1) The acceleration does not cause the symmetry breaking, it's the velocities that do.

Incorrect. The worldline of the traveling twin absolutely must not be a straight line in the spacetime diagram. Therefore the worldline must not be straight meaning that the traveling twin is accelerating. The twin could start out moving at constant speed and synchronize his clock with a traveler whose going towards Earth and then the two twins can compare clocks again when they pass by. That's one way of looking at it. But if that worldline represents an ideal clock which can instantaneously change directions without changing speed then it's still accelerating.

Please go back and read the actual document that the OP is discussing.

The question here is why does SR have an apparent violation of an assumed symmetry here. The answer is the specific velocities involved. If we consider two twins, then we have to introduce acceleration in order to change the velocity of one twin. However, the acceleration doesn't enter in to any SR calculation. We can replicate everything of importance in this scenario by replacing the twins with clocks that happen to pass by one another and happen to be synchronized when they pass by. This removes all acceleration from the scenario but preserves the difference in time dilation between clocks.

*This is because we are considering Special Relativity alone.*

Your education in physics appears to have led you to believe there is one and only one way to look at problems such as this. The following reasons are why you're wrong in this instance.

The reason that I look at this in one way is because that is the way it was laid out in the OP. The question asked in the document in question is how to properly explain the scenario without recourse to General Relativity.

1) In the first place the term **special relativity** as it is used by the majority of relativists today is that of physics in flat spacetime and not merely because the observer is accelerating. Had you extended your education to general relativity you wouldn't be ignorant of this fact.

I don't think that statement makes sense; you appear to have made at least one typo in your haste to insult me.

Regardless of the fact that we can consider Special Relativity to be a limiting case of General Relativity, if one sticks to the limiting case, then one sticks to the limiting case.

2) The only reason only SR was being considered alone was because the OP was unaware that traveling twin's point of view can be analyzed using general relativity. However most relativists would still consider this a problem in special relativity

I again suggest that you

*read* the document cited in the original post, where it is quite clear that the author is addressing a popular but unhelpful myth that the resolution of this "paradox" lies in General Relativity. This is also addressed in Bernard Schutz's relativity text, where he also points out that the scenario is purely a feature of Special Relativity alone and is entirely consistent within SR.

2) The differing rates of clocks at different heights is an effect from General Relativity which is irrelevant to this scenario. *This is because we are considering Special Relativity alone.*

Another error based on the common misconception that in modern physics (i.e. what is in current use by contemporary relativists) general relativity is defined as physics in curved spacetime, not about accelerating frames of reference.

You just reiterated my point that the difference in clock heights is a feature of GR. I said nothing about acceleration.

I wasn't talking about merely clocks. I was talking about actual physical twins, i.e. I wrote *..it is the acceleration itself which causes the stay at home twin to age more than the traveling twin...* Such twins can't accelerate instantaneously. And I was explaining the scenario from the accelerating twins perspective.

I was using a standard shortcut to talk of clock rates rather than relative time dilation.

This problem is treated *exactly as I just explained to you* in the text **Cosmological Physics** by John A. Peacock, pages 7-8. For the rest of the posters here other than you who don't have such a closed mind they can read all about this in that text which is online here - http://bookos-z1.org/book/2065579/30320e

I find it odd that you would attempt to prove your point through a citation that you assume is blocked to me in some way.

As Peacock writes, "The so-called paradox lies in the broken symmetry between the twins. There are various

resolutions of this puzzle, but these generally refuse to meet the problem head-on by analysing things from B’s point of view." Indeed, these resolutions generally refuse to do so because in the SR context alone, where is no "B's point of view" in the physical sense that there is no inertial reference frame in which B is at rest. This point is important

*because the paradox is presented as a supposed failure of the consistency of SR, so a resolution needs to show that SR remains consistent*.

Peacock shows that using the ideas of GR, one can produce a calculation that recovers the time dilation from a system of coordinates that GR can use. However, this cannot be viewed as a resolution of the "paradox" that demonstrates the internal consistency of Special Relativity.

Oyvin Gron, another well-known GR expert also treats this in the same way as I just described. It was either published or he used the notes to teach his students. I'll post it when I contact the author and get a copy again.

I am not surprised that someone might ask students to, as an exercise, run through the scenario in the context of GR. It is an exercise in Ohanion & Ruffini, since in GR, unlike in SR, one can create a system of coordinates in which the space twin is at rest in which one can work out the correct relative time dilation between the two twins. This fact is noted by Ohanion & Ruffini.

there are other ways of looking at scenarios other than the ones that you know about.

I thank you for pointing out that people might not know that when I speak of differing clock rates, that I am speaking of relative time dilation.