The Soccer Ball Problem in Relativity

[marcus]

This recent paper describes the socalled Soccerball problem in quantizing relativity.

Franz Hinterleitner
Canonical DSR
http://arxiv.org/gr-qc/0409087

It makes an attempt to solve the soccerball problem, also known as "the problem of macroscopic objects".

Here is how the problem originated.

Relativity is probably going to be quantized (there's been a fair amount of progress towards it and some interesting results about removing singularities.)

Nobody can say by what approach but ANY approach to quantum gravity, especially if it is quantizing spacetime geometry, is likely to have the Planck scale playing an essential role.

This probably means that the Planck length will have to look the same to all observers, or to a large class of observers. Not only the speed of light is invariant, in other words. Besides having an invariant speed we may also have to allow for another invariant quantity, an invariant length perhaps, or an invariant energy.

Energy and length invariants amount to much the same thing because of the relation of wavelength and frequency to energy.

So there have been appearing these various proposed multi-special relativity frameworks. And there's a widely shared expectation that whatever eventually turns out to be workable as a quantum theory of gravity is going to have some kind of DSR (double-invariant-scale SR) or multiple invariant scale SR as its flat limit.

that is the limiting case where matter is sparse enough and gravity weak enough so that space is not noticeably curved----the flat limit is our everyday reality.

So even the large distances that gammaray bursts travel to come to us are approximable not by the flat space of ordinary SR but more likely by the flat space of some DSR.

This, interestingly enough, appears to be testable!

But meanwhile there is a theoretical problem. When SR is modified to give it another invariant scale there turns out to be a limit on momentum, or atleast on momentum density The momentum limit is the Planck momentum and it is very reasonable when applied to microscopic particles.
But it would not do as a limit on the momentum of macroscopic objects. By kicking a soccer ball one can give it more than the Planck momentum.

Hinterleitner has contrived to make the limit be one on how much momentum can be concentrated in a small space. So soccerballs, because by Planck standards they are not very dense, can have all the momentum they want.

here is Hinterleitner abstract:

"For a certain example of a "doubly special relativity theory" the modified space-time Lorentz transformations are obtained from momentum space transformations by using canonical methods. In the sequel an energy-momentum dependent space-time metric is constructed, which is essentially invariant under the modified Lorentz transformations. By associating such a metric to every Planck volume in space and the energy-momentum contained in it, a solution of the problem of macroscopic bodies in doubly special relativity is suggested."

The Soccerball Problem was mentioned in several recent papers on multi-special relativity (by Smolin, Kowalski-Glikman, Livine, Girelli, Oriti and others). I first remember reading about it in a paper of Rovelli some time back, but don't remember the title.

 

[skywolf]

what about black holes, i mean what would their density, would that mean that you can't give a black hole momentum? or am i completely misunderstanding this subject?

 

[marcus]

what about black holes, i mean what would their density, would that mean that you can't give a black hole momentum? or am i completely misunderstanding this subject?

you are pointing out something I haven't been able to undertstand yet about this paper

the first reaction would be not to worry about black holes---at least not about macroscopic black holes, because
the role intended for DSR is that of a "flat limit" of quantum geometry.
DSR is just a variation on the Minkowski space of special relativity.
So it would not be used to model black holes, or any situation where there was perceptible curvature

but that only seems to dispose of the problem
the fact is I cannot resolve it at this point. Because it seems to me that this paper is envisaging at once a standard flat space, like that of SR, a Minkowski space slightly modified in how the Lorentz group works on it, and at the same time allowing for massive particles, perhaps even very small black holes, to exist in it. How could these exist in the space without deforming it.

So maybe this DSR is only good as an approximation for very mundane everyday situations where there are not high (Planckian) density objects around to make the geometry non-flat. Maybe it it only works as an approximation in very mundane circumstances where the angles of a triangle always add up to 180 degrees and all that. And it is only the formulas of this version of DSR that are set up so it looks like near-planckian densities could be plugged in.

I will look at the article some more. Have you tried it, skywolf? It seems
clearer than usual in its writing, so probably more help than I can be right now.