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The Twin Paradox Analogy in Classical Physics

VADIM N. MATVEEV, Oleg V. Matvejev

Published Jun 1, 2015• 0 citations
OpenAlex

Abstract

The article simulates Twin Paradox by means of floating boats. The boats are fitted with a pendulum clock and instruments activated by signals generated by this clock (in time with this clock). The function of the clock pendulum is performed by a high-speed shuttle continuously moving along a vertical (relative to the boat) line between the boat and the bottom. The article demonstrates, that even if two boats are sailing side by side at a speed v relative to the water, then one of them halts, waits for a while and then catches up with the boat sailing ahead, the instruments on the non-inertial boat grew less old than on the inertial one.

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The article simulates Twin Paradox by means of floating boats. The boats are fitted with a pendulum clock and instruments activated by signals generated by this clock (in time with this clock). The function of the clock pendulum is performed by a high-speed shuttle continuously moving along a vertical (relative to the boat) line between the boat and the bottom. The article demonstrates, that even if two boats are sailing side by side at a speed v relative to the water, then one of them halts, waits for a while and then catches up with the boat sailing ahead, the instruments on the non-inertial boat grew less old than on the inertial one.
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.
The simplest version of the clock paradox is the following: A and B are two adjacent atomic clocks at rest (v = 0) in a closed inertial system K. After an acceleration period, the atomic clock A travels with constant velocity va at L distance, then stops and moves contrariwise with constant velocity at L distance before slows it down and stops next to clock B. According to the standard theoretical statement, the clock in motion would run slower, therefore, after returning next to clock B, clock A shows less time elapsed as clock than clock B that remained at rest. This can be described with the frequency changes of the clocks. The frequency of the clock in motion is
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.
We propose an implementation of a twin-paradox scenario in superconducting circuits, with velocities as large as a few percent of the speed of light. Ultrafast modulation of the boundary conditions for the electromagnetic field in a microwave cavity simulates a clock moving at relativistic speeds. Since our cavity has a finite length, the setup allows us to investigate the role of clock size as well as interesting quantum effects on time dilation. In particular, our theoretical results show that the time dilation increases for larger cavity lengths and is shifted due to quantum particle creation.
It is observed that, the introduction of delayed electromagnetic interaction to account for the finite speed of "light" (actually all electromagnetic interaction) leads to different time variables where non relativistic mechanics has only one. By carefully identifying and taking these various times into account, solutions are found for certain conundrums, including in particular the twin of clock paradox. An important consequence of this analysis is that it leads to a direct generalization of mechanics including special relativistic effects.
The modern concept of spacetime usually emerges from the consideration of moving clocks on the assumption that world-lines are continuous. In this paper we start with the assumption that natural clocks are digital and that events are discrete. By taking different continuum limits we show that the phase of non-relativistic quantum mechanics and the odd metric of spacetime both emerge from the consideration of discrete clocks in relative motion. From this perspective, the continuum limit that manifests itself in 'spacetime' is an infinite mass limit. The continuum limit that gives rise to the Schrödinger equation retains a finite mass as a beat frequency superimposed on the 'Zitterbewegung' at the Compton frequency. We illustrate this in a simple model in which a Poisson process drives a relativistic clock that gives rise to a Feynman path integral, where the phase is a manifestation of the twin paradox. The example shows that the non-Euclidean character of spacetime and the wave-particle duality of quantum mechanics share a common origin. They both emerge from the necessity that clocks age at rates that are path dependent.