The train in a tunnel paradox / ladder paradox visualized

Also known as the ladder paradox, the train in a tunnel paradox challenges one's understanding of length contraction in Einstein's Theory of Special Relativity. A long futuristic train goes through a shorter tunnel and is seen from the perspective of a trainspotter on the ground and from the perspective of a passenger on the train. The two accounts of what happens are wildly different, but they are consistent.

#physics #space #time #relativity #paradox

=== Technical details ===

The train is simulated as a Born-rigid body. Each vertex in its 3x3 mesh follow a piece-wise hyperbolic trajectory.

The video shows the "measured reality" and not the "observed reality". So what you see is what an inertial observer would measure, rather than what an hypothetical camera would record. I think distortions due to the "Terrell effect" would obfuscate the relativistic physics and make it much more difficult to discern and understand. After all, even a classical camera would record image distortions if light was sufficiently slow.

=== Useful links ===

=== Soundtrack ===

World on Fire by Andy Bird

[neveroul]

Fantastic visualization, I was really surprised when I saw that you don't have much subscribers, and quality of videos that high!

[Svuem]

This is sooo nice. As a physics student, these type of problems pop into my head on a regular basis but I can never quite figure them out in my head because I lack the intuition. This helps a ton!

[OpinioNathan]

The really crazy part: send a train going the same speed down an adjacent track into the tunnel from the opposite direction at the same time. The passengers on that train will see the LEFT door shut before the right. No interpretation is wrong, the order of events is just relative to the motion.

[Deathnotefan]

What isn’t mentioned, but kind of shown, is that, no matter how fast the train is going, the light pulse will _always_ be moving at the same speed relative to an observer on the train

If you are on the train and shine a flashlight forward, the beam will travel at 299, 792, 458 m/s to both an outside observer _and_ to you

This is why the events happen at “different” times to different observers

[ivanp]

I really like the track and its synchronization to the animation

[pathemep]

0:06 All passengers are died simultaneously. They all became a meat pulp. No one can see anything from anywhere.

[marangod]

The combination of an understandable example with an excellent choice of background soundtrack really tickles my inner scientist. I ended up sharing this with a likeminded friend and we spent a solid hour discussing various interesting physics theories. It's videos like this that make me briefly wonder if I could have continued with physics after school, before I remember how little fun the calculations can be in practice. Theory is still fun though, so thanks for adding some more fuel to that particular fire

[kernicterus]

If you're wondering why 94% of lightspeed was chosen, it's because at faster than that reality becomes so crazy that the buffet car not only has all the food that you wanted, but it prepares, serves, and charges you correctly!! Mental.

[mick]

Wow! I've never heard of this before. It's really fascinating. Great explanation and visualization btw

[DrEnzyme]

the thing that is crazy to me is that no matter if you're in the train or outside of it, you both see the light pulse travelling away from you at the speed of light. No matter how fast the train goes it has no chance of ever catching up.

[trombone]

Cool new representation, new take on relativity's simultaneity ! !
Looking forward to the game developments, too.
Great vid.

[TsantoulisX]

It is not complicated at all guys!! You have to remember and understand that it's the "now" that changes for every watcher (door A, door B, train front-train back etc), our brain sees the entire system (environment as we say in Greece) and gets confused because that's the way that he learned to operate (at non-relativistic speeds). Remember: there is no paradox here! The Present is what changes, it becomes diffused, and when you understand that, then you can better understand spacetime and the changes that happen in relativistic speeds and relativity and it's effects. Also, our brain must understand that what you see is not always what is happening.

[FloMiLe]

This is a really high-quality, concise video. Thank you!

I wonder whether you might consider modifying it a bit, though. From a didactics point of view, it would be really helpful if the part in which the train crosses the tunnel really distinguished between the two perspectives. That is, for the outside frame of reference the tunnel should be at rest the whole time. And for the train's frame of reference the train should be at rest while the tunnel passes it.

And just something very minor: I think it's more common to give the acceleration in units of "g" instead of "Gs". (There isn't a plural of meters "ms" or seconds "ss" either.)

[Draxis]

At closer and closer the speed of light everything ahead of you becomes instant and anything behind you becomes stuck in time. Meaning that light experiences no time at all, as everything is instant and in the past at the same time.

[RamHornBeast]

Thank you so much for making this a 2 minute video and not padding it out to the standard 10.

[xenajin]

Thanks a lot for this. Sent it to my groupmates and will probably spend a week discussing this😂

[TonyVallad]

Looking forward to see the game since I believe not many people can really imagine relativity in their heads. Even some people that think they can.

Makes you see the universe differently once you can "easily" imagine it !

[cameron]

I don't know why this popped into my recommendations, and I'm happy it did.

[wasylbasyl]

Beautiful animation! But there is one mistake at 0:19 - the train doesn't "appear" shorter, it just IS shorter.

[SALSN]

Very good demonstration.
Looking forward to the game!