Train Tunnel Paradox Visualised (Animating Einstein's Special Relativity)

Let's visually discover the intuition behind Einstein's special relativity. Especially, the idea behind relativity of simultaneity. The train tunnel paradox, a.k.a the ladder paradox, a.k.a the pole barn paradox is an excellent example of that.

Chapters
00:00 - The Train Tunnel Paradox
02:00 - The Door Mechanism
03:24 - Visualising The Platform reference
04:47 - Visualising The Train Reference Frame
07:39 - Check out Brilliant for FREE
08:45 - Relativity Of Simultaneity
09:20 - Challenge question
10:35 - Bonus

This video is sponsored by Brilliant

[robertvangeel]

Great animation. The doors fall faster than the speed of light. But that's a minor detail that does not fundamentally change the logic, just a flaw in the animation itself.

[martinrizzo]

Years ago, I had learned this painstakingly, with vectors, formulas, etc., and some not-so-clear illustrations. But the animation you've created is pure gold!! Along with your excellent explanation, it makes everything become very intuitive and natural. Thank you very much, you are very talented, we need more science communicators like you.

[shawnharnden]

The example at the end where you and your mom being born at the same time is a bit different. The triggering mechanism is not from an outside perspective, but your mother is the trigger. This would be like one door in the tunnel triggering the other... theortically the faster the train is going, the closer the events would appear to be simultaneous, but never be simultaneous until the point v=c and after that time no longer matters anyways.

[kenhaley]

There are 3 parts to understanding special relativity. (1) Time dilation, (2) Length contraction and (3) Relativity of simultaneaty. This video does a great job of demonstrating the third. In general, without taking all 3 parts into consideration, you can always create these apparent paradoxes. Nice video!

[kookeekwisp]

Can't wait for the video later explaining what happens when you keep the doors closed.

There's objectively zero chance that i'm the only one that's curious

[rajanvenkatesh]

"Everything in relativity can be derived from that postulate (of c being constant)". Learning for the day. Well done and thank you, Mahesh.

[thrilhousesf]

This also shows that length contraction really is just relativity of simultaneity as well. Very insightful animations!

[TheKeirsunishi]

I wish you had been my physics teacher at school, your passion, excitement and ability to simplify complex concepts is second to none.

Edit: careful guys, we've got a badass in the replies below

[gustavojacobina]

This also shows how the space time interval between two events stay constant. In the first event, there is a distance d and the time between the doors closing is 0. In the second example, since the distance is shorter, the time difference has to be more than 0 to preserve space time interval.
Amazing

[kyrylosovailo]

Best visualisation of this paradox. As simple as it is genius.

[Oscar.]

Your doors seem to go faster than the speed of light. Leaving that detail aside, this is a great explanation!

[gueropalma]

I never considered a situation like this. It's really amazing how spot on relativity describes the relationships of objects in motion.

[feelthebluesgaming]

I have been diving deep into relativity and the mathematics involved, but these type of videos are so important to build the visual intuition to go along with it, thank you 🙏🏼

[HappyBeezerStudios]

My favorite example of that is the lifetime of particles. They fly further than they should, but form their perspective everything is extremely compressed.

[michigantim]

Great video I remember encountering this paradox when I was a student of physics. One slight tweak, the doors fall faster than the speed of light in your animation. I know it doesn't really affect the analysis but it still comes off a little funny.

[luiztosk]

pure genius. I was 100% stuck on a purely Newtonian worldview and didn't realize events wouldn't happen at the same "time" until you showed it.

[TheAffe]

love your videos! you are incredibly good at explaining those complex things! Keep it up

[satabdikakati]

The music you put on the background of animation is very cool❤

[loadstone]

There are a couple things I don’t agree with in this video. First of all, you don’t need a detection mechanism, you can give the doors initial velocity and constant above the tunnel. The issue is when the doors close in the video, they’re closing faster than the speed of light, which is not possible, because the doors displace a bigger distance in less amount of time compared to the light signals, clearly it’s travelling FTL. Furthermore, that’s not what the frame of reference of the train would look like. The tunnel would be distorted and distances would seem to be expanding and contracting around the train, it’s not just a length of the tunnel tunnel coming at the train, the whole tunnel has to be dilated around the train which isn’t very easy to describe with words on a YouTube comment.

[ninadgadre]

Kudos for syncing the music and key points of the simulation. Nice touch. Thanks for being the best desi science creator out there!