I Reference systems and apparent counter-explanations on Twin Paradox

[Hak]

In the Twin Paradox, I don't understand how it can be determined which of the two is moving and therefore which is the younger. What I realised is that the fact that the Earth is not an inertial system is irrelevant: just consider a planet that is stationary in an inertial system and start the shuttle from there. The Earth travels at a constant speed through space, so time always flows the same way: if we launch a manned object into spacez there are two possibilities when it returns:
if it travels faster than the Earth, the astronaut will be younger than its twin on its return; if, on the other hand, it travels at a slower speed than the Earth, the astronaut will be older on its return. But does the Twin Paradox explain the theory that the spacecraft's time should remember the accelerations and decelerations it has made?
Strictly speaking: for example, Wikipedia's explanation seems contradictory to me: in SR's it says that the Earth is an inertial system, but it is not, since the twin on Earth watches the other's journey in a continuous manner: outward journey, arrival and return. The traveller, on his way out, watches the Earth revolve around the Sun continuously until at the point of return he has lost $d''-d'$ years (one moment the Earth is at perihelion, the next, for example, at aphelion several years ahead). Why? Instead, in the one with the GR he contradicts everything he said before: the systems are now symmetrical and the dilation of time is due to the strong acceleration in the reversal of direction not to the relative velocity. And if the traveller described an arc of a circle wider than the Earth's orbit to return? If Wikipedia considered the Earth an inertial reference system, all the more reason that the traveller's should not be so?
Thanks.

 

[Ibix]

The Earth is intended to be treated as inertial, and in fact the deviation from that is tiny. If that approximation bothers you, leave the Earth out of it and just use one twin on a space station in deep space and the other on the rocket.

Neither of the twins "is moving" - both can consider themselves at rest. The whole point of the paradox is to teach you that "the fast moving clock runs slow" is not a general rule, since it would lead to a contradiction in this case. That rule only works as long as the person applying it is using an inertial frame in which they are at rest. The travelling twin is not inertial for the whole journey, so is the one making the mistake.

 

[Dale]

I don't understand how it can be determined which of the two is moving and therefore which is the younger.

Using an accelerometer.

What I realised is that the fact that the Earth is not an inertial system is irrelevant: just consider a planet that is stationary in an inertial system and start the shuttle from there. The Earth travels at a constant speed through space, so time always flows the same way

For clarity when I set up the twin’s scenario I usually say “home” rather than “earth” and simply assert that the scenario is in flat spacetime and the “home” twin is inertial.

That is the intention of the scenario, even if it is not clear. The scenario is in flat spacetime (no gravity) with one twin being inertial. That twin has an accelerometer that always reads 0. The other twin has an accelerometer that is nonzero at the turnaround. Thus the two twins are unambiguously distinguished.

if it travels faster than the Earth, the astronaut will be younger than its twin on its return; if, on the other hand, it travels at a slower speed than the Earth, the astronaut will be older on its return

The “other hand” is not possible. I encourage you to sit down with pencil and paper and work it out.

 

[ersmith]

In the Twin Paradox, I don't understand how it can be determined which of the two is moving and therefore which is the younger.

I strongly encourage you to read and digest the insight article titled "When Discussing the Twin Paradox Read This First", which is pinned at the top of the forum. As the insight points out, the solution to the twin paradox lies in comparing the lengths of the paths followed by the two twins through spacetime, *not* in determining which of the two is "moving" (motion is relative, after all).

That said, it *is* possible to analyze the basic twin paradox in terms of inertial reference frames. There are THREE inertial reference frames of interest in the twin paradox: one in which the Earth is at rest, one in which the "traveling" twin is at rest on the outbound portion of their journey, and one in which the traveling twin is at rest on the inbound (return) portion of their journey. You can analyze the situation using any of these 3 frames and the result is always the same: the "traveling" twin ages less than the Earth-bound twin. There is no inertial frame in which the traveling twin is always at rest, because in order to turn around and return to Earth they must accelerate (become non-inertial).

 

[Hak]

I strongly encourage you to read and digest the insight article titled "When Discussing the Twin Paradox Read This First", which is pinned at the top of the forum. As the insight points out, the solution to the twin paradox lies in comparing the lengths of the paths followed by the two twins through spacetime, *not* in determining which of the two is "moving" (motion is relative, after all).

That said, it *is* possible to analyze the basic twin paradox in terms of inertial reference frames. There are THREE inertial reference frames of interest in the twin paradox: one in which the Earth is at rest, one in which the "traveling" twin is at rest on the outbound portion of their journey, and one in which the traveling twin is at rest on the inbound (return) portion of their journey. You can analyze the situation using any of these 3 frames and the result is always the same: the "traveling" twin ages less than the Earth-bound twin. There is no inertial frame in which the traveling twin is always at rest, because in order to turn around and return to Earth they must accelerate (become non-inertial).

Thanks for your advice.

 

[Nugatory]

You can analyze the situation using any of these 3 frames

And at the risk of stating the obvious.... @Hak it would be a really good exercise for you to actually try doing this. You'll need the Lorentz transformations and high-school math, no more, and you will get more out of this effort than you have from all of your PF threads so far.