# Reference systems and apparent counter-explanations on Twin Paradox

• I
• Hak
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.

PeroK
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.

topsquark
Hak said:
I don't understand how it can be determined which of the two is moving and therefore which is the younger.
Using an accelerometer.

Hak said:
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.

Hak said:
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.

topsquark
Hak said:
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).

Dale, Nugatory, PeroK and 1 other person
ersmith said:
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).

ersmith said:
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.

ersmith, Ibix, Vanadium 50 and 1 other person

## What is the Twin Paradox in the context of reference systems?

The Twin Paradox is a thought experiment in special relativity where one twin travels at a high speed into space while the other stays on Earth. Upon the traveling twin's return, they find that they have aged less than the twin who stayed on Earth. This paradox highlights the effects of time dilation, where time passes at different rates for observers in different inertial frames of reference.

## How does special relativity explain the Twin Paradox?

Special relativity explains the Twin Paradox through time dilation, which is a consequence of the Lorentz transformation. When the traveling twin moves at a significant fraction of the speed of light, time for them slows down relative to the twin on Earth. Since the traveling twin changes inertial frames when they turn around to return to Earth, they experience less elapsed time compared to the twin who remains in a single inertial frame.

## Why doesn't the Twin Paradox violate the principle of relativity?

The Twin Paradox does not violate the principle of relativity because this principle states that the laws of physics are the same in all inertial frames, not that all frames are equivalent in non-inertial situations. The traveling twin experiences acceleration and deceleration, which are non-inertial phases, breaking the symmetry between the twins' experiences. Therefore, the situation is not symmetric, and the difference in aging is consistent with the principles of relativity.

## What role do reference systems play in understanding the Twin Paradox?

Reference systems are crucial in understanding the Twin Paradox because they define the framework in which measurements of time and space are made. The Earth-bound twin remains in an inertial reference frame, while the traveling twin switches between different inertial frames when accelerating and decelerating. The differences in these reference systems lead to different experiences of time, which explains the apparent paradox.

## Are there any counter-explanations to the Twin Paradox that challenge special relativity?

There are no valid counter-explanations to the Twin Paradox that challenge special relativity. Some apparent counter-explanations might arise from misunderstandings of the principles of relativity or the role of acceleration in the thought experiment. Special relativity, when correctly applied, consistently explains the differential aging of the twins without contradiction.

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