A perfectly smooth sphere

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Is rotating with whatever angular velocity we want in a vacuum, it and you being the only objects around (assume no intrinsic properties like charge/mass).

How do you tell that it's doing so? And if it has perfect rotational symmetry, does it even make sense to say that it's rotating?

This has been gnawing at me for a few months but I never thought about asking.

Any ideas? What if it has charge or mass? Could you apply any studies of say, the lens-thirring effect to deduce anything useful? I am baffled.
 
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If the sphere is really massless, then it can only travel with the speed of light. All of it's parts must also be massless and travel with c, so it can't rotate.

Let's assume it has a mass. I would try to attach a light weigt to the surface of the sphere with a spring. If the sphere is rotating, then the weigth is accelerating and the spring will extend.

But is it possible to attach something to a perfectly smooth sphere? I think not: it must be rough at least on atomic level, otherwise it can rotate without changing energy of any bond.
In this case we should carefully break the sphere into pieces without adding momentum to pieces.The pieces will fly away from each other if the sphere was rotating.
If the sphere would be charged, determining rotation would be easier, because it would produce magnetic field. It would also feel other magnetic fields: a homogeneous mag. field would cause precession (similary as with electron), which could be detected by measuring induced voltage in a coil.
An electron is in fact pretty similar to a charged perfect sphere (except that it's radious is unknown or zero).
 
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Andy Resnick
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This is a bad gedanken experiment- clearly, there has to be other things in the universe, such as a light source to see the sphere. And measuring tools?

So, one way would be to look for a doppler shift off the light reflecting from the sphere. And as you move around the sphere, the doppler shift would change as you approach the axis of rotation.
 
dst
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You can have whatever you want. As long as the sphere stays a perfect sphere. What I'm getting at is perfect rotational symmetry, not necessarily with a sphere. How does it work?
 
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Allow the sphere to split down the centre. Cut instantly in 2 halves by a laser beam

two halves will fall apart if was rotating/spinning, and they fall away from each other at constant velocity
They' ll still be spinning as they fall away into outer space.

two halves stay side by side if its not rotating/spinning
 
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berkeman
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This is a bad gedanken experiment- clearly, there has to be other things in the universe, such as a light source to see the sphere. And measuring tools?

So, one way would be to look for a doppler shift off the light reflecting from the sphere. And as you move around the sphere, the doppler shift would change as you approach the axis of rotation.
I don't think there would be a Doppler shift for visible radiation. But X-ray diffraction/reflection should be affected, for sufficiently high velocities, I would think.
 
Andy Resnick
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There's always a doppler shift, regardless of the wavelength and velocity. The trick is in measuring it. Since the OP said I could have whatever I want, I want a infinitely accurate and precise spectrometer :)
 
dst
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Would that work?

How about if we add another condition, you can't do anything to affect the rotational symmetry of the sphere itself? If you were restricted to just the space around it.

Also, does this count as a "preferred" reference frame? Anyway, in what ways would such a sphere be different from one that doesn't rotate? According to QM particles are indistnguishable (no way to say "this or that" particle) so again, can there actually be rotation?
 
Andy Resnick
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Are you thinking (or have your thought about) about Mach's principle? Newton's bucket?
 

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