Time dilation - why the observers see each other the slow one but then one of them is older or younger?

Question

I'm in trouble with time dilation: Suppose that there's two people on the Earth (A,B), they are twins and each other has a clock. (So they are at the same reference frame). B travels in a spaceship and is orbiting around the Earth, as B's speed has increased there's some time dilation. So it's supposed that if A "looks" to B, B's clock will run slower than A's, and viceversa. And if one day B decides come back to the Earth, he will be younger than his twin and the hour of his clock would be different (earlier than A's clock) because of time dilation.

My first question is, why each person see the other's clock as the slow one? (In fact, I found some information that may solved it but I'm not sure if it's the right answer, and if it is, I don't understand it. -> It's because everyone thinks about himself as the reference frame. In other words, that for B, he is the stationary and who moves is A, so he sees A's clock run slower as B is "stopped" and the same for A. B is who is moving and A the stationary.)

The other question I have is that if it's true that each one sees the other as the slow one there's something that i missed out. We all agree that B (after going to the space and came back to the Earth) he is younger than his brother. So, why B don't see A moving and aging very fast if A see his brother and his things going very slow? Let's imagine they were looking to each other all the time, if both of them see the other going slowly once they meet and "discover" B is the young one... how is that possible?

[I think that in one episode of Cosmos of Carl Sagan (though may be I'm mistaken) he said that a neutrino "borned" in the Big Bang could have seen the creation of the Universe until today in few seconds due to its high speed, here starts my doubts: or i misunderstood something or there's contradictory information]

(I don't know anything about physics, only what is taught at high school as I'm a teenager so it'd be better to answer with no kind of calculation as I'd not understand it.)

Answer 1

There are lots of questions about the twin paradox on this site, so it's probably not worth going over that material again.

What is worth saying is that where people tend to get confused is by misunderstanding what an inertial frame is and how different inertial frames can be compared. We should simplify matters a bit and put twin B on a spaceship because orbital motion is a bit more complicated. The only time A and B can directly compare anything with each other is the moment that they pass i.e. the moment that they are in the same place. If A and B stay in their inertial frames they will never meet again and indeed will get further and further apart as time passes. The only way the twins will ever meet again is if they change inertial frames i.e. if one of them accelerates.

In SR acceleration is absolute. By this I mean that velocity is relative i.e. you cannot tell whether A or B is the one moving, but it is always possible to tell which of the two is accelerating. The acceleration always introduces an assymetry so it's no surprise that when they meet again A and B will find their clocks differ.

You can treat acceleration in special relativity. See for example my answer to How do I adjust the kinematic equations to avoid reaching speeds faster than light? where I give (some of) the equations for understanding the motion of an accelerating rocket. If you do the calculation you will find that B sees A clock running fast while B is accelerating between inertial frames. See my answer to Why isn't the symmetric twin paradox a paradox? for more on this.

The question of what Carl Sagan's neutrino sees is quite a subtle one. Suppose some particle interaction shortly after the Big Bang and 13.7 billion years away produced a neutrino and that neutrino has just passed you. For the neutrino only a few seconds has passed since the Big Bang. However when the neutrino passes you it sees you at your current age, 13.7 billion years, so what's going on? The answer is that in the neutrino's frame and your frame the Big Bang happened at different times. So the neutrino can see the 13.7 billion age of the Big Bang pass in a few seconds, but not because it sees the universe's time running fast. It sees each successive bit of the universe as older because in each bit of the universe it passes through the Big Bang gets further and further back in time.