Paradox of twins (thought experiment): explanation

The main purpose of the thought experiment called "The Paradox of the Twins" was to refute the logic and validity of the special theory of relativity (STR). It should be noted right away that there is no question of any paradox in fact, and the word itself appears in this topic because the essence of the mental experiment was initially misunderstood.

The main idea of SRT

The paradox of the theory of relativity (the paradox of twins) says that a "stationary" observer perceives the processes of moving objects as slowing down. In accordance with the same theory, inertial frames of reference (systems in which the motion of free bodies are rectilinear and uniform or they are at rest) are equal in rights with respect to each other.

Paradox of twins: briefly

Taking into account the second postulate, it is assumed that the special theory of relativity is inconsistent . To solve this problem visually, it was suggested to consider the situation with two twin brothers. One (conditionally - traveler) is sent to space flight, and the other (homebody) is left on the planet Earth.

The wording of the twins paradox under such conditions usually sounds like this: according to the homebody, the time at the clock that the traveler has is moving slower, which means that when he returns, his watch will fall behind. The traveler, on the contrary, sees that the Earth is moving with respect to him (on which the homebody is with his watch), and from his point of view, it is his brother's time that will go more slowly.

In fact, both brothers are in equal conditions, which means that when they are together, their time will be the same on their watches. At the same time, according to the theory of relativity, it is precisely the hours of the traveler's brother that should fall behind. Such a violation of apparent symmetry was considered as an inconsistency of the theory's provisions.

Paradox of twins from the theory of relativity of Einstein

In 1905, Albert Einstein derived a theorem that says that when pairs of synchronized clocks are in point A, one can move one of them along a curvilinear closed trajectory at a constant speed until they again reach point A (and to this point Will be spent, for example, t seconds), but at the time of arrival they will show a shorter time than the clock that remained motionless.

Six years later the status of the paradox of this theory was given by Paul Langevin. "Wrapped up" in a visual history, 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 at an accelerated pace.

Two years later, Max von Laue was put forward a version that is not significant at all moments of acceleration of the object, but the fact that it falls into another inertial frame of reference when it is on Earth.

Finally, in 1918, Einstein was able himself to explain the paradox of the two twins through the influence of the gravitational field on the flow of time.

Explanation of the paradox

The paradox of twins explanation is quite simple: the initial assumption of equality between the two frames of reference is incorrect. The traveler stayed in the inertial frame of reference not all the time (this also applies to the history of the clock).

As a consequence, many considered that a special theory of relativity can not be used to correctly formulate the paradox of twins, otherwise inconsistencies are obtained that are incompatible with each other.

Everything was resolved when the general theory of relativity was created . She gave an exact solution for the task at hand and was able to confirm that from the pair of synchronized clocks the ones that are in motion will be lagging behind. So initially the paradoxical task was ranked as an ordinary one.

Controversial moments

There are suggestions that the acceleration time is significant enough to change the speed of the clock. But in the course of numerous experimental checks it was proved that under the action of acceleration the movement of time does not accelerate or slow down.

As a result, the segment of the trajectory, in which one of the brothers accelerated, demonstrates only some asymmetry arising between the traveler and the homebody.

But this statement can not explain why time is slowed down precisely by a moving object, and not by what remains at rest.

Practice Testing

The paradox of the twins of the formula and the theorem describes accurately, 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 extremely precise, and for minimal desynchronization they will need more than one million years. Placed in a passenger plane, they flew several times around the Earth and afterwards showed quite a noticeable lag behind those hours 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 longer life of muons (heavy electrons). 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 less than the light speed. With their true lifespan (in 2 microseconds), they would decay before they touch the surface of the planet. But in the process of flying, they live 15 times longer (30 microseconds) and still achieve the goal.

The physical cause of the paradox and the exchange of signals

Paradox of twins physics explains and more accessible language. While the flight is in progress, both twin brothers are out of reach for each other and can not in practice verify that their clocks are moving synchronously. It is possible to determine exactly how slow the traveler's movement is by analyzing the signals that they will send to each other. These are conditioned signals of "precise time", expressed as light pulses or video broadcasting of the dial of the clock.

It should be understood that the signal will be transmitted not in the present tense, but in the past, as the signal propagation occurs at a certain speed and it takes a certain amount of time to pass from the source to the receiver.

Correctly evaluate the result of the signal dialogue can only be done with the Doppler effect: when the source is removed from the receiver, the frequency of the signal will decrease, and when approaching, it will increase.

Formulation of explanation in paradoxical situations

To explain the paradoxes of similar histories with twins, two main methods can be used:

1. A close examination of the existing logical constructions for the subject of contradictions and the identification of logical errors in the chain of reasoning.
2. Realization of detailed calculations in order to assess the fact of inhibition of time 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. Here it is meant 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, a third inertial reference system may be introduced that advances in the opposite direction with respect to the traveler and is used to transfer data from its clock to Earth.

The second group includes calculations based on the fact that moments of accelerated motion are still present. This group itself is also subdivided into two subgroups: one uses gravity theory (GTR), and the other does not. If GRT is involved, it is implied that the field contains gravity field, which corresponds to the acceleration of the system, and takes into account the change in the speed of the flow of time.

Conclusion

All discussions connected with the imaginary paradox are due only to an apparent logical error. No matter how the conditions of the problem were formulated, it is impossible to ensure that the brothers are in completely symmetric conditions. It is important to take into account that time is slowing down precisely on moving clocks, which had to go through the change of frames of reference, because the simultaneity of events is relative.

Calculate how much time has slowed from the point of view of each of the brothers, in two ways: using the simplest actions within the framework of the special theory of relativity or by focusing on non-inertial frames of reference. The results of both calculation circuits can be mutually consistent and equally serve to confirm that the moving clock is slower.

On this basis, it can be assumed that when you transfer a mental experiment into reality, the one who takes the place of the homebody will really grow old faster than the traveler.