Query regarding Special Relativity

[aditya ver.2.0]

According to SR, there is no measurement that can determine whether an object is stationary or under motion. So if two metallic balls collide with each other, then aren't there motion between the two balls? Only then they will collide.

 

[Nugatory]

According to SR, there is no measurement that can determine whether an object is stationary or under motion. So if two metallic balls collide with each other, then aren't there motion between the two balls? Only then they will collide.

There is no measurement that can distinguish between these situations:
1) Left-hand ball is at rest, right-hand ball is moving right-to-left and strikes the left-hand ball
2) Right-hand ball is at rest, left-hand ball is moving left to right and strikes right-hand ball
3) Left-hand ball is moving left-to-right, right-hand ball is moving right-to-left at same speed, both balls meet in the middle.
4) ...

The first case corresponds to what an observer at rest relative to the left-hand ball sees, the second case corresponds to what an observer at rest relative to the right-hand ball sees, the third case is what an observer at rest in the center sees.

 

[ghwellsjr]

According to SR, there is no measurement that can determine whether an object is stationary or under motion. So if two metallic balls collide with each other, then aren't there motion between the two balls? Only then they will collide.

Are you asking about what happens after the two balls collide and instead of motion toward each other there is now motion away from each other?

If so, the two balls are not inertial. SR only states that it's impossible to determine if an inertial object is absolutely at rest or in motion. SR is not claiming that you cannot tell that an accelerated object experiences motion at some time.

So if we follow through on what Nugatory said, we cannot tell if each ball started out at rest and ended up in motion, or started out in motion and ended up at rest, or started out in motion and ended up in a different motion.

 

[bapowell]

According to SR, there is no measurement that can determine whether an object is stationary or under motion. So if two metallic balls collide with each other, then aren't there motion between the two balls? Only then they will collide.

Yes, there is motion between the balls -- special relativity is happy to accept that. Relativity does away with motion in the absolute sense and considers only relative motion.

 

[ghwellsjr]

Yes, there is motion between the balls -- special relativity is happy to accept that. Relativity does away with motion in the absolute sense and considers only relative motion.

Special Relativity is also happy with a single ball that starts out at rest in its own Inertial Reference Frame (IRF) and then accelerates so that now it is in motion according to that same IRF. It doesn't have to be relative motion between two objects. Motion is relative to an IRF. In fact, the object doesn't even have to start out at rest in its own IRF, it can be an inertial object moving according to some arbitrary IRF.

 

[aditya ver.2.0]

Are you asking about what happens after the two balls collide and instead of motion toward each other there is now motion away from each other?

If so, the two balls are not inertial. SR only states that it's impossible to determine if an inertial object is absolutely at rest or in motion. SR is not claiming that you cannot tell that an accelerated object experiences motion at some time.

So if we follow through on what Nugatory said, we cannot tell if each ball started out at rest and ended up in motion, or started out in motion and ended up at rest, or started out in motion and ended up in a different motion.

Sir,
How can the two balls be non- inertial as no external force is being exerted over the closed system. It all the inner forces that are being circulated.

 

[Nugatory]

Sir,
How can the two balls be non- inertial as no external force is being exerted over the closed system. It all the inner forces that are being circulated.

If the two balls collide and change directions, then there is no inertial frame in which one of the balls is at rest.

 

[sweet springs]

Hi. aditya ver2.0. SR says we can choose IFRs so that one of them stands.
Ball A is still and Ball B is moving
Ball B is still and Ball A is moving
Ball A is moving and Ball B is moving
But it does not say
Ball A is still and Ball B is still
stands.

 

[ghwellsjr]

Sir,
How can the two balls be non- inertial as no external force is being exerted over the closed system. It all the inner forces that are being circulated.

I was talking about each ball individually being non-inertial throughout the scenario. They are each inertial at the beginning and up to the moment of impact and then they are each inertial after they collide and bounce away from each other but at the moment of impact, they are each non-inertial. Since you said the two balls were metallic, I thought you wanted them to bounce away from each other as a result of their collision.

And an important point that I was making in my posts is that there is a distinction between an Inertial Reference Frame that we use to describe the motions of the object(s) in a scenario and the inertial states of the object(s). However, I don't know if that was an issue that you are concerned about or not. Do you understand that "inertial" means not accelerating or not changing its state of motion? So if a ball that starts out inertial, traveling in a straight line at a constant speed, hits another object and either changes its speed and/or changes its direction, then it has accelerated and is no longer inertial? It doesn't matter whether you consider the force that accelerates the ball to be external or internal.

 

[Dale]

Sir,
How can the two balls be non- inertial as no external force is being exerted over the closed system. It all the inner forces that are being circulated.

Each ball experiences a force. Each ball accelerates according to an accelerometer attached to the ball. Each ball is non inertial.

The center of mass of the two balls is inertial, but the balls are not inertial. Similarly, a spinning wheel in free space is not inertial even though its center of mass is.