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

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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.

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.

i am so glad that you are popularising "relativity of simultaneity " in all your videos . i always used to wonder why time dilation and length contraction were so popular, but everyone ignored relativity of simultaneity. most of the paradoxes can be resolved if people just remember to take relativity of simultaneity into account

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!

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

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.

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

Imma be honest with you Mahesh, I don't think that thumbnail train is fitting in that tunnel regardless of its proximity to c

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

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

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

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

Hey, congrats on 100k subs! So glad you're gaining so much popularity, more people need to see these videos!!

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.

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

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

Love the enthusiasm. And the visuals and your explanation makes it easy to understand. Keep 'em coming.

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 🙏🏼

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.

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

I've had an intuitive understanding of this for quite a while, but I've never seen it presented like this. This visualization will be super helpful for many people! Thank you!

Congratulations on the 100K subscribers, love the content❤

If every science teacher were as passionate as you, there would be a shortage of space in universities...

I've seen this explanation before - but it's still pretty mind blowing. I think it was one of the first times I really started to "get" relatively - how it applies equally to instances in time, as well as space, and how we each experience the universe just a little differently.

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 RU-vid comment.

This is similar to twin paradox but instead of popular idea of time dilation, we talk about the less popular idea length contraction

Your videos are always amazing!! Great work Mahesh

What an excellent video! So satisfying. I really feel like I *finally get* relativity of simultaneity. It was like the last piece of the puzzle that was missing. Thank you!

Exceptional video, great explanation. I would consider putting a static mark in the center of the light wave just to make it easier to see that how the circle expands.

Great job on the animation! A picture is definitely worth a thousand words!

I had been mulling over this idea for a while - the logic behind length contraction/ time dial action just wasn’t ’clicking’ for me, as you mentioned. I couldn’t digest how in special relativity, simultaneity isn’t absolute - it made no sense no matter how I thought of it. That’s why I’m not exaggerating when I say that this animation resolved my dilemma so well it made my eyes tear a little bit. Thank you so much, this is wonderful!

Just taught this in my modern physics class. My old teacher Johnny Evans put a twist on it to entertain us, calling it the Batman problem: Batman runs a battering ram into the Joker's hideout, but the Joker tries to trap Batman by closing two doors quickly. In Batman's frame, his battering ram no longer even fits in Joker's hideout, but it's ok bc he says the farther door closed first. Probably my favorite thought experiment in relativity.

I love how Relativity of Simultaneity always creates an illusion 😂

now we need to see the perspective of an observer walking along the train at half the speed of the train! I really would like to see the spectrum of different movement speed ratios. if we do it nicely and plot some stuff, we could be able to actually map out lorentz transformations :)

Man I Love your videos so much, u post such great vids which helps us understand the concepts easily

When I clicked on the video the first idea that came to my mind to resolve this paradox was that the doors would fall at different moments when viewed from the trains perspective... And that's no cap! Great video btw!

If we were to remove the current trigger system and replace it with a timing system would that change anything? Let's say I am able to perfectly time the doors to drop based on the time I know the train will arrive, and I have two independent clocks attached to each door that can trigger at exactly the same time without an external signal. I have now removed the signal delay that is demonstrated in this video, would there be still be delay between the two clocks that control the doors?

When there is causal relation between two events, they can't be simultaneously or change orders, no matter which reference frame you are looking from

What an incredible video, I've always found this hard to visualise but now it's hard to imagine life if light wasn't constant. It's so nice to see it all come together.

This finally helps me understand the concept. Previously I had heard something like: "the speed of light is the same to all observers" and had heard it explained in a way that would mean passengers on the train would "observe" the light traveling at the same speed if they were stationary or moving quickly, but that's probably the most confusing way to explain it. This viewpoint you show in the video-- from an "observer" outside the train-- makes much much more intuitive sense to explain it.

Mahesh sir is the Feynmann of this era as far as iam concerned because You are explaining things in a great way for everyone. Like him,you simply things in a concise way. Thank you for your teaching. Who are all agreeing ?

For anyone who has got a problem with the doors: You can also think about the experiment in a way that there are two persons, one on each end of the tunnel. The first one is located at the far end of the tunnel and the other one at the near end of the tunnel. They both have one watch each and they synchronise them with a light signal that is send from the middle of the tunnel. The one on the far end is supposed to stop his watch when the front of the train is at his position. The other one is supposed to stop his watch when the end of the train is at his position at the near end of the tunnel. From their perspective the watches start at the same time as the light reaches them at the same time. Now the train moves at a certain speed so that its length is contracted to the exact length of the tunnel. As a result both of them stop their watches at the same time and they read the same numbers on their watches. So from their point of view the front of the train was at the far end of the tunnel at the same time as the end of the train was at the near end of the tunnel. From the trains perspective the synchronization of the watches failed. The one on the far end of the tunnel starts much earlier as it moves towards the origin of the light signal and the one on the near end starts much later as it moves away from the light signal. So from the trains perspective the watch at the far end of the tunnel was already running for quite some time when the watch at the near end of the tunnel starts. Now as the tunnel moves the length of the tunnel is contracted so that it is much smaller than the train and the far end of the tunnel reaches the front of the train first. When that happens the watch at the far end of the tunnel stops. Now the tunnel moves on and the second watch stops as that end of the tunnel passes the end of the train. After stopping the watches even from the trains perspective both watches will read the same numbers on them. So between starting and stopping those watches the same amount of time passed. But from the trains perspective they didn't start at the same time in the first place. So an observer on the train would agree that both persons on the tunnel read the same amount of time on their watches but for the observer on the train the events didn't happen at the same time.

Hi, I really love your video, your videos not only answer a lot of questions I have, it also make me think about things and make me question even more, hence pushing me even further and learning more!!! I just graduated from high school this year, and only learned a little about special relativity but tried my best to make sense out of how dependent events affect one another, so that if B depend on A, B will be occuring after A from any frame fo reference (I tried) my attempt (Conclusion at the end): consider observer1 to be O, observer2 to be K Sensor A, B, and C are stationary relative to O (observer1) (these sensors light up when received light as signal), while K is in relativistic motion to O To simplify the case, let O,K,A,B to be collinear so that they are positioned like K B O A, I want B to be dependent on A, so the mechanic within can be seen as O send out light to A, upon receiving it, A then send light to B Then, as B always depends on the light sent out from A, from either frame of reference of O or K, B will be occurring after A Up to this stage, there is no issue. The main issue I had is that I always feel like I can find two events that are not dependent but look the same as A and B so that there exist a frame of reference that C happen before A So I try to see what happen if I add another sensor C that locate in the same place as B K---C--O--A Unlike other sensors, sensor C has an internal clock, such that from O's perspective, if a light is sent to C from O the moment light is sent to A, then C will light up the same time as B (This can be achieved by adding a short delay by the applying the clock) Thus, it is interesting that from O's perspective, setup like K BOA will look the same as K COA Now that C and A are independent, I want to see if i can find a frame of reference that C will happen before A Now let's investigate whether C can ever be observed by K to occur before A As it is setup like K COA, to utilize the simultaneity to let C to happen early O should be moving toward the right in some velocity v (0

I usually wait for ten good videos from someone before I subscribe, but this was a one-video subscription for me. I agree that there is much greater insight when one learns by oneself rather than learning from others. I've learned several things on my own by thinking hard about it. In some cases I already knew what the resulting answer should be, but figuring out why on my own gave me greater insight and changed my life.

We need these types of teachers who can teach physics intuitively

One inaccuracy in the animation is that the doors should be closing slower in the train's frame compared to the tunnel's frame! Great video though. I know it's the correct answer, just one small correction 😉

I love that you break this down for the layman dummies. “They”needed it. My friend said to say thanks 😢😂

I remember, in Einstein's own book, "Relativity theory" he demonstrates the relativity of simultaenity quite similarly using a train and two lighning bolt hitting the rail line simaltaenously compared to rail track. The more I know about relativity, the more I admire how far and deep that man's vision went a century before us!

But i have a question. In the trap setup's perspective, both doors fall at the same time, but in the train's perspective, the rightmost one falls first before the leftmost one. It does not make sense to me

4:41 that is not possible, because the door is closing at a speed faster than light :P

my relativity teacher used the 2m car into the 1m garage example, and the garage had a wall at the end. He showed the elegant example of the stationary garage, where the car contracted to 1 m and therefore fit the garage. Then for the other reference with the stationary car and the 0.5 m garage running towards it his very pragmatic explanation was (and as much as it was prosaic, it was essentially the same thing illustrated here) "the ass of the car has no way of realising that the face of the car has planted into the wall at the end of the garage before the whole car is smooshed into the garage, because the signal from the face can travel towards the ass at most at the speed of light" and it was so funny I still remember that 15+ years later

So I’m not entirely sure, but from my understanding relativity of simultaneity involves speed and position. So two things can only be simultaneous if they happen at the same time at the exact same position and/or the exact same speed in that specific reference frame; since your birth and your mom are at the exact same position, the only possible way they could be simultaneous in any reference frame, would be if your mum is traveling at the speed of light at her birth (compared to the observers reference frame, so she could also be standing still and the observer traveling towards her at the speed of light) and then give birth to you. Since the light is traveling at the same speed as your mom, all information about her life (and thus also your birth) gets to the observer at the same time. But since it‘s not possible to travel at the speed of light, these two events will always be after each other. Never studied physics though, so correct me if I’m wrong

Time "literally" slows down for the moving object and it becomes more noticeable as the moving object approaches the speed of light. This can be visualized by leaving the 4th dimension and coming to the 5th dimension, where we would literally be able to see "time" doing things. To a 5 dimensional being, the 4th dimension would appear as a collection of multiple "freeze" frames of time (like a video made of multiple images) and the faster one would move in the 4th dimension the lesser these frames would be, however, each of these frames would be stretched for that moving object. For example, to cover 5 years in time, an object would take 10 frames. Now as the object traveled near the speed of light, these frames would become less, now say, it took just 5 frames to reach: Travelling at a normal rate: 1 2 3 4 5 6 7 8 9 10 Travelling near 'c': 1 2 3 4 5 However, in the second case, each frames (among the 5) will be stretched and thus both arrives at 10 years into the future at the exact same instant but with a different time-elapse. 1 2 3 4 5 6 7 8 9 10 (No. of frames, when travelling at a normal rate) 1 2 3 4 5 (No. of frames, when travelling near the speed of light) Hope, this will make the visualization easy for our Mind(s), to understand and visualize the length contraction scenario.

Oh man, I thought about the doors falling at different times but animating the mechanisms make the reason intuitive.

Einstein would very likely be proud of you for this video! 👍 Thank you, this was amazing.

im sorry but it seems you're missing something critical here. you assume a requirement for "sensors" or "for the doors to trigger at exactly the right time"....and this is required for your solution. but what if none of that was relevant? what if the doors JUST SO HAPPENED to be dropping at the time, with no mechanism involved whatsoever? what if the doors dropping was a random occurence unrelated to the passing of the train?

I had actually figured it out in the first minute of the clip, funny enough I have had thought a lot about this sort of problem in my head in the past, so the solution was pretty easy for me... Some SCI-FI shows or games actually get the time dilation right as well, so when you see space ships go faster than light, they seem squish up or are streched out a crazy distance just before they hit light speed, so even from watching those shows and thinking about how and why the ships seem to squish up or are stretched out when going to light speed already helped me with this Answer

It would be fun to run the animation with a different triggering mechanism, namely, using the first light to trigger the doors directly but only after a timer count down. It would be so cool to see time dilation save special relativity from this modified version of the paradox.

This video is litrally amazing... Super excited for the future of this channel🎉

I knew the answer before the video. I remember hearing about this in high school, but I still thought to myself, "Ef, you Einstein, that trains getting cut in half." Thanks for making a video that helps me understand the answer, not just know it.

man, you have the coolest shirts ive ever seen!! where do you get these?! 😂 btw fantastic animations...this was too good !!

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

I understand why you added the slowmotions around 07:10, but for me they actually obstruct the understanding and reduce the observability. Reason: I move my screen according to the speed of the tunnel to make my brain realize that the train is at rest, while the tunnel is moving. However, due to the slowmotions it's difficult to adjust the speed of my monitor. I still appreciate the video though, don't misunderstand me :)

How was Einstein able to come up with such an exact theory? This is mindboggling.

Not sure if this comment will be seen, but 1. I understand that the speed of the doors is in consequential to the paradox. 2. I nevertheless found their apparent faster-than-light speed to be a distraction (in fact, id first intuitively wondered if their speed was going to factor into the resolution of the paradox - detracting from the actual experience of intuiting the resolution from the animation itself) I think this could be easily cleaned up, and done so i. A way that enhances the physics animation. Instead of thinking of them as doors, think of them as a light beam that shines from above and hits the detector (To scale this, the train/tunnel must be much shorter and more elongated to give the light enough time to shoot from top to bottom) But i think itd make the point just as well, without the magic doors, to present the paradox as "the train doesnt block either beam from frame where train is 'shorter' than the tunnel AND doesnt block either beam when it is 'longer'"

You have so much enthusiasm and excitement it's refreshing! and thanks for explaining this, I'd never really asked the question though DID know the threory.

Thanks @FloatHeadPhysics Great video. Just out of curiosity, what train speed did you use and what software did you use to make the animation?

Really good explanation. The visuals are perfect for this problem. Congrats!

This hangover is going to last a while. Great job Mahesh. Keep up the good work.

Mahesh, you're a gem, I understand most of these concepts, but trust me your explanations and visualization make it intuitive. Love from Lahore, Pakistan.

Great video man. I've already seen the solution to this paradox mainly by equations and lorentz transformations, but seeing from a brand new perspective is incredible. Also, while watching your video, I thought of a question on this paradox that I found interesting. What if instead of 2 separate doors, it was a box, where it was supported by a stick in the middle. Instead of a signal being created, the stick is pushed and the box released. I believe in my mind that the box being a solid object it would stay rigid and both doors would close at the same time in all referencial frames. But when whatching your video I thought that the information of the stick being taken off cannot move faster than light, hence part of the box "thinking" the stick is there while the other part of the box is already falling down. Hope Im right on this one. Keep the great content!

This's mind-blowing! 🤯 I never imagined it like this, but obviously that's exactly how it happens! There's no paradox at all, we're the paradox! 😂

i saw this one explained with a space-time-diagram ... i got it there somehow ... but yours makes it very clear!!

I love how the key events in the clip are synced with the music. And great video overall.

I remember a similar paradox on another video using light-activated railway signals. Basically, a person on a train traveling near the speed of light emits a flash of light just when he is in between two mechanical railway signals on the ground, parallel to the train. For an observer on the ground, the signals will drop simultaneously, but for the observer on the train, the signal farther in the direction of travel will trip significantly earlier than the one farther back.

Great animation! And your enthusiasm really conveys to the viewer, it was a great watch :)

This was an awesome video! The visuals really help to understand the concept!

My immediate intuition is that the people in the train just see the door at the end of the tunnel fall before the door at the beginning of the tunnel.

Wow! That truly made may jaw drop. Very intuitive explaination!

Bro... Your work is incredible. I really appreciate you explaining physics in a very perceptual way..

This is incredible.. more incredible due to the way it is presented by Mahesh.. kudos..

great video. perfect explanation. you broke it down just enough to the point where it was easy to understand but not so much that it felt repetative or oversimplified.

Whoever did this illustration Ravana, he’s more real than any Ravanas in movies. Great job 👏

Btw from this you can also clearly see that in the first refrence frame we're seeing it as an external observer who is moving with respect to time so the gates appear to close simultaneously but for the second reference frame we're seeing it from the trains perspective which is moving at the speed of light so for it time does not move simultaneously thats why the gates drop 1 by 1... The Physics of our universe is just so Brilliant yet complex..... Its Beautiful ❤

"Now at full spee-" "Did you see it?"

Beautifully explained. Fine work, sir.

Wow thats insane! The key thing to all of this, that speed doesnt actually exist, only relative velocity does. If you accelerated whole universe in one direction at 99.9999% speed of light, nothing would change.

Hello, I love your videos and you way of simplifying concepts and equations. I hope you make a video about general relativitty soon

You’re blowing my mind. I love this. Thank you 😊

What would happen in a scenario where the doors stay closed and the train stops in the tunnel? I cant quite understand because from the track perspective the train would fit inside and when it stops it would get too big for the tunnel, and from the train perspective it would be too big to fit in the first place. What is it that i am missing?

Perfect explanation and visualization!!! 👏👏👏👏

I think that visualizations on paradoxes may be the only reason i ever understood them as a kid, this made the theory of special relativity make so much more sense and make me understand that Space and Physics are nowhere near as "straightforward" (lol) as they seem, man i wish i tried harder in my physics class in school, i think i would have had a strong sense of accomplishment if i did, and if i managed to find a way to understand all of this myself.

This reminded me of the ladder in the farm paradox where the solution is "both sides are in different time events. I didn't realize that but this... This makes me understand more what he was talking about

My take on the challenge question as a youtube science enjoyer. For an outside observer travelling at some speed: depending on its speed, it would seem more and more like you and your mom were born at the same time the closer the outside observer is to the speed of light. It would certainly look like you were born at the same time if you went really fast, but there would always be a small difference where your mother would be born first. The only way to get around this is if you were to travel at actual lightspeed, which is impossible because: 1. Massive objects require infinite energy to accelerate to the speed of light 2. Imagining the reference frame of a photon, which is also impossible. Since photons travel at c, their time dilation is infinite. Which means that time does not exist for them, therefor no frame of reference since their frame of reference is instant

I wasn’t ready to have my mind blown. I learned a new way to look at time. Thank you.

For a while I imagined mechanism as solid rods and axles. (Just like in scheme of apparatus to measure speed of light). 2 conclusions came: 1) the very same rod can be straight and twisted at the same moment (but from perspective of different reference frames) 2) simple idea of measuring speed of light by sending it through holes in rotating disc then bounce back trough mirror and back to hit/miss another hole in the rotating disc IS real life example of Your Train paradox. Yet if I'm right I come onto different paradox: futon going trough the apparatus seems to experience time ( this is really hard to imagine)

Please may you make a video explaining length contraction? I think your video was great by the way.

“The speed of light is constant in all reference frames” I was caught up on this part for a while and was struggling to understand what that means I am not an expert. I have no experience with any of this other than yt videos - please tell me if I’m wrong or if any part is incorrect/inaccurate I had to reword that statement and think about it for a bit (like 2 hours) but basically, the reason this paradox (and any paradox about light) is a thing is because *light moves relative to the observer* Light will appear to move at the same speed to the one observing no matter how fast the observer is or is not moving - meaning that light will always appear to expand as a sphere with a non-moving origin relative to the observer An example: If you’re moving at 99.99% the speed of light and you create a flash of light, that flash of light will appear to expand as a sphere away from the origin(the lightbulb), which is moving with you, where any photon is always the same distance away from the origin as any other photon; but to a stationary observer, the light will appear to expand as a sphere from a stationary origin instead of the origin moving with you (where the lightbulb will be closer to the photons that are moving in the same direction as the lightbulb and be farther away from photons that are moving in the opposite direction). I know this is very wordy and not too clear but I don’t know how to explain it clearly while keeping it concise Tl;dr *The speed of light is relative to the observer, not the universe* :) Now read the rest to help you wrap your head around what that means :) Edit: I did not realize this guy has an explanation video about why “the speed of light is constant in all reference frames”, I’m going to watch it now :)

Reminds me of my problem set homework where we had to work out all the lorentz transformations for the paradox. it was a real eye opener!