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.
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