# Accelerated frames

1. Jul 14, 2007

### enridp

Hello everybody !
This is my question:
Suppose you have a mass m0 inside an ellipse (at rest).
Suposse someone see it from another frame, from this frame he will see the ellipse contracted.
I know there's no black hole, but, how can explain our observer this result?
I'm trying to see only the frame of our observer, I know he knows about relativity and he can calculate our m0, and our r0 (ellipse's radius at rest), and then conclude there's no black body. But what is seeing at really our observer? I mean, he can explain it seeing our viewpoint and noting that there's no black hole, but how can explain it from his own frame?

Thanks !

PS: I have read many times articles like:
If you go too fast do you become a black hole?
http://www.math.ucr.edu/home/baez/physics/Relativity/BlackHoles/black_fast.html
and again, I don't think there's a paradox here, I'm just trying to see what is seeing our observer.
Maybe is analogous to:
When we see a moving frame, we see their atoms contracted in the direction of motion. Then the orbitals don't follow the expected symmetry, how can be stable these "deformed" atoms?

2. Jul 14, 2007

### pervect

Staff Emeritus
This doesn't seem to have anything to do with acceleration if I'm understanding the question correctly - all you have is a standard Lorentz boost.

I'd suggest considering a much simpler problem first:

What is the electric field of a moving charge?

See http://www.phys.ufl.edu/~rfield/PHY2061/images/relativity_15.pdf
for the answer - for the mathematical details, start at

http://www.phys.ufl.edu/~rfield/PHY2061/images/relativity_1.pdf

and work you way up to slide 15.

You'll see that the electric field of a moving charge does is not radially symmetrical - it's stronger in the transverse direction. There are also magnetic forces that come into play in the moving frame. Something very roughly similar happens for gravity (including the existence of "gravitomagnetic forces"), but there are significant errors in treating gravity as a force when you get up to relativistic velocities. A fully correct treatment requires understanding gravity as a curvature of space-time, which requires differential geometry. If you don't mind potentially large errors (say 2:1 or so), you can get a very rough idea of what happens in the case of gravity by replacing the masses with charges.

Of course, you have to understand how the electromagnetic field transforms to handle even this simpler problem.

Last edited by a moderator: Apr 22, 2017
3. Jul 15, 2007

### enridp

Yes, sorry, I made a mistake, it's just a simple relative observation...
My question is: what is seeing the "moving" observer? and how ca he explain its observation from his own frame?
(could you change the subject to a better one?)

Thank you very much pervect for your links, I will read it carefully.
But I think I understood the basic idea. I was thinking that physics was not the same in the "moving" frame because we ("stationary") are seeing "stranges things" when we are observing a moving frame (black holes that not form, deformed atoms...)
But if I have understood, we see the same physics anywhere (like the firs postulate require), but the laws are not so simply now, we are treating with "covariant" and tensorial laws. Then, we can explain everything from our own frame with the same laws of physics, but we will see "extra" components from these laws...
Tell me if I'm under the right way please.
Maybe I could see it better if you explain to me how to understand this:

We have a block, solid, which is 1 meter in length at rest. At 0.866C its new
relative length would be 0.5 m. Thats OK, but what happens if you look at it in terms of atoms? Each proton, neutron and electron will decrease in length in the direction of motion. The orbits of the atoms would have to contract. The electrons now traverse elliptical orbits around the nuclei, rather than spherical. But how?, I mean, without seeing it (well, at really I don't know if we can "see" it ^_^), how can deduce these orbits?

I'm not looking for rigorous details, I don't want to exploit your time neither. But perhaps you can explain it very well with a few lines, like a "divulgation" text.

thanks again !