Act 461. Twin paradoxes

"Wait a minute, Reiner, I have a question here."

At this time, Lanchester. Stanion spoke suddenly.

"The time dilation effect occurs on an object moving at a speed close to the speed of light, and according to the principle of relativity of motion, the external observer is theoretically also using the principle of the speed of light, and the external observer also has a time dilation effect?"

Lord Stanion's words silenced the room again, and his question seemed to contain some inexplicable strangeness.

"For example, there are twins, Al and Beta, both of them grew up at the same time, exactly the same, at this time, Al obtained a spell that allowed him to move away from the planet at the speed of light and go to the universe, he experienced a brief acceleration, flew towards the universe at the speed of light, and after flying for a while, immediately slowed down, and then turned back at the speed of light."

Lord Stenion pondered his words as he spoke.

"According to the theory of time dilation, Al is in a high-speed motion close to the speed of light, he should have a time dilation effect, the one second he has passed, the beta on the ground should have passed a few seconds, if we don't discuss it with precise calculations, the moment of departure, Al and Beta are both twenty years old, and the moment of return, due to the time dilation effect, Al looks only thirty years old, but Beta is already seventy years old."

Hearing Lord Stanion's explanation, several high-level mages present pondered for a moment and nodded slightly, indicating that they agreed with such an assumption.

"But now, think about it from another angle, if we take Al as a frame of reference, then Beta has actually experienced the process of accelerating to the speed of light and then turning back, and Beta should also have a time dilation effect, and from Al's point of view, Beta should behave younger than himself."

"This creates a contradiction!"

Ludwig. Stein quickly sensed the problem, and due to the relativity of motion, the time dilation effect should be on both sides, rather than just one side of the time being inflated.

"Reiner, how do you explain this?"

Eagles. Field was equally puzzled, and Lord Stanion's paradox was quite easy to understand, but difficult to explain, because it seemed to conflict with the time dilation effect, and now no one could confidently say which one was wrong.

Everyone's eyes fell on Reiner, because among the high-level mages present, only Reiner, the proposer of the theory of relativity, knew this theory best, and it was impossible for him not to take this issue into consideration.

Reiner looked around at the crowd, cleared his throat, and stood up.

"This question is indeed in my consideration, Excellencies, to be honest, the appearance of this twin paradox is caused by the difference between the classical space-time system and the relativistic space-time system."

With a slight wave of his hand, two small clocks appeared in mid-air.

"We can simplify the problem to two clocks that are identical, one of which suddenly turns back at close to the speed of light, and the other stays still, and finds out what happens to the display time of the two clocks after the reversion, and for the sake of simplification, we assume that the process of acceleration and deceleration is almost non-existent, which is the result of two periods of uniform motion, the moving clock is called a moving clock, and the stationary clock is called a static clock."

Under the watchful eyes of the mages, Reiner ordered the point of light to repeat the movement.

"In the classical physics system, with two points of light each as a reference frame, it is natural to get the result that the other party is moving at a uniform speed relative to itself, but let's focus on the point of this movement, that is, the moving clock, the process of moving the clock away from the static clock is obvious, with the static clock as a reference, the moving clock has time dilation, and time passes more slowly, and with the moving clock as a reference, the static clock is also moving at a uniform speed, there is time dilation, and time passes more slowly."

"Isn't that a contradiction?"

Maria. Mrs. Instein asked, confused.

"But in fact, Lord Instein, the time of the moving clock and the static clock are relative, and they themselves do not feel the difference in the passage of time, just as we do not feel that time passes faster or slower than outside in the ruins, and only after the two meet, their relative time comparison is meaningful."

Once Reiner had explained this, he began to turn the distant point of light back.

"The problem lies in the process of regression, ladies and gentlemen, from the perspective of the clock, the clock is also moving at a constant speed, but from the perspective of the clock, the clock moves from its rear to its front in an instant, similar to a semicircular motion of one hundred and eighty degrees, and this movement is beyond the speed of light."

"Faster than the speed of light?"

Broly. Augustine pondered silently, Reiner's words seemed contradictory, but they also implied some facts that he did not explicitly state.

"Of course, this act of exceeding the speed of light does not have any information transmission, in other words, if the moving clock can see things at infinite distances, it will not be able to see the existence of the bell in front of it at the moment of turning, to be precise, although the still clock exists, it is not in the light cone of the moving clock at this moment."

Reiner's words caused a stir, a situation that the High Mages had never imagined, and the phenomenon Reiner was referring to was even more bizarre than the shrinkage effect and the time dilation effect.

"We define the trajectory of a particle in space-time as its world line, the world line records all the positions of this particle from the past to the future, the range of this position, I call it the light cone, the range of the light cone is determined by the speed of light, the object cannot exceed the speed of light, only the things that are located within the light cone will have an effect on the object."

Reiner came up with a concept where, at the same time, in mid-air, a point of light meanders along the coordinate axis to form a cone.

"For the moving clock, in the process of moving away, it will observe that the time of the static clock slows down, and at the moment of U-turn, the time of the still clock suddenly accelerates, and in the process of returning, the time of the still clock continues to slow down until the two parties meet, at this time, the time passed by the moving clock is still less than the time that the bell has passed, that is, Al, who flies into the sky, will eventually meet younger than Beta."

After speaking, Reiner demonstrated the phenomenon represented by his words, he drew two lines in a coordinate axis, one coincided with the vertical axis, the other was an oblique line, and there were two hyperbolas on the coordinate axis, the horizontal axis of the coordinate axis represents space X, and the vertical axis is time multiplied by the speed of light cT.

"The reason for the emergence of this phenomenon is that the moving clock and the static clock are in different world lines, in this coordinate system, the moving clock represents a diagonal line, and the still clock is a straight line, and the clock in different world lines cannot be equivalent through a simple coordinate system transformation."