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Twin Paradox 1938-2012

J. Bajnok

Published Nov 1, 2012• 0 citations
OpenAlex

Abstract

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

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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
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 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.
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.
The paper is intended to clarify operational meaning of mass and time quantities as main characteristics of an atomic clock, which is considered a quantum oscillator in association with the de Broglie wave concept. The specification of the concept of clock in quantum terms reflects the idea of relativistic mass and time complementarity, which is important for avoiding ambiguity of such notions as ``time rate'', ``time record'', and ``elapsed time'' under relativistic conditions. We used this approach in SRT Kinematics to conduct a detailed analysis of the clock paradox; results are discussed. It is also shown that in SRT Dynamics the proper mass must be acted by Minkowski force, what results in a clock rate variation.