Train Tunnel Paradox Visualised (Animating Einstein's Special Relativity)
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- Опубліковано 18 чер 2024
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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
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Hey, i saw a video from veritasium, which states that we don't actually know whether the speed of light is the same in all the directions,
Can you please make a video explaining that
Spoiler Alert
Relativistic effects are observed, not experienced. Mahesh and his mom were born at the same time only from the perspective of outside observer travelling at relativistic velocities. From perspective of Mahesh and his mom, time has passed because Earth do not travel at relativistic velocities. Length contraction is only observer effect seen from observer outside of train's frame of reference while time dilation is experienced by clocks on a moving train.
What would it look like if the experiment were set up so that from the train's perspective it would be hit by the doors falling onto it? What would the stationary observers see? Would they be able to agree where doors and the train met?
For example if there were one sensor for each door and each door was set up in such away that if a delay was needed for both doors (or detectors) to hit the top of the train from the train's perspective and they did, would the stationary and moving observers be able to agree on where the doors touched the train? If the train fits inside the tunnel from the stationary reference frame how would both doors be able to hit it, especially if the left most door has a delay?
@@sudonym2078 They would disagree on the simultaneity of the two door hits
@@LavyaBhansali Laws of physics are the same even if light does not travel at c in every direction. Perspectives of the train and the tunnel will be different in that case, but the two way result will be the same. So you have to choose your own interpretation how fast do you think light one way speed is if you want him to make a video about it because he cannot make infinite number of videos for every speed between c/2 and infinity. :)
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.
Probably an imaginary door with no mass.
I imagine it being laser beams that are cut off by the train
The doors can fall faster than the speed of light, just imagine 😅
The tunnel is long enough
If the train is moving at the speed of light how is the first light sensors light emission beating the train to the second sensor?
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
lol is this your burner account Mahesh?
Explanations are not definitions. Go ahead and Define what you are talking about...you will chase you tail into the Bill Gates pocket looking for a coin to cut it off so you can free yourself from ...hmm. anti-slavery ?!
True. Considering the last one is the most counter-intuitive.
@@manojaggarwal2773 what made you jump to that conclution?
Orodruin? Finding you is nothing short of a miracle. Don't you think?
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.
"Your mother is the trigger"
Idk why but reading your sensical comment made me laugh
@@huseyinemreeken3024 i actually took it the other way.... it's at his frame of reference point that his mother was born at the same "time"... that to him everything that occured happened at the same time he was born... or should we be using "spacetime" instead man i'm getting confused
Yup. Cause and effect. No matter the frame of reference, the effect cannot even appear to occur before the cause.
But there are actions that happen simultaneously. How does that work?
I think from people outside that train perspective we can fairly say train gets trapped if both door closes (forever) simultaneously considering door is unbreakable. Even in this frame it gets bit tricky because as train slows down inside that tunnel it's length has to increase too. Answer to all this question lies in the fact that train is not a single rigid body but can be thought to be made up of series of rectangles. (Cuboid)
So when we apply force on the back wheel of train it takes some time for that signal to propagate at front. So when all parts of train comes at rest in different times then they expands. (Again think of train as series of cuboids moving). (Assuming train proper length is smaller than tunnel length)
From train perspective though same thing happens I guess. Here brake in this frame means that part of train is moving with rest of world in opposite direction. Again that doesn't happen simultaneously for all parts of train. So train kinda gets compressed. So just think about it and it may resolve I guess in your own head.
Two key things to consider :
1) Force takes some time (max speed = c) to propagate in real bodies.
2) One can think of any bodies to be made up of series of smaller bodies.
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.
This comment deserves more likes.
Do you have a resource I can read into that? I'd love to see the math behind this!
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!
The key to understanding relativity is the geometry of the gravitational field.
Nicely put. 😊😊
i bet you tink light is a duality
@@kylelochlann5053 You mean general relativity?
@@kylelochlann5053special relativity
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
yeah i was wondering the same thing
TLDR: I'm no expert but I think the train gets crushed
I have nothing to back this up with other than intuition, but here is my take.
Since we already are in hypotethical land I've made some wild assumptions like indestructable walls and whatnot.
Perspective of the train:
The train enters the tunnel and the front wall closes. The front of the train hits the wall and before that information of speed change has propagated all the way to the back of the train, the back wall has already closed. So the whole train is now inside the closed tunnel, and at speed 0 which means the train is longer and it would be crushed by the walls that suddently seemed to contract.
From the tunnels perspective:
The train enters the tunnel and both walls close at the same time, with the full train inside. The train hits the front wall, come to a stop and immediately expand into the walls.
I mean, it crashes into the far door. From both points of view, the train is still in the tunnel when the far door closes, just when it passes by, the train can continue. If the far door closes and stays closed, the train crashes. Rapid deceleration ensues, space becomes less distorted, and the close door has already closed because the speed of matter (dont quote me on that name, but the speed at which particles collide in a solid and transfer force to the far end of that solid) is the speed of sound, meaning the whole train is in the tunnel before it slows down, crushing it inside.
Um. What happens is a lot of scrap metal...
traveling at the speed of light or anywhere near that the train would be made out of some indestructible future material and punch a hole straight through the door probably completely vaporizing it and causing a huge explosion
"Everything in relativity can be derived from that postulate (of c being constant)". Learning for the day. Well done and thank you, Mahesh.
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
Is he was my physics teacher, we would make fun of his enthusiasm and bully him.. and still top the class
@@prathameshbaviskar139You must have had really stupid classmates
@@prathameshbaviskar139 Bro you're so cool 😎😎
@@prathameshbaviskar139 I don't get why you dislike him
This also shows that length contraction really is just relativity of simultaneity as well. Very insightful animations!
😂😂😂😂
There is no simultaneity
Yes. Simultaneity rules!!
But if the doors move that fast wouldn't they contract too? Hahahaha..jk..
@@Mahesh_Shenoy There is a flaw in the simulation, IMHO: the first light signal should also hit the second button sooner, no?
Imma be honest with you Mahesh, I don't think that thumbnail train is fitting in that tunnel regardless of its proximity to c
What are you even trying to say
@@angelefrain5209 Thumbnail accuracy is lacking. It is a joke about how I am aware of what the video is about, but suggesting that the train is too big and that tunnel too small to make the length contraction feasible.
Thanks for making me explain the joke, jokes are always better when flushed out and fully explored.
😂😂😂
That’s why the thumbnail has a question mark. Learnt it from newspaper titles!😅
@@Mahesh_Shenoy "Does chocolate cure cancer? The results might shock you. And more after the weather"
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
this really boggles my mind
Hey, congrats on 100k subs! So glad you're gaining so much popularity, more people need to see these videos!!
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!
love your videos! you are incredibly good at explaining those complex things! Keep it up
Except that this explanation and all explanations are nonsensical gibberish.. Relativity is irrational BS. That is the truth.
@everythingisalllies2141 Except you can do measurements and confirm it. Muons producing in upper atmosphere manage to reach Earth's surface without decaying due to effects of special relativity. Clocks on GPS satellites move slightly slower than those on Earth (if you don't correct for that, your determined position will deviate from your real position). Maxwell's equations have been verified to an incredible precision and they contain the speed of light which is the same in every inertial reference frame.
If you don't understand special relativity and its implications (which are real and measurable) this doesn't make it BS.
@@YuriyDavygora read the ebook dave vs hal 9001 and you will learn that its not all how they claim.
@@YuriyDavygora these experiments have been debunked
My favorite example of that is the lifetime of particles. They fly further than they should, but form their perspective everything is extremely compressed.
Your doors seem to go faster than the speed of light. Leaving that detail aside, this is a great explanation!
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 🙏🏼
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.
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.
Right, haha I only focused on the x axis 😆
It'd afect the analysis since the train would hit the front door as it couldn't fall fast enough
those are really fast doors.
@@HappyBeezerStudiosyou could call it a door-dash
@@Mahesh_Shenoywhag happens if the train stops in between the doors
Congratulations on the 100K subscribers, love the content❤
This hangover is going to last a while. Great job Mahesh. Keep up the good work.
Great job on the animation! A picture is definitely worth a thousand words!
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 UA-cam comment.
A good point. The doors would have to move impossibly fast. But let's say everything was going a bit slower and the doors could move incredibly fast. Isn't the whole point to try to trap the train in the tunnel with each one being stationary? The doors close at different times in the length contracted tunnel, yet, that's not at all how the doors acted for the length contracted train and it is assumed the trains are exactly the same going through the exact same tunnel. Are the initial doors not the constant? Let's introduce another perspective of someone sitting in front of the doors watching them while the train passes by in both instances. If the doors close at the same time initially, they must in the other example, or it just doesn't make sense. Physical items are interacting with one another at that point. It is not just an illusion. I believe the answer we have came up with only makes sense because we find a way to force what we already know into it by any means. Yes it is an answer, yes it makes sense when you put the right numbers in the right place, but is it the real one? I don't believe so. Something is missing, I'm just too dumb to figure it out.
You can squeeze the system in height and get the doors that don't exceed the speed of light
@@CoyoteFeral I’m not saying it’s an illusion, I’m just saying it’s a clunky example
@@maxburmab7962 the speed of light is a constant in all reference frames, so this doesn’t make sense
@@loadstone5149 I know, I'm just saying you (in general) almost need to assume it's an illusion if the answer you believe to be correct is not one where both doors close at the same time. Someone clould be watching those doors. If at any point the doors close at a different time, something has to have changed between runs. But then you can't compare the two examples if you're changing things willy nilly. So to me it's still a paradox that starts and ends with what still seems to be impossible. Taking one physical form and turning it into a different physical form without actually changing it, or "length contraction". That's where things aren't lining up for me.
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.
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!
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 love how Relativity of Simultaneity always creates an illusion 😂
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.
Honestly, the video didn't make sense to me (at least not 100%), but this explanation did!
Thank!
Hold on can I bring something up that may or may not matter at all?
For the two stationary observers. Their clocks START when they receive the signal that goes out from the middle of the tunnel. Do they both actually 'SEE' each other's clocks start at the same time or is there a slight discrepancy in what they ACTUALLY SEE due to the same speed of light consideration? As in they implicitly know their clocks start at the same time, but...
IF the TUNNEL were 2 LIGHT YEARS across? (e.g. the time it takes for the 'light' showing the time on the other person's clock to travel to the other person)
Does this matter? Is what I'm saying valid?
@@warioman91 ok. I'll jump on the idea with the 2 light years of distance in between them.
If they had the tool, something like a huge telescope, to actually be able to read what is written on the others clock. The image they see is two years old as they are two light years apart. But they know this and so they can look at their clock and say "ok. Now I've just seen that the other clock started and it is 20th of January 2024 here on earth. So when that clock got activated it was the 20th of January 2022 and that is exactly when my clock got activated too. So they started at the same time."
If there was a huge spaceship, that only fits in that 2 light years between the two due to length contraction, and the doors were huge so you can see them from 2 light years away. You would have the door closing at your place and see the other door closing after 2 years. But as it is 2 light years away you know they closed at the same time from your point of view.
Other than when you are at exactly the same place, it will always end up like this no matter how far it is. If its 10 kilometers or 100000 kilometers or 1 million kilometers. It will allways need the information transfered by light to determine what happened simultaneously.
And as a hint towards that question at the end of the video: This is part of the explanation of the answer.
No, none of these explanations are rational, the hole theory is irrational.
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.
I never considered a situation like this. It's really amazing how spot on relativity describes the relationships of objects in motion.
This is similar to twin paradox but instead of popular idea of time dilation, we talk about the less popular idea length contraction
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 ?
Bro what?
@@danielrozario I am saying that he is explaining things in a better way ,bro.
Are you sure? You actually think they have the same intelectual capacity? I think you live in a dream.
It was the way of teaching he had compared @@gibson2623.
😂😂😂😂😂😂
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.
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!
We need these types of teachers who can teach physics intuitively
Unified Theory has existed for eternity. There is no duality in nature. The only constant, truth, is that we all live in the same system. For some reason people enjoy making things more complicated than they actually are. For monetary reasons the waste is palpable, all for science yet it to has been hijacked...Nature is simple and needs no calculator. Take your power back. You are the universe and the universe is you, end of story
No, because teaching what you see visually, or can not see is not reality.
@@Shane-qz8xi well if you wanna get all philosopical about it, reality is an illusion and you shouldn't bother learning anything.
But if you can accept that reality can be represented mathematically, then you should probably accept that maths can be represented visually.
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?
" _I have two independent clocks attached to each door that can trigger at exactly the same time_ "
if they trigger at exactly the same time in tunnel frame, then they wont trigger simultaneously in the train frame, because of relativity of simultaneity
Time is also relative. The clocks will be at different times.
time only changes with speed of light
It would still work out.
Let's say the two clocks read the same time from the tunnels frame of reference. They would trigger the doors at the same time and the train is short enough to fit into the tunnel. From the trains perspective the clocks don't read the same time but the one at the far end of the tunnel is a certain amount of time ahead. So from the trains point of view the clock at the far end of the tunnel triggers the door earlier than the clock at the near end of the tunnel triggers the door.
The reason for the time difference is basically the idea behind the second light signal in this video.
Think of the light pulses as just an aid in figuring out when things appear to be "at the same time". Let's say that the "right time" to trigger the doors is exactly 12:00:00, does it matter if a pulse of light just happens to arrive at each clock at 12:00:00? You could also say that you set up a pulse of light to be emitted so that they reach each clock at exactly 12:00:00 (independent of the trains motion). However, from the perspective of the train, it still looks the same -- the clock in front of it is ahead (because the light reaches it first), and it will trigger the door early, while the clock behind it is behind, and triggers the door later.
If every science teacher were as passionate as you, there would be a shortage of space in universities...
Your videos are always amazing!! Great work Mahesh
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
More precisely, it's when the proper time interval between two events is exactly zero.
Or simply speaking, the two events happen in the same space and time coordinates.
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 :)
Einstein would very likely be proud of you for this video! 👍 Thank you, this was amazing.
I love how the key events in the clip are synced with the music. And great video overall.
😂😂😂
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
Idea of simultaneity is relative.
“The speed of light is a constant in all frames” Remember the first animation you are observing the train, and the second you are on the train, see how the light propagates.. screwed with me for awhile too!
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.
The trap setup perspective -- only true for the MIDDLE of the trap setup (the sensor). The parts of the traps on each door perceive their own door falling sooner than the opposite door as the light from that opposite door falling takes time. Imagine if this train and tunnel are nearly a light-year across and think about it -- each door's side would see the other door as falling a YEAR later! NOT at the same time!
As for the perspective in the middle, someone from there perceives no paradox, and someone on the train perceives no paradox. So it does make sense. Because your question is really just stating relativity of simultaneity, but that is the answer. Both sides agree the doors don't get stuck, it's just relative which door fell first depending on which reference frame you're in. (The idea of "simultaneous" or "when things happen compared to when other things happen" is relative TO your reference frame.
@@logicianbones yes each door's side does not see them fall at the same time but that does not mean that those two events didn't happen at the same time. In fact for every pair of events that happen at two different places they can only happen at the same time if they are seen each with a delay from both places. If that is not the case one of the events has to have happened before the other. As they know they are one light year apart they still have the same definition of simultaneity and will say that they fell at the same time.
If someone would be one light year away from me but in the same frame of reference and he would send me a light signal, that light signal would reach me after one year and I could say "oh look he send me that signal one year ago so that was at the same time to what I did one year ago". If we look at the stars on my 27th birthday and for example there is a star that is exactly 27 light years away I could say oh look that light was emitted when I was born so any event on that star that we can see now has actually happened at the same time as when I was born.
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 😉
right, they close even faster than the speed of light 😁
I think the animation inaccuracy is the fact the train moving on a rail without any support on a floating rock in a void, and the gate fall to the direction of big mass object that is off camera at the bottom 🤓
You underestimate Mahesh's warp drive doors😎😎
@@pressaltf4forfreevbucks179 lmao you're right, my bad 😆
wow, nice catch. very intelligent observation. i did not notice that.
Thanks @FloatHeadPhysics Great video. Just out of curiosity, what train speed did you use and what software did you use to make the animation?
How you make these interactive animations?we want to know
I wasn’t ready to have my mind blown. I learned a new way to look at time. Thank you.
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.
4:41 that is not possible, because the door is closing at a speed faster than light :P
Ok, make it all shorter so is a crappy animation.
"Now at full spee-"
"Did you see it?"
Oh man, I thought about the doors falling at different times but animating the mechanisms make the reason intuitive.
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 dont know how we'd show it, but I think it will be the same as in this case (in moving frame two doors fall at different times).
Same thoughts in my brain. But i thing the solution is: it is time delation anyway. There is no such thing as simultaneity in indifferent moving frames.
IIRC there is no objective "at the same time" in relativity. So if a door just happened to drop when the train was passing through it, then it would hit.
If you needed to ensure the two doors drop at the same time, it would require a synchronization mechanism, which needs information to pass at light speed. You can use another "the same time" reference frame instead of the "at rest" one, but that just goes to show that there's no objective "same time" in relativity...
How I see that is that if the door randomly dropped at the same time from the train's perspective and thus hit it, then for that same event viewed from the tunnel's perspective they would drop at different times and also hit the train first when it enters the tunnel and then again when it leaves it
Correct @@KABOOM8800
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
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@@Spontaneouscomp you are an example of what happens when you drop out of School early.... you just spam this everywhere you go.....
Man I Love your videos so much, u post such great vids which helps us understand the concepts easily
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!
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.
I knew the answer from around the one minute mark, as soon as he showed the entire train in the tunnel I knew right away what / how it happened
And yeah I vaguely remember something like that from high school too, even tho year 12 was in 1994 for me lol
wtf ? in which freaking country is relativity taught in high school? your country men must be all geniuses.
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@@silverrahul Stay in School until year 12 ?... Schools will teach or introduce Students to a wide range of subjects...
@@xaero76 what? high schools teaching relativity? which country is that ?
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.
Really good explanation. The visuals are perfect for this problem. Congrats!
man, you have the coolest shirts ive ever seen!! where do you get these?! 😂
btw fantastic animations...this was too good !!
This is brilliant. Very well done.
I improved on a relativistic raymarching fragment shader on shadertoy, that also has sis simultaneuity-train-tunnel in it.
It simulates a slower-speed-of-light, making relativistic effects room-scale, as if the room and accellerations are larger, relative to light speed.
It shows, that length contraction depends on whether ANYTHING moves to you, or away from you.
the train/tunnel that moves towards from you becomes much longer. the train/tunnel that moves away from you becomes much shorter.
relative-Viewing-angle, relative to relative-movement direction (and the involved dot-product-projection of that) matter for length contraction, as well as acceleration (linear and angular)
while you accellerate, looking forward, things become longer and more stretched away with gained speed (while you get closer to them).
while you accellerate, looking backwards, things become shorter and pushed towards you (while you gain distance to tthings), with gained speed.
decellerating (negative accelleration) reverses both of the above effects.
Best visualisation of this paradox. As simple as it is genius.
Yoo that animation synced to the music beats was just amazing !!!
Beautifully explained. Fine work, sir.
Wow! That truly made may jaw drop. Very intuitive explaination!
Great animation! And your enthusiasm really conveys to the viewer, it was a great watch :)
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 think even if there is no dependency between events when there exists some sort of extra delay between events, a similar effect can be achieved (which is interesting if true). And this may solve the "paradox" that "why cant daughter be born before mother if I tried hard enough by moving?" since even if simulating such events by independent events, there will be delays that cause the event that corresponds to the birth of the daughter to be after mother
i saw this one explained with a space-time-diagram ... i got it there somehow ... but yours makes it very clear!!
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.
Wow this is a masterpiece, Mahesh!👍
This video is litrally amazing...
Super excited for the future of this channel🎉
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.
Some years ago I was thinking about how every reference frame is equal, and that this would mean that two observers would have contradicting opinions about which of them gets length contracted.
Going on the hunt to find out how equality of reference frames and length contraction can both be true was the most fun I had learning about physics ever.
The solution that simultaneity is relative was completely unexpected, but at that point I understood right away what such a weird concept meant and why it was inevitable.
Nice work. My left and right brain were in conflict over this, but you presented your findings in such a clear and digestible manner that it was undeniably delicious!
Nice surprise dude, im gonna study this vid. Tx for the great work !
This was an awesome video! The visuals really help to understand the concept!
Bro... Your work is incredible. I really appreciate you explaining physics in a very perceptual way..
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!
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.
The moment of realization for this problem was amazing!
This man is a gem 💎.After watching a lot of video.... finally I get to understand it properly
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.
But would it negate the conclusions : )
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
Im very excited when the special relativity series becomes/morphes into general relativity and we we'll get the amazing explaination from Mahesh and his inner einstein voice!
That's amazing ,I never thought about it
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I love that you break this down for the layman dummies. “They”needed it. My friend said to say thanks 😢😂
that explanation was Brilliant! and a lot of fun - thanks.
I guessed the solution before the explanation by imagining the Spaceship that is moving closer to the speed of light. ( Front part in past and Rear part in the future )
That's why I didn't even think that there is a paradox 😅 Thank you for this fun video!
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Very clear animation!
Perfect explanation and visualization!!! 👏👏👏👏
You’re blowing my mind. I love this. Thank you 😊
Great work man. Nice animation
How long would your doors have to be? In order to move that fast in front of the train they also would length contract.
I enjoyed that a lot. Very well done.
100k 🥳
Congratulations
I appreciate,hope next will be about bell spaceship paradox
Hello, I love your videos and you way of simplifying concepts and equations. I hope you make a video about general relativitty soon
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! 😂