# Magnets (and other things) at the speed of light

1. Oct 22, 2007

### LT07

Magnets at the speed of light.

I guess that if you propel a (natural) magnet close to the speed of light then nothing unusual happens to the magnetic field because it already exists and is accelerated along with the magnet, but what happens to an electro magnet?

If an electro magnet is traveling at 99.9999999999% the speed of light and you turn it on does the magnetic field stick to the surface in the direction of travel and radiate normally behind? The reason I ask this is because for the magnetic field to move forwards it would have to travel faster than the speed of light. (would it be a monopole?)

Rotating spheres (at the speed of light)

*NOTE to keep things simple I have reduced the speed of light to just 1,000 meters a second and I have a ball (made of anything you like) with a circumference of exactly 1 meter, if I rotate the ball at 1,000 revolutions per second the surface of the ball (in the direction of the spin) will be traveling at exactly the speed of light.

Ok now the question.

If I spin my ball to 500 RPS will it have a maximum speed of 500 MPS in the direction of the spin? is the rotational speed added to the forward motion? Or to put it another way, if my ball is traveling forwards at 950 MPS and it was spinning at 100 RPS in the direction of travel would it break the laws of physics because the surface of the ball was traveling faster than the speed of light (if you add the forward motion and the spin together)

An odd property of a ball like that spinning at 1,000 RPS would mean it would be impossible to move it in any direction (not just the direction of spin) kind of like an anchor in space.

2. Oct 22, 2007

### CPL.Luke

keep in mind that we cannot talk about objects moving at the speed of light, as no matter can move at the speed of light.

als the ball would be rotating at 2 pi c at the edge.

3. Oct 22, 2007

### LT07

I appreciate that matter cannot reach C, that's why the electromagnet is only traveling at 99.999999% of C. What I'm interested in is how the magnetic field would behave at relativistic speeds.

As for the ball rotating at 2 pi c at the edge!! It has a circumference of one meter therefore one revolution per second means the surface has traveled one meter, what I want to know is, do you add the rotational speed to the forward motion when thinking about the affects of relativity?

4. Oct 22, 2007

### Ich

You can find the transformation rules easily in the net, e.g. here.
Keep in mind that in this object's poit of view, there is nothing unusual about its electromagnetic fields, because it doesn't move at all in its own frame.
Yes, but you have to use the relativistic velocity addition, which leaves all velocities smaller than c.

5. Oct 22, 2007

### Mentz114

Magnetic fields are relativistic effects ( i.e. they depend on your frame of reference ) so different observers would see different magnetic fields from your electromagnet.

This stems from the fact that moving charges make magnetic fields, and movement is obviously relative.

6. Oct 22, 2007

### OOO

The problem with this example is that it is not as simple as it might seem.

You can't transform to the rest frame (Edit: i.e. the frame where the ball is not rotating) of the rotating ball by means of a Lorentz transform, and thus addition of velocities can't be done that easily. This is because rotation is a form of acceleration which you can't treat consistently in special relativity. One would have to use general relativity for that. If one did this one would notice that the ball's circumference gets distorted relative to the center of the ball if it approaches the speed of light (which it can't actually assume). If there is some additional translational motion near the speed of light then, obviously, there must be some additional distortion that prevents the circumference particles from exceeding the speed of light.

It's difficult to say how these phenomena look exactly, because in order to do that you would have to perform some quite heavy calculations, I guess.

Last edited: Oct 22, 2007
7. Oct 22, 2007

### Ich

It's quite easy to transform to and from the rest frame of the rotating ball. There's no problem to calculate the velocities of the ball's components in different inertial frames,too.
The problem arises when you try to transform to a frame where the ball is not rotating, because such a frame is not inertial. But you don't have to do that to answer the OP's questions.

8. Oct 22, 2007

### OOO

By the term "rest frame" I meant the system where the ball is neither rotating nor translating. I think, in order to understand how the rotating ball behaves (especially its circumference, when its tangential velocity approaches c), you have to solve it's internal equations of motion. I was assuming that one could avoid this by transforming to the rotating frame because then you "just" have to consider the ball in a curved spacetime.

I can't remember you having answered OP's question about what happens to the circumference of the ball when its tangential velocity approaches c. Are you denying that the ball undergoes a nonlinear distortion ? I assume you have good (although unexpressed) reason to claim that my answer is not necessary.

Last edited: Oct 22, 2007
9. Oct 22, 2007

### MrXow

For relativistic speeds, you cannot just use normal math. If you did rotate the ball at near the speed of light, the outer surface would have a lower angular velocity than the inside of the ball.

10. Oct 23, 2007

### Ich

And I can't remember the OP having asked about what happens to the circumference of the ball when its tangential velocity approaches c.

Given the positions and velocities of every part of the ball, it's not a big deal to transform these positions and velocities to a different inertial system. Nobody asked about the dynamics of rotating bodies, or about rotating reference frames. At least this is how I understood it.

11. Oct 23, 2007

### OOO

Huh ?

There is no way out of this paradox without pointing out, that the ball can't behave as a rigid body. So it's consequent to mention its deformation. Don't you like me to say that ? How else can I help you ?

12. Oct 23, 2007

### Ich

The only paradox is the classical "what if v=c" assumption. The examination of internal stresses and deformations as seen in a rotating frame (or by the elements of the ball) doesn't help in this case.

You're welcome to say what you like. And encouraged to read what I write. I don't have any ambitions to get into an argument with you. I simply disagree.

13. Oct 23, 2007

### OOO

Honestly, do you really think OP didn't know that ? You didn't explain how v<c is compatible with OP's assumption of a rigid body. Whereas I have tried to give a qualitative explanation. Criticizing me for that seems to be a bit overconfident.

Since you are so concerned about being helpful - would you mind giving us a description of what happens to the ball when you start to apply rotational acceleration to it so fast that its circumference approaches the speed of light ? What happens to the ball if the circumferential velocity would classically exceed the speed of light ? And what happens to the ball as you apply an additional translation to it in this state ?

Last edited: Oct 23, 2007
14. Oct 23, 2007

### Ich

I neither see the OP assuming a rigid body nor do I see the necessity to add such complications. The question was:
And the answer is: yes, but according to the relativistic velocity addition, which makes the paradox disappear.
I did not criticise you. I just wanted to make sure that the answer is in line with the question.
If you're interested in that topic, have a look at this thread.
But be aware that this is way beyond the scope of the OP's question (and my abilities) and does not help a bit to answer it.
In a state where its circumferential velocity would classically exceed the speed of light??

I see no point in continuing this debate. I did my contribution, you may take it or leave it.

15. Oct 23, 2007

### OOO

In order to enhance your ability to see the assumption of a rigid body, let's repeat what OP has proposed:

Such a behaviour (if it was real) clearly implements a constraint. What constraint should be responsible for that ? Feel free to provide any alternative explanation to mine, which is that OP assumes that the ball is contrained by rigid body conditions.

This is why OP asks himself, how can it be that the circumference moves at c when c can't be exceeded or reached. What you provided to him was just the explanation that c can't be exceeded. Well, he already knew that.

I appreciate that generally, although it should have become clear by now that my answer was well in line with the question.

We'll leave it.

Last edited: Oct 23, 2007
16. Oct 23, 2007

### Ich

Just one more thing: Maybe this is what the OP asked himself. But what he asked the pf is e.g.
So feel free to answer questions that you think the OP might ask himself, but let me answer the questions that he actually asked.

SCNR

17. Oct 23, 2007

### OOO

My balls spin at 1000 RPS and yours only spin at 500 RPS. Tee-hee. :rofl:

Just kiddin'. I think we won't feel the necessity to get in each others way from now on.

Last edited: Oct 23, 2007
18. Oct 23, 2007

### Ich

Assuming the same angular momentum, the difference is telling. :tongue:
Just kiddin'.
I really don't know what all that fuss is about. Just accept that I beg to differ. If that offends you, well, I can't help it.

19. Oct 23, 2007

### OOO

Granted.

20. Oct 23, 2007

### JesseM

I would disagree, a rotating ball can behave as a rigid body provided one does not apply any torque to it, and LT07's statement above does not require the assumption that we apply torque when attempting to "move it" (imagine using a magnetic field to pull it in the same direction as its axis of rotation, with the same magnetic force at every point inside the ball). Talking about deformations seems unecessarily complicated, given that LT07 just seems to be referring to the fact that the ball's relativistic mass has increased thanks to its rapid rotation.

Last edited: Oct 23, 2007