Matti Pitkanen (matpitka@pcu.helsinki.fi)
Mon, 3 May 1999 08:59:11 +0300 (EET DST)
On Sun, 2 May 1999, Lester Zick wrote:
> Hello to All,
>
> There are additional considerations relevant to the nature of material
> time and spatial dimensionality. Space in general is not laid out on any
> universal grid. The dimensionality of space is Euclidean in geometric
> terms, but this circumstance is simply a categorical implication of the
> ability to think and act. It is nothing more than a recognition of
> geometric necessity analogous to the application of principles of plane
> geometry to flat surfaces. Nor is it an exclusive aspect of conscious
> being because it applies equally to all aspects of being in space
> although obviously the knowledge involved is reserved to conscious
> beings.
>
> Time on the other hand is not a geometric category. Time exists because
> the present cannot be what the past was, nor can the future be what the
> present is. This is how we come to recognize the ideas of past and
> future. Everything that ever happens happens in the present. There is no
> graph of past events nor of future events waiting to happen. We only
> know of the past and future not because knowledge of either exists or is
> capable of existing in general but because the present cannot be as it
> has been nor remain as it is. And what knowledge can be had of the past
> or the future is really only knowledge of the present in the context of
> various properties associated with present phenomena.
[MP]
The concepts of spacetime and geometric have been extremely succesful
in physics. On the other hand, time does not seem to be a geometric
cathegory as you claim. I think that this paradox can be solved only by
distinguishing between subjective time and geometric time. In my own TGD
approach the flow of subjective time basically corresponds to sequence of
quantum jumps, each quantum jump is a 'tick' of subjective time. What is
new is that quantum jumps occur between quantum histories, which
correspond classically to quantum superposition of classical histories
(deterministic development of spacetime geometry and of classical fields
in it). Therefore moment of subjective time is jump between two
eternities with respect to geometric time.
I see the identification of subjective and geometric times leading to
various paradoxes as partially wrong deduction following
from approximate time localization for the contents
of our conscious experience around definite time value.
Contents of conscious experience contain also
time-non-localized contribution from
entire initial and final quantum histories (intuition?).
Simple arguments based on general coordinate invariance suggests that
contents of conscious experience shoulw be diffused over entire quantum
histories so that there would be no psychological time.
The point is that the contents of conscious experience should correspond
to locus of nondeterminism of quantum jump and nondeterminism cannot be
located in a *strictly causal theory*. Classical nondeterminism
(which one gets rid of by generalizing the concept of 3-space) of the
field equations defining classical spacetime in TGD provides a solution
to this problem and brings in psychological time. But this is another
story. (see http://www.physics.helsinki.fi/~matpitka/cbook.html)
>
> Consequently, time is not a geometric adjunct, nor is geometry the
> adjunct of time. Time has no commensuration with spatial dimensionality.
> The three dimensions exist as they do because each has some form of
> commensuration with the others. This is the only reason we can know the
> dimensions at all, because each is capable of being measured in exact
> geometric terms in relation to the others. The difference between points
> is a line, the difference between lines a plane, and the difference
> between planes a volume. And all are mutually commensurable.
>
> However, at the fourth dimension this is no longer true. The difference
> between volumes corresponds to some form of shell and is incommensurate
> with the three universal dimensions. The reason for this is that the
> integrand for the ratio between differences in volumes must include the
> natural logarithm of a non transcendental number, meaning there can be
> no exact correspondence between the volumes of shells in geometric terms
> since the natural log of a non transcendental number must itself be
> transcendental.
>
> In any event, time corresponds to no geometric dimension because it is
> simply a logical construct, the necessary implication of change in the
> context of a static spatial geometry. Space is Euclidean only in the
> sense of being subject to Euclidean concepts applicable to geometry in
> general. And that geometry can only be three dimensional in nature
> because the difference between volumes corresponds to no volume exactly
> for the reason stated.
>
> Thus I submit it is incorrect to speak of space-time or of the geometry
> of space-time or of time as some form of geometric concept. Whatever
> time may mean in ultimate terms and however it may be measured, it
> corresponds in no sense to geometric dimensionality because that
> geometry necessarily exists and can only exist whereas time measures and
> is measured by change.
>
[MP]
I agree with what you say but with little modification: I want to
replace 'time' with 'subjective time'.
Best,
Matti
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