The Einstein-Podolsky-Rosen (EPR) paradox gives an argument for the incompleteness of quantum mechanics based on a plausible criterion for reality, as well as the assumption of locality. A general view is that the argument is compromised, because EPR's premises are falsified by Greenberger-Horne-Zeilinger (GHZ) and Bell experiments. In this paper, we present an EPR argument based on premises not falsified by these experiments. First, we consider macroscopic EPR-Bohm, Bell, and GHZ experiments using spins ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{S}}_{\ensuremath{\theta}}$ defined by two macroscopically distinct states. The analyzers that realize the unitary operations ${U}_{\ensuremath{\theta}}$ determining the measurement settings $\ensuremath{\theta}$ are nonlinear devices creating macroscopic superposition states. We note two definitions of macroscopic realism (MR). For a system with two macroscopically distinct states available to it, MR posits a predetermined outcome for the measurement ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{S}}_{\ensuremath{\theta}}$ distinguishing between the states. Deterministic macroscopic realism assumes MR for the system defined prior to the interaction ${U}_{\ensuremath{\theta}}$ being carried out but is falsifiable by the macroscopic Bell and GHZ proposals. Motivated by arguments to uphold MR (without resorting to decoherence), as well as no-signaling and the properties of a meter, we define a set of premises referred to as weak macroscopic realism (wMR). Weak macroscopic realism (wMR) posits MR for the system after ${U}_{\ensuremath{\theta}}$, at the time
tf---when the system is prepared with respect to the measurement basis, ready for a ``pointer'' measurement and readout. For this system, wMR posits that the outcome of ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{S}}_{\ensuremath{\theta}}$ is determined and not changed by interactions that might subsequently occur at a remote system
B. The premise wMR also posits a weaker version of EPR's criterion for reality. Importantly, we show that the GHZ and Bell predictions are consistent with wMR. Yet, an EPR paradox arises for a macroscopic EPR-Bohm state, based on wMR. As considered by Schr\"odinger, it is possible to measure two complementary spins of system
A simultaneously, ``one by direct, the other by indirect measurement'': If we assume wMR, then once both settings are fixed, the outcomes of the two spins are both determined. We revisit the original EPR paradox and find a similar result: An EPR argument can be based on a set of premises, weak local realism, which we show are not falsifiable by GHZ or Bell experiments.
The Einstein-Podolsky-Rosen (EPR) paradox gives an argument for the incompleteness of quantum mechanics based on the premises of local realism. A general view is that the argument is compromised, because EPR's premises are falsified by Greenberger-Horne-Zeilinger (GHZ) and Bell experiments. In this paper, we present an EPR argument based on premises not falsifiable by these experiments. We propose macroscopic EPR and GHZ experiments using spins
Sθ defined by two macroscopically distinct states. The analyzers that realize the unitary operations
Uθ determining the measurement settings
θ are devices that create macroscopic superposition states. For a system with two macroscopically distinct states available, macroscopic realism (MR) posits a predetermined outcome for a measurement
Sθ distinguishing between the states. Deterministic macroscopic realism (dMR) posits MR for the system prior to the interaction
Uθ. Weak macroscopic realism (wMR) posits MR for the system after
Uθ, at the time
tf (when the system is prepared for a final "pointer" measurement), the outcome of
Sθ not being changed by interactions that might occur at a remote system
B. The premise also posits that if the outcome for
SθA of a system
A can be predicted by a pointer measurement on a system
B defined after the interaction fixing the setting at
B, then the outcome for
SθA is determined at this time. The GHZ predictions negate dMR but are consistent with wMR. Yet, an EPR paradox arises based on wMR for the set-up proposed by Schrödinger, where one measures two complementary spins simultaneously, "one by direct, the other by indirect" measurement. We revisit the original EPR paradox and find similarly that an EPR argument can be based on a weak form of local realism not falsifiable by GHZ or Bell tests.
Bohm's spin polarization modification of the paradox of Einstein, Podolsky, and Rosen has served as the basis for numerous analyses of the roles of hidden variables and Einstein locality in quantum mechanics. The present note points out how corresponding analyses can be carried out on the original formulation of Einstein, Podolsky, and Rosen (EPR) in terms of observations of position and momentum. Concrete conceptual experiments are proposed to furnish tangible illustrations of EPR tests of reality, and a position-momentum variant of Bell's inequality is formulated. Implications regarding joint measurements of position and momentum, delayed choice experiments, and superluminal communication are discussed briefly.
1 History of the Einstein-Podolsky-Rosen Paradox.- 2 Are Faster-Than-Light Influences Necessary?.- 3 All the Inequalities of Einstein Locality.- 4 Einstein-Podolsky-Rosen Experiments Using the Decays of ?c or J/? into ??? ? ?-?p?+p?.- Chapter5 Einstein-Podolsky-Rosen Paradox for the K0-K?0 and B0-B?0 Systems.- 6 Even Local Probabilities Lead to the Paradox.- 7 The Experimental Investigation of the Einstein-Podolsky-Rosen Question and Bell's Inequality.- 8 Rapisarda's Experiment: Testing Quantum Mechanics versus Local Hidden-Variable Theories with Dichotomic Analyzers.- 9 Nonlocality and the Einstein-Podolsky-Rosen Experiment as Understood through the Quantum-Potential Approach.- 10 Interpretation of the Einstein-Podolsky-Rosen Effect in Terms of a Generalized Causality.- 11 Quantum Action-at-a-Distance: The Mystery of Einstein-Podolsky-Rosen Correlations.- 12 Particle Trajectories and Quantum Correlations.- 13 Bell's Inequality and the Nonergodic Interpretation of Quantum Mechanics.- 14 An Extended-Probability Response to the Einstein-Podolsky-Rosen Argument.- 15 The Search for Hidden Variables in Quantum Mechanics.- 16 Variable Detection Probability Models for Einstein-Podolsky-Rosen-Type Experiments.- 17 Stochastic Electrodynamics and the Einstein-Podolsky-Rosen Argument.- 18 Explicit Calculations with a Hidden-Variable Spin Model.- 19 Symmetric and Asymmetric Models for Atomic Cascade Experiments.
1. Quantum Mechanics, Reality and Separability: Physical Developments of the Einstein-Podolsky-Rosen Argument.- Realism in Quantum Mechanics and a New Version of the EPR Experiment.- Discussion: M. Cini, F. De Martini, K. Kraus, T.W. Marshall, K.R. Popper, H. Rauch, M.C. Robinson, F. Selleri, J. Six, G. Tarozzi, J.-P. Vigier..- The Physical Origin of the Einstein-Podolsky-Rosen Paradox.- Does the Bell Inequality Hold for All Local Theories?.- Is it Possible to Save Causality and Locality in Quantum Mechanics?.- Einstein-Podolsky-Rosen Experiments and Macroscopic Locality.- On the Compatibility of Local Realism with Atomic Cascade Experiments.- Is the Einstein-Podolsky-Rosen Paradox Demanded by Quantum Mechanics?.- Infinite Wave Resolution of the EPR Paradox.- On Non Local Influences.- Einstein Locality for Individual Systems and for Statistical Ensembles.- Can Nondetected Photons Simulate Nonlocal Effects in Two-Photon Polarization Correlation Experiments?.- 2. The Stochastic Interpretation of Quantum Processes.- Quantum Theory of Measurement without Wave Packet Collapse.- A Causal Fluidodynamical Model for the Relativistic Quantum Mechanics.- On the Nonlinear Schrodinger Equation.- Recent Developments in de Broglie Nonlinear Wave Mechanics.- The Role of the Quantum Potential in Determining Particle Trajectories and the Resolution of the Measurement Problem.- When is Statistical Theory Causal?.- Radiation Damping and Nonlinearity in the Pilot Wave Interpretation of Quantum Mechanics.- Stochastic Electrodynamics and the Bell Inequalities.- Nonlocal Quantum-Potential Interpretation of Relativistic Actions at a Distance in Many-Body Problems.- 3. The Realistic Interpretation of the Wave Function: Experimental Tests on the Wave-Particle Dualism.- Third Kind Measurements and Wave-Particle Dualism.- Quantum Effects in the Interference of Light.- Tests of Quantum Mechanics by Neutron Interferometry.- A Unified Experiment for Testing both the Interpretation and the Reduction Postulate of the Quantum Mechanical Wave Function.- Epilogue.- Evolutionary Epistemology.