The main purpose of a thought experiment called the “Twins Paradox” was to refute the logic and validity of the special theory of relativity (SRT). It is worth mentioning right away that there is really no question of any paradox, and the word itself appears in this topic because the essence of the thought experiment was initially misunderstood.
The main idea of the service station
The paradox of the theory of relativity (the paradox of twins) says that the "motionless" observer perceives the processes of moving objects as slowing down. In accordance with the same theory, inertial reference systems (systems in which the motion of free bodies is rectilinear and uniform or they are at rest) are equal in relation to each other.
The paradox of twins: briefly
Taking into account the second postulate, an assumption arises about the inconsistency of the special theory of relativity. To solve this problem visually, it was proposed to consider the situation with two twin brothers. One (conditionally - traveler) is sent into space flight, and the other (homebody) is left on planet Earth.
The formulation of the twin paradox under such conditions usually sounds like this: according to the couch potato, the time on the watch that the traveler has is moving slower, which means that when he returns, his (traveler) watch will be behind. The traveler, on the contrary, sees that the Earth is moving relative to him (on which the homebody is with his watch), and, from his point of view, it is with his brother that time will go more slowly.
In fact, both brothers are in equal conditions, which means that when they are together, the time on their watch will be the same. At the same time, according to the theory of relativity, it was precisely the brother-traveler's clock that should lag behind. Such a violation of apparent symmetry was considered as an inconsistency of the theory.
Einstein’s twin paradox
In 1905, Albert Einstein deduced a theorem which states that when a pair of clocks synchronized with each other is located at point A, one of them can be moved along a curved closed path with a constant speed until they reach point A again (and this for example, t seconds will be spent), but at the time of arrival they will show less time than those hours that remained motionless.
Six years later, Paul Langevin gave the status of a paradox of this theory. “Wrapped up” in a visual story, it soon gained popularity even among people far from science. According to Langevin himself, the inconsistencies in theory were explained by the fact that, returning to Earth, the traveler moved accelerated.
Two years later, Max von Laue put forward the version that the moment of acceleration of the object is not significant at all, but the fact that it falls into another inertial reference frame when it appears on Earth.
Finally, in 1918, Einstein himself was able to explain the paradox of two twins through the influence of the gravitational field on the passage of time.
Paradox explanation
The twins paradox has a rather simple explanation: the initial assumption of equality between the two frames of reference is incorrect. The traveler did not stay in the inertial reference system all the time (the same goes for the story with the clock).
As a result, many felt that the special theory of relativity cannot be used to correctly formulate the twin paradox, otherwise incompatible predictions are obtained.
Everything was resolved when the general theory of relativity was created . She gave an exact solution to the existing problem and was able to confirm that precisely those that are in motion will lag behind a pair of synchronized watches. So initially the paradoxical task received the status of an ordinary.
Controversial issues
There are suggestions that the moment of acceleration is significant enough to change the speed of the clock. But in the course of numerous experimental tests it was proved that under the action of acceleration, the movement of time does not accelerate and does not slow down.
As a result, the segment of the trajectory in which one of the brothers accelerated demonstrates only some asymmetry that arises between the traveler and the homebody.
But this statement cannot explain why time slows down precisely at a moving object, and not at that which remains at rest.
Practice check
The twins paradox describes the formulas and theorems exactly, but it is quite difficult for an incompetent person. For those who are more inclined to trust practice, rather than theoretical calculations, numerous experiments were carried out, the purpose of which was to prove or refute the theory of relativity.
In one case, an atomic clock was used. They are extremely accurate, and for minimal desynchronization, they will need more than one million years. Placed in a passenger plane, they circled the Earth several times and afterwards showed a quite noticeable lag behind those watches that did not fly anywhere. And this despite the fact that the speed of movement of the first watch was far from light.
Another example: the life of muons (heavy electrons) is longer. These elementary particles are several hundred times heavier than usual, have a negative charge and are formed in the upper layer of the earth's atmosphere due to the action of cosmic rays. The speed of their movement to the Earth is only a little inferior to the light. With their true life expectancy (in 2 microseconds), they would decay before they touched the surface of the planet. But during the flight, they live 15 times longer (30 microseconds) and still achieve their goal.
Physical Cause of the Paradox and Signal Exchange
Physicist explains the twin paradox in a more accessible language. While the flight is in progress, both twin brothers are out of reach of each other and cannot, in practice, make sure that their watch is moving synchronously. It is possible to determine exactly how slow the movement of a watch’s watch is if the traveler analyzes the signals that they will send to each other. These are conditional signals of the “exact time”, expressed as light pulses or video broadcasting of the watch dial.
You need to understand that the signal will not be transmitted in the present time, but already in the past, since the signal propagates at a certain speed and it takes a certain time to go from the source to the receiver.
Correctly evaluating the result of the signal dialogue is possible only taking into account the Doppler effect: when the source is removed from the receiver, the signal frequency decreases, and when approaching, it increases.
The formulation of the explanation in paradoxical situations
Two main methods can be used to explain the paradoxes of similar stories with twins:
- A careful examination of the existing logical constructions for contradictions and the identification of logical errors in the chain of reasoning.
- Implementation of detailed calculations to assess the fact of time deceleration from the point of view of each of the brothers.
The first group includes computational expressions based on SRT and inscribed in inertial reference systems. Here it is understood that the moments associated with the acceleration of movement are so small in relation to the total flight length that they can be neglected. In some cases, they can introduce a third inertial reference system, which moves in the opposite direction with respect to the traveler and is used to transfer data from his watch to Earth.
The second group includes calculations constructed taking into account the fact that moments of accelerated motion are still present. This group itself is also divided into two subgroups: one uses gravitational theory (GTR), and the other does not. If GR is involved, it is assumed that the gravitational field appears in the equation, which corresponds to the acceleration of the system, and the change in the velocity of time is taken into account.
Conclusion
All discussions related to the imaginary paradox are due only to an apparent logical error. No matter how the conditions of the problem are formulated, it is impossible to ensure that the brothers find themselves in completely symmetrical conditions. It is important to consider that time slows down precisely on moving clocks that had to go through a change of reference systems, because the simultaneity of events is relative.
There are two ways to calculate how much time has slowed down from the point of view of each of the brothers: using the simplest actions in the framework of the special theory of relativity or focusing on non-inertial reference systems. The results of both chains of calculations can be mutually agreed and equally serve to confirm that time is moving slower on a moving clock.
On this basis, it can be assumed that when a thought experiment is transferred to reality, one who takes the place of a couch potato will really age faster than a traveler.