Re: Can anyone prove that a gravity field is infinite.

Dear Don!

I'm not quite sure what you mean by ``finite'' with respect to gravity, but from your comments on Planck's Length I assume that you imply that if there were a certain ``granularity'' of spacetime, force fields could not become infinte (for example at the centre of a black hole).

Planck's Length is the only length scale one can construct using only the ``natural constants'' G (gravity constant), h (Planck constant) and c (speed of light): L=sqrt(Gh/c<sup>3</sup>)=4.05x10<sup>-35</sup>m. It is thought to be the scale on which quantization of gravity might become important, and quantization is indeed the important point here. Consider something simpler than gravity, e.g. an electric point charge. The electric field of such a charge becomes infinitely large as you approach it, and if you calculate the overall energy that is contained in this field you get infinity! This means of course that a point charge is not a sensible concept in physics. Why do many physicists use point charges then? Well, under some (actually many) circumstances, a point charge can be a pretty good approximation to reality. If you are not interested in the energy contained in the charge's field you could be quite happy with it. That's what all physics students do when they first calculate the energy levels of the hydrogen atom: The proton in the centre is treated as a classical point charge (classical means that its quantum nature is neglected, see below), and only the electron is ``quantized''.

As soon as quantization comes into play, classical point charges have no meaning any more. The Heisenberg Uncertainty Principle forbids the simultaneous determination of location and momentum of any particle. What you must work with are particle densities, or better fields, and that provides an automatic regularization of the classical infinities described above. In this sense, Planck's Length sets the scale on which it is not sensible any more to speak of a `point mass' - you have to consider quantization effects which render your fields finite. But as this scale is to unbelievably small (it's 10²⁰ times smaller than the size of a proton!), and nobody was ever (and most probably won't be for quite some time) able to measure any processes which occur on that scale, many physicists are quite happy with the notion that the Planck Length is compatible enough with zero.

Let me finally add that it is far from established that the Planck Scale sets some ``minimal interaction distance''. In the past, dimensionality arguments like the one that leads to the value of L have often proved to be more or less reliable, but they are no substitute for a thorough theoretical investigation or experiment. And, as I have mentioned, experimental technology is still far away from reaching energies at which the Planck scale could be observed (about 10¹⁹GeV).

Hope that helps,
Georg.