[time 341] Re: [time 340] Re: [time 338] Re: [time 335] Re: [time 331] Re: [time 327] Re: [time 326] Re:[time 325] Re: Fisherinformation andrelativity

Matti Pitkanen (matpitka@pcu.helsinki.fi)
Fri, 21 May 1999 15:31:20 +0300 (EET DST)

On Fri, 21 May 1999, Hitoshi Kitada wrote:

> Dear Matti,
> The problem of negativity you proposed means, I think, that I and J have
> lost the meaning of information at the stage when Frieden changed in page 64
> his axiom from the I-theorem to his axioms 1 - 3 which are almost equivalent
> to the principle of the least action. The reason for this is that after this
> alteration of his standpoint, I is independent of time t, which means that I
> is independent of the observer's time or any other time, thus is not an
> information in any sense that can be obtained by an actual observer who has
> his own time.

This seems to be the case. Of course, in TGD the variational principle
is the absolute minimization of Kahler (Maxwell) action. I do not know
whether by some miracle Maxwell action + current term could remain

> What Frieden actually does after page 64 is to present the way how the
> action integral which suits the actual situation can be constructed from the
> I that has the quadratic form wrt q'(x) and J which should be equal to I at
> least idealistically. Frieden gives this quadratic nature of I an
> information theoretic explanation before page 64, but the explanation is no
> more than a metaphor, as there is no logical connection between the parts
> before and after the page. In this sense, the quadratic nature of I wrt
> q'(x) is one of his implicit axioms, and he does not give it any
> justification but a metaphoric reasons. His approach cannot be called an
> information theoretic one in any rigorous sense.

This seems to be the case: also the negative sign of time
component of information implies that the interpretation breaks down.

> The contribution of Frieden if any is that he gave a _pragmatic_ method of
> deriving the action integral, that has been constructed by virtue of each
> researcher's insight into the phenomenon which he studies. However, the
> quadratic nature of I is the axiom which is adopted by any researcher and is
> not a contribution of Frieden. Thus his contribution resides only in the
> complicated procedure of deriving J from I by using several physical
> considerations in addition to his axioms 2 and 3 that cannot be called
> beautiful, especially in classical problems.
I regard the general idea about classical
variational principles as a maximation of somekind of information
very attractive. The problem is at which level this occurs. For instance,
Maxwell action and Einstein Hilbert action are only low energy effective
actions designed to construct S-matrix approximately
from the point of view of most unified theories.

> The recent science becomes a kind of novels. It might be said Frieden's book
> is a novel in the sense mentioned above as well as in the point that he
> writes the book that way. Indeed the book may well be called a nursery tale
> for the modern people who have.been injured by the modern mechanical view of
> the world.


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