Universe expansion ; “big bang” or “small plop” ?
• If the “intrinsic” notion of distance must be deduced from the
structure of diagrams in permanent complexification, and if the
“natural” local framework (this within which expression of
calculations
is simpler) corresponds to the elementary scale, then the framework
that we use is with respect to that in expansion.
This expansion being reasonably proportional to the contents of the
considered structure, it would be exponential. This is perhaps not
without relation with the recent cosmological observations [1], but
the
comparison must be considered with carefulness : if our distances
measurements must be considered as “renormalized”, then one must
previously
carefully compare the respective renormalizations of the studied
phenomenon and of the measurement technique that is used (if they
are
different, their
difference comes in addition to what one believes to observe).
Such an accelerated expansion may be rather naturally connected to
the
inertial effect that is the gravitationnal force. It is therefore
normal that inertial
mass would be equal to weighting mass, and that Einstein would be
able
to describe this with a formulation in riemannian geometry, apart
from
the fact that it is often done by considering a statical metric
; is it the good choice (in particular with respect to the
description
of black holes) ?
But what is interesting within this approach, is that the considered
expansion appears as universal :
would be in expansion not only every region of space (?)
containing some mass, but every region of space containing some
energy
(some interaction diagrams, and I keep as
probable that “the space” does not exist apart from the interactions
that constitute it).
Elsewhere, the considered mechanism describes an
expansion “without expansion”, in this way that the distance between
the
galaxies grows,
but us also, and in a comparable manner. The redshift
of the light comming from far away is simply due to the fact that
the
scale reference at emission time was not the same as the one which
is
ours at receiving time. From this, Universe does not “dilute” itself
;
it is simply its “natural” reference scale which decreases. This
reference scale would be in some way the equivalent,
with respect to the law of scale invariance, to what represent the
galilean frameworks with respect to the translation invariance.
A way of presentation for this may be to consider that if the
“local”
branching degree of the diagrams increases with time, the
propagators
intervening in a later diagram carry each of them less energy (by
distribution of
this one) according to the expansion moreover connected to this
mechanism, thus the photons (among others) received now coming from
the
“past” are statistically of the less energy as they come from larger
distance. This is qualitatively coherent with the other
interpretation,
connected to the use of an expanding framework, but one cannot
conclude
more precisely without understanding in detail the renormalization
mechanism connected
to distances and perhaps also energies.
Concerning my opinion, I would be inclined to search an equation
more
or less looking like (while improving in order to respect the
invariance laws that are riquired) : dX/X = K E dt
; where X would be a quantity characteristic of space (the
metric
tensor, or the spatial part of the metric tensor, may correspond) ;
where E would be a quantity like an energy density connected to
Feynmann diagrams “passing this way” (a quantity more or less like
the
temporal component g00 of the metric tensor would not
appear
to me as absurd) and where K would be a
constant (which might be connected both to Planck's contant and to
Hubble's one).
Indispensable specification : it would not be an equation claiming
to
replace Einstein's equations associated to general relativity (which
validity is now established, at least with regard to the description
“after renormalization” of the possible quantum structure of
space-time), but to use the degree of freedom which
subsists here in order to examine more the details of the
solutions, and in particular the associated “singularities”, with
this
peculiar point of view. Someones will hurry to comment : “useless
since
all the coordinates systems solution are equivalent”... sure, but
our
manner to interpret them is not necessarily such and I don't feel
impossible that we might get a benefit from searching in this way.
• An objection to this approach comes from the speed of such an
accelerated expansion : even if considered as a kind of “average”
(remaining to specify) of interactions with the “neighbourhood”, a
gravitation field g = 9,8 m.s-2
at the surface
of earth would correspond without long delay to a redhibitory speed
of
expansion, particularly if this expansion is established since the
beginning (?) of Universe.
Another critical point lies in the comparison with cosmic
observations cosmiques : it rather seems on the contrary that the
expansion would be as unimportant as the energy density (matter
and/or
interactions) is large in the corresponding zone [2, 3]. Sure, one
may
retort that a local renormalization, according to mechanisms not yet
devised,
might modify our feeling of the phenomenon, but even would it be
necessary to found how this could be done...
• Whatever may be the mechanism considered in order to describe
expansion, one must elsewhere consider that, through the
relativistic
instantaneousness, the statistical distribution of the photons
emitted
on the future cone of a source may also depend on the distribution
density of potential detectors on this future cone. This may lead
not
only to a variation of the expansion along time flow, but also to
more
complex effects such as oscillations.
• From another point of view, if one considers a space of bipoints,
more or less corresponding to propagators, one may conceive to
define 
according to a time which begins with an initial
interaction : = 1 and t = 0 when
appears
the first propagator ; the beginning of Universe would then be a
“small
plop” rather than a “big bang”.
One may also consider 
(countable ?),
corresponding contrarily (after an indispensable
renormalization) to a fractal Universe [4], without beginning but in
continuous complexification.
• If the total number of branches is infinite, one may reasonably
consider an invariance by time reversal ; on the contrary, if it is
finite, it is very likely that only a quasi-invariance [5] may be
considered, the more near invariance as the total
number of branches increases when it is far from initial time. Thus
the
break of symmetry would not be constant but decreasing, it would
have
been larger at the beginning of Universe.
From another point of vue, the description considered here being
connected to “quantum fluctuations” of space-time, these ones could
be
in a larger proportion at the beginning of the Universe, if one
considers that the corresponding global diagram was then simpler.
The
interpretation of antimatter as some matter which “goes back in
time”
during some fluctuations then leads to consider that the
matter-antimatter proportions could be comparable at the beginning
of
Universe, but that they have anyhow very fastly evolved in such a
way
to leave almost solely matter.
__________________
References :
1. see as example :
“Accélération
confirmée”, Pour la Science n° 313, p. 14, november 2003 ;
“Que cache la constante cosmologique”, J. P. Uzan, Pour la Science
n° 326, december 2004 ;
“Pourquoi l'Univers accélère-t-il ?”, J.O. Baruch and S.
Fay, La Recherche n° 384, march 2005.
2. see as example : “Les paradoxes du Big Bang”, Pour la Science
n° 330, april 2005.
3. the geometry of space at a cosmic scale is however still a
subject
for careful tests and some deviations with respect to the theory
subsist ; see as example :
“Les amas bousculent l'énergie
du vide”, Pour la Science n° 315, p. 20, january 2004 ;
“La gravitation sous surveillance”, S.
Reynaud, Pour la Science n° 326, december 2004 ;
“L'étrange trajectoire des sondes Pioneer”, J.O. Baruch, La
Recherche n° 390, october 2005 ;
“Big Bang ; des origines de l'Univers aux origines de la vie”, S.
Katsanevas et al.,
dossiers
du
CNRS, december 2005.
4. this is perhaps to consider in connection with other approaches ;
among others :
• “The stochastic interpretation of quantum mechanics :
a
critical review”, G.C. Ghirardi, C. Omero, A. Rimini and T. Weber,
Rivista del nuovo cimento, vol 1, n° 3, 1978 ;
• “Physical foundations of quantum theory : stochastic formulation
and
proposed experimental test”, V.J. Lee, Foundations of physics, vol
10,
n°
1/2, 1980 ;
• “L'espace-temps fractal”, L. Nottale, Pour la Science n° 215,
september 1995 ;
• “La relativité d'échelle l'épreuve des faits”,
L.
Nottale, Pour la Science n° 309, july 2003.
5. see as example :
“Le miroir brisé de
l'antimatière”,
I. Mannelli, Pour la Science n° 303, january 2003 ;
“L'antimatière questionne toujours le Big Bang”, La Recherche
n° 382, january 2005.
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