Relativistic Quantum Clocks

Abstract

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. CONTENTS I. Time in quantum mechanics and general relativity 1 II. A semiclassical approach: quantum field theory in curved spacetime 3 III. A relativistic quantum clock 3 A. The clock model 3 B. Theoretical framework 4 1. A localized quantum field in curved spacetime 4 2. The covariance matrix formalism 4 3. Relativistic quantum metrology 5 C. The effect of non-inertial motion 5 D. Generalizing to curved spacetime 7 E. Physical implementation 8 IV. Conclusion 9 References 10 I. TIME IN QUANTUM MECHANICS AND GENERAL RELATIVITY * maximilian.lock12@imperial.ac.uk † Previously known as Fuentes-Guridi and Fuentes-Schuller.arXiv:1609.09426v1 [quant-ph]

Universal quantum modifications to general relativistic time dilation in delocalised clocks

“…For simplicity, we ignore the contribution due to gravity by setting g = 0, and consider only temporal measurements which correspond to a projectionvalued measure. In order to calculate the relativistic contribution to σ T (t) to leading order, we now include Hamiltonian terms up to orderp 4 /(mc) 4 (see Appendix E). Let σ T,NR (t) denote the standard deviation of the clock time in the absence of the special relativistic coupling.…”

“…One of the most important programs in theoretical physics is the pursuit of a successful theory unifying quantum mechanics and general relativity. Arguably, many of the difficulties arising in this pursuit stem from a lack of understanding of the nature of time [1][2][3], particularly the conflict between how it is conceived in the two theories [4]. For example, in general relativity a given object's proper time is defined geometrically according to that object's world line, but according to quantum mechanics such welldefined trajectories are impossible.…”

Frequency spectrum of an optical resonator in a curved spacetime

“…From equations (19) and (28), we find for the relative change of the resonance frequencies of the deformable resonator Note that the deformation of the resonator changes the coordinate position of every point inside the resonator 8 . This leads to a change in the trajectory of a light pulse within the resonator, and the whole calculation we made in section 4 would be changed.…”

“…Cases in which the effects of gravitational fields and acceleration must be considered include those in which the gravitational field is to be measured, such as in proposals for the measurement of gravitational waves with electromagnetic cavity resonators [1][2][3][4][5][6][7] or other extended matter systems [8][9][10][11][12][13][14], tests of GR [15,16] or the expansion of the universe [17,18]. Other situations are those in which the metrological system is significantly accelerated [19][20][21]. A fundamental limit for the precision of a light cavity resonator as a metrological system can even be imposed by the gravitational field of the light inside the cavity [22].…”

Retrieving the lost fermionic entanglement by partial measurement in noninertial frames

“…As a matter of fact, the state-independent strategy is not restricted to the specific quantity of entanglement or quantum discord, hence it can be exported to a huge variety of physical quantities, for instance, quantum coherence [59] or quantum Fisher information [60] under Unruh decoherence. The later aspect is of both theoretical and applied significance as the maintenance of quantum Fisher information is a central problem in relativistic quantum metrology [61,62] and relativistic clock synchronization [63,64].…”