Hitoshi Kitada (email@example.com)
Mon, 22 Mar 1999 16:54:41 +0900
I am glad to have seen in the communications between you and Stephen that we
have many common points in your theory and my theory. In this note I just
comment on some points you find problems:
From: Matti Pitkanen <firstname.lastname@example.org>
To: Stephen P. King <email@example.com>
Cc: firstname.lastname@example.org <email@example.com>
Date: Sunday, March 21, 1999 11:24 PM
Subject: [time 41] Re: [time 37] Re:The ordering of spatial states and
>On Sat, 20 Mar 1999, Stephen P. King wrote:
>> Dear Matti,
>> Matti Pitkanen wrote:
>> > The paper co-authored by Hitoshi and Lance Fletcher
>> > (http://www.kitada.com/time_III.html) explains all of the basic thinking
>> > involved in LS. It is rather revolutionary and goes against the grain of
>> > conventional physical thinking, but, that all said, it does provided a
>> > starting point with which to address many other difficulties in modeling
>> > consistently our world.
>> > An example, the primitive ideas are examined:
>> > "1.We begin by distinguishing the notion of a local system consisting of
>> > a finite number of particles. Here we mean by "local" that the
>> > positions of all particles in a local system are understood as defined
>> > with respect to the same reference frame."
>> > Here we do not assume any particular properties of the
>> > other than what is explicitly stated and use the standard definition of
>> > a "particle"; some entity existing at the locus of an set of
>> > coordinates, but we do not assume any properties yet...
>> > [MP]
>> > There is clear analogy with many sheeted spacetime. In TGD elementary
>> > particles correspond to so called CP2 type extremals of size of order
>> > Planck lengths. They have metric with Euclidian signature but lightlike
>> > curve as M^4_+ projection. These tiny 3-surfaces are glued by
>> > sum to 3-surface which is roughly like a piece of Minkowski space with
>> > size of order Compton length and possessing outer boundary. This process
>> > leads to massivation of elementary particle described by p-adic
>> > thermodynamics. It seems that one could think CP2 type extremal as a
>> > local system and piece of M^4_+ as spacetime. Am I correct?
>> Yes! I would like to understand this "topological sum" better. Could
>> you explain it to us?
>Topological sum for two n-dimensional surfaces is formed as follows.
>Cut balls D^n from both surfaces. The boundaries of these
>holes are spheres S^(n-1). Connect the boundaries of the
>holes by the cylinder D^1xS^(n-1) along its ends. In two dimensional case
>you remove disks from the two surfaces and connect them by a cylinder by
>gluing its ends to the boundaries of the holes.
>I looked at the references you mentioned. There seems to be also a
>difference. Local clocks are introduced at each spacetime point
>by replacing X^4 with X^4xR^6 (R^6 phase space of particle).
>I do not attach local system to *every point* of background spacetime.
>Local system would represent topological nonhomegenuity of
>spacetime surface in TGD approach. But these spacetime sheet 'glued'
>to background space represent in good approximation their own universes
>and in good approximation one can construct their physics discarding
>the interactions with external world. In this manner one obtains
>QCD, low energy hadronic physics, nuclear physics, atomic physics,...
>Also our starting point could be seen as same. The failure of Newtonian
>spacetime applied in standard QM in General Relativistic context.
>My solution is to give up totally the idea about physical state as
>time=constant snapshot and describe quantum state as quantum history
>and try to understand the emergence of psychological time ('clocks')
>as a problem of consciousness theory: why the contents of conscious
>experience is located around some value(s possibly) and why this value
>of time tends to increase at least locally. Here the nondetermism of
>Kahler action, which generated this discussion, is in fundamental role.
>Quantum jumps for which nondetermism is located in finite time interval
>give conscious information about that time interval and hence conscious
>experiences with time localized experiences become possible. Without
>nondeterminism experience would contain information diffused over entire
>intial and final quantum histories.
>What troubled me in local system approach were the following points.
>Dirac equation for atoms gives predictions which are verified
>experimentally and replacing Dirac equation with Schrodinger equation does
>not seem promising.
My point in choosing Schroedinger equation is in that Dirac eqaution cannot
treat many body problem. As far as I know, it is an equation for one partcile
(an electron) in an exterior field. This is the reason why I had to choose
Schroedinger equation as a starting point of a description of nature inside a
local system. The relation among plural number of local systems is derived
from this equation, and I obtained some halfly-relativistsic equatIon.
But if we can take a standpoint that Stephen stated in [time 22] as follows,
we might be able to start with Dirac or any other relativistic QM equation.
form [time 22]:
>> Also electromagnetic aspect is a quanutm mechanical one, where classical
>> treatment breaks (e.g. the stability of matter (atoms, molecules,...) does
>> hold in classical electromagnetic theory). Further Weyl seems to be able to
> >treat only one body problem (i.e. it can treat only the external forces,
> >cannot conisder the interactions between plural number of particles, which
> >essentially the same as Einstein's GR.)
>While the emmition and absorbtion of photons is a QM phenomena, the
>light cone structures are not "internal" to LS as classical
>trajectories. They are, as Hitoshi said before, perspectivist, e.g. a
>means to observe. Weyl's treatement of only a single body, IMHO, is not
>a problem in the context that such is an LS seen from the outside; it
>would be a classical "particle."
>When thinking about this and we shift from internal LS QM behaviour to
>external LS classical behaviour we must keep track of what is happening.
>It can be very tricky! :)
Here Stephen considers that what is observed is just "one" LS. If we take this
view, we may have no problem in the description of the behavior of an LS when
observed as a single classical particle. (Though still a problem seems to
remain in the description of physics inside an LS.)
>Secondly, Why R^6, why not only R^3 if local system
>obeys nonrelativistic QM?
The description related with R^6 is used in the introduction of some of my
papers to explain my theory. I used it to indicate that what is fundamental
in QM is the six componets: three configurations x_1, x_2, x_3 and three
components of momentum p_1, p_2, p_3 canonically conjugate to x_1, x_2, x_3
for the case of a single particle. This is some rhetorical expression. Since
p_1, p_2, p_3 are determined by x_1, x_2, x_3 by canonical conjugacy, what is
necessary is just R^3 as you pointed out. I chose my expression just to
emphasize the point above, and might have been slightly away form the
rigorousness in the expression.
>> > Hierarchy continues: for instance, quark like 3- surfaces are glued to
>> > hadronic 3-surfaces, and so on. At human length scales my body is a
>> > 3-surface with outer boundary identifiable as my skin glued to a larger
>> > 3-surface.
By the way, may I ask the non-abbreviated terms for TGD? What is the original
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