We study the quantum version of the classical twin paradox in special relativity by replacing the twins with quantum detectors, and studying the transitions and entanglement induced by coupling them to a quantum field. We show that the \textit{changes} in direction of acceleration leave imprints on detector responses and entanglement, inducing novel features which might have relevance in black hole spacetimes.
We study the quantum version of the classical twin paradox in special relativity by replacing the twins with quantum detectors, and studying the transitions and entanglement induced by coupling them to a quantum field. We show that the \textit{changes} in direction of acceleration leave imprints on detector responses and entanglement, inducing novel features which might have relevance in black hole spacetimes.
We propose a novel framework for understanding quantum entanglement as a phenomenon fundamentally dependent on the proper-time histories of entangled particles. Drawing an analogy to the classical twin paradox of special relativity, we hypothesize that entanglement persists only when particle worldlines remain synchronized in their accumulated proper time. When differential aging occurs due to relative velocity or gravitational time dilation, quantum correlations degrade in a predictable, oscillatory manner. This “Entangled Twin Paradox” makes testable predictions that distinguish it from standard quantum mechanics, which treats entanglement as independent of relativistic effects.
Abstract In the twin paradox of special relativity, an observer that travels along an accelerated trajectory at a high velocity will experience a smaller amount of elapsed time than an observer that remains at rest. This illustrates the fact that time is relative unlike the situation in classical physics where time is absolute. In a recent paper, Bushev et al (2016 New J. Phys. 18 093050 ) showed that the twin paradox can also be demonstrated using a single electron that functions as a quantum-mechanical clock. The wave function of the electron can travel along two different paths simultaneously, which allows a measurement of the difference in proper times along the two trajectories using a single particle. Quantum interference effects show that time cannot be thought of as a classical parameter even when associated with a single clock or observer.
One consequence of the cosmic censorship conjecture is that any topological structure will ultimately collapse to within the horizons of a set of black holes, and as a result, an external classical observer will be unable to probe it. However, a single two-level quantum system [Unruh–DeWitt (UDW) detector] that remains outside of the horizon has been shown to distinguish between a black hole and its associated geon counterpart via its different response rates. Here, we extend this investigation of the quantum vacuum outside of an ℝP2 geon by considering the entanglement structure of the vacuum state of a quantum scalar field in this spacetime, and how this differs from its Banados–Teitelboim–Zanelli (BTZ) black hole counterpart. Employing the entanglement harvesting protocol, where field entanglement is swapped to a pair of UDW detectors, we find that the classically hidden topology of the geon can have an appreciable difference in the amount of entanglement harvested in the two spacetimes for sufficiently small mass. In this regime, we find that detectors with a small energy gap harvest more entanglement in the BTZ spacetime; however, as the energy gap increases, the detectors harvest more entanglement in a geon spacetime. The energy gap at the crossover is dependent on the black hole mass, occurring at lower values for lower masses. This also impacts the size of the entanglement shadow, the region near the horizon where the detectors cannot harvest entanglement. Small gap detectors experience a larger entanglement shadow in a geon spacetime, whereas for large gap detectors, the shadow is larger in a BTZ spacetime.
Abstract We consider two Unruh-DeWitt detectors interacting with a massless, minimally coupled scalar field in a (1+1) dimensional Reissner-Nordstrom black hole spacetime. In particular, one of the detectors, corresponding to Alice, is moving along an outgoing null trajectory. While the other detector carried by Bob is static. With this set-up, we investigate the entangling condition and the measure of the entanglement, concurrence, in the nonextremal and extremal scenarios. Our observations suggest, as expected, a qualitative similarity in characteristics of the entanglement between these two scenarios. However, we find a distinct and consistent quantitative feature between the nonextremal and extremal concurrences for a broad range of black hole charges. With moderately large detector transition energy, the extremal background always accounts for the larger entanglement than the nonextremal one. In contrast, with low detector transition energy, entanglement on the nonextremal background can be greater. Therefore, by adjusting the detector transition energy, one can perceive optimum entanglement from either the extremal or the nonextremal background.
The Classical Twin Paradox is widely dealt in literature and neatly resolved. In addition, it is also well known that, when looking at two systems which are boosted relative to each other, the concept of the simultaneous effect of a quantum measurement in space-time causes some discrepancies in the cause-effect behavior. However, these discrepancies have been thought not to cause any apparent paradox except for violating the Free-Will postulate. In this paper we suggest that using the local t axis, all over space, as the axis in which the quantum measurement is thought to be simultaneous, we do reach a kind of true "Twin Paradox". The resolution of this paradox requires the introduction of a global proper time into a covariant quantum theory.
Demonstrations of quantum entanglement which confirm the violation of Bell's inequality indicate that under certain conditions action at a distance is possible. This consequence seems to contradict the relativistic principle of causality, which asserts that an effect never precedes its cause, in any reference frame. By analyzing a numerical example of Bell's experiment with entangled pairs of photons, we show how observers in two inertial reference frames can disagree about the causality relation between two events. One observer claims that event 1 is the cause of event 2, while the other claims that event 1 is the result of event 2. The solution we suggest to the paradox is that in entangled systems, one can find pairs of "entangled events" which have symmetrical causality relations. Each of the events can serve as a cause or as an effect, depending on the frame of reference in which they are observed.