[time 743] Holy trinity summarizes the mathematical structure of quantum TGD

Matti Pitkanen (matpitka@pcu.helsinki.fi)
Sat, 11 Sep 1999 09:13:46 +0300 (EET DST)

Dear Matti, Lance, Stephen et al.,

To me three kinds of time of Matti look like a taxonomy of phenomena.
Matti, do you have any relations between these three times?

[MP] These three times emerge automatically from the basic
structure of theory. They are by no means assumed in ad hoc manner.

Holy trinity basically follows from 'holy trinity' of
a) General Coordinate Invariance,
b) existence of Poincare invariant and GCI S-matrix and
c) existence of classical physics, not as approximation, but
exact part of quantum theory. The existence of classical
physics actually follows from the definition of configuration
geometry in GCI invariant manner so that

*it is basically Poincare invariance and GCI which lies behind holy

At least for me it was shock to realize how enormously forceful
principle GCI is when combined with spacetime as 4-surface idea.

Here are some details.

a) *General Coordinate Invariance* makes impossible to define
state as t=constant snapshot. States are configuration space
spinor fields in entire configuration space consisting of 3-surfaces
in M^4_+x xCP_2 with all possible values of lightcone proper time.
Thus the phrase "quantum history".

Quantum histories would be the description of manyworld enthusiast for the
entire universe: I think we know that this approach does not lead to any
understanding of consciousness and splitting of worlds is at least to me
intolerably ill defined concept.

b) Quantum jumps between quantum histories occur.

This sequence of quantum jumps is subjective time development and
time is measures as quantum jumps occurred after say wakeup of some self.

Quantum jumps *CANNOT* occur just as


This would be totally inconsistent with which we know about quantum
field theories which summarizes the predictions of the theory. Rather,
each quantum jump involves unitary 'time' development acting
in the space of quantum histories.

Psi_i-->UPsi_i -->Psi_f,

U =exp (iL_0(tf-ti)),

tf--> infty, tf-->-infty.

The 'time' t is just group theoretical parameter like parameter
characterizing element of Lie-group in some unitary representation
of group. It has nothing to do with experienced time. As far
actual calculations are considered, this is precisely its role
also in standard quantum field theory. 'Time' t runs from -infty
to +infty in experiment. Usually this is taken as approximation:
interactions are 'turned on' at ti--> -infty and
'turned off' tf--> infty: this of course makes no sense but is
handy manner to get to the formula of S-matrix,
which is mathematically obvious.

Note: One could avoid use of t totally, by just speaking about
S-matrix. The definition of S-matrix leads to introduction
of t and it is indeed possible to speak about information
currents associated with t-development. An open question is whether
this is really useful or not.

Note: The form of U follows in TGD from the requirements of General
Coordinate Invariance, Poincare invariance and Super Virasoro
invariance and guaranteese that S-matrix of the theory
is algebraically very 'stringy' and hence also yields the S-matrix
reducing at low energy limit to that of standard model
in good approximation. Thus the form of U is *NOT* any adhoc

Note: One can call U as 'informational time development' since
information difference between final and initial states
defining information gain of conscious experiences results
from U.

c) Geometric time is associated with spacetime surfaces as time
coordinate. Geometric time is highly nonunique by GCI.
It can be taken as lightcone proper time in most cases and at least

'Holy trinity' is *NOT* starting point of TGD approach,
there is nothing 'religious' associated with this
term. Holy trinity and tripartism is not starting point of
TGD, these concepts only sum up the philosophy first by the
only known consistent mathematical formulation of quantum TGD.

Matti Pitkanen <matpitka@pcu.helsinki.fi> wrote:

Subject: [time 735] Which was first: clock or time?

> Dear Matti, Stephen, Hitoshi, et al.:
> Because I am too busy with practical affairs to follow this discussion
> closely, much less to participate actively, I apologize if the following
> comment is inappropriate, but I could not let the following pass without
> some comment:
> Somebody (I think Stephen) wrote:
> > I see LS's as fundamental clocks, and thus it
> > should be possible to consider an "ensemble of clocks" as given by a
> > ensemble of LSs. But, I am very sketchy in my thinking of this. :-(
> To which Matti replied:
> >
> > [MP] I cannot say. One should need a quantative model for clock.
> > Clock as oscillator is a nice model but based on rythe existence of
> > time! You want to derive time from the existence of clocks, I
> > am happy in deriving the existence of clocks from the existence
> > of time!
> My comment is this: Matti's reply does indeed identify the core issue.
> The only problem I have with Matti's comment is that it seems rather
> casual, so it doesn't alert the reader to how fundamental the
>disagreement here is.

> This was casual comment. I have talked a lot about TGD based
> time concept in earlier discussions and I did not bother to repeat
> all that. In any case, the disagreement is fundamental.
> It is not that I would believe that geometric time is enough: the point
> is that there are *three times*.
> a) Subjective time "measured" as a number of quantum jumps occurred.

You seem to think/assume that quantum jumps exist. You often identifies
them with our waking up in the morning. I have another view to the
so-called quantum jumps from the point of view of observer: They just look
like existing but do not occur as far as they are observable. The jump is
a jump from one eigenstate to another, but if this jump could be
observable, the observed system that jumped must be in scattering state
(that is orthogonal to eigenstates), hence this is not a jump.

[MP] One must distinguish between quantum jumps and selves carefully. I
assume quantum jumps. Wake-up means generation of self
which is able to stay self (p-adically unentangled): wake-up can
occur either spontaneously (U develop p-adically vanishing entanglement)
or by quantum jump.

Your view is possible and certainly the only one if one sticks
with dualism or materialism. Equally well I could formulate my belief
as belief in existence of free will. I am however worried
about whether your approach is really consistent with quantum
measurement theory.

> b) Geometric time, this is the good old Einsteinian time and combines
> with space to form spacetime.

Geometrical time appears only in observation and this time is the
observer's time that observes the geometry of other systems. Thus
geometrical time is a time of a local system when it is in a state of
observation of others.

[MP] Yes, I understand your view: here we simply have different

Einstein himself talked about 'events' in formulation of Special
Relativity and this suggests that he identified time with observer's
time. He however introduced proper time concept as observer's subjective
time and this definition involved also the motion of observer.
This is step to the same direction of subjective time
as I define it freeing it from geometry totally. The view
of Einstein about observing was surprisingly close to mine: he states that
our observations give only very partial accounts about the reality
behind, in particular that our concept of time
reflects this. I however disagree with Einstein's belief
about given unique spacetime.

> c) And also the time *parameter* t of unitary time
> evolution operator U: this parameter is purely group theoretical and has
> absolutely nothing to do with our psychological time. t runs from -inty
> infty during each quantum jump Psi_i--> UPsi_i-->Psi_f.
> U defines S-matrix and predictions of quantum physics. Already
> realized that the time evolution associated with S-matrix has nothing to
> do with time evolution as we experience it. All calculations assume
> that t runs from -inty to infty but take this as 'technical'
> therefore TGD predicts precisely same general form of S-matrix
> as standard physics. Interpretation is only different.

Unitary time is the proper time of a local system, existing as a
clocking/living of itself. This time is the fundamental one, from which
the geometrical time arises in the act of observation. Quantum jumps is an
illusion of the present physicists. Thus my formulation combines these
three kinds of time of yours.

[MP] Here TGD differs from you view decisevely but is completely
consistent with how S-matrix is always defined.

You approach is subject to obvious criticism: does it really yield
the predictions of standard measurement theory. Born rule, probability
interpretation. It if does, I would be interested to know how it
achieves this feat. As we know, already the Bell inequalities and
the fact that only eigenstates of observables occurs as outcomes
of measurements, seem to simply exclude the possibility to reproduce
quantum measurement theory without actually assuming quantum jump.

> In standard physics all these times are identified as single time: it is
> easy to understand what a mess results!

I do not see your theory cleans up the mess.


a) The fact that quantum jumps occur between quantum histories
solves the "determinism of quantum jump-determinism of Schrodinger
equation" paradox. Schrodinger equation does not cease to hold
for a moment: rather entire solution of Schrodinger is replaced
with a new one.

[This interpretation is by the way consistent also with
the structure of S-matrix in standard QFT: integrations
over entires spacetime]

b) Dissipative time development means phenomenological description
replacing the sequence of final state spacetimes (macroscopically
equivalent by localization in zero modes) with single macroscopic
spacetime, which is like envelope for set of curves. Not quite
exact envelope solving the reversible equations of motion
is in question: hence one must introduce various parameters
characterizing irreversibelity (diffusion constants, paraters
characterizing friction, etc...).

c) The loss of geometric time occurs in GRT because configuration
space consists of 3-geometries. Configuration space of 3-surfaces
differs from Wheeler's super space: one can associate with 3-surface
center of mass time coordinate. This gives me geometrical
time lost in quantum GRT.

Classical nondeterminism of Kaehler action is crucial
for undestanding of *psychological time* characterizing
cm time coordinate for the contents of cs experience.
Without classical nondeterminism the information contents
of our experiences would not be concentrated around any value
of geometric time.

Classical nondeterminism however makes possible cognitive
spacetime sheets with finite time duration and q uantum jumps for
which nondeterminism is concentrated
to a finite interval of geometric time: and these
quantum jumps correspond to conscious experiences with time localized
content. This is how psychological time emerges. As center of mass time
coordinate for contents of conscious experience.

Note that I assume no a priori experiencers: experiencer is defined
by the contents of experience. In dualistic approch mind and
matter are assumed apriori.

There are many other items in the list of 'time anomalies' but I will
not go to these here.

> *************

> In Hitoshi's first statements on the subject of Local Times one of the
> things that attracted my attention (as a philosopher) was his comment
> the problem of time in contemporary physics is essentially a
> problem, not a physical or mathematical problem. Matti's comment here
> perfectly illustrates the validity of Hitoshi's assertion about the
> of the problem of time. What is at issue is really how we understand the
> fundamental nature of time. In our joint article in Apeiron, Hitoshi
> I were completely explicit about the fact that our position was in
> opposition to the conventional understanding. Here is what we wrote:
> "...the proper clock is the local system itself,
> and it is a necessary manifestation of that local system.
> In this sense, “clockingEis the natural activity of any
> local system. It follows from this that to be an existing
> thing in the world necessarily involves clocking, without
> which there is no interaction. In these respects, our position
> is in complete opposition to the conventional understanding
> of time measurement, where time is given a
> priori and the measurement of time by clocks is viewed as
> an incidental activity of intelligent observers. Contrary to
> the conventional understanding, our view is that all beings
> are engaged in measuring and observing, and the activities
> of measuring and observing are not incidental, but
> pertain to the essence of all interactions. If we are permitted
> to express it somewhat boldly, we have turned things
> completely around: It is not that things exist and their
> duration is incidentally expressed by clocks. According to
> our formulation, clocks exist and their operation is necessarily
> expressed by duration."
> (to which we might have added, Time, as measured or counted duration, is
> what results when certain local systems or certain sets of interactions
> are chosen as the standard in terms of which other durations are
> described, much as monetary value comes into existence when one
> commodity
> is chosen as the unit in terms of which the exchange relations of other
> commodities are expressed.)

> Thank your for a nice phrasing of your viewpoint.
> I agree in many aspects with what you say. I have however
> 'neuropsychology' oriented starting point. LS as self, if it
> time must have subself waking up periodically. We have a lot of
> them, typically mental images representing mental images, recur
> periodically. After images are a good example. Self can
> however be in state of whole body consciousness and have no subselves:
> in this case it has no clock: hence explanation for the reports about
>'no time' experiences by meditators.
> I could paraphrase you comment about turning things completely around.
> Selves exists as heaps of cs experiences associated
> with quantum jumps and give rise to experience of *subjective time*.
> Each self waking up periodically is clock of some larger self.
> One could also say that quantum jump is basic tick of subjective
> time (not directly experienced as such however) and subjective time
> is created by the syncronized ticking of all the subjective clocks of
> this infinite universe. But as I said, I assume also the existence of
> geometric time and formal time parameter t associated with the unitary
> evolution operator U. I believe that only this 'holy trinity' makes

I notice that you have been sticking to "the holy trinity" from the
beginning of your discussion. This sounds like you have a kind of
religious starting point as Kepler, et al.

As I noticed, I use "holy trinity" only to summarize the philosophical
interpretation for the outcome of mathematical formulation of quantum TGD.

> it possible to resolve all the paradoxes related to the concept
> of time.
> ********

> Now, to come back to Matti's comment: It is entirely in order to
> challenge Hitoshi and me to flesh out our claims -- to show that we can
> offer an intelligible and serviceable, quantitative model of a clock --
> and it is particularly apt for Matti to demand that we show that our
> model is not an instance of circular definition. However, I am less
> comfortable
> when Matti says, "I am happy in deriving the existence of clocks from
> the existence of time!" The reason I am uncomfortable with that is that
> it seems to me that it simply begs the question. I am not saying he is
> wrong. I am simply saying that we need to acknowledge that this is what
> in dispute. From our point of view, Matti's claim looks just as
> as ours looks to him.

> OK. My statement was casual already because I have
> all these three times instead of only one (as if single time would
> not produce enough head aches(;-)) and was meant only to
> pinpoint the difference in views.

I feel this is not a difference but a lack of unifying view point. Three
kinds of time do not seem to help us to understand the universe.

[MP] Here I disagree but I can give only the arguments supporting
my view, which I think are convincing. I am of course grateful for
any detailed demonstration of how my framework fails.
In any case, I do not want to take any role of guru. Anyone must discover
the truth personally, if not in this life, then in the next(;-)!


> Best,
> MP

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