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New Journal of Physics

Quantum-mechanical twin paradox

J. D. Franson

Published Oct 1, 2016• 5 citations
Publisher

Abstract

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.

DOI
10.1088/1367-2630/18/10/101001

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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.
With Einstein’s interpretation, “everything is relative”, the so-called twin experiment discloses what is called a paradox, when the travelling twin returns and they compare watches (and aging). Some assign the solution to acceleration, which they claim should be taken into account so that the paradox evaporates. However, it’s easy to construct an experiment in which any acceleration lays outside the considered part of the experiment, so that within the measured part we have only constant velocities. We can then have one observer at rest, and two travelers who run through the travelling twin’s route, but without acceleration. Within a hypothetical absolute underlying medium, particles oscillate slower for an observer who moves through the Aether than they do for an observer at rest. An acceleration free experiment can be made in which all three agree on that. The conflict appears if the traveling ‘twins’ measure how fast the first observers clock runs, based on their respective lines of simultaneity, because then the travelling ‘twins’ then insist that A’s particles oscillate slower than their own. Even without the physical experiment, the thought experiment itself discloses that the twin-paradox is a product of the “everything is relative” interpretation.
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.
Vacuum fluctuations in quantum field theory impose fundamental limitations on our ability to measure time at arbitrarily short scales. To investigate the impact of universal quantum field theory effects on observer-dependent time measurements, we introduce a clock model based on the vacuum decay probability of a finite-sized quantum system. This model defines an effective notion of proper time that depends on the microscopic properties of the clock and on how it samples vacuum fluctuations along its trajectory. We show that, in the long-time regime, this notion of time reduces to the usual proper time of special relativity. However, by studying a microscopic twin-paradox scenario, we find that, in general, time is not determined solely by the trajectory connecting two events, but also by how vacuum fluctuations interact with the internal structure of the clocks.
The role of the observer is essential in determining the reality as well as making measurements of the state of a physical situation. This observation becomes important in elaborating a long-standing paradox of physics known as the Twin Paradox of the Special Theory of Relativity (STR). Einstein showed that the time interval between two events determined by a moving observer is greater than that determined by a stationary observer. The effect is known as time dilation. However, it leads to the paradox that a twin brother returning from a space trip is younger than his twin sister who had stayed home. The resolution of the paradox is assisted by introducing a new requirement of physics called the “reality test.” This states that whatever an observer measures must be real. It also reveals that discrepancies in time measurements can be attributed to the change of state the traveling twin undergoes as he changes velocity over the journey.
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.
The phase of matter waves depends on proper time and is therefore susceptible to special-relativistic (kinematic) and gravitational (redshift) time dilation. Hence, it is conceivable that atom interferometers measure general-relativistic time-dilation effects. In contrast to this intuition, we show that (i) closed light-pulse interferometers without clock transitions during the pulse sequence are not sensitive to gravitational time dilation in a linear potential. (ii) They can constitute a quantum version of the special-relativistic twin paradox. (iii) Our proposed experimental geometry for a quantum-clock interferometer isolates this effect.