This recent paper describes the socalled Soccerball problem in quantizing relativity.(adsbygoogle = window.adsbygoogle || []).push({});

Franz Hinterleitner

Canonical DSR

http://arxiv.org/gr-qc/0409087 [Broken]

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 invariantspeedwe may also have to allow for another invariant quantity, an invariantlengthperhaps, 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 thatwhatevereventually 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 itsflat 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 onmomentum densityThe 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 dont remember the title.

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# The Soccer Ball Problem in Relativity

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