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arXiv:1102.0016

A Quantum Twin Paradox

Doron ludwin

Published Jan 31, 2011• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.1102.0016

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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.
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.
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.
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.
This paper outlines a ‘paradox’ in quantum measurement theory, illustrated with two different types of systems. If this paradox cannot be resolved in ordinary quantum mechanics (as I currently think), it is alarming. If it can be resolved, it can be added to a long list of examples that show the internal consistency of quantum mechanics, and in this case I hope the correct analysis will be an interesting example for students. The immediate paradox involves a failure of Lorentz invariance for measurements on certain types of single particle systems. It seems to show that an absolute frame of reference is required to describe wave function collapse. But if the argument is correct, quantum measurement theory is not merely dependant on the frame of collapse - it is inconsistent, and experimental tests would have to be done to verify whether the apparent non-local effects predicted are real.
In recent decades it was established that the measurements of physical quantities in space-time points divided by large space-like intervals can be correlated.The correlation is created by the measurements while their mutual influence requires the corresponding supraliminal velocities.This situation is commonly known as the violation of the Bell inequality in the Bohm version of Einstein-Podolsky-Rosen paradox.Nearly 40 years the question remains disputable with a variety of contradicting views.The most frequently the violation is explained by the existence of some momentary action at a distance which obliges the quantum mechanics (as well as all nature) to be nonlocal.We find the "common cause in the past" as the origin of the observed quantum correlation which so far was unnoticed either by the partisans of quantum non-locality or their opponents.The novelty of our approach is the accent on the expressions for the observed physical quantities rather than on the "entangled" two-particle wave functions.We show the crucial role of phases in the correlation process that is hard to notice using the traditional approach.
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.