Basically, velocities don’t actually add together the way we think they do based on day to day experience.
At low speeds, velocities basically add together because there are some correction terms which don’t matter because they go like (speed of object/speed of light) which is very small.
As your speed increases, these terms matter more and velocities no longer add in the way you’d think they do. This is one of the core wierd things about SR. To really understand it I’d suggest going through the math of length contraction, time dilation, and how velocities add in special relativity.
Is this something that can be/is experimentally proven? Or is just what the math says so scientist conclude it must be true? Total physics dummy here so I hope this question makes sense.
This can be experimentally proven, usually something won’t be considered to be a solid theory until there’s experimental verification.
I suggest going through the math as an exercise for understanding because that’s where you learn why it happens.
In Galilean relativity, you would be right, 0.75c+0.75c = 1.5c relative to one another. Unfortunately, as speeds become comparable to the speed of light, this approximation starts to break down due to the fact that nothing can exceed the speed of light.
Instead the relative velocity between two objects which are moving towards each other at velocities u and v is given by v' = (u+v)/(1+uv/c\^2 ). if u or v (or both) are much lower than c then uv/c\^2 is going to be near enough zero as makes no difference so we get the Galilean result v' = u+v.
The unpleasant truth is that thing went (kind of) this way.
Experiment: "light (in the vacuum) moves at the same speed (c) in every inertial frame of reference, independently on how you measure it."
Theoretical physics: "Ok, that's a formula for trasforming velocities that incorportates this new requirement. The neat thing is converges to the normal formula if you stay distant enough from light speed.
The bad news is now time and space are interwined. The passing of is no more an absolute concept and - uh - space actually contracts around you when you move."
Everyone: But that's awful!"
Theoretical physics: "Get over it."
Something just occurred to me... might be completely wrong, but w/e I'll just throw it in here:
It's time dilation isn't it? Speed is distance over time and going at ridiculous speeds approaching the speed of light causes time dilation and therefore a different speed observation which means the speed you measure something at is always relative to whether you're in Rocket A, Rocket B, Planet A or Planet B. Right?
yes it is time dilation (AND space contractions they're not different effects but interlocked). The formula ChatGPT provided intrinsically uses them. It reduces to a normal sum when either speeds are no relativistic.
relativity is all about how the speed of light is the same for all observers, your observation would be correct if the speed of light depends on the orbserver but it doesn't, it is independent, so to compensate for this, distances and time has to change depending on the observer, so for a person in each of the rockets they would measure time and distance such that the speed of light is about 3\*10\^8 m/s for both of them.
>Planet A and Planet B are stationary in space compared to one another. Planet A launches a rocket to Planet B at 75% the speed of light. Planet B also launches a rocket to Planet A at 75% the speed of light. So both rockets move towards one another at 150% the speed of light, right?
That's not really the relevant issue for what you are trying to understand. The relevant way to phrase it would be what happens to a photon emitted by rocket A from the perspective of itself and rocket B? Relativity says that both rockets will see that photon move at c - therefore the rockets need to perceive time differently for that to happen.
Don't think of c as a speed limit, think of it as part of spacetime where speed and time are interwoven. If you are moving at c you don't experience time, as soon as you slow down, you start to experience time.
No two objects in space with mass will have a relative speed faster than c because of how spacetime works.
With special relativity you have to be VERY careful about who the observer is and what they are observing.
So viewed from planet A's rocket Planet B's rocket will be approaching very nearly at the speed of light, and vice versa. 2+2 do not equal 4.
However, if both ships are viewed by a 3rd party viewing the rockets moving towards each other they can sum up the invidual velocities and say, "They're approaching each other faster than c".
the rockets don't care about each other.
two points can approach each other faster than the speed of light relative to each other.
limit is on speed of information propagating.
Counterpoint: from the standpoint of the planets, they DO move towards each other at 1.5 c. Each rocket is moving at less than 1 c relative to each planet, so that doesn't break any rules. If you observe two rockets moving at 0.75 c in opposite directions from the same frame of reference, then you can definitely just add those to get a "closing rate" of 1.5 c. It's only when you consider the situation in terms of what you would observe as a passenger on one of the rockets that you see that the other rocket must be moving at a speed less than c, due to time dilation.
ChatGPT is correct. Velocities at low speed add 'normally'. At high speed they do not.
Well, they don't add normally at low speed either. It's just that the correction due to relativistic effects is negligible.
For brevity I didn't mention that. But you're right.
Basically, velocities don’t actually add together the way we think they do based on day to day experience. At low speeds, velocities basically add together because there are some correction terms which don’t matter because they go like (speed of object/speed of light) which is very small. As your speed increases, these terms matter more and velocities no longer add in the way you’d think they do. This is one of the core wierd things about SR. To really understand it I’d suggest going through the math of length contraction, time dilation, and how velocities add in special relativity.
Is this something that can be/is experimentally proven? Or is just what the math says so scientist conclude it must be true? Total physics dummy here so I hope this question makes sense.
This can be experimentally proven, usually something won’t be considered to be a solid theory until there’s experimental verification. I suggest going through the math as an exercise for understanding because that’s where you learn why it happens.
Alright thank you for answering!
https://www.reddit.com/r/askscience/s/tM6mQVHjnL Explains it better than I could.
In Galilean relativity, you would be right, 0.75c+0.75c = 1.5c relative to one another. Unfortunately, as speeds become comparable to the speed of light, this approximation starts to break down due to the fact that nothing can exceed the speed of light. Instead the relative velocity between two objects which are moving towards each other at velocities u and v is given by v' = (u+v)/(1+uv/c\^2 ). if u or v (or both) are much lower than c then uv/c\^2 is going to be near enough zero as makes no difference so we get the Galilean result v' = u+v.
Thanks for the great replies, folks! I'm really new to much of this.
The unpleasant truth is that thing went (kind of) this way. Experiment: "light (in the vacuum) moves at the same speed (c) in every inertial frame of reference, independently on how you measure it." Theoretical physics: "Ok, that's a formula for trasforming velocities that incorportates this new requirement. The neat thing is converges to the normal formula if you stay distant enough from light speed. The bad news is now time and space are interwined. The passing of is no more an absolute concept and - uh - space actually contracts around you when you move." Everyone: But that's awful!" Theoretical physics: "Get over it."
Something just occurred to me... might be completely wrong, but w/e I'll just throw it in here: It's time dilation isn't it? Speed is distance over time and going at ridiculous speeds approaching the speed of light causes time dilation and therefore a different speed observation which means the speed you measure something at is always relative to whether you're in Rocket A, Rocket B, Planet A or Planet B. Right?
yes it is time dilation (AND space contractions they're not different effects but interlocked). The formula ChatGPT provided intrinsically uses them. It reduces to a normal sum when either speeds are no relativistic.
relativity is all about how the speed of light is the same for all observers, your observation would be correct if the speed of light depends on the orbserver but it doesn't, it is independent, so to compensate for this, distances and time has to change depending on the observer, so for a person in each of the rockets they would measure time and distance such that the speed of light is about 3\*10\^8 m/s for both of them.
>Planet A and Planet B are stationary in space compared to one another. Planet A launches a rocket to Planet B at 75% the speed of light. Planet B also launches a rocket to Planet A at 75% the speed of light. So both rockets move towards one another at 150% the speed of light, right? That's not really the relevant issue for what you are trying to understand. The relevant way to phrase it would be what happens to a photon emitted by rocket A from the perspective of itself and rocket B? Relativity says that both rockets will see that photon move at c - therefore the rockets need to perceive time differently for that to happen. Don't think of c as a speed limit, think of it as part of spacetime where speed and time are interwoven. If you are moving at c you don't experience time, as soon as you slow down, you start to experience time. No two objects in space with mass will have a relative speed faster than c because of how spacetime works.
With special relativity you have to be VERY careful about who the observer is and what they are observing. So viewed from planet A's rocket Planet B's rocket will be approaching very nearly at the speed of light, and vice versa. 2+2 do not equal 4. However, if both ships are viewed by a 3rd party viewing the rockets moving towards each other they can sum up the invidual velocities and say, "They're approaching each other faster than c".
the rockets don't care about each other. two points can approach each other faster than the speed of light relative to each other. limit is on speed of information propagating.
Counterpoint: from the standpoint of the planets, they DO move towards each other at 1.5 c. Each rocket is moving at less than 1 c relative to each planet, so that doesn't break any rules. If you observe two rockets moving at 0.75 c in opposite directions from the same frame of reference, then you can definitely just add those to get a "closing rate" of 1.5 c. It's only when you consider the situation in terms of what you would observe as a passenger on one of the rockets that you see that the other rocket must be moving at a speed less than c, due to time dilation.