It is demonstrated how classical properties of the intrinsic time variable in minisuperspace of quantum gravity would emerge in the sense of a continuous measurement process solely through interaction with fermionic degrees of freedom. This measurement is much less effective than that by bosons considered in a previous paper. Continuous measurement by fermions would not lead to classical properties for values of intrinsic time near the singularity of a Friedmann universe. It is argued that this result remains true for the full quantum theory of gravity.
It is demonstrated how classical properties of the intrinsic time variable in minisuperspace of quantum gravity would emerge in the sense of a continuous measurement process solely through interaction with fermionic degrees of freedom. This measurement is much less effective than that by bosons considered in a previous paper. Continuous measurement by fermions would not lead to classical properties for values of intrinsic time near the singularity of a Friedmann universe. It is argued that this result remains true for the full quantum theory of gravity.
This chapter applies the path-integral approach to the quantum theory of continuous measurements to investigate the quantum Universe, taking into account its self-measurement. It describes the way to apply the path-integral theory of continuous measurements in quantum cosmology in a general form and develops a minisuperspace model. The path-integral approach can be applied to describe the measurement of a quantum field. The measurement of curvature in the framework of quantum gravity has been considered in such a way by Mensky using a functional integral over configurations of the gravitational field. The chapter considers the possible influence of self-measurement on the dynamics of the quantum Universe. The influence could be caused by reduction of the wavefunction of the Universe in the process of continuous measurement. Therefore the time evolution of the quantum Universe makes sense in quantum cosmology provided its self-measurement is correctly taken into account.
Macroscopic observables allow the recovery of intrinsic dynamics from stationary quantum states. I show that, by interpreting the squared amplitude as the probability density for each definite value of intrinsic time, a curvature emerges in the time direction. For example, from the perspective of intrinsic quantum time, the Friedmann-Lemaître-Robertson-Walker cosmological model emerges from spherically symmetric stationary solutions in four-dimensional Euclidean space, without presupposing gravity. If there is no unique direction of time, curvature emerges in all spacetime dimensions, without presupposing gravity, from the variable amplitude of the stationary wavefunction alone. This opens a new possibility that general relativity or some modification of it emerges from intrinsic time observables.
The unsatisfactory status of the interpretation of the wave function of the Universe in canonical quantum gravity is reviewed. The ``naive interpretation'' obtained by straightforwardly applying the standard interpretive rules to the canonical quantization of general relativity is manifestly unacceptable; the ``WKB interpretation'' has only a limited domain of applicability; and the ``conditional probability interpretation'' requires one to pick out a ``preferred time variable'' (or preferred class of such variables) from among the dynamical variables. Evidence against the possibility of using a dynamical variable to play the role of ``time'' in the conditional probability interpretation is provided by the fact (proven here) that in ordinary Schr\"odinger quantum mechanics for a system with a Hamiltonian bounded from below, no dynamical variable can correlate monotonically with the Schr\"odinger time parameter t, and thus the role of t in the interpretation of Schr\"odinger quantum mechanics cannot be replaced by that of a dynamical variable. We also argue that the interpretive problems of quantum gravity are not alleviated by the incorporation of observers into the theory. Faced with these difficulties, we seek a formulation of canonical quantum gravity in which an appropriate nondynamical time parameter is present. By analogy with a parametrized form of ordinary Schr\"odinger quantum mechanics, we make a proposal for such a formulation. A specific proposal considered in detail yields a theory which corresponds at the classical level to general relativity with an arbitrary, unspecified cosmological constant. In minisuperspace models, this proposal yields a quantum theory with satisfactory interpretive properties, although it is unlikely that this theory will admit sufficiently many observables for general spacetimes. Nevertheless, we feel that the approach suggested here is worthy of further investigation.
In order to empirically test the quantum nature of gravity, it is essential to explore the construction of classical gravity theories that are as consistent with experiments as possible. In particular, the classical gravity field must receive input regarding matter distribution. Previously, such input has been constructed by taking expectation values of the matter density operator on the quantum state, or by using the outcomes of all measurements being performed on the quantum system---or by using information obtained by auxiliary observers (like those that lead to the continuous spontaneous localization and Diosi-Penrose collapses) that continuously monitor the quantum dynamics. We propose a framework that unifies these models, and argue that the Causal Conditional Formulation of Schr\"odinger-Newton (CCSN) theory, which takes classical inputs only from experimental and environmental channels---without auxiliary observers---is a minimum model within this framework. Since CCSN can be viewed as a quantum feedback control scheme, it can be made explicitly causal and free from pathologies that previously plagued Schr\"odinger-Newton theories. Since classical information from measurement results are used to generate classical gravity, CCSN can mimic quantum gravity better than one would naively expect for a classical theory---making it more subtle to perform tests of the quantum nature of gravity. We predict experimental signatures of CCSN in two concrete scenarios: (i) a single test mass continuously monitored by light, and (ii) two objects interacting via mutual gravity, each monitored separately. In case (i), we show that the mass-concentration effect of self classical gravity still makes CCSN much easier to test than testing the establishment of mutual entanglement, yet the signatures are more subtle than previously thought for classical gravity theories. Using time-delayed measurements and nonstationary measurements, which delay or suspend the flow of classical information into classical gravity, one can make CCSN more detectable. In case (ii), we show that mutual gravity generated by CCSN can lead to correlations that largely mimic signatures of quantum entanglement in steady-state measurements. Rigorous protocols that rule out local operation and classical communication channels, which are experimentally more challenging than simply testing steady-state entanglement, must be applied in order to completely rule out CCSN.
I take non-locality to be the Michaelson Morley experiment of the early 21st Century, assume its universal validity, and try to derive its consequences. Spacetime, with its locality, cannot be fundamental, but must somehow be emergent from entangled coherent quantum variables and their behaviors. There are, then, two immediate consequences: i. If we start with non-locality, we need not explain non-locality. We must instead explain an emergence of locality and spacetime. ii. There can be no emergence of spacetime without matter. These propositions flatly contradict General Relativity, which is foundationally local, can be formulated without matter, and in which there is no “emergence” of spacetime.If these be true, then quantum gravity cannot be a minor alteration of General Relativity but must demand its deep reformulation. This will almost inevitably lead to: Matter not only curves spacetime, but “creates” spacetime.We will see independent grounds for the assertion that matter both curves and creates spacetime that may invite a new union of quantum gravity and General Relativity.This quantum creation of spacetime consists in: i. Fully non-local entangled coherent quantum variables.ii. The onset of locality via decoherence. iii. A metric in Hilbert Space among entangled quantum variables by the sub-additive von Neumann Entropy between pairs of variables. iv. Mapping from metric distances in Hilbert Space to metric distances in classical spacetime by episodic actualization events.v. Discrete spacetime is the relations among these discrete actualization events. vi. “Now” is the shared moment of actualization of one among the entangled variables when the amplitudes of the remaining entangled variables change instantaneously.vii. The discrete, successive, episodic, irreversible actualization events constitute a quantum arrow of time. viii. The arrow of time history of these events is recorded in the very structure of the spacetime constructed. ix. Actual Time is a succession of two or more actual events.The theory inevitably yields a UV cut-off of a new type. The cut-off is a phase transition between continuous spacetime before the transition and discontinuous spacetime beyond the phase transition.This quantum creation of spacetime modifies general relativity and may account for Dark Energy, Dark Matter, and the possible elimination of the singularities of General Relativity.Relations to Causal Set Theory, faithful Lorentzian manifolds, and past and future light cones joined at “Actual Now” are discussed.Possible observational and experimental tests based on: i. the existence of Sub- Planckian photons, ii. knee and ankle discontinuities in the high energy gamma ray spectrum, and iii. possible experiments to detect a creation of spacetime in the Casimir system are discussed. A quantum actualization enhancement of repulsive Casimir effect would be anti-gravitational and of possible practical use.The ideas and concepts discussed here are not yet a theory, but at most the start of a framework that may be useful.
Inspired by the holographic theory of gravity originating from the microscopic degrees of freedom of black holes, as well as the profound connection between quantum entanglement and space-time revealed by the AdS/CFT correspondence, this paper attempts to establish a connection among quantum measurement, quantum entanglement, and space-time, thereby proposing a "Multi-Space-Time" scheme. Under this scheme, the "problem of the preferred basis" and the "problem of definite outcomes" in quantum measurement can be solved simultaneously. Furthermore, it reveals that classical space-time originates from quantum measurement. However, a derived result of this scheme is that the number of classical space-times in the universe is not unique; rather, there may exist a multitude of them. The "Multi-Space-Time" scheme demotes measuring instruments or observers to a status of parity, establishing an egalitarian relationship between the measured system and the measuring instrument. Nevertheless, the proposal remains largely a conceptual or epistemic framework at present, and its verification relies on the establishment of quantum gravity. Yet, it provides a potential direction for future quantum gravity research when dealing with classical space-time, quantum measurement, and quantum entanglement simultaneously.