WDEshleman@aol.com
Mon, 6 Sep 1999 06:26:52 EDT
In a message dated 9/5/99 9:58:53 PM Eastern Daylight Time,
hitoshi@kitada.com writes:
> Dear Bill,
>
> I have a question.
>
> Bill <WDEshleman@aol.com> wrote:
>
> Subject: [time 674] Re: [time 664] Reply to NOW/PAST question
> >
> > [MP]
> > a) I could not quite understand you NOW= PAST + x*PAST. If one starts
> > from Schrodinger equation one has -i dPsi/dt= HPsi.
> > Psi(t+deltat) = Psi(t) + i*HPsi(t)*Deltat = (1+ iH*delta t )*Psi(t)
> >
[HK]
> If you set like this, this x is equal to
>
> x = - i Deltat H.
>
> (You forgot minus sign in the above).
>
> In this setting, we have an exact identity
>
> Psi(t+Deltat) = exp(-i Deltat H) Psi(t) = exp (x) Psi(t)
>
> according to the Schroedinger equation. This equals
>
> Psi(t+Deltat) = (1+ x + x^2/2! + x^3/3! + x^4/4! + ...) Psi(t),
>
> which seems different from your calculation:
>
> > Psi(t+Deltat)/Psi(t) = [ 1/(1 - x) ],
>
> i.e.
>
> Psi(t+Deltat)=(1+x+x^2+x^3+x^4+...)Psi(t)
>
> Do you mean to imply what we actually observe is different from the exact
> physical process to this amount? If so, then why/how?
>
> Best wishes,
> Hitoshi
>
Hitoshi, Matti, and Stephen,
I wish I had said that. We are discussing some competing
notions of change. Hitoshi's result for Schroedinger case,
Psi(t+Deltat) = exp(x) * Psi(t)
= (1+ x + x^2/2! + x^3/3! + x^4/4! + ...) Psi(t), (A)
is partitioned between the extremes,
Psi(t+Deltat) = (1 + x) * Psi(t) (B)
and,
Psi(t+Deltat) = Psi(t) / (1 - x) (C)
And A is very close to the average of B and C, below x = 0.1 .
B implies that the future is entirely determined by full knowledge
of the present. Or, FUTURE = (1 + x) * PRESENT.
C implies that the present is determined by knowledge that
will only be complete upon arriving at the present. Or,
NOW = PAST + x * NOW => NOW = PAST/(1 - x).
A implies that the future is entirely determined by knowledge
of the present and additional knowledge of the past (or at
least past knowledge of the properties of exp(x) ).
Given a choice, I choose C because it is suggested
by Relativity. Eg., M^2 = (M_0)^2 + (v^2/c^2) * M^2
=> M^2 = (M_0)^2 / (1 - v^2/c^2). Because it
seems to be a reason for believing that it is the
possibilities of the future that attract the present
to it. And because I some interesting notions
and additional identities concerning 1/(1 - x).
Now, if Relativity turned out to be, as in A,
M^2 = exp(v^2/c^2) * (M_0)^2,
I could see a unification by the similarity of their
"first principle of change." Since this does not appear to be
true for Relativity, I am then prone to at least question
and speculate whether we ought to consider wave equations that
do follow C's notion of change? If you reply with a wave
equation for the notion of C, I will appreciate it alot.
Why/how? Because I am at a stage where consistency is far
more important than being correct.
Sincerely,
Bill
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