Re: Susskind on 'variation in Planck length'?

stargene@xxxxxxxxxxxxx wrote:

IF the authors are actually suggesting that the Planck length
might vary under certain conditions in our universe, they are
then also suggesting changes in one or more of the 'constants'
on the right hand side of the above equation. Unfortunately,
they do not expand on this statement any further in the book,
as far as I can tell.

Is this interpretation correct? Do some theorists posit a varying
Planck length?

Anyone who is thinking of varying dimensionful constants should read
the following trialog on a related topic:

Trialogue on the number of fundamental constants
Authors: M. J. Duff, L. B. Okun, G. Veneziano
http://arxiv.org/abs/physics/0110060

Personally, I side with Duff's opinion that there are zero fundamental
dimensionful constants. So a statement about a change in some of them
would be rather vacuous. While others may disagree about precisely how
many and which dimensionful constants are fundamental, what everyone
does agree on is that only comparisons between dimensionless numbers
are meaningful. For example, if we are comparing two lengths, say 1km
and 1cm, we would have to divide each by a reference length, say 1m,
and then compare the dimensionless ratios, 1km/1m = 1000 and 1cm/1m =
0.01.

So, to rigorously address the question of whether the Planck length can
be different in different parts parts and eras of our universe, you
need two ingredients: (1) a way to measure the Planck length in
different parts of the universe and (2) a reference length that can be
assumed to be the same everywhere and everywhen. However, satisfying
both these requirements is not as easy as it might seem at first,
mostly because you have to avoid circular definitions. And you still
need to make some kind of assumption in part (2).

I'm not saying this can't be done, but it is more subtle than a lot of
people realize. This kind of analysis was done for the fine structure
constant (alpha, since it is already dimensionless part (2) becomes
much simpler). And there are now very tight bounds on how much it could
have changed in the history of the universe. Over the past two billion
years, alpha has not changed more than 2 parts in 100 million, thats <
2x10^(-8). See:

http://www.eso.org/outreach/press-rel/pr-2004/pr-05-04.html

So, yes, some theorists are considering changes in *dimensionless*
fundamental constants and are able to put constraints on these
variations from available data. But, the Planck length by itself is not
dimensionless, we'd have to add another constant of dimension length to
detect any changes in it. Susskind's book, which you cited, seemed to
treat the string length as another fundamental constant. So it should
be meaningful to consider the variation of the *ratio* of the Planck
length to the string length.

Hope this helps.

Igor

.

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