Do Objects in Motion Share the Same Time Reference?

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The discussion centers on the relationship between motion and time reference in the context of the theory of relativity. It posits that two objects moving at the same speed, such as those on a table rotating with the Earth, share a common time reference. When one object is lifted, it alters its speed and thus its time reference, leading to a separation from the other object. This concept suggests that objects remain connected not solely due to speed but because they exist within the same temporal framework.

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I've just started to understand the theory of relativity. Since the speed of light is the only constant in the speed of anything and time is a variable, just as much as distance is a variable, I'm starting to wonder about the time of individual objects. If an object traveling at 3 mph has a slower time than an object not traveling (faster than the rotation of the earth), however infinitesimal, that object would essentially be in a different 'time.'

Two objects not connected but pushed up against each other are sitting on a table, traveling at the speed of the rotation of the earth. At the same speed, they would have the same time reference. When one of the objects is picked up, it suddenly increases speed and thus enters a different time reference, all of the bits of that object move along with it into the same time reference. The object still on the table is no longer in the same time reference and thus separates from it. Similarly if we were to split the moving object in half, it would separate only because the atoms at the separation points were no longer in the same time reference.

So in a way we could say that things move together not because they have the same speed in the same direction, but rather that they stay within the same time reference, they move at the same 'time.'

Is this an idea that has been explored by anyone?
 
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