Matti Pitkanen (matpitka@pcu.helsinki.fi)
Sun, 8 Aug 1999 08:08:24 +0300 (EET DST)
Dear Stephen and All,
Below A little piece of text about how internal clock could be realized
in TGD framework.
Best,
MP
***********
How fast time runs?
It is not at all clear whether the wake-up state is continuous:
it might well be that self exists only a fraction of time.
The identification of subjective memory as short term memory actually
forces this conclusion: the duration of short term memory seems to be of
order second so that the periods of, at least, sensory wake-up should be
of order second. Also during sleep self or some subselves probably exist
some small fraction of time: dreams are good example of this.
In highly alert state this wakeup fraction would be near unity while
in drowsy state it becomes small.
An interesting challenge is to understand the relation of
the subjectively experienced time to the psychological time
(essentially geometric time). In order to experience
time self must have a clock. The simplest assumption is that the
sequence of quantum jumps defines the sequence of ticks for the
clock. Therefore subjective time would be measured
as the number n of quantum jumps occurred after the wake-up of
the self. The rate for the running of subjective
time would be dn/da, number of quantum jumps per geometric time,
and just the inverse for the rate
of running for psychological time and same
for all systems if the average duration of chronon is
of order of CP_2 time: this is certainly not consistent
with the fact subjectively experienced time can run faster
or even stop. One could also kill this naive hypothesis by
noticing that self should be
able to distinguish between the ticks of the clock:
obviously we cannot experience quantum jumps as separate
events.
A more realistic model is based on the idea that the average
time interval Delta a between two wake-ups of a 'clock' subself,
which exists periodically in a wake-up state defines a
natural unit of subjective time. The number N of ticks for the
clock is given by the age of self divided by the duration of single
wake-up period for the 'clock' self
N(a)= a/Delta a .
N(a) would naturally define a measure of
subjectively experienced time. Slowing down of subjective time would
correspond to the slowing down of the internal clock
in the sense that Delta a increases.
Consider now whether this simple model can explain basic facts
about experienced rate of subjectively experienced time.
a) Experienced time is said to run slowly, when we
get bored and drowsy. Actually the situation is just the opposite
since the number of ticks of the internal clock
per unit of psychological time must be large. In order
to understand what might be involved,
assume that also the internal clock gets
drowsy so that the average wake-up period Delta a_W
for the internal clock gets shorter. If
internal clock wakes up spontaneously, one can assume
that the average duration Delta a_S
for the sleeping periods for clock self
is not changed. Hence Delta = Delta a_W+Delta a_S
is reduced so that N(a) propto 1/Delta a increases
and geometric time is experienced as longer.
b) Quite different situation is encountered, when
person is in the state of whole-body-consciousness.
In this kind of situation
there is no internal clock and one can indeed say that
there is no time! This would explain the reports
of meditators about state of 'timelessness' [notime]
Oliver Sacks has described in his book 'Awakenings'
patients who have lived for years in 'no-time' state with frozen
contents of conscious experience, which
presumably meant that everything in the external
world seemed to happen extremely slowly.
It would be natural to assume that
the lifetime Delta a of the 'clock' self was very long
in this kind of situation or even that person was in
the state of whole-body-consciousness.
The only clock is person itself and the entire experience
corresponds to single tick of this clock.
There are also reports that when person is in
dramatic situation like traffic accident, time is experienced
to stop. The simplest explanation is that person
experiences state of whole-body consciousness.
One could also try to understand why persons
at older age feel that time runs faster. This statement is
clearly not about what person immediately experiences
but impression about what has happened. One possible
explanation is however that the period Delta a of
the internal clock indeed gets longer at older age.
This could be caused by the increase of the period Delta a_S of
the sleeping period of the internal clock. Perhaps
the deviation of the entanglement of the internal
clock from critical entanglement increases
gradually when person ages and it becomes increasingly difficult
to wake-up. Thus, if the total fraction of geometric time spend by
the person and his/her subselves in wake-up state decreases when
person gets older, one can understand why the time is experienced to
run faster at the older age.
Best,
MP
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