Relativity implies that a moving clock experiences less passing time than a resting clock (relative to an observer). The "slowness"-factor gets higher the closer you get to light speed, reaching infinity (i.e. impossible) precisely at light speed.
In the example the one twin travels to a distant star with an appreciable fraction of light speed, thus ages slower. Then, the twin travels back, again with an appreciable fraction of light speed, and still ages slower.
This is basic relativity theory. Maybe I understand the article wrong, but from what I read I understood that the twin should somehow "catch up" on his travel back.
It implied that the temporal effect of the final deceleration was analogous to how when you throw a ball up in the air and catch it, it only momentarily feels heavier than before you threw it. The twin only momentarily looks younger because the clock has to speed back up during the final deceleration and a naive calculation neglects this step.
This isn't that bus that will explode if it gets slower than 60 mph.
According the the article, during the final deceleration, the space traveller will age 20 or so years. In other words, for the traveller, that deceleration phase is going to last 20 years.
Or they just burst into flames. It is like burning up on re-entry.
You are thinking of acceleration in the same way you were taught to think about velocity, but that doesn't work in this case.
In the example the one twin travels to a distant star with an appreciable fraction of light speed, thus ages slower. Then, the twin travels back, again with an appreciable fraction of light speed, and still ages slower.
This is basic relativity theory. Maybe I understand the article wrong, but from what I read I understood that the twin should somehow "catch up" on his travel back.
I'd love to be corrected.