Dr Lubos Motl, string theorist, responds to me with a weird message, probably because he is stuck with the string length and cannot do anything about it in the string community: http://motls.blogspot.com/2005/09/crichton-in-senate.html

Nigel said...
Dear Lumo,

You say 'Your 10^{-58} meters as an alternative for string scale is nonsense, and you can't justify it, and no one can reproduce it.'

I said it was the black hole size, R = 2GM/c^2

Putting in the electron mass gives something on the order 10^-58 m.

I did explain this is black hole size.

The Planck size is determined by dimensional analysis to find the smallest possible length from fundamental constants.

It is disproved, because the black hole size of an electron is smaller than the Planck size.

Planck evidently did not think of proposing the combination of units MG/c^2 to get length, with M the electron mass.

If you want theoretical justification for the black hole electron, check out my internet site. [http://nigelcook0.tripod.com/] However, there is no justification for the Planck size experimentally or theoretically. It is nonsense to use this unit in ST.

This doesn't need a DSc. It is obviously an error on the ST background which is ignored.Best wishes,Nigel

7:06 AM
Lumo said...

Dear Nigel,

the black hole whose mass equals the mass of the electron definitely can't be described by a trustworthy solution with the radius 10^{-58} meters.

As you say correctly, there are many new effects that become important at distances much longer than 10^{-58} meters and that prevent one from considering these very short distances. The Planck scale will definitely come to rescue if nothing else.

Of course that there are ways to multiply and divide the elementary constants without any rational thinking to obtain more or less anything - but it does not mean that anything is relevant for physics.

All tbe best
Lubos