# [time 595] Clocks etc,

Matti Pitkanen (matpitka@pcu.helsinki.fi)
Mon, 23 Aug 1999 07:54:15 +0300 (EET DST)

Hi Stephen,

the subject test is not the original. I hope it does not confuse.

snipping

Matti Pitkanen wrote:
>

> > > On Wed, 18 Aug 1999, Stephen P. King wrote:

>
> [SPK]
> > Ok, what Hitoshi and I are contending is that if it is
impossible
> > to define a clock, there is no such quantity as time! You said:
"Geometric
> > clock is impossible and is not even needed.", thus the notion of a
> > "geometric time" is meaningless! Unless we are referring to the M^4-
> > past light cone, them I agree with you...
[MP]
> Perhaps I formulated inaccurately what I wanted to say. What I wanted to
> say that manifold measuring the values of its own coordinates is
> conceptual impossibility. Already by general coordinate invariance:
which
> would be the preferred coordinates which manifold measures. Clock
> is a concept which cannot be reduced to Riemann geometry, which
> happily exists without clocks. The concept of clock involves the
> concept of quantum jump and self: theory of consciousness.

[SPK] A clock seems to require a comparison between at least two
manifolds
such that variations of one can be given against another, that acts like
the standard scale. I think that a clocking action involves a
tripartiteness: A manifold X, that acts as the object of observation, a
manifold A that acts as the reference standard, and a mapping X <-> A
that compares the two. I think that a minimal mathematical relation for
X and A is that there is a basis such that X is orthogonal to A. This
would make the operation X <-> A a projection operator.
We could easily see that your q-jump would meet this if we could
show that the initial and final sheets are orthogonal in some basis, since
the jump itself looks like a projection or I <-> F.

[MP] Your clock is based on comparison with reference standard.
X is mapped to A. Your clock could equally well measure length.
Everything is pure geometry. A,X and comparison mapping X-->A.

I want to compare to my own clock to your clock to see whether I could
buy it. My basic unit of subjective time is single quantum jump,
which corresponds in statistical sense to 10^4 Planck times: this is
however microscopy. Real biological clock of self is subself, which wakes
up periodically with period t and falls asleep gain. The behaviour of
clock self is rather predictable by quantum statistical determinism but
its wake-up time t_W can vary (e.g, it gets shorter when self and
presumably also clock subself gets drowsy). Geometric time T (your X)
corresponds to the subjectively experienced time measured as the number N
(your A) of wakeup periods occurred during T.

There is *no explicit* comparison map giving N = T/t: the duration of
time is just experienced subjectively. This is essential: there is no
geometric map since contents of conscious experience is not describable by
a formula. Here our approaches differ.

>
> [SPK]
> > If "geometric time" does not have the qualities of "[an] arrow,
> > 'clockability, [and] irreversibility", what qualities does it have
that
> > allow us to think of it as time? I really don't understand! :-( The
> > "dynamics of reading [writing] of the Turing [machine] head", for me,
> > speaks to the interaction of matter and information; it is the
> > operations of record generation that are an essential aspect of any
> > observation. H. H. Pattee's work gets into the specifics of this.
> > http://ssie.binghamton.edu/~pattee/
> >
>
> [MP] I think that Riemann geometry abstracts all the needed properties
> of geometric time. There is no essential difference between time and
> space. Clockability and irreversibility are properties of subjective
> time. Psychological time inherits its values from geometric time and
> its irreversibelity and clockability from subjective time.
> Psychological time is hybrid of these two times.

[SPK]
I am still not sure what you mean here in that "Riemannian geometry
abstracts..." I do not agree with your statement "there is no essential
difference between time and space"! How? space is given by the
"extensional" quantities and time by the "duration" quantities.

[MP] The problem is that you assume single time. I assume two.
Subjective and geometric. There is no difference between geometric time
and space. Our experiences correspond to spacetime volume: the temporal
duration of this volume is only very short. Taking volume of order L=
meter the simplest guess is L/c=about 10^-9 seconds. This is of course
just guess.

[SPK]
There is
a basic difference! "Extensionality" involves transformations of
relational placements of events/states and "durationality" involve
comparisons of the "before and after" of the transformations of
relational placements. So it seems that the two are interdependent but
not reducible...

[MP] What you say applies to subjective time, the time we experience.
It would be better to introduce completely different name for the
geometric time: call it just fourth spatial coordinate.

[SPKK]
I just wonder how the distribution of the g_ij of the Riemannian
geometry are given ab initio...

> >
> [SPK]
> > I really don't understand how you relate emotions to
"geometrical
> > time".
>
> [MP]
> The point is that conscious experiences are determined by initial
> and final quantum histories and classically they correspond to
> spacetime surfaces. This implies that sensory experiences involve
> expectation of what occurred and occurs: intuition, intentionality.

[SPK] Umm, this makes sense. Expectations are an important aspect of
statistics. Umm, I am wanting to explore the work of Amari with regards
to a connection discovered between statistics and geometry. :-) A
teaser: what is the difference between the distribution of expected
values and the measured distribution of values given an ensemble?
Can we think of an ensemble of points as a manifold having a
metric?

[MP] BTW, the our memories seem to be to a high degree combinations of
geometric, theorizing and subjective memories, which are
genuine but piecewise. Persons who are victims of accidents can lose
their subjective memory and just fabulate (or 'geometrize') without
realizing
that they are fabulating.

Geometric memory is purely TGD:eish phenomenon: absolute minimization of
Kaehler action assigns to given 3-surface Y^3 spacetime surface X^4(Y^3),
simulation for what happened and will happen.

I cannot relate your question directly to my picture. Instead of expected
distribution I am thinking prediction of physicists for what
my body would do if all my motor activities would cease.
Instead of measured distribution I am thinking of what my body really
does in presence of motor activities and spontaneous decisions
to do this or that.

I did not understand what you mean with 'the ensemble of points'...

> [SPK]
> > From what the neurophysicists tell us, emotions involve
> > variations in neurotransmitters and seem to involve specific areas of
> > the brain, the limbic system (I think). Emotion seem to be
"valuations"
> > that weigh sense impressions in the short term memory, associated with
> > the limbic system, in a way that looks like the creation of a basis
and
> > inner product for vectors.
>
> [MP]
> Emotions like disappointment, relief, etc... result from comparisons
> of what happened and what was expected to happen. Intentionality is
> essential. Computationalist might perhaps model limbic system as
> a set of flags: the value of flat is 1 for expected=actually occurred
and
> 0
> for expected not= actually occurred. The distribution of flags
> would determine the emotion. I believe that this picture, although
> extremely simplified, has some truth in it.

[SPK]
Me too! I think that Amari's work will help us with this! See
http://mijuno.larc.nasa.gov/dfc/biblio/gstatB.html

[MP] Ok.

> It could be that neurotransmitters and hormones just
> communicate the values of flag variables and cause the most primitive
> emotions like rage and fear from comparison of single bit
> to expected value of the bit.

[SPK]
This makes sense. :-) I just think that we are trying to cover too
much
with a single perspective...

[MP] Might be! I just started updating of 'Strong form of NMP': I must
admit that I was relieved to throw away some sections: I had tried
explain too many things using NMP. What remains
is the basic mathematical formulas and general interpretation
and new views about self necessary for proper interpretation.
I think it is however necessary to try to apply new ideas to all possible
context to see how widely they apply. Is is phantastic to see
how new concept, now 'self', clears the air.

> [SPK]
> > Emotions are usually not "chosen", that would require the
ability
> > to choose the valuation and it appears to be out of the reach of the
> > awareness. Persons are very rarely "aware of themselves being aware".
> > This takes a lot of effort!
>
> [MP]
> This is certainly true. Basic objection against quantum jump as moment
> of consciousness was that sensory experiences and emotions do not
involve
> conscious selection. The concept of self solved the problem. Although
> invidividual quantum jump is nondeterministic, the fact that
> experience is integrated from all quantum jumps after wake-up of
> self (typically 10^40 for self of age of one second!) brings
> in quantum statistical determinism. The volitions associated
> with the selection of density matrix eigenstate averages out in
> the experience which is 'sum' over all these experiences.
> Only the volition related with the selection
> between degenerate absolute minima of Kaehler action (classical
> nondeterminism) remains.

[SPK] This look to me that the 10^40 gives a time-series window within
which
a "self" can be reflected. I think that there would be a "ensemble" that
is "equivalent" to this time-series in terms of the information content
involved. I still do not understand what "absolute minima of Kaehler
action" has to do with "classical
nondeterminism". :-( Frankly I don't see how classical physics is
"nondeterministic". I am confused. :-(

[MP] Standard classical physics is deterministic. Kaehler action
is nondeterministic *in the sense* that absolute minima of Kaehler action
are degenerate. This is like several soap films spanned by same frame
and spanning same minimum area. Now only 4-dimensional and having
frames at lightcone boundary. Huge vacuum degeneracy of Kaehler
action gives rise to this degeneracy: actually
degeneracy is due to the cognitive spacetime sheets glued to the material
spacetime sheets: thoughts geometrically!

To make things even more complicated: one can *save classical determinism*
by *generalizing the definition of 3-surface*: allow spacelike 3-surfaces
with *timelike* separations. These 'association
sequences' are geometric models for thought, they are simulations,
predictions for future behaviour and bring in intetionality and
intuition. They are the geometric counterparts
of quantum jump sequences of selves.

Ontogeny recapitulates phylogeny: self as sequence of quantum jumps <-->
association sequence as sequence of 3-surfaces with timelike separations.

snip
MP]
> You are quite right. TGD is however not QED or QCD. One of
> the basic differences between TGD and standard model is that TGD
> predicts the existence of classical electroweak gauge fields and
> classical color fields. Of course also quantum fields are predicted: TGD
> predicts practically same world in elementary particle length scales
> (there are also new physics effects). Situation changes at very low
> energies. The possibility of classical Z0 and color fields is
> crucially important difference and implies new effects at low energies.

[SPK] Interesting! I would like to see an explicit calculation of this!
:-)

[MP] For instance, 'TGD and nuclear physics' (in
descriges some effects of classical Z^0 fields.

In fact, classical color fields are given apart from numerical
constant by G^A_alphabeta = H^A J_alphabeta, where J_alphabeta
is Kahler form and below cell length scales apart
from numerical constant equal to classical em field. H^A is
color Hamiltonian associated with particular generator
of color Lie algebra (8 alltogether). The strenght of classical
color field is essentially same as that of classical em field.
Compared to gluonic fields inside hadrons these fields
are very weak.

> Consider first what the new effects related to weak interactions are.
>
> a) Neutrino physics at eV energy range changes dramatically since
> Z^0 long range force provides long range interaction between neutrinos.
> The requirements that parity breaking effects in hadronic, nuclear and
> atomic physics are (extremely) small, that Z^0 force does not explode
> condensed matter, and the experimental data about neutrino mass squared
> differences, fix the scenario completely.

You mean no ultraviolet divergence caused by the Z^0 interaction?

[MP] No. Nuclei have classical Z^0 charges. If neutrinos do not screen
this charge there is huge net charge density and huge repulsive
Z^0 energy. The screening must occur at the spacetime sheet
at which neutrinos topologically condensed. It is the spacetime
sheet associated with epithelials sheets (essentially cell length scale
is in question).

> Quarks must feed their Z0 gauge fluxes to same
> spacetime sheet at which neutrinos topologically condense. This
> corresponds to the length scale of epithelial sheets from the recent
> constraints on neutrino mass (p=about 2^k, k=169=13^2).

[SPK] "Epithelial"?? "They are contiguous (i.e., the cells are attached
to
one another)"????
http://www.mc.vanderbilt.edu/histo/BasicTissue/Epith.char.html

[MP]Epithelial sheets are double cell layers and much like
cell membranes: various organs, also skin, are bounded by them. p-Adic
scale corresponds to p=about 2^169. Something roughly like 4*10^-6 meters.
Epithelial sheets was next step after the development of monocellulars.
Multicellulars organized to epithelial sheets.

> b) Chirality selection, complete mystery in standard physics context,
> finds an elegant explanation in terms of classical Z^0 force, which
> has chiral coupling to fermions and hence breaks parity.

[SPK] How does p-adic TGD model the chirality of the three generations
of
neutrinos and their masses? Can you explain this explicitly?

[MP] The empirical imput from neutrino masses comes from experiments
done during last years. The only possible conclusion in TGD context
is that *all* 3 neutrino generations topologically
The reason is that mass scale is exponentially sensitive to integer k.

Mass calculations using p-adic thermodynamics can be found in chapter
'P-adic mass calculations: elementary particle masses'

Chirality is essentially handedness. In standard model with massless
neutrinos neutrinos are left-handed (left-handed screw visualizes this).
Massive neutrinos are mixtures of left and right handed components
but neutrinos created in typical particle reactions
are in good approximation massless and left handed since mass
is so small: 10^7 times smaller than electron mass.

In standard model the mystery is what makes neutrinos massive<-->
mixes their Minkowski chiralities. In TGD this occurs automatically.
The conserved chirality is not M^4_+ chirality but
H=M^4_+xCP_2 chirality. It corresponds to quark and lepton numbers:
proton is stable (proton stability is causing troubles for standard
unifiers).
M^4_+ chirality is not conserved and this gives the general prediction
that all fermions are massive.

> c) Solar neutrino puzzle finds explanation in terms of dispersion
> caused by solar and terrestial Z0 magnetic fields on neutrino beam
> coming from the solar core. In particular, the observed correlation
> of solar neutrino intensity with solar spot activity and magnetic
> (actually Z0 magnetic) fields of Earth finds explanation. Also the fact,
> the intensity of solar neutrinos is different in Kamiokande and in
> Homestake can be understood.

[SPK] "Z0 magnetic"? Could you elaborate?

[MP] Classical Z^0 field obeys essentially the same mathematics as
classical
electromagnetic field. There is Z^0 electric field and Z^0 magnetic field.
Since the 4 CP_2 coordinates determinedinduced classical gauge fields,
there is very close connection between ordinary magnetic and Z^0 magnetic
fields. In fact, typically they are proportional to each other
if on same spacetime sheet. The simplest assumption is that Earth's
magnetic field could be accompanied by Z^0 magnetic field in same
direction: this
is also implied by the fact the currents creating the field are probably
very
similar.

Homestake is rather near to magnetic North Pole. If Z^0 magnetic
field is indeed essentially similar to ordinary magnetic field,
this means that neutrinos coming to Homestake couple to stronger
Z^0 magnetic field than those coming to Kamiokande, which
is much farther from the magnetic North Pole. The anticorrelation
of neutrino flux with Earth's magnetic field (actually ^Z^0 magnetic)
has been indeed observed. In Kamiokande no effect has been observed.

> d) Tritium beta decay anomaly and its variation with period
> of year (physics of planet system must be somehow involved!)
> finds also explation in terms of classical Z0 force.

[SPK] Could you give me some references on this anomaly?

This reference is not newest one related to tritium beta decay anomaly.
V. M. Lobashev {\it et al}(1996), in {\em Neutrino 96} (Ed. K. Enqvist,
K. Huitu, J. Maalampi). World Scientific, Singapore.

There was neutrino conference in Tokyo for year ago: Neutrino 98', in
which
newest data was represented relating to the annual variation
of the anomaly, which is competely absurd effect from the point of view
of standard model.

> e) For roughly year ago came also report from NASA telling
> that the acceleration of space crafts in outer space
> is not quite what it should be. Classical Z0 force leads
> to an explanation of the effect.

Has the "effect" been confirmed?

The gathering of information took 25 years. The problem is
finding explanation for it. I saw some explanation based on claim
that some effect related to space craft could explain the effect:
the people who published the data about effect did not take seriously
the explanation. Standard model physicists probably took it seriously
because they have no explation.

Here is reference to the effect.
J. D. Anderson {\it et al}(1998), Phys. Rev.Lett. Vol. 81, No 14,p. 2858.

> f) Just week ago I learned from labotory scale effect
> in which spinning disk in accelerated rotation induces
> rotation of the second disk above it in oppposite direction.
> Explanation in terms of Faraday induction associated
> with Z0 field suggests itself. The time varying Z^0 magnetic
> field created by the rotating disk generates Z0 electromotive force.
> The field lines of induced Z^0 electric field rotate along the axis of
> Z^0 magnetic field and create torque forcing the second disk
> to rotate in opposite direction (from minimization of Maxwell
> action).

[SPK] Any references on this? That about the gravitational shielding
effect
that has been reported in connection with spinning superconductor disks?

[MP] This is different effect. Here is relevant piece of text from email.
http://www.electrogravity.com/index1.html gives
second accelerating disk (Comments of Jerry Bayles
about Harvey Morgan's paper in IEEE Aerospace and
Electronic Systems" (AES) of January 1998, pages 5 to 10, "Now we can
explore the Universe".

The gravitational shielding effect was observed by Podkletnov in
Finland, at Tampere. He lost immediately his job. Probably the
Finnish physics colleagues would have killed him unless he had not escaped
immediately(;-). Later NASA got interested and Podkletnov is now in NASA,
I think.

> Classical color fields accompanying classical em fields
> are second prediction of TGD.
> In http://www.physics.helsinki.fi/~matpitka I have proposed a model
> of color vision in which quark color directly corresponds to
> the color of color vision.
>
> The basic observation came from mathematician Barbara Shipman who
> discovered that the model for honeybee dance leads to a connection with
> flag manifold SU(3)/U(1)xU(1) associated with color group: as
> if quarks might have something to do with how honeybees see
> the world!

Could you post this notion explicitly?

> I did not take seriously the quark hypothesis first but it indeed seems
> that quarks could be involved: the reason is that quarks feed
> their Z0 charges to the spacetime sheet corresponding
> to epithelial sheets since neutrino Z0 charge is there
> and must be neutralized in order to avoid Z^0 explosion.

[SPK] Umm, this looks a bit ad hoc...

[MP] This is just applying general physics thinking. Condensed matter
must be stable. The data about neutrino mass differences fix
completely the p-adic prime of spacetime sheet at which most
of neutrinos reside. The Z^0 charge of neutrinos must screen
in excellent approximation quark Z^0 charge. For instance, if
quarks would feed their Z^0 charge to nuclear spacetime sheet, nuclear
and atomic parity breaking effects would be huge. They are
extremely small and found to be just what standard model predicts.

Manysheeted spacetime is of course absolutely essential for the
mechanism to work. Smallness of parity breaking effects
and stability of condensed matter fix essentially unique the
general picture about manysheeted universe in condensed matter length
scales.

> Hence quarks couple directly to classical
> color fields: this generates small color magnetic polarization
> at the level of nucleons (protons and neutrons): proton and neutron
> change very little but this is enough. Epithelial sheets are
> the p-adic level where I have located our consciousness!
>
> Therefore the mysterious quarks, which we have believed to be
> completely outside of the realm of sensory experience make possible our
> color vision! Neutrinos, which we have believed to be completely elusive
> particles in turn make our thinking and hearing possible. Neutrinos
> are indeed ideal candidates for realizing thoughts since
> dissipation is practically completely absent since coupling to
> Z0 quanta is extremely weak (they are extremely massive).

[SPK] Is it necessary to require a "particle" to "realize thoughts"?!

[MP] It would be better to say 'realize logical mind'.
The starting point is that logical mind corresponds to Boolean
algebra. Fermionic Fock state basis forms Boolean algebra:
yes= fermion number one, no=fermion number 0.
Therefore it is tempting to assume that fermions make
thinking possible.

In order to easily manipulate the Boolean algebra statements represented
by fermions, one needs pairs of fermion and antifermion at different
spacetime sheets: spacetime sheets contain statement and its negation
pairs are created by the decay of wormholes to fermion-antiferion pairs.

Electrons and nuclei are excluded since huge energies
would be involved in this kind of process. Neutrino and antineutrino are
however light. The decay of Z^0 wormholes to neutrino-antineutrino pairs
connecting spacetime sheets of cell membrane and epithelial sheet is nice
mechanism for manipulating Boolean statements. Boolean
statement decomposes to statement and its conjugate at different
spacetime sheets so that negation of statement is automatically
consciously experienced (as it indeed is!)

Even more, neutrino pairs should have vanishing total energy in order that
they could exists finite time (cognitive spacetime sheet has
finite duration). Neutrino indeed has negative energy in condensed
matter! The reason is essentially that its rest mass is so small
and its interaction energy with nuclei is much larger.
No other elementary particle fits these requirements!

What is amazing that the length scale of double cell layers
is the length scale at which the model predicts that logical
thought appears first time. Also vision appears at this spacetime
sheet since quarks must feed their Z^0 charges at same spacetime
sheet!

> Classical Z0 force makes possible the coding of sound oscillations
> to thoughts and coding of sounds to auditory experiences (oscillating
> nuclei generate oscillating Z^0 fields which couple to neutrinos).

[SPK]I don't follow... :-(

[MP] Sound wave means that nuclei oscillate. Nuclei have Z0 charges
and oscillating Z^0 charges create oscillating classical Z^0 electric
fields. Neutrino Cooper pairs in turn couple to these classical
oscillating
Z^0 electric fields and therefore 'experience' the frequency of
oscillation.

snip
[SPK]
> > Interesting, this picture looks similar to Hitoshi's, except for the
> > details about CP_2 extremals and "em neutral spacetime sheets"... In
> > Hitoshi's model all "direct" observations give classical situations,
QM
> > behavior can only be inferred from "corrections". This corresponds to
> > your statement that the self can not be modeled, we can only infer its
> > properties, bounds, etc. ...
> >
> [MP]
> Yes. The Feynmann diagrammatics has direct topological counterpart.
> Lines of Feynmann diagrams are thickened to 4-manifolds.

[MP] Can we think of the "thickening" as a consequence of considering
velocities distributions, e.g. greater than zero (null) lengths between
events?

[MP] No. What is involved is transition from quantum field theory
to TGD. For point like particles lines of Feynmann diagram are
just lines. When particle becomes small 3-surface, lines become
orbits of 3-surfaces and hence 4-manifolds.

snip
[MP]
> Ability to measure time with accuracy of 10^(-40) seconds would require
> quite a lot of intelligence(;-). System should also be able to form the
> concept of time, etc... Only experience of passing of time
> and short term memory is involved at basic level.
>
> The clock reading comes from sensory observations (clock in the wall)
and
> subjective memory telling that the pointer indeed moves. Subjective
memory
> made possible by self concept is crucial for this.

[SPK] This is a clocking between the "perception of the clock on the
wall"
and the "memory of a clock"... I agree that subjective memory is very
important here. I think of memory as a finite and variable subset
partitioned out from the Set of all possible Minds by the clocking
action. It is a selective act resulting from am interaction between
object (subuniverse) and subject (Self). What we have to understand is
that we have no unique Self and no unique clocking, we have infinite
equivalence classes of each! Also the subject-object relation is
symmetric!

[MP] I think that one should be very cautious of not requiring the clock
to have properties, which are possessed by us only! I explained
already earlier my model of biological clock as subself waking up
periodically.

[SPK]
> > Observers get around this by making records of events
> > that are observed and the recordings are arranged in posets, thus the
> > observer can infer its "clocking rate", but it can not observe it
> > directly. This is directly related to an observer's inability to
> > directly observe itself. "I can only see a reflection of my face, not
my
> > face it self."
> >
> [MP]
> In TGD framework situation is different. I experience my subselves
> as thoughs, sensory experiences, mental images. An example
> of clocklike phenomenon are periodical after (mental) images:
> subselves waking up periodically. Also we are mental images
> of higher level selves waking up periodically. Also particle
> physics community is mental image of a higher level self waking
> up periodically. I hope I knew when it does this next time.

[SPK] Sure, but like I said, we can not experience the subsets
"directly" we
can not "know what it is like" to be such in a first-person sense...

[MP] We can experience them directly if they
are our immediate subselves! Even mental images
are clocks of this kind. Look at bright light and close your
eyes. You find that the after images comes periodically back:
it is subself which wakes up and slees again. Same is true
for all mental images. Think some word for some time and you find
that it comes back to your mind periodically.

[SPK]
We can only represent what it would be like in terms of our experiences,
e.g. we use our own experiences as the building block to model the
expected observations of the subselves, we do not use the experiences of
the subselves.

[MP] We experience abstractions of the experiences of subselves.
They are kind of averages. Our experiences contain
both self and subself level: this division might well correspond
to reflective and proto levels of consciousness. (Situation
is not quite so simple: also fermions
could correspond to reflective level)

snip
[SPK]
> > Can you isolate why "Fundamental physics predicts reversible world"?
Is
> > it because of the use of infinitesimal calculus and the association of
> > "time" to an absolute external parameter of change?
>
> [MP] The basic reason is that fundamental physics relies on variational
> principles: there is no other way to formulate quantum theory. One
> cannot formulate the dynamics of dissipative systems in terms
> of variational principles. Quantum theory of dissipative systems
> simply does not make sense: parameters characterizing dissipation
> are results of quantum calculations relying on quantum statistical
> determinism and quantum measurement theory, which goes
> outside the Schrodinger equation. What one typically does is to
> calculate reaction rates using reversible quantum physics and then use
> Boltzman equations and alike to calculate various parameters
> characterizing irreversibility and then to replace the reversible world
> with irreversible one. Ugly!

[SPK] I think that we need to look more carefully at the time-energy
uncertainty relation! Prigogine and Schommers have suggested the use of
semigroups in order to make irreversibility primitive in the model. It
is obvious, at least to some, that the traditional formulation of QM is
too heavily dependent on classical assumptions!

[MP] I think that the essential property of subjective time
is that it is not metrizable. It it were one would have just two
different geometric times and this we do not want!

I will continue in separate posting

Best,
MP

This archive was generated by hypermail 2.0b3 on Sat Oct 16 1999 - 00:36:30 JST