Would two asteroids tied together with string and rotating around each other in an empty Universe generate centrifugal force?

See Mach’s Principle, which in turn influenced Einstein’s formulation of general relativity. It can be stated, “Local physical laws are determined by the large-scale structure of the universe.” Great question.

As long as the laws of gravity still applied, yes they would generate centrifugal force.

Seems to me the tension on the string is an indicator of actual spinning around the center-of-mass of the two part system. If there is no tension there is no spinning. If there is tension then there is spinning and the amount of tension would help you determine exactly how much spinning is going on. No external reference point needed.

@dabbler We are trying to predict, in advance, whether there will be tension on the string.

Assuming an “empty universe” is, of course, an extraordinary thought experiment far from reality. Newton would have said it doesn’t matter, but not Einstein.

A vacuum is filled with a whole bunch of particles that are created and destroyed almost instantly, which would seem to me to mean that where there is space, there is matter and energy. So, EITHER the universe does not extend past the asteroids, OR the universe does not have the same physical laws.

In the second case, there is absolutely no way for me to predict what will happen.

In the first option, EITHER there needs to be space through which the asteroids will rotate, OR the fabric of space-time rotates with the asteroids.

This first option would violate the whole “no space beyond asteroids” idea.

With this second option, the setup is EITHER identical to the asteroids not moving at all, OR it is not because the universe is rotating relative to the multiverse.

In the first case, NO.

In the second case, I have no idea.

GQ.

Assuming physics operated as it does in this universe, then yes. If you were there and had some light to see it with, it would be seen spinning. Translation movement is relative, but rotational movement is not. If you had a force measure on the string, it would show the amount of force the string was subjected to by the asteroids being pulled by the string preventing them from going on their own ways instead of being kept spinning together by the string.

Note you’d need an extremely strong string to actually restrain an asteroid.

@CaptainHarley Gravitational force would only be a small force with compared to the typical size and motion of asteroids.

The question has to do with inertia and is similar to asking if a body in an empty universe would possess inertia. According to Mach it wouldn’t, as inertia is caused by all the surrounding matter in the universe. Bodies are affected gravitationally by all other matter in the universe so this idea isn’t at all crazy. As far as I can make out inertia is still not properly understood and it isn’t incorporated in Einstein’s theories of relativity and so no one knows for sure what would happen.

@Zaku Once you have imagined an empty universe imagining very strong string should be easy.