*WDEshleman@aol.com*

*Mon, 6 Sep 1999 06:26:52 EDT*

**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**Stephen P. King: "[time 695] Re: [time 691] ... Re: [time 686] Time operator?"**Previous message:**Hitoshi Kitada: "[time 693] Correction to [time 692] re [time 686] Time operator?"**In reply to:**Stephen P. King: "[time 686] Time operator?"**Next in thread:**Hitoshi Kitada: "[time 697] Re: [time 694] Re: [time 674] Reply to NOW/PAST question"

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

**Next message:**Stephen P. King: "[time 695] Re: [time 691] ... Re: [time 686] Time operator?"**Previous message:**Hitoshi Kitada: "[time 693] Correction to [time 692] re [time 686] Time operator?"**In reply to:**Stephen P. King: "[time 686] Time operator?"**Next in thread:**Hitoshi Kitada: "[time 697] Re: [time 694] Re: [time 674] Reply to NOW/PAST question"

*
This archive was generated by hypermail 2.0b3
on Sat Oct 16 1999 - 00:36:39 JST
*