Hitoshi Kitada (hitoshi@kitada.com)
Thu, 11 Nov 1999 00:50:56 +0900
Dear Koichiro, Matti, Bill, et al.,
I apologize my delay in response: I had to be present at wake and funeral of my
uncle, and after that I had to write a long Japanese reply to a Japanese
physicist. As you may know Japanese requires tedious, complicated input
processes and needs much rhetorical expression :-).
Koichiro Matsuno <kmatsuno@vos.nagaokaut.ac.jp> wrote:
Subject: [time 979] RE: [time 978] a fundamental question on QM time
> Stephen King and Hitoshi Kitada have let me know this mailing list.
> Although I am a novice here, the point Hitoshi just raised has intrigued me
> for long.
You are already famous here :-) Stephen introduced your site and Matti responded
that he has ever met you at somewhere in Finland.
>
> >In actuality what one is able to
> >observe is scattering process, but not the eigenstates as the final
> >states of the process.
>
> Perhaps, we may need to pay some attention to a linguistic prerequisite
> to the issue of dynamics, whether it is classical or quantal. Any dynamics
> in its making is in the present progressive mode. Then, it has been
> transformed into the past progressive mode, some of which has consistently
> been frozen into the completed record in the perfect tense. The point here
> is that there is always some leftover which cannot be frozen in the record
> in the completed perfect mode.
Could you explain in concrete examples what kind of leftover is?
> The leftover constantly serves as an impetus
> for moving the subsequent progressive mode.
How does the "impetus" move "the subsequent progressive mode?"
> Strangely enough, however, both
> CM and QM start from the categorical statements made in the present tense,
> and the present progressive is simply taken to be a derivative from the
> present tense there.
I think you are talking of "usual" QM, not any of its variants as Matti's or
mine or any others'?
>
> CM and QM anchored at the present tense necessarily have to presume the
> presence of globally synchronous time out of the blue, otherwise no
> categorical statements to be made in the present tense.
I seem to agree.
> CM is completely
> consistent at least conceptually in dismissing whatever in the progressive
> mode, though not very well founded empirically.
I agree insofar as we admit the consistency means not a precise mathematical
one.
> In contrast, QM is quite
> ambivalent in that it has already assumed the role of the present
> progressive mode even unwittingly, especially in the form of operations or
> operators.
Yes.
> This must be a source of headaches. QM as we know of it today
> seems to be pretty schizophrenic in getting time and dynamics from both the
> present and the present progressive tense rather in a hodgepodge manner.
I agree. And time that implies the exact relation x=tv would be the one that
should be talked about in present tense and thus is a classical notion that
remains in QM which should be talked of in the present progressive mode?
> Hitoshi's emphasis on scattering process seems to me an appraisal of time as
> a derivative from the present progressive tense instead of from the present,
> in which the non-frozen leftover from the preceding progressive mode is
> constantly driving the succeeding one.
Yes, that's the point.
> I might have muddied the waters a
> bit.
No, you made an important remark. I think Stephen whould be interested in your
comment, seeing he has been interested in the understanding of "emergence" of
classical time from the communication process between local systems (LS's).
Matti Pitkanen <matpitka@pcu.helsinki.fi> wrote:
Subject: [time 980] Re: [time 978] a fundamental question on QM time
snip
> > Let us consider quantum mechanical case where the space-time coordinates
> > are given a priori. Then the velocity of a particle should be defined as
> > something like v=x/t. This is a definition, so this must hold in exact
> > sense if the definition works at all. However in QM case, the
> > uncertainty principle prohibits the position and momentum from taking
> > exact values simultaneously. That principle is based on the notion of
> > position and momentum operators that satisfy the canonical commutation
> > relation. In the point that the space and momentum are given by
> > operators, the definition of velocity v above does not apply to QM.
> > Further the uncertainty principle tells that there is a minimum value
> > for the product of the variances of the position and momentum from their
> > expected values, and thus tells that there is an absolute independence
> > between the notions of position and momentum. I.e. the principle does
> > not say anything about the relation like x=tv, but instead just tells
> > that they have to be away from their expectation values.
>
> This is very real problem.
>
> a) Your definition of velocity is classical and applies in practice
> to point like particles. In case of field momentum it does not work.
You are right. I think usual QM is the fountain of general problems of QM.
>
> b) One could try to avoid the problem is by defining
> velocity as a parameter characterizing symmetry transformation, in this
> case Lorentz boost. Given velocity would only characterize
> the transformation relating too states. In this case velocity
> appears only in the transformation formula defining how energy and
> momentum are changed in Lorentz boost. Velocity of particle can be defined
> in terms of the components of four momentum.
Certainly in relativistic case.
>
> c) This definition is not operational definition in style "v=x/t"
> but it can be used to assign velocity parameter to quantum
> particle. Note that velocity is purely geometric quantity
> in Minkowski geometry since velocity corresponds to hyperbolic
> angle.
>
>
> >
> > This observation seems to suggest that, if given a pair of a priori
> > space and time coordinates, QM becomes contradictory, and that the
> > independent quantities, space and momentum operators, have to be taken
> > as the fundamental quantities of quantum mechanics. As time t can be
> > defined as a ratio x/v in this view, time is a redundant notion that
> > should not be given a role independent of space and momentum.
> >
>
>
> I regard this as important question. Following monolog does not
> provide "final" solution to the problem!
>
>
> In TGD framework there are several time developments.
>
> a) "Time development" U in single quantum jump (I am speaking
> about TGD now) defining S-matrix is considered. It seems that there
> is not need to assign Schrodinger evolution to this time development:
> just S-matrix characterizes it. S-matrix conserves four-momenta.
I think this S-matrix is the one we have discussed before?
> Negentropy Maximization Principle need not be consistent with momentum
> conservation and could force final states to consists of wave packets
> around average momentum.
>
>
> b) Time development by quantum jumps. Poincare invariance guarantees
> conservation of four-momentum in quantum jump, that is U connects
> states with same Poincare quantum numbers. This is what particle
> physicist needs. NMP might imply that momentum is not precisely
> conserved in the sequence of quantum jumps so that the evolution
> of the Universe is not restricted by momentum conservation.
Is this a composite one consisting of many jumps in a)?
>
>
> c) Geometric time development defined by absolute minimization
> of Kaehler action. One can assign to spacetime sheets classical
> momenta and they are conserved.
Then you have two kinds of time as you have claimed?
>
>
> The basic problem is how quantum mechanical Poincare quantum numbers
> relate to the momenta and energies measured in laboratory using classical
> physics notions.
>
> a) In TGD framework one can assign to quantum particles
> four-momenta. Quantum state corresponds to a superposition of spacetime
> surfaces. Quantum particle corresponds to spacetime sheets moving on this
> surface classically so that one can assing to particles
> also classical momenta and velocities.
If these momenta are classical, they are free from the uncertainty principle?
>
> b) Since final state of quantum jump is superposition of
> *macroscopically* equivalent spacetime surfaces (localization in "zero
> modes"), it seems that the particle like spaceetime sheets must have
> sharp directions and values of velocities.
So the final state is also classical?
> This in case that particle
> orbits are of macroscopic size. What "macroscopic" means is presumably
> defined by p-adic length scale hypothesis: macroscopy begins at length
> scale L(p).
>
>
> c) If the four-velocities for classical spacetime sheets
> are same as for corresponding quantum particles, one achieves
> quite nice correspondence at purely kinetical level. Feynmann
> diagrams have precice geometric realization.
>
>
> d) If one requires that classical masses
> are same as quantum masses, the correspondence is even more tight.
> An interesting question is should one also require that classical
> conserved quantities are identical for various spacetime sheets for all
> spacetime surfaces in superposition.
>
>
> e) Also the masses of particles are determined classically in
> particle physics experiments, say by putting charged particle in
> magnetic field. Could one require that the classical mass of particle is
> same as quantum mass?
Maybe, but this seems to depend on what assumption you adopt.
> One should be very cautious here since the mass of
> particle results from small p-adic thermal mixing of massless
> particle with 10^(-4) Planck mass excitations. Therefore
> it would seem that particle mass as we usually define it
> is quantum statistical parameter.
>
>
>
> In any case, the fact that classical physics is genuine part of
> quantum theory in TGD framework, seems to provide solution
> to the problem.
Then in your context how is the uncertainty principle understood?
> The basic technical problem seems to be about how
> precise correlation between classical and quantum numbers results from
> consistency arguments (localization in zero modes being the most important
> one and implying the "classicality" of the final states
> of quantum jump)
Is only the "final state" observable in your context?
snip
Bill Eshleman <WDEshleman@aol.com> wrote:
Subject: [time 981] Re: [time 978] Stealing time
> In a message dated 11/8/99 11:38:09 AM Eastern Standard Time,
> hitoshi@kitada.com writes:
>
> > Or in more exact words,
> > the usual QM theory is an overdetermined system that involves too many
> > independent variables: space, momentum, and time, and in that framework
> > time is not free from the classical image that velocity is defined by
> > v=x/t.
> >
> > Best wishes,
> > Hitoshi
>
> Hitoshi, et. al.,
>
> When I read or hear that so and so person is "too busy" to get around to
> something, I feel that this person is not "too busy," but is not willing to
> "steal time" from other things.
Yes, I agree we "feel" so. But the classical "fact" might be different :-)
> That is, when things interact, they steal
> time
> from each other; and when things do not interact, they are not capable of
> stealing time from each other. Photons do not steal time from each other
> nor do they share time with other photons and therefore do not interact
> with each other.
How about the spontaneous emission of photon from an atom? Is this not thought
as a QM interaction of photon with matter and thus able to steal time?
>
> Matter, on the other hand, does interact with matter and by the definition
> above, some sort of "time sharing" seems to be going on that curves
> trajectories that would otherwise be straight lines. Classical mechanics
> might be an example of a most efficient sharing of time; like computers
> share time between multiple processes.
>
> But quantum mechanics seems to be more like how I manage my own
> projects; i.e., I don't share time with other projects, I steal time from
> other projects and sometimes finish a project at the expense of every
> other project. This is like proposing that the evolution of the state of a
> particular object is subjected to a constant Hamiltonian that is static
> in time. That, x=vt and v=x/t can't be determined at the same time
> is because we cannot determine what random time sharing is going on.
So you reduce the uncertainty principle to the ambiguity or unobservability of
the QM process of "time sharing?"
> Is reality being like me, or is it I being like reality?
Both are the same thing. Either one would imply another :-)
Best wishes,
Hitoshi
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