[time 325] Re: Fisher information and relativity

Matti Pitkanen (matpitka@pcu.helsinki.fi)
Tue, 18 May 1999 11:48:07 +0300 (EET DST)

Dear, Hitoshi,

sign of the time derivative term. See the question below.

[MP]
> > Here I am wondering how the negative sign in (\partial_tp)^2/p
> > relateed with time derivative term comes.

[Hitoshi]
> This comes from
>
> (\partial p/ \partial_{ict})^2= - c^{-2} (\partial p/ \partial_t)^2
>
> since x_0=ict. Frieden considers the sum
>
> I = \int dx \sum_{\nu=0}^3 (\partial p/ \partial_{x_\nu})^2/p(x)
>
> for the PDF (probability density function) p(x) = p(x_0,x_1,x_2,x_3) that
> are functions of multiple variable x=(x_0,...,x_3). This I gives the free
> part of Klein-Gordon equation.
>
[Hitoshi]
> As I wrote in the original post [time 321] of [time 320] (that was cut
> because I put a period at the top of a line), Frieden makes an ad hoc
> assumption that space-time is relativistic. This is because Frieden thinks
> the observation only, as his concern is solely with the explanation of how
> the relativistic Lagrangian appears in physics and the relativistic
> Lagrangian is the quantity that describes how nature looks, at the observer.
>
> In my thought consciousness must be Euclidean because we, inside ourself,
> think space Euclidean. Or because what we think as space has been called
> Euclidean since Greek age. This I think is a mental property of humans. If
> we did not have in mind a Euclidean space as an origin geometry, how could
> we imagine the curved geometry?
>

Interesting idea. One could also argue that the development of
mathematical consciousness starts by discovery of simple structures
and then proceeds to more complex structures and that Euclidian
flat spacetiem is simplest thing one can imagine (without any algebraic
tools).

>
> Is Fisher information
> > still in question when one uses imaginery coordinate x0 =it?
> >

Coordinates correspond to kind of parameters in Fisher
information: unfortunately I have not clear picture
about what kind of parameters are in question. What troubled and
still troubles me is whether the imaginary
value of parameter is indeed consistent with this
interpretation.

MP

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