A theoretical question about something that may or may not be relative.?

Question

This is about an imaginary universe in which the laws and properties of matter are equal to ours.

If you only have two objects in this universe, an observer who observes a round object spinning wildly. This second object is spinning about so quickly that any increase in its spin would cause it to lose coherence and break apart into small pieces.

If this situation had one change only, nothing else is changed in this scenario; namely, the observer is somehow removed from this universe so that only the spinning object remains left in this universe the following questions arise:

Does the object still spin? If yes what does it spin in relation to? How can you tell it is spinning?

If no, what happened to the energy that the spin clearly endowed the object with?

Answer 1

Good question. If there were only one object with mass in the universe, it could not have angular momentum. Now, this is not obvious, but is implied by General Relativity. There is a theorem called Mach's Principle which states that the total angular momentum of an entire universe has no observable consequences and, therefore, may as well be set to zero.

The reason for this has to do with something called "frame dragging". It's important to remember that in GR, it is the mass in the universe that determines the space-time metric. If there were only one mass and you imagine it spinning, the metric would be dragged around with it, relaxing any centripetal forces holding it together. That is, it would behave as if it were not spinning, so you might as well say it wasn't.


Removing a second object from the universe is a red herring because that would violate conservation of energy, of which mass is a form. With such magical powers, you can assume anything you wish will happen. You should not be surprised, for example, that violating conservation of energy causes a violation of conservation of energy.

Answer 2

This is not a good theoretical construct, but I'll try and answer it anyway. I assume the objects are not atomic or subatomic, but it doesn't really matter when talking about spin.

One of our physical laws is the law of conservation of Angular Momentum, so the answer is, observer or no, the object will spin just the same.

This is akin to asking "If a tree falls in a forrest, and nobody is around to hear it, does it make a sound"

That question is more philosophical than scientific. Any falling body has to impact something with a certain amount of energy. The result would have to make some sound.

Answer 3

Oh wow... that's a pretty good question. My best answer is that if you say that it is no longer spinning then you're changing the inertial reference point, and you can't do that.