Hitoshi Kitada (hitoshi@kitada.com)
Mon, 6 Sep 1999 11:00:00 +0900
Dear Bill,
I have a question.
Bill <WDEshleman@aol.com> wrote:
Subject: [time 674] Re: [time 664] Reply to NOW/PAST question
> Matti,
> Here is some fixing up.
> Bill
>
> [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)
>
> What troubles me is the identification of x. I would identify
> it as operator. My formula was also for infinitesimal time interval
> delta t. Perhaps we understand by z quite different things.
>
> [WDE]
> Yes, the name operator for v^2/c^2 is imprecise, it is a true factor,
> not the mathematical convenience, operator. Let me try to escape
> this imprecision. First evaluate the operator and write it this way:
>
> Psi(t+Deltat) = Psi(t) + [ i*HPsi(t) ] * Deltat
>
> normalize,
>
> Psi(t+Deltat) = Psi(t) + [ i*HPsi(t) / Psi(t) ] * Deltat * Psi(t)
>
> then x = [ i*HPsi(t) / Psi(t) ] * Deltat
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?
>
> I cannot think of a name other than "operator", but Stephen
> might call it a "propagator". It is simply just a factor.
> And,
>
> Psi(t+Deltat) = Psi(t) + x * Psi(t)
>
> But what I suggest is that we subjectively see,
>
> Psi(t+Deltat) = Psi(t) + x * Psi(t+Deltat)
> = Psi(t)
> + [ i*HPsi(t+Deltat) / Psi(t+Deltat) ] * Deltat * Psi(t+Deltat)
>
> or, Psi(t+Deltat)/Psi(t) = [ 1/(1 - x) ]
> = 1/ { 1 - [ i*HPsi(t+Deltat) ] * Deltat / Psi(t+Deltat) }
>
> or, Psi(t+Deltat)
> = Psi(t) / { 1 - [ i*HPsi(t+Deltat) ] * Deltat / Psi(t+Deltat) }
>
> because of an objective multiplicity of other-worlds that
> trick observers into believing that the NOW is attracted
> to the FUTURE.
>
> Matti,
> If I made another error in the algebra, please don't give up.
>
> [MP]
> Is your fomula really consistent with Schrodinger equation?
>
> [WDE]
> I suspect not, but it might be, and I suggest that it should be.
>
> Sincerely,
>
> Bill
>
>
Best wishes,
Hitoshi
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