Two myths about the Twin Paradox

Abstract

The theory of relativity (SRT and GRT), created by Albert Einstein more than a hundred years ago and one of the two main foundations of 20th century physics, still excites the minds of “subversives” to this day. For the general public, the most well-known and at the same time the most odious consequence of the SRT is the so-called “twin paradox”, which is associated with two myths.

Myth One. “There is symmetry between the Astronaut and the Homebody”.

If, based on the principle of relativity, the Astronaut is considered to be at rest, and the Homebody is considered to be moving, then applying Lorentz transformations to the movement of participants should lead to the answer that the Homebody's clock will record a shorter travel time than the Astronaut's clock.

Reasoning about the presence of symmetry is erroneous, since the Homebody remains in the same ISO for the entire period of waiting for the Astronaut, and the Astronaut moves from Earth to the target in one ISO, and returns to Earth by moving to another ISO, which indicates the inequality of participants. Regardless of which of the participants will be considered conditionally at rest and who will be considered conditionally moving, the correct application of Lorentz transformations always leads to the answer that the Astronaut’s watch displays a shorter travel time than the watch of the Homebody. The reason for this lies in the Astronaut’s travel times “there” and “back” being measured by clocks related to two different ISO: one of which is accompanying for him on the way “there”, and the other is accompanying on the way “back”. On the way “there”, both events – the start from Earth and the finish at the target – for the Astronaut occur at the same point in space – at the origin of the ISO coordinates, which is accompanying for him on the way “there”. The distance between the start and finish events in this accompanying ISO is zero. Therefore, the time period on the way “there” is a period of his own time, which is shorter than the time period according to the clock of any other ISO, relative to which these events occur at different points in space. In particular, this is the Homebody’s ISO, in which the same start and finish events are separated by the distance from the Earth to the target: the start event of the Astronaut in the Homebody’s ISO occurs at the origin of its coordinates, and the event of the Astronaut’s finish at the target occurs at the distance of the target. And the time period according to the watch of the Homebody, not being the period of his own time, is longer than according to the watch of an Astronaut. A similar situation occurs during the return movement. On the way back, the events of starting from the target and finishing on Earth for the Astronaut also occur at the same point in space – at the origin of the ISO coordinates, which for him is accompanying on the way back. The distance between these events in this accompanying ISO is also zero. And the time period on the way “back” is also the period of his own time. But for the Homebody, these events are separated by the same distance between the Earth and the target, and therefore the time period between them, not being the period of their own time, is longer than according to the Astronaut’s watch. The time periods between the events of starts and finishes measured by the Astronaut’s watch will always be periods of his own time, unlike the periods of non-own time measured by the watch of the Homebody. A detailed analysis indicating the fallacy of this myth, based on the Lorentz transformations and the concept of an interval, is carried out in section 4 of the article.

Myth two. “To analyze the accelerated motion of an Astronaut, it is necessary to use GRT.”

Since when an Astronaut moves from one ISO to another ISO to return to Earth, he experiences acceleration, he is affected by inertial forces, which, like gravitational forces, affect the pace of time. Therefore, to analyze the Astronaut’s movement, it is necessary to take into account the effects of GRT.

The myth is based on a misunderstanding of the fact that GRT is a theory of gravity, but not a theory of accelerated motion. Therefore, the statement about the need to use GRT to analyze the accelerated motion of an Astronaut is illiterate. The foundations of GTR are the already constructed SRT and the equivalence principle established by Galileo and Newton, which allowed Einstein to apply the constructions of STR to describe gravitational interactions, which he called GTR. At the same time, the equations that describe the accelerated motion of objects when they reach speeds commensurate with the speed of light in the absence of gravity remain a consequence of only STR. To create them, the principle of equivalence is not required, and due to the fact that accelerated motion, unlike gravity, is spatially homogeneous and does not lead to space curvature, its description does not require complex mathematical constructions based on tensor analysis and differential geometry, but almost school mathematics in relation to flat pseudo-Euclidean geometry within the framework of the kinematics of STR is quite sufficient. This applies equally to the accelerations of an Astronaut as he moves from one ISO to another to return to Earth, as well as to the accelerations acting on an Astronaut during dispersal and deceleration from the Earth towards the target and back from the target towards the Earth. A detailed analysis of the Astronaut’s movement with accelerations during his acceleration and deceleration on the way “there” and “back”, indicating the fallacy of this myth, based on the relations of the accelerated motion of SRT (see L. D. Landau, E. M. Lifshits. Field theory, §7, Solution of the problem // M.: Nauka. 1967) was carried out in section 6 of the article.

Since the twin paradox for the general public is the most famous and most odious consequence of SRT, in order to reduce the amount of speculation around STR and GTR, this “paradox” should be given the greatest attention and all its nuances should be considered in the most careful manner in popular science literature, intended primarily for scientifically educated layers of society. However, this has not been done by professional theoretical physicists. It is difficult to say how useful the attempt of the author of this article, who is not a theorist, to analyze in detail the two most odious myths that have developed around the twin paradox will be.

Translation into English was made using online translators.