discussion

About the "Twin Paradox"

In many popular descriptions about the so-called "twin paradox" (which is not really a paradox) the message is that what makes the difference is that one of the twins is accelerated. And what many laymen learn from such descriptions is that it is that phase of the acceleration which makes the difference, which somehow leads to the difference in the age of the twins.

This is completely misleading. And this can be easily shown, by the following variant of the twin paradox, where above twins have completely similar acceleration and deceleration events, but end up anyway differently aged.

Look at the picture at the right side: Here, above twins travel, at least a little bit. Only the red twin travels much longer time, and stays at the final place much shorter time. So, there is a long time when the red twin is travelling but the gree twin is at rest. And this is what matters: The clock of the travelling twin is going slower. All imaginable clocks - inclusive his own aging as a biological clock. And therefore he ends up younger when they meet again.

This is simply what the Lorentz ether interpretation tells us. And in the Lorentz ether interpretation where is no such animal as a "twin paradox".

And this is also what the formula for "proper time" (the German original is "Eigenzeit", which translates more accurately as own, private, separate time) tells us: Acceleration does not matter at all, what matters is velocity: \[ \tau = \int \sqrt{1 - \frac{v^2}{c^2}} dt\]

But what about the "twin paradox" in the spacetime interpretation?

But does that mean there is something wrong with the relativistic picture? For the travelling twin, tells the "twin paradox", it looks like the other twin moves, thus, his clock should be slower. This happens if he flies away, but also as he flies home. Thus, if we take everything together, it is the twin at home which will stay younger. Not?

The point which is missed in this description is what really changes if the travelling twin makes his turn. He makes a switch from one inertial frame to another inertial frame. But this change of the inertial system used changes also what is considered, by the travelling twin, what looks like "now" for the twin at home.

It is the difference between these two different opinions what is "now" which makes the difference, and what is forgotten in the description above. It is easy to forget it, because we do not change in our everyday experiences our opinion what is "now". We live in a world where "now" makes sense as defined by Nature, independent of our behaviour. And, so, we would not change, if we would travel, our opinion what is "now" for the twin who remains at home. There would be no point doing this.

The problem with Einstein synchronization

The problem behind this is the use of Einstein synchronization to define what is now. Einstein synchronization is a way to establish what is "now" for far away places by using the fastest signals we have. We send a signal with light to the place, which is returned by a mirror or a friend there. Then we assume that the light ray needs the same time back and forth. So, the moment when the light signal was send back will be the same as the middle between sending the signal and receiving the answer. Reasonable? Yes.

But only if we assume that we are at rest. If we move, the light ray has to do different distances on his way back and forth. And, therefore, will need different time. So, our synchronization will be wrong if we move.

The very point of relativity is that we will be unable to find out if we move. If we, by error, think that we are at rest, we will get a lot of things wrong: We will get a wrong synchronization. We will make wrong assumtions about clocks, thinking that the (really faster) clock of the twin at rest is going slower, and that his rulers are Lorentz-contracted. But all this conspires in such a way that we do not observe any error in our wrong constructions.

But all this is relevant only as long as it makes sense for us to believe we are in rest. For the travelling twin, it makes no sense to assume as before, as after the turn that he is at rest. This would be obviously inconsistent. He can make the error to assume that he is at rest if he drives away from the Earth. But in this case, he will not assume that he is at rest travelling home, but assume a much larger speed than that of the twin at Earth. Or he can make the other error, thinking that he was at rest when he travels home. But in this case, he would assume that then he was driving away from Earth he had a much higher speed than the Earth.

In above cases of error, there would be no nonsensical immediate change of the assumption what is "now" for the twin at Earth. There would be a wrong but finally consistent picture, where one half of the trip he was at rest, with the clock of the Earth twin going slower, and the other half of the trip he moving himself faster than the twin on Earth, and therefore his own clock going slower. So much slower that the result would be the same number as the correct one predicted by assuming the twin on Earth is at rest.