# More twin paradox and acceleration

#### DiracPool

I just came across this video today with Brian Greene talking about how time slows down for an observer near a black hole relative to an observer who is farther away. See the first two minutes:

It reminded me of another video I saw recently by David Butler where he states that the twin paradox can be resolved by looking at the time dilation factor of the traveling twin as being essentially fully a result of the turnaround acceleration effect producing more the equivalent of a gravitational time dilation effect (see 24:40):

Edit: I forgot to add this video, which is where he explains the resolution (see 17:17 in):

Such an effect would be similar to the one in the Brian Greene video. Thus, David Butler's position is that the twin paradox is not explained by Lorentzian time dilation due to relative velocity differences but rather to the acceleration effects of the turnaround. However, having read numerous threads in this forum on the twin paradox over the years, the consensus here seems to be that acceleration effects of the turnaround are not a significant factor in the time dilation effect but rather that it is simply the longer world line of the traveling twin that accounts for the paradox.

To be honest, the acceleration resolution makes more conceptual sense to me than the world-line solution does. If you look at the Brian Greene video and replace the black hole with a long, strong turnaround with high acceleration, it seems to make great sense. To this day I can't put my head around the world-line solution only to say that it seems to work mathematically and I'll have to take it on faith.

Is David Butler wrong? Please explain how. More generally, the question is what is responsible for or what makes a greater contribution to the age differences in the classic twin paradox experiment, gravitational time dilation or SR-velocity related time dilation?

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#### A.T.

Thus, David Butler's position is that the twin paradox is not explained by Lorentzian time dilation due to relative velocity differences but rather to the acceleration effects of the turnaround.
If you describe the whole journey from the non-inertial twin's frame perspective, you will have to account (along with Lorentzian time dilation) for non-inertial-frame-effects (like position dependent time flow rate) to get the right age difference. Form any inertial frame Lorentzian time dilation is sufficient.

More generally, the question is what is responsible for or what makes a greater contribution to the age differences in the classic twin paradox experiment, gravitational time dilation or SR-velocity related time dilation?
Depends on the reference frame.

#### Dale

Mentor
To be honest, the acceleration resolution makes more conceptual sense to me than the world-line solution does.
I don't think that you can have the acceleration resolution without the world line solution. You have to use the worldline solution in order to calculate the amount of time dilation in the acceleration solution. I.E. the acceleration solution is simply a subset of the worldline solution.

#### PeterDonis

Mentor
If you look at the Brian Greene video and replace the black hole with a long, strong turnaround with high acceleration, it seems to make great sense.
Until you actually look at the underlying math, which makes it obvious that the two cases are very different, and that what similarities there are between them do not generalize to other cases. The "worldline solution", OTOH, is completely general; you can use it in any scenario whatsoever, even curved spacetime scenarios where neither twin feels any acceleration at all, but they still are different ages when they meet up again, which the "acceleration solution" can't explain at all.

This is why it's not a good idea to try to learn science from pop science sources. The video is a pop science source, even though Brian Greene is a scientist. Greene is a particular bete noire of mine in this regard, because he pushes the limits in his pop science more than just about any other scientist I know of. If you look at Greene's actual published, peer-reviewed papers, you won't find him saying the things he says in his pop science videos and books, because he knows he would never get away with them; his scientist peers would call him on it. But his pop science book publishers and video producers don't care, as long as it sells.

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#### Janus

Staff Emeritus
Gold Member
More generally, the question is what is responsible for or what makes a greater contribution to the age differences in the classic twin paradox experiment, gravitational time dilation or SR-velocity related time dilation?

If you are the traveling twin, then you could use the gravitational time dilation approach during acceleration, but you will still have to factor in time dilation due to velocity. You also have to factor in the fact that the distance between you and your sibling is changing during your acceleration.
Remember, gravitational time dilation is tied to the difference in potential. So if you have a uniform gravity field, a higher clock is at a higher potential and runs faster(even if the strength of gravity does not change with height). For the accelerating observer, his acceleration is equivalent to a uniform gravity field and since his sibling is higher in that field, his clock runs faster( the further away he is, the higher in the field and the faster his clock runs as measured by the accelerating observer.) But since our observer is accelerating, two other things are occurring, the distance between him and his sibling is changing(thus changing the gravitational time dilation factor), and the velocity between the twin are changing(introducing a velocity dependent time dilation).

If you are the stay at home twin, you just need to deal with the velocity dependent time dilation. It is only for the accelerating twin that the equivalent gravity field used above exists.

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