Contraction of length under relativity proven wrong

[Semjase]

Here's an example of contraction of length of a moving object

proven wrong.

 

If you have a ring with a radius of 1m spinning at a velocity of (.75)^.5 of c,

under relativity it's radius should appear to be .5m to a stationary observer.

Now if you have a clock hand with a radius of 1m with it's outside tip

spinning at at a velocity of (.75)^.5 of c then the clock hand should also

appear to have a radius of .5m to the stationary observer. If you take

an instantaneous snap shot of the moving clock hand, taking into account the x,y

velocities of the clock hand when the clock hand in line with the x axis,

the clock hand should narrow and shrink radially very little.

Taking the ring into consideration the with the same logic the circumference

of the ring should half. In reality they would both have to shrink radially the

same since the are in essence one in the same. So why does relativity

predict this difference in radial shrinkage in the clock hand and the ring?

[swansont]

Here's an example of contraction of length of a moving object

proven wrong.

 

If you have a ring with a radius of 1m spinning at a velocity of (.75)^.5 of c,

under relativity it's radius should appear to be .5m to a stationary observer.

 

Why? Length contraction is along the direction of motion. The standard argument is that there is a problem with the circumference, not the radius.

 

http://en.wikipedia.org/wiki/Ehrenfest_paradox

 

Now if you have a clock hand with a radius of 1m with it's outside tip

spinning at at a velocity of (.75)^.5 of c then the clock hand should also

appear to have a radius of .5m to the stationary observer. If you take

an instantaneous snap shot of the moving clock hand, taking into account the x,y

velocities of the clock hand when the clock hand in line with the x axis,

the clock hand should narrow and shrink radially very little.

Taking the ring into consideration the with the same logic the circumference

of the ring should half. In reality they would both have to shrink radially the

same since the are in essence one in the same. So why does relativity

predict this difference in radial shrinkage in the clock hand and the ring?

 

Because your prediction is wrong.

[Iggy]

Taking the ring into consideration the with the same logic the circumference

of the ring should half. In reality they would both have to shrink radially the

same since the are in essence one in the same. So why does relativity

predict this difference in radial shrinkage in the clock hand and the ring?

 

The circumference doesn't shrink (if I understand you) -- it increases. If observers take rulers onto the spinning ring and lay them along the circumference, the rulers will shrink from the perspective of a static observer. More of the shrunken rulers (that move along with the ring) will fit along the circumference than static rulers (which don't move along with the ring). More rulers = more distance,

 

The radius doesn't length contract to the same extent. The ratio between the circumference and radius is therefore not pi, which is what I think you mean when you say "difference in radial shrinkage in the clock hand and the ring". This isn't a paradox. It just means that the spinning disk isn't Euclidean in the spinning frame.

 

They call your thought experiment Ehrenfest's paradox

[Semjase]

I don't buy into Eisteins explanation for Ehrenfest's paradox

any 3D motion can be made up of x,y and z velocities with respect

to the observer and the length contraction should be applied

to the x,y and z axes velocities accordingly, a spinning disk shouldn't be treated

any differently.

[SamBridge]

But in a circular motion the direction is always changing, so the relative length contraction at any point is along a different relative angle at an instantaneous moment so you would get different results. Sometimes it would be contracting towards you, sometimes away from you, and all the places in between.

Edited January 13, 2013 by SamBridge