Matti Pitkanen (email@example.com)
Thu, 2 Sep 1999 12:42:37 +0300 (EET DST)
> > Here are some of my thoughts about change pulled from my abstract.
> > This proposal begins with the argument that the linear operators (x),
> > dictate the evolution of the state of an object, are themselves
> > present states (NOW), not past states (PAST). That is, if NOW = PAST
> > PAST, then NOW/PAST = 1 + x, a trivial result allowing all values of
> > the other hand, if it realized that it is more logical and consistent
> > NOW = PAST + x * NOW, then NOW/PAST = 1/(1 - x), a most interesting
> > result that prevents x from achieving unity.
> Very neat! So is unity achieved asymptotically in the infinite limit,
> Lim i -> \inf. : x = 0 ? I am having a hard time with the math. :-(
> (dyslexia sucks!)
Associating x with PAST states,
if NOW = PAST + x * PAST => NOW = PAST * (1 + x)
=> NOW/PAST = (1 + x), this is classical (common sense) change.
Or associating x with NOW states,
if NOW = PAST + x * NOW => NOW - x * NOW = PAST
=> NOW * (1 - x) = PAST => NOW/PAST = 1/(1 - x),
this is relativistic (singularity) change. That is,
NOW = PAST/(1 - x). Not, NOW = PAST * (1 + x)
> Can we think of worlds in terms of different NOW/PAST pairs?
I don't think of worlds as NOW/PAST pairs, but you may have
something there. I see the PAST as always gone and that
associating a "change operator" with the PAST is relativistically
wrong (or relativity suggests that it's wrong). Matti, if you are
reading this your help would be appreciated. I may be
misguided, but I look at this as a relativistic first principle,
independent of geometry.
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)
Psi(t) wold represent past in this and x=1+iH*delta t would represent
x. I do not know whether I have understood correctly.
Psi(t) could be also understood as Psi(t)=U(t-t')*Psi(t'<t), where U(t-t')
=exp(iH(t-t')) is exponent of time indenependent Hamiltonian.
b) Certainly Schrodinger equation is not consistent with relativistic
ideas. Already because one has selected preferred time coordinate (one
can however consider the possibility of preferred time coordinate
fixed by symmetries: in TGD lightcone proper time is this kind of
time coordinate). In relativistic classical field theory
one can solve the time development of field equations defining past
of point as past lightcone and Now depends only on the field values
in Past defined by this past lightcone.
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