Matti Pitkanen (matpitka@pcu.helsinki.fi)
Fri, 3 Sep 1999 13:47:02 +0300 (EET DST)
On Fri, 3 Sep 1999 WDEshleman@aol.com wrote:
>
>
> [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)
[MP] Sorry for lacking "=" in the formula above.
>
> 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] Yes in terms of unitari time development operator, which is
exponent of Hamiltonian.
>
> [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 GRT framework it is not possible to introduce any preferred
time coordinate like lightcone propertime so that Schrodinger does
not make sense as general coordinate invariant concept.
In TGD context there is and I believed for long time that lightcone
proper time or some function of it is the time parameter appearing in
time development operator of TGD defined by exponentiating
so called Virasoro generator L_0 (not energy but rather mass
squared operator). This operator does not act in spacetime but
on configuration space spinors.
My worries were related to Poincare
invariance and it turned out that lightcone proper time
was not in question: the time parameter is purely group theoretic
parameter having interpretation as lightcone coordinate.
It is not possible to identify it with experienced time. The
really great relief was that I get Poincare invariant S-matrix despite the
fact that Poincare invariance is broken globally by
the presence of lightcone boundary.
>
> [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.
>
Best,
MP
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