On Wed, Oct 31, 2007 at 05:11:01PM -0700, George Levy wrote:
> 
> Could we relate the expansion of  the universe to the decrease in 
> measure of a given observer? High measure corresponds to a small 
> universe and conversely, low measure to a large one.  For the observer 
> the decrease in his measure would be caused by all the possible mode of 
> decay of all the nuclear particles necessary for his consciousness. 
> Corresponding to this decrease, the radius of the observable universe 
> increases to make the universe less likely.
> 
> This would provide an experimental way to measure absolute measure.
> 
> I am not a proponent of ASSA, rather I believe in RSSA and in a 
> cosmological principle for measure: that measure is independent of when 
> or where the observer makes an observation. However, I thought that 
> tying cosmic expansion to measure may be an interesting avenue of inquiry.
> 
> George Levy
> 

There is a relationship, though perhaps not quite what you think. The
measure of an OM will be 2^{-C_O}, where C_O is the amount of
information about the universe you know at that point in time
(measured in bits). The physical complexity C of the universe at a point
in time is in some sense the limit of all that is possible to know
about the universe, ie C_O <= C.

C is related to the size of the universe by the equation H = C + S,
where S is the entropy of the universe (measured in bits), and H is
the maximum possible entropy that would pertain if the universe were
in equilibrium. H is a monotonically increasing function of the size
of the universe - something like propertional to the volume (or
similar - I forget the details). S is also an increasing function (due
to the second law), but doesn't increase as fast as H. Consequently C
increases as a function of universe age, and so C_O can be larger now
than earlier in the universe, implying smaller OM measures.

However, it remains to be seen whether the anthropic reasons for
experiencing a universe 10^9 years and of large complexity we
currently see is necessary...

-- 

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