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Parallelisms : Neurophenomenology - Quantum mechanics -
Thermodynamics - Holotomography - Higgs field -
Accounting - Stability
Neurophenomenology - Quantum
mechanics
The present parallelism has
been only motivated by the aim of providing a simple and
accessible analogy. However it may constitute an additional
questioning aspect in relation with an underlying brain process
related to an intermix of quantum field - like already mentioned
at the page
3.3 .
The present parallelism is not at
making more prospective assumptions about possible links between
neurophenomenology and
quantum mechanics per se, but at highlighting the co-existence of
several scales of time - say time-cycles of reference - in a
dynamical set - say a "big data t-inversion or update" may result
from a large collection of very many tiny ones.
In example, the above
described the "night-time" inversion like a big "t-inversion"
cycle - say a "big overnight update of the data in our accounting
system". It will be shown now that a same similar process can be
seen as a "very tiny" part of any "motion" or "transition" process.
Let's first describe the
procedure in accounting terms as following: the sequence consists
at transferring first the actual data in a two [u] accounts so
that the accounts for the operational records become free and
second at reifying the adequate portion in the real account space
so that the time inversion become effective and finally "dropping
the rest" within a [v] so that the obsolete data vanish and that
the balance is maintained.
The point is that this
procedure may apply for an "big overnight update" but it may also apply when we describe the
single motion of a particle from a point to another
- i.e. like we did from q1 to q2 at the page
4.2 and
4.3 .
While
the object is crossing the motion-cluster border, we do not know
where it stands - as this position has been conventionally
eliminated as being an observable at the
page 2.4
- so that we can reflect the particle position with two [u] accounts and
when it fully lands within the motion-cluster, we may reify it on
one motion account and balance the reification by a record in a [v] account.
Of course the same happens again when the object quits motion to
land in q2.
We can so identify several "time-scales":
the frame owns its global time frame - say one year in our former
example - and several time-frames distributed within the frame
border. The observer
owns one or several data "update" cycles - says one or several
double-inversions cycles.
Still remains the time-cycles
that correspond to the passage of particles into the complete uncertainty
state and the following reification that has always a [v]
companion.
We illustrated that this "uncertainty cycle"
surrounds any motions and we can observe that it surrounds in fact
any item-cluster on a map.
Those cycles looks like being everywhere -
say like a non localized item with non defined shape, nor
size, cost, mass or any tangible
property. They only look like mediators between clusters.
It looks also like [u] and [v]
are surrounding the clusters borders as it is illustrated in the
figure here below:
It suggests an
alternative vision that is: at each cluster lines - say at each
world components - one can associate one [v] and one [u] that
surround them like in the figure.
So a motion traveling from
one cluster to another and forth would design a sequence of "mile
stoned" by [u] and [v].
When we translate it by the
following expression [v] - [1] - [u], we can see the parallelism
that exist with the metric base [ ] - [1] - [i] that we introduced
at the page 3.5
.
So we will say equivalently
that "[v] and [u]" or "[ ] and [i]" are our "world closures" - say
where [ ] is the empty set and [i] the "uncertainty principle.
Noticeable is to remark that "[v] and [u]"
are owning properties that are similar to the ones owned by
actions - say like [p] has been introduced previously at the
page 4.2 .
They are distributed everywhere, they reify only when an action
occurs between two coordinates and they reify in association with
a time cluster set in between those two coordinates.
Say that
"[v] and [u]" are like actions.
Thermodynamics
- Quantum dynamics
If our development suggested
and borrowed so far many parallelisms with quantum mechanics, it
is suggested here also a parallelism with thermodynamics.
This kind of parallelism is
not per se so astonishing as it has already been considered in
several occurrences - i.e. by J. Von Neumann who introduced an
entropy definition in quantum statistical mechanics.
To frame our argument, we can
remind that classical mechanics historically developed his
accuracy within systems made of a limited number of individualized
bodies.
Classical mechanics developed
next and conversely a statistical extension for the cases where
the bodies number was so high that an individualized treatment of
them would not be efficient. In principle, this statistical
approach is not different in nature and "only" consists at dealing
with variables means and averages.
To our knowledge, there are
two noticeable domains where those classical statistical methods
failed to describe the physical observations.
The first one is quantum
mechanics - to which we already extensively referred and where the
statistical nature appeared different in regard to the classical
one.
The second noticeable case is
thermodynamics where a conservative description of the system was
not enough to characterize it in a complete manner. In short
thermodynamics introduced a distinction between two kinds of
mechanical inefficiencies: one that is conservative - i.e. like
friction that can be transformed in heat that is reversible in
mechanical work - and the one that is non-conservative - i.e. that
can not be recovered and that leads to irreversibilities and to
spontaneous evolution in only one direction.
This duality led to the
co-existence of two principles for isolated systems: the first
principle states that the amount of energy that can be transformed
in work is constant and the second principle states that the
energy that can not be transformed in work can naturally only
increase and reaches a maximum at system equilibrium.
Those two noticeable cases
have in common that they both maintain a law of conservation - the
Hamiltonian in the case of quantum and the first principle in the
case of thermodynamics - and also in common that they needed to
introduce a statistical principle to enable a correct description
of the observed reality - the "uncertainty principle" in quantum
mechanics and the "second principle or the Entropy principle" in thermodynamics.
One can of course have the
question whether those two statistical additions - to classical
mechanics - own a similar or a different nature.
In the case of our holotomial
analysis that only deals with an observation space, we exhibited a
case were [u] was objectively in relation with an non resolvable
uncertainty -
see page 4.7 . We exhibited also its link with [v] that we see
now being as an internal part of a cluster - see above figure.
It is then not unfair to
investigate whether [v] could not be treated in a equivalent
manner than we can handle the entropy in thermodynamics.
The entropy has been
interpreted as representing the number of configurations that a
system can possibly achieved so that the second principle states
that a system naturally tends to always "round trip" equivalently
between all its possible configurations.
In this sense the entropy
represents also the uncertainty we have upon which configuration
owns a system at given moment. This uncertainty is maximum at equilibrium because all
the configurations become equivalently probable and because the
maximum possible number of configurations is also achieved at this point.
Obviously our maps - i.e. in
particular the
P-maps - exhibits at once a vision of all the possible
configurations of a given system in so - implicitly - included the
uncertainty because a map does not tell about which one is
eventually reified.
We introduced [u] and [v] at
the only aim of maintaining our description complete. So we
had no reason to recall for a differentiation of natures between
them - both can be always equivalently used in any given role of
closure.
We only made a distinction
when we introduced the uncertainty - see
page 4.7 -
because one observed situation was obligatory inferring the
mobilization of two of those account.
We adopt [u]-[u] to recognize this
case and let the usage of [v] for the cases of single or isolated
occurrence. This convention
still does not argue for a different nature between [u] and [v] and any other
permutations would have led us to the same results - i.e. like
[v][v]-[u], [u][v]-[u] or [u][v]-[v].
As said in our complete space
system, [u] and [v] play a similar role and the above figure is
now highlighting that the only difference between the single
and the obligatory double occurrence may find its origin only because
one occurrence is internal and the other is external.
It is like if a cluster has
only one such account inside and only one outside and so when we
describe several clusters, all the outside instances connect so
that the outside clusters appear like pairs.
In our table at the
page 4.7 ,
our cluster being in a complete description, the second [u]
account corresponds to the outside instance of "the rest of the
world" as introduced - at the
page 2.2 -
for constructing a single-item holotomy.
They are two manners to
suggest that in our observation space [v] is effectively related
to an entropy and to an uncertainty.
The first manner is to simply
consider multiple holotomy - say an organic space - : as shown in
the above figure, pairs of [u] will joint all the clusters.
Say that we set a given number
of bodies occupying locations in this space. This set of location
is one of the particular configuration of the system in the sense
of thermodynamics. Of course we can move all those bodies in
successive motions so that we finally end up at having occupied
all the system particular configuration.
Of course, as shown previously,
each of those motions will mobilized the [u] - and [v] - accounts
so one can say that [u] is having links with the number of
configurations because it allows them to be achieved. [v] being
related to [u] and having possibly a same nature, both [u] and [v] can be in relation with the entropy of the whole system.
The other manner to apprehend
that [v] may have a link with the entropy concept is to recall to
the possibility we have to incorporate several clusters within a
cluster. In example, we may consider a [furniture] cluster which
own its internal [v].
When we insert in this
clusters others clusters like [chairs], [table] and [desk], the
[v] cluster of the [furniture] cluster will vanish and be replaced
by [u] pairs that liaise the different elements of the newly
defined cluster.
Hence we can seemingly replace
[v] by pairs of [u] so that we can estimate that [v] may
effectively reflect an incertitude and a kind of entropy.
Holotomography
We can easily replace the
previous figure by the following so that we clearly see how the
above recalls for our previously introduce base [ ] - [1] - [i]:
We can see that [v] and [u]
are playing roles similar to [ ] and [i]. Hence [ ] and [i] are
also "like actions".
According to what has been
said in the previous paragraph, we may investigate whether an even
simpler base would not be enough at handling our system - i.e.
like [ ] - [1] or [1] - [i].
In principle we do not see any
real theoretical objection but in practice it may first lead to
forget the necessity of the 3 dimensions required by a complete
description and - more important - we may loose a means to
indicate directions - i.e. like inside-to-outside.
In - advanced - practices, the
adopted view tends to keep and even to enforce the initial
proposition based on three components. This view point is
introduced in the next paragraph.
Accounting - Holotomography -
Higgs field
Let's introduce this aspect in
several steps:
1. We will convene to
designate a cluster by [1] - say the blue line in the above figure
- and two companions that are [ ] - [i] - one inside and the other
one outside.
This convention enables to
describe directions of possible motions .
2. Imagine the we have an
horizontal motion that goes from left to right. With the above
conventions of the previous point 1, it may look like in the
figure here below.
Conversely we may write the
motion out of a cluster on the base of the following expression:
[ ] x [1] x [i]
where "[ ]" stands for
"inside" and "[i]" for "outside".
3. We may of course also have
other motions than only an horizontal one - say we may have
motions in any directions. Known is - from vectorial analysis -
that we may describe them like the composite of an horizontal and
a vertical component. So with the same convention, the case may be
illustrate like in then next figure.
4. We may like to correct the
above image so that it expresses better that we do not consider
any motion but only the horizontal one. So we transform the former
figure into the next one:
5. From the two above figures
- and without entering into more discussions that rely mostly on
dynamics and not at recording "snapshots" -, the
motion out of a cluster may now be written as an extension of the
previous relation - say the relation will extended at the
one or both of the following:
[ ] x [1] x [i]
x [ ]
[ ] x [1] x [i]
x [i]
The left "[ ]" stands for
"inside", the "[i]" at the third position still stands for "outside" and the right "[ ]"
or [i] stands also for "outside".
We can regard the above
relation also at saying that the two left signs represent the
"cluster" and that the two right signs represent the "outside
world" - say "the rest of the world" to highlight that we are back
at our initial single-item holotomy description - see
page 2.2 .
This relationship also
perfectly complies with the double-entry accounting - as
introduced at
page 3.3 - its both central component [1] x [i] are the
accounts' titles introduced on this page - say the "assets" and
"liabilities" - and that those accounts are only here surrounded
by two "voids".
This coherent feedback on
our initial start point means that since we introduced the concept
of a single-item complete view - say a single-item holotomy - we
remained in coherence with it when we deduced the other concepts
that all in turn led us to this time-inversion concept and its non
resolvable uncertainty pairs [u]-[v] or [ ]-[i].
Out the scope of the present introduction, we
mention here that we may seemingly recover a parallelism to the
Higgs field if we write the above in the form [u] x [v] x [1] x
[u] - say in the sense the [u], [v] and [u] are massless while [1]
would be a mass unit.
Stability
If we get back on our
horizontal motion like in the above figure, we can say that the
motion is like the result of a field - say like [i] would attract
out of the cluster from [v] and next would invert over the small
vertical line between the two [i] | [i] to push it towards then
next [v] and so on.
Of course, one can see that a
similar field may exist vertically so that if our motion is
actually horizontal and stable in this direction, it means that
the vertical field is at least weaker than the horizontal field or
better that the vertical field helps to keep the motion
horizontal.
We will not enter here in much
more details along the view point of analyzing the stability of a
motion but we will underline that when we describe a regular or
stable motion, only describing the motion along its direction will
not "explain" all of it and that a complete description will need
to embed the description of what confers this motion with its
stability.
In this sense, care must be
taken that classical mechanics makes a large usage of descriptions
that remain only constrained by initial conditions so that they do
not embed the what make the resulting motion stable - i.e. the two
bodies or the pendulum problem in their usual formulation.
It does not says that those
descriptions are erroneous - and certainly not that they are
useless - but it only says that they are not complete - i.e. in a
spherical manifold [q] x [p] x [t] those motions might not
appeared as regular when described as a part of a larger system.
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