboration with Leinaas) that the effective black-body radiation seen by an accelerated observer in an electromagnetic vacuum - the "Unruh effect" - had already been observed experimentally in the partial depolarization of electrons traversing circular orbits.     

Demonstrating superior discrimination of locally prepared states using nonlocal measurements

We experimentally demonstrate the superior discrimination of separated, unentangled two-qubit correlated states using nonlocal measurements, when compared with measurements based on local operations and classical communications. When predicted theoretically, this phenomenon was dubbed "quantum nonlocality without entanglement." We characterize the performance of the nonlocal, or joint, measurement with a payoff function, for which we measure 0.72 +/- 0.02, compared with the maximum locally achievable value of 2/3 and the overall optimal value of 0.75.     

Nonlocal nonreciprocal optomechanical circulator

A nonlocal circulator protocol is proposed in a hybrid optomechanical system. By analogy with quantum communication, using the input-output relationship, we establish the quantum channel between two optical modes with long-range. The three-body nonlocal interaction between the cavity and the two oscillators is obtained by eliminating the optomechanical cavity mode and verifying the Bell-CHSH inequality of continuous variables. By introducing the phase accumulation between cyclic interactions, the unidirectional transmission of quantum state between the optical mode and two mechanical modes is achieved. The results show that nonreciprocal transmissions are achieved as long as the accumulated phase reaches a certain value. In addition, the effective interaction parameters in our system are amplified, which reduces the difficulty of the implementation of our protocol. Our research can provide potential applications for nonlocal manipulation and transmission control of quantum platforms.