Do Rotating Bodies Near Light Speed Exhibit Relativistic Effects?

[spidey]

Will there be any relativistic effects on a rotating body which rotates at velocity close to c...

 

[Fredrik]

There's always Lorentz contraction and time dilation when high speeds are involved, and if the object is massive (any actual physical object is), there will also be general relativistic effects: curvature, frame dragging, etc.

The most interesting special relativistic effect is that there's always a forceful stretching of the material when the angular velocity is changed.

There actually are no rigid bodies in SR. Turn a bicycle upside down and give one of the wheels a spin. The wheel is now getting Lorentz contracted along its circumference, but it stays the same length in the original rest frame (we can be sure of that because the symmetry of the situation guarantees that all the points along the circumference have identical world lines), so it must be getting forcefully stretched. This means that anything that rotates isn't even approximately rigid (or even approximately Born rigid).

 

[spidey]

There's always Lorentz contraction and time dilation when high speeds are involved, and if the object is massive (any actual physical object is), there will also be general relativistic effects: curvature, frame dragging, etc.

The most interesting special relativistic effect is that there's always a forceful stretching of the material when the angular velocity is changed.

Does a rotating body have magnetic field? if so, will the magnetic field also gets contracted?

 

[stevebd1]

There's a (very) short video from the Spitzer website called 'Spitzers spin on stars' which you can find on Youtube. Alternatively, you can download it directly from the NASA website-

http://www.nasa.gov/multimedia/podcasting/universe_video_archive_1.html

While not massively informative, it does answer your question.

regards
Steve

 

[Merlinus]

We know neutron stars spin rapidly - so what of the objects we define as black holes?

What happens when the centrifugal force & gravitational force reach equilibrium? - this would imply that singularities will not form, only that a star might only collapse to a given size.

Thoughts, please.

 

[Dale]

I think the singularity of a Kerr black hole is supposed to be a ring rather than a point, but it is still supposed to be a singularity (0 thickness).

 

[Merlinus]

Yes, you're correct - why stop at rings when there's spheres, hypertoroids and other higher dimensional geometric singularities?

I think the singularity of a Kerr black hole is supposed to be a ring rather than a point, but it is still supposed to be a singularity (0 thickness).

 

[Dale]

Because they are not solutions to the EFE.

 

[Merlinus]

Why limit oneself to Einsteins field equations?

Because they are not solutions to the EFE.

 

[Dale]

Why limit oneself to Einsteins field equations?

Because you are talking about black holes.

 

[spidey]

Does a rotating body have magnetic field? if so, will the magnetic field also gets contracted?

 

[Naty1]

Does a rotating body have magnetic field? if so, will the magnetic field also gets contracted?

Since an electromagnetic field can be thought of as consisting photon quanta and photons are curved by gravity, gravitational forces DO curve electromagnetic fields. But gravity is I believe on the order of 10^80 times weaker than EM forces, so it's a negligible effect under most circumstances.

 

[Naty1]

What happens when the centrifugal force & gravitational force reach equilibrium? - this would imply that singularities will not form, only that a star might only collapse to a given size.

It's possible, nobody knows for sure...The mechanism of collapse is still a matter of debate:
From Peter Bergmann's THE RIDDLE OF GRAVITATION, PG 133:

Therorists have speculated whether matter, once compression reaches extreme values, might not build up enormous counterpressures, so that eventually collapse is halted...Sufficiently rapid rotation might prevent collapse, but if too vigorous would tear the quasi-stellar body asunder. Whether there are states of rotation that will maintain arbitrarily large masses stable remains to be settled...

And he discusses interesting theoretical calculations conducted by Oppenheimer and Einstein...neitherof which was able to resolve the issue.

 

[Naty1]

Does a rotating body have magnetic field?

Wiki sez:
http://en.wikipedia.org/wiki/Planet#Magnetosphere

Magnetosphere

One important characteristic of the planets is their intrinsic magnetic moments which in turn give rise to magnetospheres. The presence of a magnetic field indicates that the planet is still geologically alive. In other words, magnetized planets have flows of electrically conducting material in their interiors, which generate their magnetic fields

I can't think of a a reason for a non relativistic rotating solid body to otherwise have a magnetic field, but I would not rule it out. It's easier to visualize a viscous body perhaps having dipole's formed at higher rotational velocities.

Also keep in mind that electric field in one reference frame is a magnetic field in another; so a static charge on a rotating body will have a perceived magnetic field component.

 

[spidey]

Since an electromagnetic field can be thought of as consisting photon quanta and photons are curved by gravity, gravitational forces DO curve electromagnetic fields. But gravity is I believe on the order of 10^80 times weaker than EM forces, so it's a negligible effect under most circumstances.

But i asked in SR perspective not GR..rotating body experiences length contraction and so will the magnetic field also gets contracted from SR perspective?

 

[Naty1]

so will the magnetic field also gets contracted from SR perspective?

I'm pretty sure,Yes.

But the exact mechanism is not clear to me.

In THE RIDDLE OF GRAVITATION Peter Bergmann says:

In electricity the apparent contradiction between relativity and the law of electric forces is resolved by the discovery that Coulomb's law holds rigorously only if the charged bodies do not move with respect to each other...Whenever the charged particles move relative to each other Coulombs law must be replaced by a much more complex interaction which can best be described in terms of the fields generated by the interacting charges."

Maybe it can be thought of " as r changes due to relativistic effects, the particle separation changes and so the field must change"

 

[spidey]

I'm pretty sure,Yes.

But the exact mechanism is not clear to me.

In THE RIDDLE OF GRAVITATION Peter Bergmann says:



Maybe it can be thought of " as r changes due to relativistic effects, the particle separation changes and so the field must change"

Is rotation motion an inertial motion? Is rotational motion equivalent to object at rest and object at constant velocity?

 

[Jonathan Scott]

Is rotation motion an inertial motion? Is rotational motion equivalent to object at rest and object at constant velocity?

No, rotation is related to acceleration so a rotating frame of reference is not inertial. Mathematically, rotation is like an imaginary acceleration, or equivalently acceleration is like an imaginary rotation.

Rotation is related to acceleration in the same way that magnetic fields are related to electric fields.

The gravitational field of a moving or rotating body includes a "gravitomagnetic" part which has the effect of making a test object experience an apparently rotating frame of reference, which is known as "frame dragging". Gravity Probe B has been attempting to measure this tiny effect as caused by the Earth's rotation.

 

[Naty1]

Is rotation motion an inertial motion? Is rotational motion equivalent to object at rest and object at constant velocity?

I agree with Jonathan's post.

How do you know rotational motion is NOT inertial?? because you feel a FORCE!

Constant velocity is unaccelerated motion, that is constant speed, in a straight line. You can think of rotational motion as constant speed (magnitude) with acceleration via a change in direction. Or to say the same thing another way, the radial acceleration radially exerts a force acting perpendicular to the direction of motion (tangential speed along the circumference).

 

[Naty1]

Does a rotating body have magnetic field?

I had not thought of this before: If a rotating body did always have a magnetic field, we could rotate a piece of wood, for example, and produce a magnetic field to generate power...

 

[spidey]

No, rotation is related to acceleration so a rotating frame of reference is not inertial. Mathematically, rotation is like an imaginary acceleration, or equivalently acceleration is like an imaginary rotation.

Rotation is related to acceleration in the same way that magnetic fields are related to electric fields.

The gravitational field of a moving or rotating body includes a "gravitomagnetic" part which has the effect of making a test object experience an apparently rotating frame of reference, which is known as "frame dragging". Gravity Probe B has been attempting to measure this tiny effect as caused by the Earth's rotation.

If rotation is not inertial then it should not have relativistic(SR) effects correct..why it is having

 

[Jonathan Scott]

If rotation is not inertial then it should not have relativistic(SR) effects correct..why it is having

Not correct.

Relativistic effects in SR are primarily related to velocity. Rotation and acceleration result in velocities which are not constant, and therefore make it more complicated to calculate some of the effects, but velocity-dependent effects are still present exactly as for inertial frames of reference.

 

[||spoon||]

This is to do with another topic, but it is relativity and roation based so thread name kinds fits...

Anyway, if there is a cube at rest with respect to your reference frame, you can only see a maximum of 3 sides, disregarding mirrors etc...
I was recently told that if the cube were traveling at speeds comparable to that of light with respect to your reference frame you would be able to see more sides than this; and further that the object would appear to rotate as it passed you.

Is this true? If so, could someone give an explanation of why?

Thanks,

-spoon

 

[Naty1]

If a body reaches near light speed, it's mass become huge...and may bend/curve light...like a planet which moves much more slowly...bending light might reveal more about the object...see my thread LIGHT WITH GRAVITY AND MIRRORS ...for a reference including a sketch...
such would be analogous to gravitational lensing...

I don't know why it might appear to rotate.

 

[matheinste]

Hello spoon

The thing you are looking for is Terrell Rotation.

Matheinste.

 

[DrGreg]

This is to do with another topic, but it is relativity and roation based so thread name kinds fits...

Anyway, if there is a cube at rest with respect to your reference frame, you can only see a maximum of 3 sides, disregarding mirrors etc...
I was recently told that if the cube were traveling at speeds comparable to that of light with respect to your reference frame you would be able to see more sides than this; and further that the object would appear to rotate as it passed you.

Is this true? If so, could someone give an explanation of why?

Thanks,

-spoon

See Terrell rotation and Penrose-Terrell Rotation.

 

[Naty1]

Interesting read on Penrose Terrell...So it sounds like that deswcription ignores the gravitational lensing idea I used...Is that reasonable; that is, is the gravitational curving of light insignificant compared to the Penrose effects.

 

[DrGreg]

Interesting read on Penrose Terrell...So it sounds like that deswcription ignores the gravitational lensing idea I used...Is that reasonable; that is, is the gravitational curving of light insignificant compared to the Penrose effects.

See also "If you go too fast, do you become a black hole?". Note that article, and your question, use "mass" to mean "relativistic mass", which includes kinetic energy, but most physicists use "mass" to mean "rest mass" which excludes kinetic energy. Although the article refers to black holes, the same principle applies to gravitational lensing.

 

[||spoon||]

Thanks that was what i was talking about :)

On a side note, if you can see more than three sides... How many could you see as a maximum?

-Spoon