# Are objects moving relative to each other?

## Main Question or Discussion Point

We have 3 clocks A, B and C. They are in a straight line (Time 1). Clock A rotates around it's axis and clocks B and C rotates around clock A at distance L1 and L2 respectively. Distance L2 > L1. Clocks B and C rotates around clock A so they stay in straight line. Clock A rotates around it's axis so clocks B and C are in front of it. Because of distance L1 and L2 clocks B and C travel different distances R1 and R2 at same amount of time. R2 > R1. Thus, the speed of clocks B and C differ.
Are clocks A, B and C stationary relative to each other or not?
Will clocks A, B and C show same time at line (Time 2)? If clocks at line (Time 1) were synchronized.

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Ibix
Are clocks A, B and C stationary relative to each other or not?
Clearly not. Or do you think the moon is stationary with respect to the Earth?
Will clocks A, B and C show same time at line (Time 2)? If clocks at line (Time 1) were synchronized.
No they won't, because all of the clocks are in relative motion.

I advise not trying to think about rotational motion in relativity until you are confident with linear motion. The complexities of rotating reference frames are a large part of what lead Einstein to develop General Relativity, which is a whole order of mathematical complexity worse than Special Relativity.

Clearly not. Or do you think the moon is stationary with respect to the Earth?
No they won't, because all of the clocks are in relative motion.
Does that mean my friend in tenth floor of building is moving relative to me if I am in first floor of building? Even if we do not move?
Well, point A can be earth. Point B are me in first floor of building and point C is my friend in tenth floor of building. Earth rotates around it's axis, so we move in circular rotation around earth, but at different distances from earth axis.

I was reading about linear motion and that tow objects moving in same direction at same speed will be stationary with respect to each other. They do not see that they move with respect to each other (because they don't). And I thought that objects moving in rational motion do not see that they move with respect to each other (but they do).

Ibix
Does that mean my friend in tenth floor of building is moving relative to me if I am in first floor of building? Even if we do not move?
Typically, "not moving" means at rest in an inertial frame of reference, and there is no inertial frame of reference in which all of the objects are at rest. However, you make a fair point that you can adopt a rotating frame of reference in which you are not moving. But the price of doing so is the emergence of so-called "fictitious forces" such as centrifugal force and, in relativity, serious complications related to clock synchronisation. Generally, you'd consider someone "at rest in a rotating frame" to be moving because they themselves can detect the acceleration even if they were shut in a box.

Well, point A can be earth. Point B are me in first floor of building and point C is my friend in tenth floor of building. Earth rotates around it's axis, so we move in circular rotation around earth, but at different distances from earth axis.
Earth is big enough and moves slowly enough that you can largely treat yourself as standing on a Euclidean plane at rest in an inertial reference frame. That's why you can treat your friend as stationary without worrying yourself about details. But if you make sufficiently precise (or sufficiently large scale) measurements, you'll be able to see effects from the fact that you are approximating. Notably, hurricanes.

I was reading about linear motion and that tow objects moving in same direction at same speed will be stationary with respect to each other. They do not see that they move with respect to each other (because they don't). And I thought that objects moving in rational motion do not see that they move with respect to each other (but they do).
It depends what you mean by "moving", basically. When you say that you and your friend aren't moving you are implicitly adopting a rotating frame of reference. If one adopts a non-rotating frame then you are both moving at different speeds. See my first paragraph.

Rotating frames have a lot of complications compared to inertial frames. For example, clocks at relative rest in an inertial frame tick at the same rate. Clocks at rest in a rotating frame tick slower the further from the axis they are - and you can't even be at rest when you are far enough from the axis that "at rest in the rotating frame" means "moving at or above light speed in an inertial frame". And clock synchronisation is a complicated topic. All this is why I suggest getting to grips with linear motion first.

Dale
Thanks.