Can the Ehrenfest Paradox Occur for a Rotating Body with Relativistic Speeds?

[vin300]

For a body of
m=1kg, v=0.1c, and rotating with r=1m, lorentz factor =1/0.99
the centripetal force is (c^2 *10^-2)/0.99 N
This force creates enough stress in the body to break it apart
This effect reduces at values of r comparable to c^2 which again is purely fictitious like the "superluminal scissors"

 

[Dale]

Yes, the stress in a material disk will become infinite before the rim reaches c.

 

[vin300]

Most strong metals have an ultimate strength of a few hundred megapascals, but a velocity enough to consider length contraction stresses the material way beyond to be intact.

 

[atyy]

Isn't the Ehrenfest paradox supposed to illustrate how acceleration can mimic warped space? And surely the disc is warped after it's broken :tongue2:

 

[vin300]

If the disk is not in place, where will you set up the born rigid rods?

 

[vin300]

Natural disks disintegrate at velocities comparable to c so there is no Ehrenfest's paradox.Is this okay?

 

[JesseM]

Natural disks disintegrate at velocities comparable to c so there is no Ehrenfest's paradox.Is this okay?

No, the Ehrenfest paradox does not depend on the outer rim of the disc actually reaching c, only on going at some relativistic speed like 0.5c. There's no theoretical reason why this should be impossible, even if it might be difficult in practice.

 

[vin300]

No, the Ehrenfest paradox does not depend on the outer rim of the disc actually reaching c, only on going at some relativistic speed like 0.5c.

Post#1. 0.1c is way far from enough to do it.

 

[vin300]

If this is correct and agreed, I need help to forward it

 

[JesseM]

Post#1. 0.1c is way far from enough to do it.

It's a theoretical paradox, so even if we don't happen to have any materials that would withstand the stress above 0.1c (and I'm not sure if this is true, you don't give any references about tensile strength or anything along those lines in post #1--also, why do you only consider a small disc or radius 1m? Why not a disc of 1 km or 1 light-year, for example?), this is irrelevant as long as such a supermaterial is not forbidden by the laws of physics.

 

[vin300]

Also, the length contraction is contributed by elongation perpendicular to motion due to the stress, in both frames(if the disk riding observer is alive in theory)

 

[vin300]

The considerations of a large radius, a supermaterial at lesser radii, length contraction and elongation of radius due to stess do not appear in any text of the paradox

 

[JesseM]

The considerations of a large radius, a supermaterial at lesser radii, length contraction and elongation of radius due to stess do not appear in any text of the paradox

That's because they are irrelevant to the theoretical principles the Ehrenfest paradox is supposed to illustrate, much like how discussions of the twin paradox never explain what type of fuel is used by the traveling twin's rocket.

 

[atyy]

The considerations of a large radius, a supermaterial at lesser radii, length contraction and elongation of radius due to stess do not appear in any text of the paradox

http://books.google.com/books?id=fUj_LW51GfQC&dq=rindler+relativity&source=gbs_navlinks_s

See page 71, and footnote 5 on page 72.

 

[vin300]

(Almost) unstressed disks can be created, but the tensile strength is compensated.
As for the supermaterial, it can undergo close-to-infinite extension for close-to-infinite stresses which is out of the range of electromagnetic attraction