Nature is full of amazing things and paradoxes. And one of them, associated with movement with the speed of light, is called the "paradox of twins."
You are probably familiar with the phenomenon of half-life: many subatomic particles are unstable and after a short time decay (transform into something else). The half-life of a particle is the time it needs to "wait" to reach a 50% chance of decay.
For example, the half-life of muons is 2.2 microseconds. If you had 100 muons, there would be only 50 muons left in 2.2 microseconds, right? In fact, not necessarily.
2.2 microseconds is the elapsed time for a muon. If you have a handful of 100 stationary muons, then after 2.2 microseconds there will be about 50. But if you have a friend who is flying in a rocket at 50% of the speed of light, then when 10 seconds pass for you, it will take 8, 66 seconds.
It turns out that this also applies to muons. So if your 100 muons are not static, but are moving in a particle accelerator at 50% the speed of light, then after 2.2 microseconds from your side, it will be about 1.9 microseconds for muons. This means that by this time you will have about 55 muons.
In your frame of reference, 2.54 microseconds would pass, while 2.2 microseconds would pass for muons. So you have 50 muons left after 2.54 microseconds.
What does the twins have to do with it?
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Perhaps you are reading and thinking: what have twins and paradoxes to do with it? You know, this is a very good and timely question.
Imagine you have a twin brother. And even in your youth, you learned that he was a villain and planned to take over the world. To rid the planet of his monstrous plans, you pump him sleeping pills, put him in a rocket and send him 90% of the speed of light away from Earth.
Unfortunately, due to the time dilation effect on your twin, time passes significantly more slowly. In your nine years, only four years pass for him. If, after nine of your years, he manages to turn the ship around and return at the same speed, you will age 18 years, and he - only eight!
Usually this is the end of discussions about the paradox, which was first proposed in 1911 by Paul Langevin as a thought experiment, and this is where it all ends. However, upon closer examination of the "twin paradox" an interesting question arises.
Paul Langevin.
From the point of view of your evil twin, the Earth and you were moving at 90% of the speed of light. Thus, after nine years for him, only four years should pass for you. In other words, if your twin thinks eight years have elapsed from departure to return for him, then it should have been only three and a half years for you!
So, when your villainous twin returns, which one of you will be the older one? This is precisely the paradox.
It may seem that this question is a verdict for the Special theory of relativity. Some today devote entire websites to "exposing" the SRT. However, we can scientifically prove that one of the twins will actually age more.
The Twin Paradox is one of those problems that has a single elegant solution (or, one might say, an answer). As you may have already understood, this task involves relativistic time dilation according to the theory of special relativity.
Decision
Approaching the solution to the paradox, first imagine that you and your twin have a watch in your arms, and your girlfriend can keep track of the time on your and his watch. You can independently keep track of the time on your watch, and your twin on his: everyone is where he is. But this is an unusual clock: it ticks only once a year - on the day of the anniversary of the Earth's salvation from your evil copy. On this day, you can also exchange messages in the form of an electromagnetic pulse (you are a family after all). And here it is worth noting that the light from the telescope and the electromagnetic signal that you send move at the same speed.
Now, if we draw a time-space diagram for you and your twin, we get this:
Twin Paradox Diagram / Science ABC / Naked Science.
In the picture on the left, you are with your own frame of reference. On the right we see two frames of reference corresponding to the departure and return of your brother.
We will carry out calculations corresponding to your frame of reference. Let's say your twin is 2.67 light-years in one direction. Now that we know the distance and the speed with which it is moving, we can calculate the time it took to travel: a little over two and a half years. From your point of view, the twin's journey took about six years.
So, it turns out that the evil twin brother will return to Earth to wreak havoc in about six of your years, although it will be a little over two and a half years for him. Consequently, the more the speed of objects approaches the speed of light, the more their "experience" slows down in comparison with other objects that do not move at speeds relatively close to the speed of light, be it a man or a muon.
Vladimir Guillen
