Quantum Locality?

Robert Griffiths has recently addressed, within the framework of a ‘consistent quantum theory’ that he has developed, the issue of whether, as is often claimed, quantum mechanics entails a need for faster-than-light transfers of information over long distances. He argues that the putative proofs of this property that involve hidden variables include in their premises some essentially classical-physics-type assumptions that are not entailed by the precepts of quantum mechanics. Thus whatever is proved is not a feature of quantum mechanics, but is a property of a theory that tries to combine quantum theory with quasi-classical features that go beyond what is entailed by quantum theory itself. One cannot logically prove properties of a system by establishing, instead, properties of a system modified by adding properties alien to the original system. Hence Griffiths’ rejection of hidden-variable-based proofs is logically warranted. Griffiths mentions the existence of a certain alternative proof that does not involve hidden variables, and that uses only macroscopically described observable properties. He notes that he had examined in his book proofs of this general kind, and concluded that they provide no evidence for nonlocal influences. But he did not examine the particular proof that he cites. An examination of that particular proof by the method specified by his ‘consistent quantum theory’ shows that the cited proof is valid within that restrictive version of quantum theory. An added section responds to Griffiths’ reply, which cites general possibilities of ambiguities that might make what is to be proved ill-defined, and hence render the pertinent ‘consistent framework’ ill defined. But the vagaries that he cites do not upset the proof in question, which, both by its physical formulation and by explicit identification, specify the framework to be used. Griffiths confirms the validity of the proof insofar as that pertinent framework is used. The section also shows, in response to Griffiths’ challenge, why a putative proof of locality that he has described is flawed.     

Some further comments on the Selleri-Tarozzi proof of the nonlocality of quantum mechanics

A recent proof, by Selleri and Tarozzi, of the nonlocality of quantum mechanics is reexamined within a general ensemble interpretation. It is concluded that there is no reason at all to doubt the compatibility between quantum mechanics and Einstein locality in the sense of Einstein's relativity principle (propagation of physical influences with finite velocity).     

The significance of a hidden variable proof and the logical interpretation of quantum mechanics

This paper examines the logical interpretation of quantum mechanics. Since this interpretation is based on a proof by Kochen and Specker that purports to demonstrate that hidden variable theories for quantum mechanics are excluded, the proof and its significance for the understanding of hidden variable theories and standard quantum mechanics are discussed.Work supported by the National Science Foundation.     

Nonlocality and conservation laws in hidden variable theories

It is shown that any hidden variable model that reproduces quantum mechanics for a single particle must either be nonlocal or violate conservation of momentum. This is established by deriving an inequality which must hold in any local, momentum-conserving hidden variable model for a modified form of the double-slit experiment. It is then shown that any hidden variable model that reproduces quantum mechanics must violate the inequality. The inconsistency between the classical and quantum views of the world is therefore demonstrated in a new way.     

On the structure of quantal proposition systems

I define sublaltices of quantum propositions that can be taken as having determinate (but perhaps unknown) truth values for a given quantum state, in the sense that sufficiently many two-valued maps satisfying a Boolean homomorphism condition exist on each determinate sublattice to generate a Kolmogorov probability space for the probabilities defined by the slate. I show that these sublattices are maximal, subject to certain constraints, from which it follows easily that they are unique. I discuss the relevance of this result for the measurement problem, relating it to an early proposal by Jauch and Piron for defining a new notion of state for quantum systems, to a recent uniqueness proof by Clifton for the sublattice of propositions specified as determinate by modal interpretations of quantum mechanics that exploit the polar decompostion theorem, and to my own previous suggestions for interpreting quantum mechanics without the projection postulate.     

No-broadcasting theorem and its classical counterpart

Although it is widely accepted that "no-broadcasting"-the nonclonability of quantum information-is a fundamental principle of quantum mechanics, an impossibility theorem for the broadcasting of general density matrices has not yet been formulated. In this Letter, we present a general proof for the no-broadcasting theorem, which applies to arbitrary density matrices. The proof relies on entropic considerations, and as such can also be directly linked to its classical counterpart, which applies to probabilistic distributions of statistical ensembles.     

Hadron Structure Within the Point Form of Relativistic Quantum Mechanics

We present an outline of recent developments in the field of hadron form-factor calculations within constituent-quark models using the point form of relativistic quantum mechanics. Our method to calculate currents and form factors is exemplified by means of the weak B → D transition. We present results for weak B → D transition form factors in the space- and the time-like momentum-transfer region. We discuss how wrong cluster properties, which one has to deal with when employing relativistic quantum mechanics, affect these form factors and we estimate the role non-valence, Z-graph contributions may play for decay kinematics.     

对于“包含在连续谱量子体系中的决定论性”一文的讨论

对于具有连续能谱的单粒子量子体系,“包含在连续谱量子体系中的决定论性”一文用所谓“双波函数”来描述处于能量本征态的粒子系综中各粒子的量子行为,并且在所谓的“等价定理”中称:双波函数描述在经典极限下将化为经典力学描述.然而,此描述所给出的系综力学量观测值统计分布的预言与通常量子力学不相容;并且,该文对其“等价定理”的证明是不正确的,这个“定理”实际上不成立 关键词： 连续能谱量子体系 双波函数 经典极限     

Morse theory interpretation of topological quantum field theories

Topological quantum field theories are interpreted as a generalized form of Morse theory. This interpretation is applied to formulate the simplest topological quantum field theory: topological quantum mechanics. The only non-trivial topological invariant corresponding to this theory is computed and identified with the Euler characteristic. Using field theoretical methods this topological invariant is calculated in different ways and in the process a proof of the Gauss-Bonnet-Chern-Avez formula as well as some results of degenerate Morse theory are obtained.     

Compound objects as particles in quantum mechanics

The property of fundamental mechanical theories which allows one to treat compound objects as particles under suitable conditions is considered. It is argued that such a property, called composition invariance, is a nonreleasable property of any fundamental mechanical theory. The proof that standard quantum mechanics enjoys composition invariance is reviewed. Finally, it is shown that the requirement of composition invariance allows one to choose between two alternative forms of quantum mechanics with spontaneous localization.     

Effect of irreversible atomic relaxation on resonance fluorescence,absorption, and stimulated emission

Even for a single isolated constituent of matter, a recent generalization of quantum mechanics, called quantum thermodynamics, postulates the existence of new nonmechanical individual states, not contemplated within conventional quantum mechanics, for which the time evolution is governed by a novel nonlinear equation of motion, which entails an irreversible, energy-preserving internal redistribution mechanism of relaxation towards stable equilibrium. For a single two-level atom interacting with the quantum electromagnetic field, we show that such irreversible internal redistribution mechanism entails interesting corrections to the conventional quantum electrodynamic predictions on absorption, resonance fluorescence, and stimulated emission. For a two-level atom driven near resonance by a nearly monochromatic laser beam, we estimate the corrections implied on the spectral distribution of resonance fluorescence and on the absorption and stimulated emission line shape. We submit that our predictions call for further high-resolution studies of atom-field interactions. For example, the value or a lower bound to the value of the only unknown constant of the theory, namely, the internal redistribution time constant, can only be established by a quantitative experimental study.     

Quantum Hamilton mechanics: Hamilton equations of quantum motion, origin of quantum operators, and proof of quantization axiom

This paper gives a thorough investigation on formulating and solving quantum problems by extended analytical mechanics that extends canonical variables to complex domain. With this complex extension, we show that quantum mechanics becomes a part of analytical mechanics and hence can be treated integrally with classical mechanics. Complex canonical variables are governed by Hamilton equations of motion, which can be derived naturally from Schrödinger equation. Using complex canonical variables, a formal proof of the quantization axiom p → pˆ = −i, which is the kernel in constructing quantum-mechanical systems, becomes a one-line corollary of Hamilton mechanics. The derivation of quantum operators from Hamilton mechanics is coordinate independent and thus allows us to derive quantum operators directly under any coordinate system without transforming back to Cartesian coordinates. Besides deriving quantum operators, we also show that the various prominent quantum effects, such as quantization, tunneling, atomic shell structure, Aharonov–Bohm effect, and spin, all have the root in Hamilton mechanics and can be described entirely by Hamilton equations of motion.     

RQM description of PS meson form factors,constraints from space-time translations and underlying dynamics

The role of Poincaré covariant space-time translations is investigated in the case of the pseudoscalar-meson charge form factors. It is shown that this role extends beyond the standard energy-momentum conservation, which is accounted for in all relativistic quantum mechanics calculations. It implies constraints that have been largely ignored until now but should be fulfilled to ensure the full Poincaré covariance. The violation of these constraints, which is more or less important depending on the form of relativistic quantum mechanics that is employed, points to the validity of using a single-particle current, which is generally assumed in calculations of form factors. In short, these constraints concern the relation of the momentum transferred to the constituents to the one transferred to the system. How to account for the related constraints, as well as restoring the equivalence of different relativistic quantum mechanics approaches in estimating form factors, is discussed. Some conclusions relative to the underlying dynamics are given in the pion case.     

Determinism,realism, and Stapp's 1985 proof of nonlocality

Two recent criticisms of Stapp's 1985 proof of an incompatibility between locality and quantum mechanics are clarified. One of these criticisms (charging that the proof requires determinism) is supported by a detailed logical analysis of the locality conditions in the proof. The other criticism (charging that the proof assumes realism) is shown to be based upon a misinterpretation of the rôle of counterfactuals in the proof. Further, Stapp's own replies to these criticisms are shown to be inadequate.     

Two-time correlation functions: stochastic and conventional quantum mechanics

An investigation of two-time correlation functions is reported within the framework of (i) stochastic quantum mechanics and (ii) conventional Heisenberg-Schr?dinger quantum mechanics. The spectral functions associated with the two-time electric dipole moment correlation functions are worked out in detail for the case of the hydrogen atom. While the single time averages are identical for stochastic and conventional quantum mechanics, differences arise in the two approaches for multiple time correlation functions.     

Calculating the C Operator in PT-symmetric Quantum Mechanics

It has recently been shown that a non-Hermitian Hamiltonian H possessing an unbroken PT symmetry (i) has a real spectrum that is bounded below, and (ii) defines a unitary theory of quantum mechanics with positive norm. The proof of unitarity requires a linear operator C, which was originally defined as a sum over the eigenfunctions of H. However, using this definition it is cumbersome to calculate C in quantum mechanics and impossible in quantum field theory. An alternative method is devised here for calculating C directly in terms of the operator dynamical variables of the quantum theory. This new method is general and applies to a variety of quantum mechanical systems having several degrees of freedom. More importantly, this method can be used to calculate the C operator in quantum field theory. The C operator is a new time-independent observable in PT-symmetric quantum field theory.     

Bell’s Theorem Without Inequalities and Only Two Distant Observers

A proof of Bell's theorem without inequalities and involving only two observers is given by suitably extending a proof of the Bell-Kochen-Specker theorem due to Mermin. This proof is generalized to obtain an inequality-free proof of Bell's theorem for a set of n Bell states (with n odd) shared between two distant observers. A generalized CHSH inequality is formulated for n Bell states shared symmetrically between two observers and it is shown that quantum mechanics violates this inequality by an amount that grows exponentially with increasing n.     

Positive Commutators in Non-Equilibrium Quantum Statistical Mechanics

The method of positive commutators, developed for zero temperature problems over the last twenty years, has been an essential tool in the spectral analysis of Hamiltonians in quantum mechanics. We extend this method to positive temperatures, i.e. to non-equilibrium quantum statistical mechanics. We use the positive commutator technique to give an alternative proof of a fundamental property of a certain class of large quantum systems, called Return to Equilibrium. This property says that equilibrium states are (asymptotically) stable: if a system is slightly perturbed from its equilibrium state, then it converges back to that equilibrium state as time goes to infinity. Received: 27 December 2000 / Accepted: 21 June 2001