Relativity states that nature doesn't depend on how we look at things, and a physical process is the same no matter what perspective we choose to think about it in, and frame of reference is a set of criteria or stated values in relation to which measurements or judgments can be made. Don't these two contradict each other? I'm confused because I'm taking a course that says that a stationary ball is hit by a train going 200 km/hr, and so the ball goes 200 km/hr from a passenger on the train's viewpoint. But then from a bystander's viewpoint, the ball ends up going 400 km/hr. My understanding was because the bystander is looking at it where they are stationary, too, the ball goes twice as fast from of the force from the train. The passenger is already going 200 km/hr, so the ball goes 200 km/hr for them, so it would just be 200 km/hr added to the 200 km/hr the train is already traveling. So I don't understand how relativity works here? Wouldn't it just depend on where you were when this happened? I've read a lot of answers to similar questions, but I can't quite get a grasp of this concept. If the speed of the ball can change depending on where you are in the situation, the perspective and how you look at it does matter, or am I just overthinking this? Help!
-
1This may help - Gravity Assist Analogy – mmesser314 Nov 19 '21 at 02:40
-
Yes, observed speed does "change" depending on the observer, it is not a unique number; that is what relativity means! Galilieo describes the idea of relativity very well here: https://en.wikipedia.org/wiki/Galileo%27s_ship#The_proposal. Hope that helps. – m4r35n357 Nov 19 '21 at 10:05
3 Answers
From the point of view of the bystander next to the track, the ball is stationary until it is hit, after which it goes at 400km/hr, so its change of speed arising from the collision is 400km/hr.
From the point of view of the passenger, the ball is coming towards them at 200km/hr before the collision, then rebounds at 200km/hr in the other direction after the collision, so again its change of speed is 400km/hr.
In both cases, each observer sees that the collision has the same effect on the speed of the ball.
The principle of relativity says the laws of physics are the same in all reference frames, but that doesn't mean that all physical quantities are the same in all reference frames. If the passenger walks down the corridor of the train at 2km/hr, clearly their speed in that frame is different from their speed in your frame, where it is either 202km/hr or 198km/hr depending on whether they are walking towards the front or the rear of the train.
- 26,161
I'm not sure I really understand your train example, but the principle of relativity specifically states that the laws of physics in your local neighborhood do not depend on your state of motion. As a consequence of this, certain things are invariant with respect to who is observing them (i.e. all observers will agree on): the speed of light, the spacetime interval between two events, the order of events if one causes the other. Some things they won't agree on: time interval or spatial distance between objects or events, speed of objects, dimensions of objects (i.e. spatial distance between two points).
- 9,096
How relativity works in your example:
The situation ("nature") is absolute: when describing what happens either from the perspective of a passenger or that of a bystander, we do not get the feeling that they live in two different worlds - intuitively, it is clear that we just look to the same event (a train hitting a ball) and that no observer would say to the other "what you observe does not make any sense, I have no idea what you are talking about". The two observers agree they share the same world where this event is happening.
That's the "nature doesn't depend on how we look at things" part.
Now speed is relative, which means that in itself it does not make any sense to talk about the ball speed, either before or after the collision. For that matter, it does not make any sense to speak of the train speed either: this speed is 200 km/h for the bystander, zero for the passenger. The notion of "speed" only takes a meaning in relation to a specific observer.
That's the "frame of reference is a set of criteria or stated values in relation to which measurements or judgments can be made" part: we need the criteria "I am identifying to the bystander" vs "I am identifying wth the passenger" to measure the ball (or train) speed.
Each observer is in itself a frame of reference, each has a specific relation to what happens in an absolute way, and that is what "relativity" is about.
- 3,742