It is currently unknown whether the laws of physics permit time travel into the past. While general relativity indicates the theoretical possibility of causality violation, it is now widely accepted that a theory of quantum gravity must play an essential role in such cases. As a striking example, the logical paradoxes usually associated with causality violation can be resolved by quantum effects. We ask whether the explicit construction of a theory that allows causality violation might in turn teach us something about quantum gravity. Taking the toy model of Deutsch as a starting point, in Part I we argue that, despite being a nonlinear modification of quantum mechanics, the model does not imply superluminal signalling and its predictions can be operationally verified by experimenters within an appropriate ontological setting. In Part II we show that the model can be directly applied to scalar quantum fields, provided the fields are sent back in time by an amount much larger than the coherence time of the wavepackets. We propose a generalisation of the model that lifts this constraint and recovers the predictions of standard quantum field theory when the size of the temporal jump is much smaller than the coherence time of the wavepackets. Finally, we discuss an extension of the model to ordinary gravitational time dilation. The resulting model generalises and extends earlier work on the topic and can be tested experimentally using current technology.
It is currently unknown whether the laws of physics permit time travel into the past. While general relativity indicates the theoretical possibility of causality violation, it is now widely accepted that a theory of quantum gravity must play an essential role in such cases. As a striking example, the logical paradoxes usually associated with causality violation can be resolved by quantum effects. We ask whether the explicit construction of a theory that allows causality violation might in turn teach us something about quantum gravity. Taking the toy model of Deutsch as a starting point, in Part I we argue that, despite being a nonlinear modification of quantum mechanics, the model does not imply superluminal signalling and its predictions can be operationally verified by experimenters within an appropriate ontological setting. In Part II we show that the model can be directly applied to scalar quantum fields, provided the fields are sent back in time by an amount much larger than the coherence time of the wavepackets. We propose a generalisation of the model that lifts this constraint and recovers the predictions of standard quantum field theory when the size of the temporal jump is much smaller than the coherence time of the wavepackets. Finally, we discuss an extension of the model to ordinary gravitational time dilation. The resulting model generalises and extends earlier work on the topic and can be tested experimentally using current technology.
We add nonlinear and state-dependent terms to quantum field theory. We show that the resulting low-energy theory, nonlinear quantum mechanics, is causal, preserves probability and permits a consistent description of the process of measurement. We explore the consequences of such terms and show that nonlinear quantum effects can be observed in macroscopic systems even in the presence of decoherence. We find that current experimental bounds on these nonlinearities are weak and propose several experimental methods to significantly probe these effects. The locally exploitable effects of these nonlinearities have enormous technological implications. For example, they would allow large-scale parallelization of computing (in fact, any other effort) and enable quantum sensing beyond the standard quantum limit. We also expose a fundamental vulnerability of any nonlinear modification of quantum mechanics---these modifications are highly sensitive to cosmic history and their locally exploitable effects can dynamically disappear if the observed universe has a tiny overlap with the overall quantum state of the universe, as is predicted in conventional inflationary cosmology. We identify observables that should persist in this case and discuss opportunities to detect them in cosmic ray experiments, tests of strong field general relativity and current probes of the equation of state of the universe. Nonlinear quantum mechanics also enables novel gravitational phenomena and may open new directions to solve the black hole information problem and to uncover the theory underlying quantum field theory and gravitation.
Gell-Mann and Hartle (GMH) have recently considered time-neutral cosmological models in which the initial and final conditions are independently specified, and several authors have investigated experimental tests of such models. We point out here that GMH time-neutral models can allow superluminal signaling, in the sense that it can be possible for observers in those cosmologies, by detecting and exploiting regularities in the final state, to construct devices which send and receive signals between space-like separated points. In suitable cosmologies, any single superluminal message can be transmitted with probability arbitrarily close to one by the use of redundant signals. However, the outcome probabilities of quantum measurements generally depend on precisely which past and future measurements take place. As the transmission of any signal relies on quantum measurements, its transmission probability is similarly context dependent. As a result, the standard superluminal signaling paradoxes do not apply. Despite their unusual features, the models are internally consistent. These results illustrate an interesting conceptual point. The standard view of Minkowski causality is not an absolutely indispensable part of the mathematical formalism of relativistic quantum theory. It is contingent on the empirical observation that naturally occurring ensembles can be naturally pre-selected but not post-selected.
The problem of time in quantum gravity is often presented as a consequence of applying quantum theory to general relativity. These notes adopt a broader perspective. We first examine how time enters classical mechanics, relativity, quantum theory, and quantum field theory, distinguishing three principal aspects: causal order, temporal duration, and the present. This analysis shows that the conceptual difficulties associated with time do not arise only when gravity is quantised. Tensions between causal structure, clocks, observables, and measurement are already present in the theories from which quantum gravity is constructed. We then survey responses to the problem of time across the principal approaches to quantum gravity. These include canonical and Wheeler-DeWitt quantisation, path-integral and histories formulations, perturbative and background-dependent approaches, causal sets, and twistor theory. The programmes are compared according to whether they retain an external time, render time problematic through quantisation, or incorporate causal or temporal structure into their foundations. Particular emphasis is placed on questions arising from quantum foundations and relativistic quantum information. We conclude by examining linearised gravity and weak-gravity quantum systems. This regime shows that the problem of time is not confined to Planck-scale physics, but arises already in attempts to provide a predictive and operationally meaningful quantum description of spacetime near flat geometry.
It has been claimed that quantum mechanics is a non-local theory, i.e., that the predictions of quantum mechanics are at odds with a conception of the world where all the interactions are mediated by local mechanisms. The cited reason is the violation of the Bell inequality in cases where measurements are performed on quantum systems of particles that have interacted in the past. Quantum mechanics predicts that the state of the particles in such a system are correlated, a result obtained from considering a thought-experiment often known as EPR. In this thesis, I will argue that the violation of the Bell inequality in EPR forces us to either accept that causes sometimes act both backwards and forwards in time, or give up some widely-held assumptions about causal relations or the role of causal explanations. First, I will present three principles regarding causality that I take be widely accepted. I will then present the background for the claim the quantum mechanics is a non-local theory, and discuss the implications of non-local causal influences in light of the Special Theory of Relativity. One argument against a causal explanation of the EPR-correlations will be discussed, and different models for the causal structure of EPR will be assessed. I will argue that a retrocausal model – models that include instances of retrocausation, where the direction of causation is the opposite of the direction of time – is the only viable option if we want to uphold the three principles presented in chapter 1. I will discuss the plausibility of rejecting one of these principles, and argue that at least one of the can be restricted in a way that still accounts for our commitment to it. Finally, I will assess the non-local models against the retrocausal models, and argue that a retrocausal model offers interpretational advantages over the non-local alternatives.
Quantum mechanics and general relativity have been extensively and independently confirmed in many experiments. However, the interplay of the two theories has never been tested: all experiments that measured the influence of gravity on quantum systems are consistent with non-relativistic, Newtonian gravity. On the other hand, all tests of general relativity can be described within the framework of classical physics. Here we discuss a quantum interference experiment with single photons that can probe quantum mechanics in curved space-time. We consider a single photon traveling in superposition along two paths in an interferometer, with each arm experiencing a different gravitational time dilation. If the difference in the time dilations is comparable with the photon's coherence time, the visibility of the quantum interference is predicted to drop, while for shorter time dilations the effect of gravity will result only in a relative phase shift between the two arms. We discuss what aspects of the interplay between quantum mechanics and general relativity are probed in such experiments and analyze the experimental feasibility.
PROSPECTIVE The concern of this paper will be different from that of most studies of quantum gravity. There will be no discussion of the problem of quantizing the gravitational field equations, hence nothing about the modifications which quantization requires of space-time structure at distances of the order of the Planck length (∼ 10 −33 cm). The emphasis will be rather upon the implications of quantum mechanics for certain general properties of events and processes which occur in the theatre of space-time, specifically with non-locality and nonlinearity . Quantum mechanics is undoubtedly a non-local theory when it treats correlated spatially separated systems. When one examines closely the character of this non-locality, however, one does not find reasons for modifying the causal structure of space-time as described by special or general relativity theory, but rather reasons for refining the concept of an event. The occurrence of definite outcomes of measurements implies that there are processes in nature governed by nonlinear laws. Nonlinearity is very peculiar from the standpoint of quantum mechanics, since it is contrary to the linearity of the time-dependent Schrödinger equation, which is commonly assumed to govern the dynamics of any isolated physical system. Hence it is necessary to inquire whether a rational treatment of the occurrence of outcomes is possible without some modifications of current quantum mechanics. Whatever decision is reached on this question, however, it does not appear to bear directly on space-time structure, but rather on the general character of processes.