Re: What's wrong with loop quantum gravity

rof_at_maths.tcd.ie
Date: 09/24/04 

Date: Fri, 24 Sep 2004 13:13:19 +0000 (UTC)

Aaron Denney <wnoise@ofb.net> writes:

>On 2004-09-22, Lubos Motl <motl@feynman.harvard.edu> wrote:
>> It would be a sad outcome, but if we happen to see that a point in the
>> "landscape" is the only way how to describe the real world without jumping
>> to theories with infinitely many arbitrary parameters, we will have to
>> take this possibility seriously.

>A point in an high-dimensional "landscape" sounds like just another way
>of describing a theory with many arbitrary parameters to me.

Quite right. In fact, there's a quantitative way to see how good a theory
is. Take the amount of information (measured in bits, or digits if you
prefer) required to specify the theory (and any auxiliary parameters,
for example, a point in the landscape) and compare this to the
amount of information correctly predicted by the theory. If the
former is not smaller than the latter, then the theory has failed
to compress the observed data, and should be discarded.

For example, if somebody starts using string theory to predict the numerical
values of the fundamental constants, but needs to first specify a point
on the landscape, then the amount of information needed to specify
the point (in digits) had better not exceed the total number of digits
successfully "explained". Given that the known fundamental constants
give us less than 100 digits of information altogether, even complete
certainty that an explanation lies somewhere in a discretuum of
10^100 possible choices shouldn't convince us of anything. Of
course, digits in fundamental constants aren't everything - you
need a few more bits to specify which gauge groups describe the
observed fields, dimensionality of observed space and so forth, but
most of the information is in the constants (log log n digits for
the order of magnitude and one digit for each known digit).

A vacuum selection principle is needed, and anthropic arguments
will never be predictive, since they basically tell us that
the universe must be as it is, so go looking (among the 10^100
possibilities) for something which looks like our universe. If
there are 70 digits to be explained, then we'll find an explanation
(by chance) once for every 10^70 options we examine, leaving
us with 10^30 different universes to choose from; take any
two of these selected universes - the chance that they will
agree on the next digit of alpha will be one in ten. That is,
there'll be no predictive power.

R.

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