Related papers: Physical Hilbert Spaces in Quantum Gravity
The appearance of Hamiltonian constraint in the canonical formalism for general relativity reflects the lack of a fixed external time. The dynamics of general relativistic systems can be expressed with respect to an arbitrarily chosen…
Einstein's theory of general relativity is based on the premise that the physical laws take the same form in all coordinate systems. However, it still presumes a preferred decomposition of the total kinematic Hilbert space into local…
The basic tenet of the present work is the assumption of the lack of external and fixed time in the Universe. This assumption is best embodied by general relativity, which replaces the fixed space-time structure with the gravitational…
Beginning with the principle that a closed mechanical composite system is timeless, time can be defined by the regular changes in a suitable position coordinate (clock) in the observing part, when one part of the closed composite observes…
In general relativity, the picture of spacetime assigns an ideal clock to each worldline. Being ideal, gravitational effects due to these clocks are ignored and the flow of time according to one clock is not affected by the presence of…
The standard formulation of quantum theory relies on a fixed space-time metric determining the localisation and causal order of events. In general relativity, the metric is influenced by matter, and is expected to become indefinite when…
Time dilation is a difference in measured time between two clocks that either move with different velocities or experience different gravitational potentials. Both of these effects stem from the theory of relativity and are usually…
It is often conjectured that a choice of time function merely sets up a frame for the quantum evolution of gravitational field, meaning that all choices should be in some sense compatible. In order to explore this conjecture (and the…
A proper time observable for a quantum clock is introduced and it is found that the proper time read by one clock conditioned on another clock reading a different proper time obeys classical time dilation in accordance with special…
We investigate how the quantum dynamics of gravitational models depends on the internal clock employed in quantisation. Our previous result on the quantum Friedmann-Lemaitre model demonstrates that almost all physical predictions from the…
It is expected that a quantum theory of gravity will radically alter our current notion of spacetime geometry. However, contrary to what was commonly assumed for many decades, quantum gravity effects could manifest in scales much larger…
In this article, we discuss how to carryover gravitomagnetic clock effect from classical general relativity to quantum theory and how to calculate this effect in quantum mechanics. Our calculation is valid for semi-classical regime and can…
Clocks play a special role at the interface of general relativity and quantum mechanics. We analyze a clock-interferometry thought experiment and go on to theoretically derive and experimentally test a complementarity relation for quantum…
It has recently been reported [\textit{PNAS} \textbf{114}, 2303 (2017)] that, under an operational definition of time, quantum clocks would get entangled through gravitational effects. Here we study an alternative scenario: the clocks have…
Time in relativity theory has a status different from that adopted by standard quantum mechanics, where time is considered as a parameter measured with reference to an external absolute Newtonian frame. This status strongly restricts its…
We discuss a new approach to the problem of quantum gravity in which the quantum mechanical structures that are traditionally fixed, such as the Fubini-Study metric in the Hilbert space of states, become dynamical and so implement the idea…
Quantum theory and relativity offer different conceptions of time. To explore the conflict between them, we study a quantum version of the light-clock commonly used to illustrate relativistic time dilation. This semiclassical model combines…
The nature of time in quantum mechanics is closely related to the use of a complex, rather than say real, Hilbert space. This becomes particularly clear when considering quantum field theory in time dependent backgrounds, such as in…
We review two approaches to the definition of the Hilbert space and evolution in mechanical theories with local time-reparametrization invariance, which are often used as toy models of quantum gravity. The first approach is based on the…
A practical way to deal with the problem of time in quantum cosmology and quantum gravity is proposed. The main tool is effective equations, which mainly restrict explicit considerations to semiclassical regimes but have the crucial…