Ok so since there’s a bunch of science nerds on here and I’m sleep deprived I’m gonna ask my dumb ftl question.
If you’re on a train and you walk towards the front of the train, your speed measured from outside of the train is the speed of the train (T) plus the speed of you walking (W).
So if there was a train inside of that train, and you walked inside of that, you’d go the speed of the outside train, plus the speed of the inside train, plus your own walking speed.
So what if we had a Russian nesting doll of trains, so that the inner most train was, from the outside, going as fast as light and you walked towards the front? Wouldn’t you be going faster than light if you measured your speed from the outside?
Didn’t come at me with how hard it would be to build a Russian nesting doll of super trains it’s a hypothetical and I’m tired.
The idea that the velocity of a person walking forward on a train is simply the velocity of the train plus the velocity of the person walking with respect to the train is called “Galilean relativity”.
Einstein realized that Galilean relativity has a big problem if you take for granted the idea that the speed of light is the same for all observers, regardless of reference frame, and people had a lot of reasons at the time to suspect this to be true.
In particular, he imagined something like watching a train passing by him, but on board the train is a special clock which works by shooting a pulse of light at a mirror directly overhead which reflects back down and hits a sensor. Every time the light pulse hits the sensor, the clock ticks up by one and another light pulse is sent out. People usually call this the “light clock thought experiment” if you want to learn more about it.
Anyway, Einstein realized if he was watching the light clock as the train passed by him while he’s standing on the station, the path the light beam traces out will take the form of a zigzag. Meanwhile, for a person standing on the train, it will just be going straight up and down. If you know anything about triangles, you will realize that the zigzag path is longer than the straight up and down path. So if everyone observes the speed of light to be the same exact thing, it must be the case that it will take the light a longer amount of time to traverse the zigzag path. And so the person standing on the platform will see that clock ticking slower than the person on the train will. This phenomenon is called “time dilation”.
From this point, you can apply some simple trigonometry to figure out just how much slower things would be appearing to move on the train. And it turns out that the velocity the person watching the train observes the person walking on the train to have is not the velocity of the train plus the velocity of the person walking on the train. But rather, it’s something like that velocity, but divided by 1 + (train velocity)•(walking velocity)/c^2, where c is the speed of light (and this is called “Lorentzian relativity” if you want to read more about it).
It’s important to notice that since trains and walking come nowhere close to the speed of light, the value you’re adding to one is very small in these kinds of situations, and so what you’re left with is almost exactly the same thing you would get with Galilean relativity, which is why it still is useful and works. But when you want to consider the physics of objects that are moving much much faster, all of this is extremely important to take into account.
And lastly if you wanna read more about this stuff in general, this is all part of “the theory of special relativity” and there’s probably helpful YouTube videos covering every single thing that I’ve put in quotation marks.
Things get really unintuitive when you go near the speed of light. Einstein’s “Special Relativity” is describing that. Watch a couple of videos on the topic. It’s mindbending but seriously cool.
In short: The speed light is always constant FOR EVERY OBSERVER. That means, if you would hold a flashlight in a very fast moving train, the light would travel as the same speed for you as for a stationary person that is watching your flashlight from outside the train.
But how could that be? Aren’t you “adding” the trains speed to your flashlight? So shouldn’t the light in your train travel faster in your train? Or maybe slower? No. Light speed is always constant - but what is NOT constant is space and time. It is relative to the observer. Time and space can stretch/dilate to make up for what seems to be a paradox. E.g. your trains would shrink in length the faster you go. But it would look different to you than it does to an outside observer.
As I said, it’s mindbending, but there are a couple of cool and simple videos on the internet to get a better grasp on the matter.
Relativity would prevent this. If the train moves at the speed of light, then nothing inside it will move because time will stop. The amount of trains inside trains doesn’t really change much except the effect of time dilation (slowdown) on each train. You can’t actually accelerate to the speed of light.
as a software engineer that watches too much youtube, this is the first time it’s clicked for me:
If the train moves at the speed of light, then nothing inside it will move because time will stop.
the pieces of information:
time moves slower the faster you travel, and
nothing can travel faster than the speed of light
have never been concretely connected in my head, but this makes a lot of sense now: time moves slower (for you) the faster you travel BECAUSE that’s the thing that stops you from moving faster than the speed of light… AND that holds true from all perspectives because it’s like… a trade-off?
Because of relativistic effects, from your point of view on the train you would just walk forward. But you would notice a strange effect while the trains were accelerating: your atomically synchronized wristwatch the clock you can see out the window has slowed down and stopped counting time. So it seems that your journey to the front of the train takes no time at all.
From someone standing on the side of the tracks catching a glimpse of you and the train as you whizz by, the front of the train is moving at light speed. You’re at the back of the train completely frozen still, unable to move forward because the front of the train is moving away at light speed.
Weird things happen when you’re talking about the limits of physical reality.
your atomically synchronized wristwatch has slowed down and stopped counting time.
Wait, surely time would move at a normal speed within your own reference frame. The act of you walking to the front of the inner-most train you are in would be a normal occurence to you, but if you looked out of the window you would see a completely frozen scene.
Only once you measure time afterwards with an observer would you notice the gaping time difference.
Not a science nerd. But I would assume the inner trains would like to push forward, stealing some kinetic energy from the outer train because it pushes itself away from the outer train and making the outer train slower or even push back.
That’s a great guess when you try to answer the problem with traditional (Newtonian) physics. However, space and time do not behave in a way we would expect when we go nearly at light speed. So Newtonian laws do not apply in the same sense anymore.
Ok so since there’s a bunch of science nerds on here and I’m sleep deprived I’m gonna ask my dumb ftl question.
If you’re on a train and you walk towards the front of the train, your speed measured from outside of the train is the speed of the train (T) plus the speed of you walking (W).
So if there was a train inside of that train, and you walked inside of that, you’d go the speed of the outside train, plus the speed of the inside train, plus your own walking speed.
So what if we had a Russian nesting doll of trains, so that the inner most train was, from the outside, going as fast as light and you walked towards the front? Wouldn’t you be going faster than light if you measured your speed from the outside?
Didn’t come at me with how hard it would be to build a Russian nesting doll of super trains it’s a hypothetical and I’m tired.
The idea that the velocity of a person walking forward on a train is simply the velocity of the train plus the velocity of the person walking with respect to the train is called “Galilean relativity”.
Einstein realized that Galilean relativity has a big problem if you take for granted the idea that the speed of light is the same for all observers, regardless of reference frame, and people had a lot of reasons at the time to suspect this to be true.
In particular, he imagined something like watching a train passing by him, but on board the train is a special clock which works by shooting a pulse of light at a mirror directly overhead which reflects back down and hits a sensor. Every time the light pulse hits the sensor, the clock ticks up by one and another light pulse is sent out. People usually call this the “light clock thought experiment” if you want to learn more about it.
Anyway, Einstein realized if he was watching the light clock as the train passed by him while he’s standing on the station, the path the light beam traces out will take the form of a zigzag. Meanwhile, for a person standing on the train, it will just be going straight up and down. If you know anything about triangles, you will realize that the zigzag path is longer than the straight up and down path. So if everyone observes the speed of light to be the same exact thing, it must be the case that it will take the light a longer amount of time to traverse the zigzag path. And so the person standing on the platform will see that clock ticking slower than the person on the train will. This phenomenon is called “time dilation”.
From this point, you can apply some simple trigonometry to figure out just how much slower things would be appearing to move on the train. And it turns out that the velocity the person watching the train observes the person walking on the train to have is not the velocity of the train plus the velocity of the person walking on the train. But rather, it’s something like that velocity, but divided by 1 + (train velocity)•(walking velocity)/c^2, where c is the speed of light (and this is called “Lorentzian relativity” if you want to read more about it).
It’s important to notice that since trains and walking come nowhere close to the speed of light, the value you’re adding to one is very small in these kinds of situations, and so what you’re left with is almost exactly the same thing you would get with Galilean relativity, which is why it still is useful and works. But when you want to consider the physics of objects that are moving much much faster, all of this is extremely important to take into account.
And lastly if you wanna read more about this stuff in general, this is all part of “the theory of special relativity” and there’s probably helpful YouTube videos covering every single thing that I’ve put in quotation marks.
Dang there goes my patent
Things get really unintuitive when you go near the speed of light. Einstein’s “Special Relativity” is describing that. Watch a couple of videos on the topic. It’s mindbending but seriously cool.
In short: The speed light is always constant FOR EVERY OBSERVER. That means, if you would hold a flashlight in a very fast moving train, the light would travel as the same speed for you as for a stationary person that is watching your flashlight from outside the train.
But how could that be? Aren’t you “adding” the trains speed to your flashlight? So shouldn’t the light in your train travel faster in your train? Or maybe slower? No. Light speed is always constant - but what is NOT constant is space and time. It is relative to the observer. Time and space can stretch/dilate to make up for what seems to be a paradox. E.g. your trains would shrink in length the faster you go. But it would look different to you than it does to an outside observer.
As I said, it’s mindbending, but there are a couple of cool and simple videos on the internet to get a better grasp on the matter.
That’s wack af
That’s where time dilation will kick in
Relativity would prevent this. If the train moves at the speed of light, then nothing inside it will move because time will stop. The amount of trains inside trains doesn’t really change much except the effect of time dilation (slowdown) on each train. You can’t actually accelerate to the speed of light.
as a software engineer that watches too much youtube, this is the first time it’s clicked for me:
the pieces of information:
have never been concretely connected in my head, but this makes a lot of sense now: time moves slower (for you) the faster you travel BECAUSE that’s the thing that stops you from moving faster than the speed of light… AND that holds true from all perspectives because it’s like… a trade-off?
https://www.quora.com/What-if-you-walk-forward-on-a-ship-moving-at-light-speed#%3A~%3Atext=You+would+experience+nothing.%2Cof+travel+wouldn't+exist.
Because of relativistic effects, from your point of view on the train you would just walk forward. But you would notice a strange effect while the trains were accelerating:
your atomically synchronized wristwatchthe clock you can see out the window has slowed down and stopped counting time. So it seems that your journey to the front of the train takes no time at all.From someone standing on the side of the tracks catching a glimpse of you and the train as you whizz by, the front of the train is moving at light speed. You’re at the back of the train completely frozen still, unable to move forward because the front of the train is moving away at light speed.
Weird things happen when you’re talking about the limits of physical reality.
Wait, surely time would move at a normal speed within your own reference frame. The act of you walking to the front of the inner-most train you are in would be a normal occurence to you, but if you looked out of the window you would see a completely frozen scene.
Only once you measure time afterwards with an observer would you notice the gaping time difference.
You are correct, I should have said there was an atomic clock out the window that the walker looked out at.
Not a science nerd. But I would assume the inner trains would like to push forward, stealing some kinetic energy from the outer train because it pushes itself away from the outer train and making the outer train slower or even push back.
That’s a great guess when you try to answer the problem with traditional (Newtonian) physics. However, space and time do not behave in a way we would expect when we go nearly at light speed. So Newtonian laws do not apply in the same sense anymore.