"Every creation" hypotheses, instead of every computation
or every mathematical structure.
I favor a variant of the everything idea, which I would like
to call the "every creation" approach. In some sense it
creates every "computational moment". Computations are
not required as fundamental entities. Almost all you need is
a natural definition to make new creations from pairs of
creations. This determines the evolution of an avalanche of
creations. Creations inside the avalanche may be aware only
of those creations to which they are in relative equilibrium.
As with other approaches, a consequence seems to be the
emergence of the laws of Physics.
Let me start with the following 4 hypotheses:
1. There is an underlying time.
2. There are creations (creation objects).
3. There is a natural creation operation defined, which
creates new creations from existing creations.
4. Every natural creation operation happens.
Some more words on these hypotheses:
(1) There is an underlying time, which is discrete. This
makes it easy to talk about creation operations, as if they
happened in our time. I will do this.
(2a) New creations can be made (created).
(2b) Creations do not get deleted.
(2c) Creations can be made in multiple copies. Creations
have multiplicities. Whether a creation can be made does
not depend on (can not be prevented by) the preexistence
of an identical creation.
(3) For any two creations x and y, there is a natural
creation operation [x,y] defined, which makes a creation z.
Lets call x the operator, and y the operand. I do not specify
the definition of the natural creation operation here. I have
given one of my favorite definitions, using replacement
operators, in a previous posting, where [(x1 x2),y] creates
a copy of y and replaces every occurrence of x1 by x2.
(4a) Every-creation hypotheses. The natural creation
operation [x,y] is happening for every existing creation x
and for every existing creation y.
(4b) Every existing creation x has equal chance to become
the operator in [x,y].
(4c) Every existing creation y has equal chance to become
the operand in [x,y].
Let's also make the assumption that creations are (directly)
responsible for our awareness and our perceptions of the
world. What are the consequences of such a hypotheses?
Creations may perceive other creations only indirectly and
only if the later possibly play a role in the creations'
histories. We may not perceive properties which depend
on the underlying time Tau. But we may be able to perceive
invariant properties, which do not change when the
underlying time Tau is getting larger and larger. We can be
indirectly aware of creations who's multiplicities are on
average in relative equilibrium with the multiplicities of the
creations which are directly responsible for our
awareness.
Thus the observable universe consists, possibly only, of
creations who's multiplicities grow on average at the same
rate.
Multiplicity(creation,Tau) = phi(creation) * growth_factor(Tau)
Multiplicity (observer,Tau) = phi(observer) * growth_factor(Tau)
The relative multiplicity,
Multiplicity (creation,Tau) /Multiplicity (observer,Tau) =
= phi(creation) / phi(observer),
is independent of Tau.
For creations inside the avalanche, the importance of
the initial conditions depends on the number of possible
equilibrium states (or the number of certain equivalence
classes of possible equilibrium states.) If there is only one
possible equilibrium state, then the initial conditions are
not relevant at all.
Let's assume that Tau is large enough, so that the
equilibrium is reached for the creations under
consideration. The growth factor can be calculated when
we make the simplifying approximation that every operation
[x,y] just creates one new copy of y. In that case trivially all
creations are in equilibrium, as required. If one of the
operations [x,y] does not create a new copy of y, but
instead another creation z, the equilibrium is broken. There
is one creation y missing and one creation z too much. This
is as if the creation y had been moved from y to z. The
effective movement can be compensated by an effective
movement back. There could be another operation [x2,z]
which creates a creation y. Adding loops of effective
movements does not change the equilibrium.
May a set X of creations x_i form a pattern, and the
operations among these creations may produce another
pattern Y of creations y_i. Lets call this an effective particle
P moving from X to Y. The broken equilibrium can be
restored by an effective particle moving from Y to X. Let
me call this the effective antiparticle P_bar moving into the
opposite direction as particle P is moving.
The choice of naming is intended to remind you of the
Feynman-Stückelberg interpretation of E<0 Solutions of
equations like Dirac or Klein-Gordon Equation:
Negative-energy particle solutions going backward in time
*describe*,
positive-energy antiparticle solutions going forward in time.
In short, this interpretation claims that
P(-E) *describes* P_bar(E).
But the equilibrium argument claims that
the existence of P *requires the existence* of P_bar,
P_bar also moving into the opposite direction.
This suggest a new(?) interpretation of the equations
where the two possible solutions are not only two ways of
describing reality. They correspond to two parts of reality.
They are based on two processes, which require each
other in order to keep the equilibrium. For every particle
with energy E there is an antiparticle with energy -E, and
the total energy is E = 0.
In a Feynman graph, there are lines that, according to
Feynman, do correspond to a particle, *or* do correspond to
an antiparticle moving into the opposite direction. However,
according to the equilibrium argument, the line should be
interpreted as a loop(s) composed of a particle, moving in
one direction, *and* an antiparticle, moving backwards in
time, back to the original space-time point.
Feynman, with his lines, draws kind of one-dimensional
projections of such loops. The additional dimension, which
is not visible in his graphs, corresponds to transformations
between spaces, which you may call "invention space" and
"feedback space", or covariant and contravariant space.
This additional degree of freedom may be what is needed
to explain the additional imaginary component of quantum
mechanical amplitudes -- to explain them from multiplicities,
which are given as natural numbers.
Covariant and Contravariant Spaces are not two
descriptions of one reality which can be transformed into
each other. They are rather two parts of reality which
require each other in order to keep the equilibrium growth
intact.
Does the Hilbert space corresponds to that part of the
creation space which is already in equilibrium?
The following ideas may rely on the definition of the natural
creation operation.
Einstein's field equation might be understood as equations
stating that effects of all loops going through one creation,
such as all gravitation loops and all loops from energetic
pattern movements, cancel each other and have no effect
on that particular creation, except for its equilibrium growth.
What is gravitation? Creations lead to new creations by
the continuing inflation, plus continuing shrinking, plus
rotations, and other transformations of space-time, at any
space-time point in the remembered history of those
creations. This gives a kind of diffusion effect, which could
be responsible for gravitation. Do today's gravitation fields
evolve according to the dynamics of "the past", in particular
the dynamics of the Big Bang?
By the way, at the moment I favor space-time generator
"definitions" which result in non-projectable dimensions.
(Projections can not be done easily with few operations.)
The projections to the border which I have mentioned in a
previous posting may correspond to other degrees of
freedom though.
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Received on Tue May 08 2007 - 12:08:09 PDT