Re: QM

From: <GSLevy.domain.name.hidden>
Date: Tue, 18 Jul 2000 18:36:30 EDT

In a message dated 07/11/2000 7:44:22 PM Pacific Daylight Time,
meekerdb.domain.name.hidden writes:

> > Well, we must start somewhere. But it is fun.
> >
> > How about casting the SE with Psi as a relative quantity just like
> position
> > or velocity? In other words we would be always talking about Delta Psi =
> Psi1
> > - Psi0 rather then absolute Psi, where Psi0 would correspond to the
> > (coordinate system of the) observer.
>
> I think that would need to be the ratio, not the difference, since psi
needs
> to
> represent the square-root of a probability.
>
> Brent Meeker
>
>

Brent, taking a ratio is interesting! Going one step further and taking the
logarithm of the ratio Psi1/Ps0 generates something that looks like
information. Information can be added and subtracted in a linear fashion
just like velocity and position.

In other words SE can be converted to express a wave of information.

Psi can be converted to probability but only after normalization which
involves taking the ratio (|Psi|**2 Dx)/Integral(|Psi|**2 dx. This is done to
make sure that the range of probability is between 0 and 1.

The mutual information between two events x and y can be expressed by taking
the log of the ratio of their square of the normalized Psis. In other words:

Mutual Information between event x and event y
                           = log ( |Psi(y|x)|**2 / |Psi(y)|**2 )
                           = log ( |Psi(x|y)|**2 / |Psi(x)|**2 )
                           = log ( |Psi(x,y)|**2 /( (|Psi(y)|**2) (
|Psi(y)|**2)))

To get the above, I just applied the equation defining mutual information to
the relationship between probability and normalized Psi.

We see now that information can range from + infinity to - infinity and can
be added or subtracted in a linear fashion. Measure expressed in terms of
infomation is relative not absolute.

I will expand on this when I have more time.

George
Received on Tue Jul 18 2000 - 15:45:50 PDT