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The conflict between quantum theory and the theory of relativity is exemplified in their treatment of time. We examine the ways in which their conceptions differ, and describe a semiclassical clock model combining elements of both theories. The results obtained with this clock model in flat spacetime are reviewed, and the problem of generalizing the model to curved spacetime is discussed, before briefly describing an experimental setup which could be used to test of the model. Taking an operationalist view, where time is that which is measured by a clock, we discuss the conclusions that can be drawn from these results, and what clues they contain for a full quantum relativistic theory of time.
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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 different masses and energy gaps, which would produce time difference via gravitational interaction. The proposal of quantum clock synchronization for the gravity-induced time difference is discussed. We illustrate how the stability of measurement probability in the quantum clock synchronization proposal is influenced by the gravitational interaction induced by the clock themselves. It is found that the precision of clock synchronization depends on the energy gaps of the clocks and the improvement of precision in quantum metrology is in fact an indicator of entanglement generation. We also present the quantum enhanced estimation of time difference and find that the quantum Fisher information is very sensitive to the distance between the clocks.
Real clocks are not perfect. This must have an effect in our predictions for the behaviour of a quantum system, an effect for which we present a unified description encompassing several previous proposals. We study the relevance of clock errors in the Zeno effect, and find that generically no Zeno effect can be present (in such a way that there is no contradiction with currently available experimental data). We further observe that, within the class of stochasticities in time addressed here, there is no modification in emission lineshapes.
We investigated the effects of the global monopole spacetime on the Dirac and Klein-Gordon relativistic quantum oscillators. In order to do this, we solve the Dirac and Klein-Gordon equations analytically and discuss the influence of this background which is characterized by the curvature of the spacetime on the energy profiles of these oscillators. In addition, we introduce a hard-wall potential and, for a particular case, determine the energy spectrum for relativistic quantum oscillators in this background.
The notion of time is given a different footing in Quantum Mechanics and General Relativity, treated as a parameter in the former and being an observer dependent property in the later. From a operational point of view time is simply the correlation between a system and a clock, where an idealized clock can be modelled as a two level systems. We investigate the dynamics of clocks interacting gravitationally by treating the gravitational interaction as a classical information channel. In particular, we focus on the decoherence rates and temporal resolution of arrays of $N$ clocks showing how the minimum dephasing rate scales with $N$, and the spatial configuration. Furthermore, we consider the gravitational redshift between a clock and massive particle and show that a classical channel model of gravity predicts a finite dephasing rate from the non-local interaction. In our model we obtain a fundamental limitation in time accuracy that is intrinsic to each clock.
Time plays a fundamental role in our ability to make sense of the physical laws in the world around us. The nature of time has puzzled people -- from the ancient Greeks to the present day -- resulting in a long running debate between philosophers and physicists alike to whether time needs change to exist (the so-called relatival theory), or whether time flows regardless of change (the so-called substantival theory). One way to decide between the two is to attempt to measure the flow of time with a stationary clock, since if time were substantival, the flow of time would manifest itself in the experiment. Alas, conventional wisdom suggests that in order for a clock to function, it cannot be a static object, thus rendering this experiment seemingly impossible. We show, counter-intuitively, that a quantum clock can measure the passage of time even while being switched off, lending support for the substantival theory of time.
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