Because of the non-locality of quantum entanglement, realist approaches to completing quantum mechanics have implications for our conception of space. Quantum gravity also is expected to predict phenomena in which the locality of classical spacetime is modified or disordered. It is then possible that the right quantum theory of gravity will also be a completion of quantum mechanics in which the foundational puzzles in both are addressed together. I review here the results of a program, developed with Roberto Mangabeira Unger, Marina Cortes and other collaborators, which aims to do just that. The results so far include energetic causal set models, time asymmetric extensions of general relativity and relational hidden variables theories, including real ensemble approaches to quantum mechanics. These models share two assumptions: that physics is relational and that time and causality are fundamental.
I propose that quantum entanglement may reflect relational connectivity at a level where ordinary spatial distance is not fundamental. In the geometric framework considered here, particle pairs arise from an underlying field, retain a shared quantum structure, and participate in a network from which three-dimensional space emerges. Spatial separation in the emergent description need not imply complete independence at the underlying level. I formulate this idea as a conceptual hypothesis and distinguish it from established quantum mechanics, from classical common-cause explanations, and from specific proposals relating entanglement to spacetime geometry. Standard entanglement, Bell correlations, and the no-signalling condition provide consistency requirements; they are not derived from the proposed framework. No graviton-mediated mechanism, dynamical law, or experimentally distinguishable prediction is established in this paper. The hypothesis motivates a research programme requiring a defined state space, a rule for emergent geometry, a treatment of measurement and decoherence, and a quantitative comparison with quantum theory.
The general view is that all fundamental physical laws should be formulated within the framework given by quantum mechanics (QM). In a sense, QM therefore has the character of a metaphysical theory. Consequently, if it is possible to derive QM from more basic principles, these principles should be of general, philosophical nature. Here, we derive the formalism of QM from well-motivated epistemic principles. A key assumption is that a physical theory that relies on entities or distinctions that are unknowable in principle gives rise to wrong predictions. First, an epistemic formalism is developed, using concepts like knowledge and potential knowledge, identifying a physical state
S with the potential knowledge of the physical world. It is demonstrated that QM emerges from this formalism. However, Hilbert spaces, wave functions and probabilities are defined in certain well-defined observational contexts only. This means that the epistemic formalism is broader than QM. In the fundamental layer of description, the physical state
S is a subset of a state space
S={Z}, such that
S always contains many elements
Z. These elements correspond to unattainable states of complete knowledge of the world. The evolution of
S cannot be determined in terms of the individual evolution of the elements
Z, unlike the evolution of an ensemble in classical phase space. The evolution of
S is described in terms of sequential time
n∈N, which is updated according to
n→n+1 each time an event occurs, each time potential knowledge changes. Sequential time
n can be separated from relational time
t, which describes distances between events in space-time. There is an entire space-time associated with each
n, in which
t represents the knowledge at sequential time
n about the temporal relations between present and past events.
There are pressures that are coming from a number of quarters in quantum cosmology to view space or space-time as an emergent structure. But in recent years in the foundations of standard, non-relativistic quantum mechanics, interpretations have emerged that treat space as emergent. My primary purpose is (i) to make explicit the considerations stemming from quantum mechanics alone, that are pushing in the direction of viewing space (or space-time) as an emergent structure, and (ii)to clarify exactly what it means to say that space is emergent in the sense that this chapter is interested inhere. Itdoes that by presenting some simple low-dimensional models that reproduce central features of quantum phenomena, and analyzing the examples with attention to the difference between two different kinds of explanation: one in which the correlations emerge from a more fundamental (and not ultimately spatial) description and one in which correlations are explained by influences that pass through the space in which the correlated events are situated.
In 1935, Albert Einstein and two colleagues, Boris Podolsky and Nathan Rosen (EPR) developed a thought experiment to demonstrate what they felt was a lack of completeness in quantum mechanics (QM). EPR also postulated the existence of more fundamental theory where physical reality of any system would be completely described by the variables/states of that fundamental theory. This variable is commonly called hidden variable and the theory is called hidden variable theory (HVT). In 1964, John Bell proposed an empirically verifiable criterion to test for the existence of these HVTs. He derived an inequality, which must be satisfied by any theory that fulfill the conditions of locality and reality. He also showed that QM, as it violates this inequality, is incompatible with any local-realistic theory. Later it has been shown that Bell’s inequality (BI) can be derived from different set of assumptions and it also find applications in useful information theoretic protocols. In this review, we will discuss various foundational as well as information theoretic implications of BI. We will also discuss about some restricted nonlocal feature of quantum nonlocality and elaborate the role of Uncertainty principle and Complementarity principle in explaining this feature.