A _perfectly_ symmetric twin paradox cases

[Boing3000]

In a centrifuge, the direction of "down" changes; in a rocket accelerating in a straight line, it doesn't.

Direction with respect to who ? Is a 6 degree of freedom G-meter able to distinguish (small patch locally) that we are in a centrifuge and not in a ship ?

Also, in the OP's scenario with an observer on the surface of the Earth and an observer making a round trip from orbit to surface and back, it is impossible for the second observer's G to match the first, in either magnitude or direction, for the entire experiment.

Yes, I spot that error too, and that's why I came up with another setup which was supposed to fix this problem (by trying to make it symmetrical)

 

[Boing3000]

If your proposal was one large/fast centrifuge and one small/slow centrifuge. But you cannot apply a combination of the above 10 operations to get from one to the other, so they are not symmetric.

Thanks, that's clear now. I was applying the symmetry to each "voyager clock" separately (and locally, as the OP I think) and not appling it to transform one into the other (which seem to requires an external frame of reference, not just a local G-meter to assert symmetry)

 

[Dale]

Is a 6 degree of freedom G-meter able to distinguish (small patch locally) that we are in a centrifuge and not in a ship ?

Yes. They measure three directions of linear acceleration and three axes of rotation.

 

[PeterDonis]

Direction with respect to who ?

A gyroscopically stabilized local reference frame.

Is a 6 degree of freedom G-meter able to distinguish (small patch locally) that we are in a centrifuge and not in a ship ?

Yes. See Dale's response.

 

[stefanbanev]

So when we are talking about symmetry in physics this is not what we mean. In physics we talk about the symmetry of the laws of physics and the symmetry of the boundary conditions.

Well, apparently I'm not talking about "symmetry in physics" in general; in this particular context, the "symmetry" is not in the "symmetry in physics" but rather a specific reference to x2(two) records from x2(two) G-force meters observer on the Earth and observer on the rocket compare after round trip. Though, I definitely appreciate your lecturing regarding to "symmetry in physics" yet, I failed to see how it relates to the particular context, pls excuse me for my profound stupidity...

 

[Dale]

yet, I failed to see how it relates to the particular context

The particular context is a supposed difficulty with a "perfectly symmetrical" case. I was pointing out that the case is not perfectly symmetrical. So there is no difficulty. There is no expectation that the two non symmetric results should be the same.