Abstract ‘Saved by Gravity’ shows how exotic gravitational effects could enable our escape from quantum death, by creating particles that violate quantum mechanics and Born’s formula. We begin with a review of quantum gravity and of the notorious ‘problem of time’. We explain why the theory is unable to give a mathematically consistent account of quantum probability. We propose that the problem can be solved if we accept that there is no quantum death, and no Born’s formula, at the deepest level of quantum gravity. The chapter ends by showing how quantum-gravitational effects can create violations of Born’s formula, in particular for radiation from exploding primordial black holes.
Abstract ‘Saved by Gravity’ shows how exotic gravitational effects could enable our escape from quantum death, by creating particles that violate quantum mechanics and Born’s formula. We begin with a review of quantum gravity and of the notorious ‘problem of time’. We explain why the theory is unable to give a mathematically consistent account of quantum probability. We propose that the problem can be solved if we accept that there is no quantum death, and no Born’s formula, at the deepest level of quantum gravity. The chapter ends by showing how quantum-gravitational effects can create violations of Born’s formula, in particular for radiation from exploding primordial black holes.
We argue that in quantum gravity there is no Born rule. The quantum-gravity regime, described by a non-normalisable Wheeler-DeWitt wave functional Ψ, must be in quantum nonequilibrium with a probability distribution P=∣Ψ∣2 (initially and always). A Born rule can emerge only in the semiclassical regime of quantum systems on a classical spacetime background, with normalisable Schrödinger wave functions ψ. Conditioning on the underlying quantum-gravitational ensemble yields a nonequilibrium distribution ρ=∣ψ∣2 at the beginning of the semiclassical regime, with quantum relaxation ρ→∣ψ∣2 taking place only afterwards. Quantum gravity naturally creates an early nonequilibrium universe. We also show how small corrections to the Schrödinger equation yield an intermediate regime in which the Born rule is unstable: an initial distribution ρ=∣ψ∣2 can evolve to a final distribution ρ=∣ψ∣2. These results arise naturally in the de Broglie-Bohm pilot-wave formulation of quantum gravity. We show that quantum instability during inflation generates a large-scale deficit ∼1/k3 in the primordial power spectrum at wavenumber k, though the effect is too small to observe. Similarly we find an unobservably large timescale for quantum instability in a radiation-dominated universe. Quantum instability may be important in black-hole evaporation, with a final burst of Hawking radiation that violates the Born rule. Deviations from the Born rule can also be generated for atomic systems in the gravitational field of the earth, though the effects are unlikely to be observable. The most promising scenario for the detection of Born-rule violations appears to be in radiation from exploding primordial black holes.
Abstract ‘Beyond Quantum Physics’ delves into some detail about the new physics that could be accessed if ever we were able to escape from the restrictive state of quantum death. We begin with a deeper discussion of the ‘quantum conspiracy’, which prevents us from using nonlocality for signalling. We explain precisely why the conspiracy is a peculiarity of the state of quantum death as described by Born’s formula, and we show how superluminal signalling inevitably arises in more general ‘nonequilibrium’ conditions. We also give more details about how quantum relaxation to Born’s formula takes place. The chapter ends with a discussion of other properties of ‘subquantum matter’ (matter breaking Born’s formula), in particular how it could be deployed to circumvent the uncertainty principle.
A consistent theory including gravitational effects in quantum mechanics has not been found. Although many different approaches have been proposed for theory of quantum gravity, several authors have suggested that gravity may be fundamentally classical. As there is no experimental evidence for a fundamentally quantum vs. fundamentally classical theory of gravity, it is hoped that investigating the consequences of semiclassical gravity, one may propose an experiment to distinguish between the quantum or classical nature of gravity. As opto- and electromechanical devices allow quantum limited measurement and control over massive, mechanical degrees of freedom, they are ideal systems to test violations of standard quantum mechanics arising from gravitational effects. After a brief introduction to the background theory and literature review, we begin by introducing a semiclassical model of gravity based on quantum measurement and control. We show under which conditions the theory behaves like a collapse model, and how a Newtonian potential is recovered in the multi particle case.We then go on to analyse our semiclassical model in two scenarios: firstly in a cosmological setting, and secondly by considering quantum clocks on the surface of the earth. In the cosmological description, we show that a violation of energy conservation, resulting from our model, can be reinterpreted as a dark energy fluid in the spacetime, suggesting that perhaps local violations of conservations of energy may be resolved in a cosmological framework. Secondly, we derive a minimum, gravitational dephasing rate for quantum clocks under the semiclassical model, which unsurprisingly, is is well below the resolution of current state of the art clocks. The next chapters diverge from analysing the gravitational model, and instead focus on novel methods of manipulating and measuring micromechanical devices, that may be used to experimentally probe the results of the semi-classical theory. Firstly we show that a sequence of coherently controlled pulses in an optomechanical system can be used to directly probe the momentum of an oscillator - opening up the possibility for direct detection of momentum diffusion, which is a consequence of the semiclassical gravity model. Secondly, we introduce an electro-mechanical device, and sequence of control operations, that may be understood as an interferometer for the wave function of a mechanical oscillator coupled to a qubit. We show how the resulting interference pattern can distinguish between unitary evolution, thermalisation/decoherence, and a purely classical description of the mechanical oscillator. We also show how the qubit-oscillator interaction can be used generate arbitrary wave functions of the mechanical oscillator, using only classical qubit driving.
The possibility that a classical space-time and quantum matter cohabit at the deepest level, i.e., the possibility of having a fundamental and not phenomenological semiclassical gravity, is often disregarded for lack of a good candidate theory. The standard semiclassical theory suffers from fundamental inconsistencies (e.g., Schr\"odinger cat sources, faster-than-light communication and violation of the Born rule) which can only be ignored in simple typical situations. We harness the power of spontaneous localization models, historically constructed to solve the measurement problem in quantum mechanics, to build a consistent theory of (stochastic) semiclassical gravity in the Newtonian limit. Our model makes quantitative and potentially testable predictions: we recover the Newtonian pair potential up to a short distance cutoff (hence, we predict no one-particle self-interaction) and uncover an additional gravitational decoherence term which depends on the specifics of the underlying spontaneous localization model considered. We hint at a possible program to go past the Newtonian limit, towards a consistent general relativistic semiclassical gravity.
Abstract ‘Black Holes and the Edge of Physics’ delves into the mysteries of black holes, and shows how these enigmatic objects may transcend quantum physics. We begin with a review of how black holes form and eventually evaporate, resulting in the notorious problem of ‘information loss’. We show how pilot-wave theory could solve the problem by allowing information to escape at superluminal speeds. We describe an experiment that could test these and related ideas, involving astrophysical black holes in space. The chapter ends with an account of the life cycle of black holes and the role they may play in ‘reprocessing’ our quantum universe.
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.