Unravelling the Mysteries of Spinning 1-Spheres

[yourdadonapogostick]

am i missing something here?
we have a circle: $$(x-h)^2+(y-k)^2=r^2$$ where (h,k) is the center and r is the radius. we now spin the circle about an axis that is perpendicular to the plane on which the circle lies and it runs through the center of said circle. gravity contracts length (and my the equivelance principle, so does acceleration), so as the 1-sphere spins about the axis, the distance between any two points on it decreases while the radius stays the same. since $$\pi=\frac{c}{2r}$$, where c is circumference and r is radius, $$\pi$$ no longer is a constant. the circle shrinks, but the radius stays the same. what is going on? does the circle turn into a cone?

that post got me thinking. would such change in geometry change the way a string vibrates? if so, that would cause predictable changes in the properties of a particle spun arund an axis that runs through the center of the string and perpendicular to the plane on which it exists. so, spin a bunch of particles and eventually you will get one to spin in the correct manner. if you find the predicted change in particle properties, wouldn't that be evidence for string theory?

 

[yourdadonapogostick]

well, i thought it was a good idea. any ideas on why it is or isn't?

 

[Berislav]

I'm not sure what you mean by spinning particles, but quantum mechanical spin has nothing to do with spinning.

 

[Igor_S]

well, i thought it was a good idea. any ideas on why it is or isn't?

I'm not sure about the strings, but I know there are some problems in defining rigid bodies in special relativity. I think you have to pinpoint the exact location from where did the circle began spinning (what point of the circle is the first one to experience force) and that would be complicated. I had this problem in my course in electrodynamics, but as I remember we "solved" it by stating that there is a problem of defining a rigid body. Maybe someone else knows ?

However, the QM spin is magnetic moment of a particle, therefore it's not related with the shape, but with EM properties (of "strings", if you like ).

 

[Berislav]

I'm not sure about the strings, but I know there are some problems in defining rigid bodies in special relativity. I think you have to pinpoint the exact location from where did the circle began spinning (what point of the circle is the first one to experience force) and that would be complicated. I had this problem in my course in electrodynamics, but as I remember we "solved" it by stating that there is a problem of defining a rigid body. Maybe someone else knows ?

I don't know about that. I heard that spinning bodies aren't well defined in context of general relativity, as in the Riemann geometry the Ricci curvation tensor must be symmetric; this causes problems with exchange of orbital angular momentum and spin because the momentum tensor shouldn't be symmetric in such cases.

but with EM properties (of "strings", if you like ).

One also has Ramond and Neveu-Schwarz sectors which play a part in determing the spin associated with open and closed strings.

P.S.
Pozdrav! Kako sve na PMF-u?

 

[Igor_S]

I don't know about that. I heard that spinning bodies aren't well defined in context of general relativity, as in the Riemann geometry the Ricci curvation tensor must be symmetric; this causes problems with exchange of orbital angular momentum and spin because the momentum tensor shouldn't be symmetric in such cases.

I have a rather weak knowledge of GR (and it don't contain many-body or rigid systems), so I don't know. The problem in SR is in the fact that different parts of the rigid body do not (in general cases) accelerate simultaneously.

 

[yourdadonapogostick]

I'm not sure what you mean by spinning particles, but quantum mechanical spin has nothing to do with spinning.

i was talking about actually spinning them around an axis, not qm spin.