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The problems connected with a causality of space-time universe and with the paradox of Einstein, Podolsky, and Rosen are considered. A main philosophical problem and its possible solutions are briefly discussed. A concept of unified local…

We discuss the problem of hidden variables and the motivation for introducting them in quantum mechanics. These include determinism, and the problem of meassurement and incompleteness. We first discuss Von-Neumann's imposisbility proof and…

The enigmatic nonlocal quantum correlation that was famously derided by Einstein as "spooky action at a distance" has now been experimentally demonstrated to be authentic. The quantum entanglement and nonlocal correlations emerged as…

In the 80 years since the seminal Einstein, Podolsky, and Rosen (EPR) paper, physicists and philosophers have mused about the `spooky action at a distance' aspect of quantum mechanics that so bothered Einstein. In his formal analysis of…

Bell's theorem has fascinated physicists and philosophers since his 1964 paper, which was written in response to the 1935 paper of Einstein, Podolsky, and Rosen. Bell's theorem and its many extensions have led to the claim that quantum…

It is shown that the Einstein, Podolsky and Rosen (EPR) correlations for arbitrary spin-s and the Greenberger, Horne and Zeilinger (GHZ) correlations for three particles can be described by nonlocal joint and conditional quantum…

This chapter of the Handbook of Quantum Gravity aims to illustrate how nonlocality can be implemented in field theories, as well as the manner it solves fundamental difficulties of gravitational theories. We review Stelle's quadratic…

In this chapter we discuss the Einstein Podolsky Rosen theorem and its strong relation with Bell's theorem. The central role played by the concept of beable introduced by Bell is emphasized. In particular we stress that beables involved in…

Conventionally, one interprets the correlations observed in Einstein-Podolsky-Rosen experiments by Bell's inequalities and quantum nonlocality. We show, in this paper, that identical correlations arise, if the phase relations of…

Quantum correlations between two parties are essential for the argument of Einstein, Podolsky, and Rosen in favour of the incompleteness of quantum mechanics. Schr\"odinger noted that an essential point is the fact that one party can…

Unarticulated, implicit hypotheses in Bell's analysis of Einstein, Podolsky and Rosen (EPR) correlations are identified and examined. These relate to the mathematical-analytical properties of random variables, the character of the relevant…

The Einstein-Podolsky-Rosen nonlocality puzzle has been recognized as one of the most important unresolved issues in the foundational aspects of quantum mechanics. We show that the problem is resolved if the quantum correlations are…

It is argued that while quantum mechanics contains nonlocal or entangled states, the instantaneous or nonlocal influences sometimes thought to be present due to violations of Bell inequalities in fact arise from mistaken attempts to apply…

A fruitful way of studying physical theories is via the question whether the possible physical states and different kinds of correlations in each theory can be shared to different parties. Over the past few years it has become clear that…

Characterization and categorization of quantum correlations are both fundamentally and practically important in quantum information science. Although quantum correlations such as non-separability, steerability, and non-locality can be…

The present standard interpretation of quantum mechanics invokes nonlocality and state reduction at space-like separated points during measurements on entangled systems. While there is no understanding of the physical mechanism of such…

We carry out a thought experiment in an imaginary world. Our world is both local and realistic, yet it violates a Bell inequality more than does quantum theory. This serves to debunk the myth that equates local realism with local hidden…

Since Bell's theorem we know that quantum mechanics is incompatible with local hidden-variable models, the phenomenon known as quantum nonlocality. However, despite steady progress over the years, precise characterization of the set of…

It is shown that when properly analyzed using principles consistent with the use of a Hilbert space to describe microscopic properties, quantum mechanics is a local theory: one system cannot influence another system with which it does not…

Recent work has shown that non-local modifications of the Einstein equations can have interesting cosmological consequences and can provide a dynamical origin for dark energy, consistent with existing data. At first sight these theories are…