The theory of
general relativity already contains and explains the possibility of a
finite and unlimited universe, that possibility pretends to be a
discovering and development from the quantum mechanics, it is
proposed as a possibility that can only be generated from the theory
of the quantum gravity, however the general theory of relativity
already proposes it but by being proposed by Einstein together with
the hypothesis that the radius of the universe would be independent
of time, it was completely discarded with the discovering of an
expanding universe.
This idea is not
quite right because the solutions of Friedman of an expanding
universe do not (in any way) exclude the idea of a universe finite
but unlimited, this is it does not imply that the universe should be
infinite or with a limit or singularity completely defined.
Given that the
idea of a finite and unlimited universe contains without any trouble
the ability of this to be under expansion. However the idea of a
finite and unlimited universe under expansion seems to be not
comprehended completely, as well as its considerations about the
beginning of the same.
In fact a finite
and expanding universe leads inevitably to a initial state where the
distances in between anything would be null, this is in a concept
similar to the Bing-Bang; in the other hand an infinite universe
would prevent this inevitable consequence because there would be no
center on which the whole universe could concentrate in, because any
point could be considered the “center” inside a infinite
universe; however it is necessary to comprehend that an infinite
universe should be infinite since the beginning of the “time”
because in any other way it would have to be finite without any
possibility of mistake; it is not the same an infinite quantity and a
quantity that reaches the infinite, this is that the universe could
be expanding and had started with a finite magnitude means that it is
still finite and would become infinite only if it keeps expanding
during a interval of time infinite.
Because of this,
an infinite universe would exist since ever or would be there
forever. In the other hand a finite universe expanding would have
consequently a point in time that could be called the “beginning of
time” whatever that would mean. Under these perspectives we can
divide the possible models of the universe in the following way:
A) An infinite
universe which by definition is unlimited, because as much as you
travel the universe in one given direction there always be more
universe to travel, this does not imply in any way that it would be
possible to return to the starting point because as it can be
observed, an infinite universe has no limits or singularities which
will define the frontier of the universe. Also an infinite universe
(even under expansion) should be infinite at any given time, and by
which there's no place for a singularity such as the Big-Bang to
generate it, the infinite universe is infinite independent of the
time. In this way the concept of “universe under expansion” is
not well defined as the universe is infinite since ever and forever.
B) In other way, a
finite universe can be limited or unlimited, if it is unlimited it
implies that there is not frontier or singularity on which the
universe ends, in this case the expansion means that at the beginning
this could be collapsed into a point of length zero; and it was
created indeed in a singularity such as the Big-Bang, and could end
in a Big-Crunch, given that being finite in extension, exists
therefore a center to collapse; or perhaps it could keep expanding
forever, reaching an infinite extension at the end of time.
C) The last case implies a finite and
unlimited universe; this case if it were not expanding it will
illustrate the primary model (defined by Einstein), where obviously
there is no place for a singularity, such as the Big-Bang because in
fact, the universe is static; this is it is not expanding. However,
in the case of a finite and unlimited universe that is expanding the
panorama changes radically; because necessarily it begins in a
singularity such as the Big-Bang where unavoidably the universe hast
a null magnitude.
Now, before explaining why this is the
case, first we should account that the universe, either will
continue expanding forever or finally it will collapse around itself
in a Big-Crunch; going back to the beginning of the universe in a
singularity, let's assume a tri-dimentional universe (this is, two
spatial coordinated and one temporal coordinate) which is finite and
unlimited, meaning, the universe is formed exclusively by the
surface of a ellipse (or a sphere as well, however the ellipse
generalizes the model, because it does not pre-establishes the
perfection of the shape of a sphere), because obviously it has two
spatial coordinates; in this case the expansion of the universe is
given by the increase of the radius of the sphere that “contains”
our universe, as you can clearly see this means that the expansion
should have started with a radius of null size, which in consequence
will yield a null surface; meaning, a state where the universe
collapsed around itself in a null space; this describes clearly the
image of the Big-Bang; if we translate the analogy to a
quadric-dimensional the consequences are the same.
As you can see this theory does not
completely clarify the initial state of the universe, the
difficulties are still there.
In another way,
the ideas of a universe in contraction remembering the future; are
equally unnecessary and absurd; because in any case for a person in
this state; simply their “past” will be what we know their
“future” and vice versa; this would imply in the case of a
universe that at any moment it would stop expanding, that in the
precise moment where the universe stops its expansion to start its
compression there should exist a singularity in which “time”
would stop to start its backwards flow; this is absurd, it would
imply that truly the universe will return to its initial state from
that point on.
However, the
previous problem is defined by thermodynamic questions related to the
entropy, these complications can be eliminated if we conceive a
closed cyclical universe; this is, in the initial state totally
chaotic and unordered of the universe, it emerges in an instant of
time a state of “apparent order” (meaning an ordered state just
as we perceive it); which favors and starts the evolution of the
universe of which we are part of; of course at that instant we could
identify that the disorder or entropy of the universe, not really
being null, it is in a minimal state; through the evolution process
of the universe the entropy of the universe starts to increase
through the destruction of stars, primitive planets, etc.; which
gives birth to galaxies and new systems, and of course to us,
obviously we keep contributing more entropy to the universe.
The universe keeps
its expansion and after all with a natural transition it starts its
contraction; its entropy keeps growing, until the unavoidable
happens; the collapse of the universe in the Big-Crunch, of course in
this state planets are so close to each other that the start to
collide between each other, generating their destruction and
augmenting the entropy, stars explode, finally the universe collapses
disintegrating matter as we know it and augmenting the chaos; there
is a time where chaos is total, there is a state where only elemental
particles coexist; from this state of chaos, which we don't know how
long it will last; it will be generated at any moment a state of
“apparent order” and the cycle will start again.
This model that
could be supported by quantum mechanics developed under the premises
of the general relativity and its definition of the relativity
fields; would be also naturally supported by the unified theory.
It is my opinion
that there is no sufficient empirical knowledge that prevents
supporting quantum mechanics through the general relativity theory;
contrarily it everything seems to signal that this is possible; even
generating conclusions about the origin of the universe.
First draft originally
written in Spanish during Feb 2006
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