I Is the Scientific American Article on the Twin Paradox Accurate?

[Sorcerer]

I know this publication is not peer reviewed, but when I saw this article it was exactly the same way I came to “understand” the twin paradox myself. I literally did this exact calculation (with a different gamma value).

So I was wondering if the article was valid. If it isn’t, where isn’t it? That way I can correct any misunderstandings that I don’t know I have. Here is the article. Thanks for those who take the time to read it and reply.

https://www.scientificamerican.com/article/how-does-relativity-theor/

 

[Borg]

I am no expert on the Twin Paradox but the article actually cleared up some issues that I had with understanding it. Was there something in particular that you were concerned about?

 

[Sorcerer]

I am no expert on the Twin Paradox but the article actually cleared up some issues that I had with understanding it. Was there something in particular that you were concerned about?

Just want to make sure there are no hidden subtleties I might have missed. As I said, working out an identical problem is how I came to understand whatever I do about it, and I just want to make sure there are no easy to miss subtleties.

 

[Borg]

I don't see anything wrong with it but I pinged one of the members that is more versed in the topic. He should be along soon enough.

 

[Ibix]

The Scientific American article covers the Doppler way of explaining it, yes. It's nice because it's firmly rooted on observations made by the twins.

I'd say the only thing missing is why naive time dilation leads to a paradox, which is just that if the traveling twin wishes to "stitch together" the inbound and outbound inertial frames he needs to remember that "at the same time as he turns round, on Earth" refers to two different times. Accounting for that time difference accounts for the age difference.

 

[phinds]

I think Borg may overestimate my knowledge in this area but I see the article as a correct explanation. I have always found it unnecessary to take acceleration into account in the twin paradox. As nearly as I can tell, acceleration is mentioned because a real traveler WOULD have to experience acceleration to get back and it's a good way to point out the asymmetry in their worldlines. Contrarily, I like to think instead of a "Traveler's clock time" as making the trip, as follows (using the figures in the article)

Traveler1 passes Earth at .6c, syncing his clock with that of Homebody exactly as he passes Earth, and when he get to the destination, Traveler2, who is traveling at the same speed but in the opposite direction, syncs his clock with that of Traveler1. Traveler 2 then makes the trip back to Earth and all is as explained in the article expect that it is only "clock time" that makes the physical trip and there is no acceleration involved. The "Traveler's clock time" at the end of the trip (as Traveler2 passes Earth) is 16 years and the Homebody's clock reads 20 years.

Post 24 in this thread:
https://www.physicsforums.com/threads/twin-paradox-and-the-body.940272/page-2
Shows a spacetime diagram that you might also find helpful.

LATER EDIT: and by the way, I should note for the sake of completeness, that although the scenario I presented avoids acceleration, it does NOT (and cannot) avoid the asymmetry of the situation, which in my scenario is due to the fact that the Traveler1's clock and Traveler2's clock are in different rest frames.

 

[vanhees71]

I think, the article is essentially correct making again much ado about nothing. Everything can be described by the standard hypothesis that an ideal clock shows its proper time and a living being ages according to this well-defined (scalar!) time measure, i.e., you can calculate each twin's aging by using the simple formula defining the proper time along each twin's time-like worldline
$$\tau=\frac{1}{c} \int_{\lambda_1}^{\lambda_2} \mathrm{d} \lambda \sqrt{g_{\mu \nu}\dot{x}^{\mu} \dot{x}^{\nu}},$$
which is even true in the most general case of GR.

Of course, the author is also right in stressing that you don't need GR to describe accelerated motion as long as no gravity is essential for the situation under investigation.

 

[robphy]

Yes, the article looks correct... and, as others have pointed out, it uses a Doppler approach (although not fully following Bondi's k-calculus treatment since it appeals to length contraction. [Bondi was quoted at the top of the article.]).
Note the clock comparisons are "visual comparisons of clockface readings", which involve the Doppler factor (k=2 for v=(3/5)c).
(The more typical textbook comparisons use "time dilation", which involve the time-dilation gamma factor (\gamma=5/4 for v=(3/5)c).)

Here's the spacetime diagram shown in the SciAm article
(which I pasted here because I couldn't easily see it in my browser..(maybe a pop-up blocker is running?) I had to manually build the URL).

Here is my version of the diagram (taken from my PF Insight https://www.physicsforums.com/insights/spacetime-diagrams-light-clocks/ ),
where each diamond would represent two ticks in the article's setup.
The diagram includes enough data that can be used with practically any explanation that works [including an arc-length calculation of proper time].

To see the apparent distance "4.8" in the article (which would be 2.4 on my diagram above), one has to draw a line parallel to Bob's space-axis (the spacelike diagonal of his diamond), then construct Bob's diamonds along it.

I've drawn it below in full-scale [so the homebody interval is 20 and the distance is 4.8].