The main purpose of the thought experiment called "Twin Paradox" was to refute the logic and validity of the special theory of relativity (SRT). It is worth mentioning right away that there is actually no question of any paradox, and the word itself appears in this topic because the essence of the thought experiment was initially misunderstood.
Main idea of SRT
The paradox of the theory of relativity (the twin paradox) states that a “stationary” observer perceives the processes of moving objects as slowing down. In accordance with the same theory, inertial frames of reference (frames in which the motion of free bodies occurs in a straight line and uniformly, or they are at rest) are equal relative to each other.
The twin paradox in brief
Taking into account the second postulate, there is an assumption about the inconsistency of the special theory of relativity. To allowthis problem clearly, it was proposed to consider the situation with two twin brothers. One (conditionally - a traveler) is sent on a space flight, and the other (a homebody) is left on planet Earth.
The wording of the twin paradox under such conditions usually sounds like this: according to the stay-at-home, the time on the clock that the traveler has is running slower, which means that when he returns, his (the traveler's) clock will lag behind. The traveler, on the contrary, sees that the Earth is moving relative to him (on which there is a homebody with his watch), and, from his point of view, it is his brother who will pass the time more slowly.
In fact, both brothers are in equal conditions, which means that when they are together, the time on their clocks will be the same. At the same time, according to the theory of relativity, it is the brother-traveler's watch that should fall behind. Such a violation of the apparent symmetry was considered as an inconsistency in the provisions of the theory.
Twin paradox from Einstein's theory of relativity
In 1905, Albert Einstein deduced a theorem that states that when a pair of clocks synchronized with each other is at point A, one of them can move along a curved closed trajectory at a constant speed until they again reach the point A (and this will take, for example, t seconds), but at the moment of arrival they will show less time than the clock that remained motionless.
Six years later, the paradox status of this theoryprovided by Paul Langevin. "Wrapped" in a visual story, it soon gained popularity even among people far from science. According to Langevin himself, the inconsistencies in the theory were explained by the fact that, returning to Earth, the traveler moved at an accelerated rate.
Two years later, Max von Laue put forward a version that it is not the acceleration moments of an object that are significant, but the fact that it falls into a different inertial frame of reference when it is on Earth.
Finally, in 1918, Einstein was able to explain the paradox of two twins himself through the influence of the gravitational field on the passage of time.
Explanation of the paradox
The twin paradox has a rather simple explanation: the initial assumption of equality between the two frames of reference is wrong. The traveler did not stay in the inertial frame of reference all the time (the same applies to the story with the clock).
As a result, many felt that special relativity could not be used to correctly formulate the twin paradox, otherwise incompatible predictions would result.
Everything was resolved when the general theory of relativity was created. She gave an exact solution for the problem at hand and was able to confirm that of a pair of synchronized clocks, it was the ones in motion that would fall behind. So the initially paradoxical task received the status of an ordinary one.
Controversial issues
There are suggestions thatthe 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 influence of acceleration, the movement of time does not accelerate or slow down.
As a result, the segment of the trajectory, on which one of the brothers accelerated, demonstrates only some asymmetry that occurs between the traveler and the homebody.
But this statement cannot explain why time slows down for a moving object, and not for something that remains at rest.
Test by practice
The twin paradox formulas and theorems describe 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 have been carried out, the purpose of which was to prove or disprove the theory of relativity.
In one case, an atomic clock was used. They are highly accurate, and for a minimum desynchronization they will need more than one million years. Placed in a passenger plane, they circled the Earth several times and then showed quite a noticeable lag behind those watches that did not fly anywhere. And this despite the fact that the speed of movement of the first sample of the clock was far from light.
Another example: the life of muons (heavy electrons) is longer. These elementary particles are several hundred times heavier than ordinary particles, have a negative charge and are formed in the upper layer of the earth's atmosphere due toaction of cosmic rays. The speed of their movement towards the Earth is only slightly inferior to the speed of light. With their true lifespan (2 microseconds), they would have decayed before they touched the surface of the planet. But in the process of flying, they live 15 times longer (30 microseconds) and still reach the goal.
Physical cause of paradox and signal exchange
Physics explains the twin paradox in a more accessible language. During the flight, both twin brothers are out of range for each other and cannot practically make sure that their clocks move in sync. It is possible to determine exactly how much the movement of the traveler’s clocks slows down if we analyze the signals that they will send to each other. These are conventional signals of "exact time", expressed as light pulses or video transmission of the clock face.
You need to understand that the signal will not be transmitted in the present tense, but already in the past, since the signal propagates at a certain speed and it takes a certain time to pass from the source to the receiver.
It is possible to correctly evaluate the result of the signal dialogue only taking into account the Doppler effect: when the source moves away from the receiver, the signal frequency will decrease, and when approached, it will increase.
Formulating an explanation in paradoxical situations
There are two main ways to explain the paradoxes of these twin stories:
- Attentiveconsideration of existing logical constructions for contradictions and identification of logical errors in the chain of reasoning.
- Performing detailed calculations to evaluate 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 frames of reference. It is assumed here that the moments associated with the acceleration of motion are so small in relation to the total flight length that they can be neglected. In some cases, they can introduce a third inertial frame of reference, which moves in the opposite direction in relation to the traveler and is used to transmit data from his watch to Earth.
The second group includes calculations built taking into account the fact that moments of accelerated motion are still present. This group itself is also divided into two subgroups: one uses the gravitational theory (GR), and the other does not. If general relativity is involved, then it is assumed that the gravitational field appears in the equation, which corresponds to the acceleration of the system, and the change in the speed of time is taken into account.
Conclusion
All discussions related to the imaginary paradox are due only to a seeming 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, which had to go through a change in frames of reference, becausesimultaneity 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 within the framework of the special theory of relativity or focusing on non-inertial frames of reference. The results of both chains of calculations can be mutually consistent and equally serve to confirm that time passes more slowly on a moving clock.
On this basis, it can be assumed that when the thought experiment is transferred to reality, the one who takes the place of a homebody will indeed grow old faster than the traveler.
