Einstein Locality

Howard M. Wiseman

In this Einstein Year of Physics it seems appropriate to look at an important aspect of Einstein's work that is often down-played: his contribution to the debate on the interpretation of quantum mechanics. Contrary to physics ‘folklore’, Bohr had no defence against Einstein's 1935 attack (the EPR paper) on the claimed completeness of orthodox quantum mechanics. I suggest that Einstein's argument, as stated most clearly in 1946, could justly be called Einstein's reality – locality – completeness theorem, since it proves that one of these three must be false. Einstein's instinct was that completeness of orthodox quantum mechanics was the falsehood, but he failed in his quest to find a more complete theory that respected reality and locality. Einstein's theorem, and possibly Einstein's failure, inspired John Bell in 1964 to prove his reality – locality theorem. This strengthened Einstein's theorem (but showed the futility of his quest) by demonstrating that either reality or locality is a falsehood. This revealed the full non-locality of the quantum world for the first time.

Martin A. Roos

Jeremy Butterfield

I discuss various formulations of stochastic Einstein locality (SEL), which is a version of the idea of relativistic causality, that is, the idea that influences propagate at most as fast as light. SEL is similar to Reichenbach's Principle of the Common Cause (PCC), and Bell's Local Causality.My main aim is to discuss formulations of SEL for a fixed background spacetime. I previously argued that SEL is violated by the outcome dependence shown by Bell correlations, both in quantum mechanics and in quantum field theory. Here I reassess those verdicts in the light of some recent literature which argues that outcome dependence does not violate the PCC. I argue that the verdicts about SEL still stand.Finally, I briefly discuss how to formulate relativistic causality if there is no fixed background spacetime. 1. Introduction2. Formulating Stochastic Einstein Locality2.1. Events and regions2.2. The idea of SEL2.3. Three formulations of SEL2.3.1. The formulations2.3.2. Comparisons2.4. Implications between the formulations2.4.1. Conditions for the equivalence of SELD1 and SELD22.4.2. Conditions for the equivalence of SELS and SELD23. Relativistic Causality in the Bell Experiment3.1. The background3.1.1. The Bell experiment reviewed3.1.2. My previous position3.2. A common common cause? The Budapest school3.2.1. Resuscitating the PCC3.2.2. Known proofs of a Bell inequality need a strong PCC3.2.3. Two distinctions3.2.4. Szabó's model3.2.5. A common common cause is plausible3.2.6. Bell inequalities from a weak PCC: the Bern school3.3. SEL in the Bell experiment3.3.1. PCC and SEL are connected by PPSI3.3.2. The need for other judgments3.3.3. Weak vs. strong SELD4. SEL in Algebraic Quantum Field Theory4.1. The story so far4.2. Questions4.2.1. Our formulations4.2.2. The Budapest and Bern schools5. SEL in Dynamical Spacetimes5.1. SEL for metric structure?5.2. SEL for causal sets?5.2.1. The causal set approach5.2.2. Labelled causal sets; general covariance5.2.3. Deducing the dynamics5.2.4. The fate of SEL

Henry Pierce Stapp

Robert B. Griffiths

Shasanka Mohan Roy, Virendra Singh

For multiparticle systems we formulate the notions of signal locality (i.e., absence of faster-than-light signaling) and Einstein-Bell locality (or local realism) and obtain inequalities between experimental correlation functions to test them. Quantum theory obeys signal locality but violates Einstein-Bell locality by a factor ${2}^{(\mathit{n}\mathrm{\ensuremath{-}}1)/2}$ for n-particle systems.