WDEshleman@aol.com
Fri, 3 Sep 1999 04:36:25 EDT
[WDE]
Here are some of my thoughts about change pulled from my abstract.
This proposal begins with the argument that the linear operators (x),
that
dictate the evolution of the state of an object, are themselves
measured in present states (NOW), not past states (PAST). That is, if
NOW = PAST+ x * PAST, then NOW/PAST = 1 + x, a trivial result
allowing all values of x.
On the other hand, if it realized that it is more logical and consistent
that, NOW = PAST + x * NOW, then NOW/PAST = 1/(1 - x),
a most interesting result that prevents x from achieving unity.
[SPK]
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!)
[WDE]
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)
[SPK]
Can we think of worlds in terms of different NOW/PAST pairs?
[WDE]
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.
[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)
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.
[WDE]
Yes, except that,
x = i*HPsi(t)*Deltat (1+ iH*delta t )
=> NOW/PAST = Psi(t+deltat)/Psi(t)
= 1 + x = 1 + i*HPsi(t)*Deltat (1+ iH*delta t )
but, from seeing how relativity works, I suggest,
NOW/PAST = Psi(t+deltat)/Psi(t) = 1/(1 - x)
= 1/{ 1 - i*HPsi(t)*Deltat (1+ iH*delta t ) }
not very much of a difference if,
i*HPsi(t)*Deltat (1+ iH*delta t ) is small relative to 1,
but as i*HPsi(t)*Deltat (1+ iH*delta t ) approaches 1,
NOW/PAST = Psi(t+deltat)/Psi(t) approaches infinity,
and I suggest that this is one of the requirements
for unification of Relativity and QM.
That is, if x = v^2/c^2,
then, { ( M ) }^2 = { (M_0)^2 } / (1 - x),
and, { ( T ) }^2 = { (T_0)^2 } / (1 - x),
and, { ( L ) }^2 = { (L_0)^2 } * (1 - x).
suggest the necessity to do the same for QM.
[MP]
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.
[WDE]
This is a re-formulation, is it not?
[MP]
b) Certainly Schrodinger equation is not consistent with relativistic
ideas.
[WDE]
I do not suggest that we attempt to find a relativistic Wave equation,
but I do suggest that we treat it relativistically. This all started because
Stephen refused to understand some simple algebra, claiming dislexia
(one of the best traits of a philosopher or quantum mechanic) :-|
Of course, I need some reasons to assume the relation 1/(1 - x),
(it's what my infinite product is equal to) and I'll go to any lengths
of relative absurdity to make it deductive. :-)
[MP]
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).
[WDE]
Is this or is it not an agreement or disagreement?
[MP]
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.
[WDE]
To me this is an oxymoron, kind of like a subjective/objective theory.
Sincerely
Bill
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