Does acceleration solve the twin paradox?

Special relativity is known to make mind-blowing predictions, perhaps most notably the Twin Paradox, in which two individuals claim that the other person’s clock is doing something funny. There have been many explanations, including two videos, one here on the Fermilab channel and one by fellow YouTuber Sabine Hossenfelder. These two videos seem to contradict each other, but they really don’t. In this video, Fermilab’s Dr. Don Lincoln explains how the two videos can be reconciled.

Sabine’s video

Don’s first twin paradox video (with math)

Don’s second twin paradox video (without math)

Fermilab physics 101:

Fermilab home page:

[disgruntledwookie]

It took me way too long to understand the twin paradox and I have to say that the biggest cause of this delay was from science educators trying to avoid the math, using metaphors, simplifications, etc. As soon as I understood the Minkowski metric, things fell into place. Suddenly this whole debate about acceleration being the cause of time dilation or not seemed to be missing the point. The key detail of the twin paradox is that the two twins end up in the same reference frame but one of them travels through multiple reference frames (at least 2, assuming infinite acceleration at the turn around). But I think this is much easier to understand if we go one step further and assume that the two observers start at the same event and end at the same event (same point in spacetime), which is implied by the usual setup of the twin paradox. So we have two worldlines (paths in spacetime) which start in the same place and end in the same place, but one of them is a straight line and the other is not. Then you just need to account for the Minkowski metric and you see that the shortest (straight line) path between two events is actually the one with the longest proper time, any other path experiences less time. I realise this is a bit more involved but I think with some nice graphics and a slightly friendlier explanation it would help a lot of people get their heads around it. I don't think you can really appreciate what's happening without understanding the way distances (proper times) are calculated in spacetime.

[ankitjhunjhunwala]

This is a very elegant explanation. "Change in frame = acceleration" that's a great way to look at it. With this simple concept, you resolved the discrepancy between your and Sabine's analysis. Thanks!

[grievouserror]

I love when content creators respond to challenges to their videos raised by other creators. I especially love it when they're both held in such high esteem. Thank you for addressing the apparent tension between these two entries, it had been bothering me.

[josephmann]

Very cool sir; you are, once again, a truly fine physics teacher. Thanks for letting us tag along on the journey. May you and Sabine live long, prosper & continue to inspire!

[GuyNamedSean]

Oh man I love seeing dialogue between science educators like this. Doesn't matter to me if someone was wrong or someone had a better or worse way to explain things. Discussions like this only help me understand complex subjects better.

[walnutclose]

I like the "no acceleration" gedanken experiment you describe in your earlier video. Another way of showing that the time dilation does not occur specifically in the acceleration phases of the trip is to use a set of triplets. Leave number one on earth, accelerate number two toward the distant star, but as soon as you've reached cruising speed, turn her around and send her back to earth, and send number three on the entire trip to the star and back. You can make the accelerations experienced by two and three identical. When all three are back together again in one's rest frame, two will have aged less than one, but three will have aged less than either, showing definitively that the time dilation occurred during the entirety of the trip, including during the non-accelerated "cruise" phases. Just as in your experiment, it is the motion that matters, not the acceleration.

One way to show why acceleration itself doesn't explain the paradox is the use of two similar experiments, where we let the twin travel twice the distance, but still using the same acceleration.

In that case, the effect will approximately double. And so it can't be explained by the acceleration as we used the same acceleration.

[gareththompson]

I really liked what you said about how two people can say things that appear to be in conflict, but aren't. I have no idea how many times people have thought that I was disagreeing with them, when in fact I was offering my own perspective on why I thought they were right. But it has gotten pretty frustrating.

[MitzvosGolem]

Let's all say prayers for Physics girl channel Diana...She is very sick again in Hospital ICU long COVID again..

[Voimies]

But can we really say that its the rocket that inhabits two frames (without thinking about the acceleration)? I can see that everyone agrees that there are 3 frames, but couldn't you name them also as "stationary rocket", "the outgoing earth" and "incoming earth"? This paradox would be easier to understand by imagining two rockets in an empty space. The other one goes high speed in one direction and comes back. We can see that there are three different reference frames but the only way to decide which rocket experiences two frames is by an experiment that demonstrates the acceleration of the moving rocket. So the acceleration really is the thing that breaks the symmetry and it plays a key part in solving this paradox.

[tilik]

Thank you Don! I got in a lot of arguments over the twin paradox and always referred my opponents to your excellent video on the subject where you model the same scenario with 3 reference frames.

[xjuhox]

The only way to truly comprehend the "paradox" is to calculate the proper times of the two spacetime paths in terms of Minkowski metric. That is, the solution is a mathematical calculation.

[jakobthastum]

Being a huge fan of both you and Sabine... I'm so happy that you were both right - Keep producing these amazing videos

[Mr.Not_Sure]

There's another explanation I found in the book "Philosophy of physics". It's just as simple as:
Time passed for an observer is just length of his world line in Minkovski metric. And if you calculate, you'll see that observer in the rocket has shorter world line.

[EugeneKhutoryansky]

You are only talking about Special Relativity. In General Relativity, a single non-inertial reference frame is allowed for the spaceship’s entire journey. The person in the spaceship can believe that he is standing still by believing that there is a gravitational field present throughout all of space, and that gravitational time dilation is what causes him to be older than his twin.

[kbjerke]

Love both your and Sabine's channels! My mind *needs* stimulation! LOL Thanks for the video!

[rahularyaphysicist]

I love this channel and prof.Don sir’s explanation
So amusing, it’s been 3 years since I’m watching his videos…

[jean-marclugrin]

Thanks. I found your explanation much more enlightening, Adding acceleration makes a nice story with twins, but the clocks are much simpler to understand. Or at least to have a feeling of understanding. Good luck with some comments of FB physicists 🙂

[rkalle]

There are not only 3 reference frames but infinite many. The key point is that you have to stay in your chosen reference frame to do the math (how fast clocks are running). The travelling twin is changing velocity (from away from earth to back to earth) at one point regardless which reference frame you are choosing as long as you don't change this once choosen.
Yes, changing velocity is acceleration. And it will complicate the math to deal with a time consuming finite ac- or deceleration of the travelling twin. But all can be done just using the formulas of Special Relativity and some calculus.

[kabongpope]

Definitely think yours is clearer! Showing each object as being in a separate frame of reference makes a lot of sense.