双子のパラドックスへの反論

The Illusion of Relativistic Time

Counterargument to the Twin Paradox (Written by Katsunari Takada )

Suppose twin brothers are separated at birth; the older brother is sent into space on a ship that instantly reaches light speed, heading in one direction through the cosmos. It is decided that every year, both parties will exchange teletransmission photos. The younger twin on Earth will see images of his older brother in the spacecraft, growing each year. However, the older brother in the spacecraft, lacking a means of communication faster than light speed, is traveling at the same speed as the first teletransmission photo sent from Earth. Consequently, unless he slows down somewhere, he cannot observe the growth of his younger brother on Earth.

Thirty years later, the older brother on the stopped spacecraft will see a photo of his grown brother from Earth every year. Thirty years after that, when the older brother sees the 30-year-old figure of his younger brother on Earth, his own age will be 60.

Suppose the older brother in the spacecraft does not slow down midway, but turns around 30 light-years away and returns to Earth. Since he will return while receiving teletransmission photos sent from Earth along the way, every time he travels half a light-year back, he can see a photo from Earth that is approaching him every year (totaling one light-year for both). The figures in the photos sent from Earth over the 60-year round trip of the spacecraft will gradually approach the current figure, and I believe the times of the two will return to the same when the spacecraft arrives on Earth. I think the “Twins Paradox” is a theory held by people who mistakenly believe that even after the U-turn, photos are always sent from behind the spacecraft (through the spacecraft’s past trajectory) rather than from the front.

If one does not have a means of observation faster than light, it may just look (be observed) that way, while the reality might be different. Distance = Time × Velocity.

In Einstein’s book “Relativity: The Special and General Theory,” an example of a rod moving in space is given to explain the relativity of time.

“Let us suppose that at each end (A and B) of the rod, a clock is placed. These two clocks are synchronized with each other when viewed from the stationary system. Suppose there are two observers, one with each clock, traveling along with them. First, at time \(t_A\), a ray of light is emitted from A, reflected at point B at time \(t_B\), and at time \(t’_A\), this ray returns to A. Using the principle of the constancy of the velocity of light, the following relations hold:

\(t_B – t_A = \frac{r_{AB}}{c – v}\)

\(t’_A – t_B = \frac{r_{AB}}{c + v}\)

Here \(r_{AB}\) signifies the length of the moving rod as viewed from the stationary system. Looking at the above relations, when viewed by the observers traveling with the rod, the two clocks A and B are not synchronized. On the other hand, viewed from the observer sitting in the stationary system, both clocks show the same time.”

In short, if signals are transmitted simultaneously from the front and rear of a high-speed train in motion, the signals will reach a person living along the line at the same time. However, for a person moving at the same speed as the train, the signal from the front will arrive faster than the signal from the rear (the velocity at which the observer moves forward + the speed coming from the front). If that means the passage of time for a person living along the line and a person moving at the same speed as the train deviates, I believe the “Twins Paradox” is nothing more than a time lag that occurs during the exchange of information via light.