Nonlocality as a feature of the physical world

Aprediction puzzle leads to a form ofnecessary realism which forces the rejection of a central tenet of the Copenhagen interpretation. This leads to reconsidering conceptual difficulties related to Bell's locality premise. It is shown that aparadox of elementary probability theory puts new light on Bell's assumption that causality and statistical independence are mutually incompatible. Nemo dat quod non habet : No one can offer more than he has ability to give; in that spirit, this paper is dedicated to the memory of J.S. Bell.     

A comment on “critique of home and sengupta's derivation of a Bell inequality”

We clarify some aspects of our derivation of a Bell-type inequality, in response to a paper by Elby.The following comments refer to Andrew Elby's discussion note immediately following our present paper.(a) We wish to stress that physical distinction between NC and LC is particularly important in the case of local realist theories violating NC for any single system but satisfying LC for any correlated many-component system. Arguments given by Elby do not rule out a reasonable theory violating NC but obeying LC. Therefore, a physically meaningful possibility exists that while Bell's inequality derived from NC is violated for a single system, the inequality derived from LC is satisfied for correlated and spatially separated (non-interacting) systems. It is precisely this possibility which was explored by HS in deriving Bell's inequality from NC.(b) Since Elby's formulation of locality condition necessarily involves a relativistic constraint at the level of individual measurements, it is pointless to discuss its compatibility with predictions derived from non-relativistic quantum mechanics, which is well known to allow superluminal communication by mechanisms such as wavepacket travel or spread. Recently this aspect has been discussed in depth by P. Ghose and D. Home,Phys. Rev. A 43, 6382 (1991). It needs to be stressed that our formulation of LC is in line with the separability condition articulated by Einstein in different contexts; see, for example,J. Franklin Inst. 221, 349 (1936), reprinted inIdeas and Opinions (Crown, New York, 1954), pp. 290–323.On leave from: Department of Physics, Bose Institute, Calcutta 700009, India.     

An exact,finite, gauge-invariant,non-perturbative approach to QCD renormalization

A particular choice of renormalization, within the simplifications provided by the non-perturbative property of Effective Locality, leads to a completely finite, non-perturbative approach to renormalized QCD, in which all correlation functions can, in principle, be defined and calculated. In this Model of renormalization, only the Bundle chain-Graphs of the cluster expansion are non-zero. All Bundle graphs connecting to closed quark loops of whatever complexity, and attached to a single quark line, provided no ‘self-energy’ to that quark line, and hence no effective renormalization. However, the exchange of momentum between one quark line and another, involves only the cluster-expansion’s chain graphs, and yields a set of contributions which can be summed and provide a finite color-charge renormalization that can be incorporated into all other QCD processes. An application to High Energy elastic pp scattering is now underway.     

The Bell inequalities and the joint measurement of incompatible observables

A quantum-mechanical theory of joint nonideal measurement of incompatible polarization observables is applied to an EPR-like experiment. It is demonstrated that this experiment yields both information satisfying and information violating the Bell inequalities. The measurement is also discussed in the context of a local hidden-variables theory. It is argued that the violation of an additional assumption of reproducibility of the hidden variable rather than violation of locality may be responsible for the violation of the Bell inequalities.     

On the Consequences of Retaining the General Validity of Locality in Physical Theory

The empirical validity of the locality (LOC) principle of relativity is used to argue in favour of a local hidden variable theory (HVT) for individual quantum processes. It is shown that such a HVT may reproduce the statistical predictions of quantum mechanics (QM), provided the reproducibility of initial hidden variable states is limited. This means that in a HVT limits should be set to the validity of the notion of counterfactual definiteness (CFD). This is supported by the empirical evidence that past, present, and future are basically distinct. Our argumentation is contrasted with a recent one by Stapp resulting in the opposite conclusion, i.e. nonlocality or the existence of faster-than-light influences. We argue that Stapps argumentation still depends in an implicit, but crucial, way on both the notions of hidden variables and of CFD. In addition, some implications of our results for the debate between Bohr and Einstein, Podolsky and Rosen are discussed.     

POPPER'S EXPERIMENT, UNCERTAINTY PRINCIPLE, SIGNAL LOCALITY AND MOMENTUM CONSERVATION

An experiment proposed earlier by Karl Popper in his critique of the Copenhagen interpretation was realized recently by Kim and Shih. We show that the Copenhagen interpretation is consistent with the results, contrary to Popper's expectation. We examine the role of signal locality and momentum conservation in Popper's experiment and in the realization by Kim and Shih.     

Finite speed of propagation and local boundary conditions for wave equations with point interactions

We show that the boundary conditions entering in the definition of the self-adjoint operator describing the Laplacian plus a finite number of point interactions are local if and only if the corresponding wave equation has finite speed of propagation.