Operational quantum theory without predefined time

The standard formulation of quantum theory assumes a predefined notion of time. This is a major obstacle in the search for a quantum theory of gravity, where the causal structure of space-time is expected to be dynamical and fundamentally probabilistic in character. Here, we propose a generalized formulation of quantum theory without predefined time or causal structure, building upon a recently introduced operationally time-symmetric approach to quantum theory. The key idea is a novel isomorphism between transformations and states which depends on the symmetry transformation of time reversal. This allows us to express the time-symmetric formulation in a time-neutral form with a clear physical interpretation, and ultimately drop the assumption of time. In the resultant generalized formulation, operations are associated with regions that can be connected in networks with no directionality assumed for the connections, generalizing the standard circuit framework and the process matrix framework for operations without global causal order. The possible events in a given region are described by positive semidefinite operators on a Hilbert space at the boundary, while the connections between regions are described by entangled states that encode a nontrivial symmetry and could be tested in principle. We discuss how the causal structure of space-time could be understood as emergent from properties of the operators on the boundaries of compact space-time regions. The framework is compatible with indefinite causal order, timelike loops, and other acausal structures.Comment: 15 pages, 7 figures, published version (this version covers the second half of the original submission; the first half has been published separately and is available at arXiv:1507.07745

Causal Fermion Systems: A Quantum Space-Time Emerging from an Action Principle

Causal fermion systems are introduced as a general mathematical framework for formulating relativistic quantum theory. By specializing, we recover earlier notions like fermion systems in discrete space-time, the fermionic projector and causal variational principles. We review how an effect of spontaneous structure formation gives rise to a topology and a causal structure in space-time. Moreover, we outline how to construct a spin connection and curvature, leading to a proposal for a "quantum geometry" in the Lorentzian setting. We review recent numerical and analytical results on the support of minimizers of causal variational principles which reveal a "quantization effect" resulting in a discreteness of space-time. A brief survey is given on the correspondence to quantum field theory and gauge theories.Comment: 23 pages, LaTeX, 2 figures, footnote added on page

A causal model of radiating stellar collapse

We find a simple exact model of radiating stellar collapse, with a shear-free and non-accelerating interior matched to a Vaidya exterior. The heat flux is subject to causal thermodynamics, leading to self-consistent determination of the temperature $T$. We solve for $T$ exactly when the mean collision time $\tau_{c}$ is constant, and perturbatively in a more realistic case of variable $\tau_{c}$. Causal thermodynamics predicts temperature behaviour that can differ significantly from the predictions of non-causal theory. In particular, the causal theory gives a higher central temperature and greater temperature gradient.Comment: Latex [ioplppt style] 9 pages; to appear Class. Quantum Gra

Beyond the causal theory? Fifty years after Martin and Deutscher

It is natural to think of remembering in terms of causation: I can recall a recent dinner with a friend because I experienced that dinner. Some fifty years ago, Martin and Deutscher (1966) turned this basic thought into a full-fledged theory of memory, a theory that came to dominate the landscape in the philosophy of memory. Remembering, Martin and Deutscher argue, requires the existence of a specific sort of causal connection between the rememberer's original experience of an event and his later representation of that event: a causal connection sustained by a memory trace. In recent years, it has become apparent that this reference to memory traces may be out of step with memory science. Contemporary proponents of the causal theory are thus confronted with the question: is it possible to develop an empirically adequate version of the theory, or is it time to move beyond it? This chapter traces the recent history of the causal theory, showing how increased awareness of the theory’s problems has led to the development of modified version of the causal theory and ultimately to the emergence of postcausal theories