# Why is Einstein solution to the twin paradox different from the one on the internet?

The solution to the twin paradox found on the internet is that the twin on Earth is on 1 frame the entire journey, while the twin in space is in 2 frames for the duration of the journey. However, in his own paper:

Einstein gives a totally different explanation. He says that what matters is the moment of acceleration. So even if the acceleration happens in 1 second from 0 to 290.000km/s that's the only second that truly matters. So if Einstein says like this, how can anyone bring other explanations ?

• Isn't that the same thing? Einstein is saying that it's the acceleration that matters, which is the same thing as saying the traveling twin switches inertial frames. – Javier May 4 '15 at 22:54
• No. You can talk about the frame switching without saying anything about acceleration. You just draw 2 lines in a Minkowski diagram and that's it. Then you just apply the equations of special relativity and presumably you obtain the correct result. But Einstein says otherwise. That you have to use the equations of general relativity for the moment of acceleration (even though it is only 1 second or 1 year) and only then you obtain the correct results. So who should I trust ? – Abc2000ro May 4 '15 at 23:00
• @Abc2000ro: they're equivalent because the acceleration connects two different inertial frames. The paradox would also be resolved if the first twin sent information about their age to someone travelling in a rocketship moving in the opposite direction. You don't really have any acceleration in that case, but you still have a frame shift. Acceleration is just a special case of switching sets of inertial frames. – Jerry Schirmer May 4 '15 at 23:06
• Who you should trust is a deep question, but you should never fetishize anyone. Remember that Einstein installed a cosmological constant in his explanation of the sturcture of the universe to make it agree with the then popular steady-state model, removed it after Hubble showed that there were problems with SS, and it's being put back in now as a possible way to treat the phenomena known as "dark energy". No one is infallible. – dmckee --- ex-moderator kitten May 4 '15 at 23:07
• @dmckee Rule 34 says Einstein is already fetishized – Jim May 8 '15 at 18:38

The paradox is: As each twin may consider herself in a distinct inertial reference frame, then each should see the other moving at a relativistic speed, and each should see the other appearing younger than herself, a patently impossible outcome.

There is more than one way to resolve this seeming paradox. But regardless of which logical method is used to debunk the paradox, experiments with atomic clocks in different inertial reference frames, as well as with particles traveling inside accelerators, have shown that relativistic time dilation is a real feature of the natural world.

The clearest way to debunk the paradox may be to compute the Proper Time between the events of leaving and returning. Proper Time is measured by a clock following the world line of each event, rather than by clocks in the inertial reference frame of either. See Example 1 in the Wikipedia article on Proper Time: http://en.wikipedia.org/wiki/Proper_time.

There is "more than one way to skin a cat". Just because Einstein used general relativity to debunk this seeming paradox of special relativity doesn't mean either is internally inconsistent.

Acceleration itself isn't what causes time dilation, what it does do is it adjusts the rate at which a reference frame passes through time. It's still the physical movement through space that causes the passing through time though. Of course in actuality you can't have acceleration without the movement, but the concept of acceleration on it's own only adjusts the coefficient that determines how fast a perspective progresses through time.

The initial acceleration does not matter at all. You could completely leave it out by assuming an incoming human A on his spaceship at Vrel which just happens to be of the same age when he passes another human B sitting on earth.

A will see B's clock move slower, as in calculate it to move slower (time dilation)

B will see A's clock move slower, as in calculate it to move slower.

This is a symmetrical situation. It would have been the same if B was formerly at rest and then decided to instantaneously accelerate towards a direction away of A.

So who will be the younger one, even though both see(as in calculate) each other as aging slower.

It will be whoever of the two accelerates into the inertial frame of reference, the other is at rest in, in the second phase. So if A accelerates into B's rest frame after some time, A will be younger one.

If B accelerates into A's rest frame after some time of moving apart, then B will be the younger one.

This is phase two.

In phase 3 one of them would decide to accelerate back and meet up again. Again, whoever decides to do that acceleration or to state it more precisely, whoever decides to switch into a different rest frame, will end up being younger.

But it's not the acceleration which does the trick. If it was the acceleration, accelerating instantaneously into another frame, and then back again instantaneously, you should end up younger. Which is not the case, because locally your clocks remain in sync with whichever clock you left in the former rest frame.

It's the switching of your rest frame which is what causes the age difference.

Let's check phase 3 isolated.

B is at a distance to A. Assume they are both of the same age.

There is a long line of clocks going out from B to A. All clocks will be synced, so B's clock, A's clock and all other clocks along the path now display zero. B plots this scenario on a x,t diagram.

B instantaneously accelerates to Vrel. He is now in a different rest frame. He can plot another x,t diagram and calculate what each clock along the path to A will display along the x axis (at the same time, in the classical sense) He will soon find out, that none of the clocks are in sync anymore. His clock displays zero still, but clocks towards A have a higher count with A's clock at the end having the highest count. That's what relativity of simultaneity is about. No two events which are space separated and happen at the same time in the classical sense (events that are on a line parallel to the x axis - therefore, having the same t value) do happen at the same time seen from an observer in a different rest frame.

And even though B will see A's clock (as in calculate using SR) to be ticking slower than his clock, it won't be enough to make up for the time shift of A's clock, he calculated, when switching his rest frame, until he reaches A.

A on the other hand did not switch his rest frame. All he calculates while B is approaching, is B's clock ticking slower. The acceleration of B at a distance had no effect on A other than just B now approaching at Vrel towards him.

And so B will end up to be the younger one when they meet.

So SR can fully explain this scenario, but it's not a really good explanation, allowing you to fully understand what is going on. One has to understand what switching of a rest frame means geometrically and for that he would have to be able to imagine spacetime as a hypercube. Because this switching of the rest frame is merely a perspective change on this 4 dimensional construct. In reality there is no motion at all. Spacetime is absolute with us looking at different slices from different perspectives.

If you were able to map all events that happened and will ever happen within this hypercube, there won't be anything moving. It's static/absolute with all events causally linked. We are all looking at the same hypercube, no matter which rest frame we are in. It just looks different to us depending on the perspective which is what rest frames are in essence. A perspective change. Acceleration causes this perspective change, but we do not really know how exactly it does that. We explain it with motion caused by electrons repelling each other and so on, but i don't think that goes deep enough.