Matti Pitkanen (matpitka@pcu.helsinki.fi)
Fri, 21 May 1999 08:23:32 +0300 (EET DST)
Dear Hitoshi,
Still some comments about Fisher information, mostly from the point of
view of TGD. Kahler function is absolute minimum of Kaehler action, which
is Maxwell action for induced Kahler form, which satisfies identically
the topological half of Maxwell's equations. The primary variables
are however imbedding space coordinates rather than vector potential
itself.
Frieden's theory would suggest the interpretation of Kahler function as
available information I, whereas J would vanish identically since no
external currents are present. On the other hand, absolute minimization
of Kahler action favours negative values of Kaehler action (with
action density proportional to B^2 -E^2 and generation of Kaehler
electric fields indeed makes Kaehler action negative.
Therefore available information I would be *negative* as a rule. This does
not make sense to me.
[My own proposal for information theoretic interpretation starts from
quite different basic philosophy and it is the NEGATIVE of Kahler action,
which has interpretation as a measure for cognitive resources of system:
therefore the problem is not encountered.]
Also for ordinary Maxwell electrodynamics the situation is problematic.
Consider point like charge at rest generating only electric field,
described by Coulomb potential. In this case I is negative since it
is proportioal to the negative of electric energy (which actually
diverges). You told that I = J/2 holds true so that also J is negative
(actually I diverges).
MP
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