CRITIQUE
of
THE UNIVERSE
The Friedmann Equations, FLRW Metric,
Hubble’s Law Acceleration and Dark energy
Note that using the “Standard Model of Cosmology” with its necessary assumption
of a Hubble constant, Ho, to compute an accelerating
universe expansion rate, with Ho
≠ k, is self-contradictory.
The
Friedmann equations (FE) and the Friedmann/Lemaitre/Robertson/Walker (FLRW)
metric upon which the FE are based have been described as a “first
approximation” but, this is misleading. Both the FE and the FLRW metric, as they
are always presented, contain so many layered unstated assumptions as well as
some acknowledged “guesstimates” that the result is not merely a “first
approximation”, but is a blatant mistake. The hidden postulates and unstated
assumptions are far more important then the explicit ones.
The
Introduction and the Solutions sections of Wikipedia’s the FLRW Metric and the FE
describe the substrate matrix and substance of the universe together as
comprising a fluid. Due to the required properties (such as frictionlessness) of
any such substrate matrix for the whole universe, what they mean by a “fluid” is
really an “ideal” or “perfect” fluid. Both matter/energy and the spacetime
continuum under general relativity comprise this fluid1, which can
only be described as an ideal gas2 simply because no other metaphor
is appropriate.
The
universe is described as comprising a continuum, an entity which is really
unlike any solid, liquid or gas. Therefore, to refer to the universe and the
continuum together as expanding without limit or as having a pressure or
density, per se, is pure expedience. Einstein described
the space-time continuum as a matrix of infinitesimal (infinitely small, infinitely
closely spaced and infinitely numerous) massless particles having no mutual affinity3
(so, it must have the nature of an infinitely deep fractal chaos, completely
unlike a gas). Yet, the universe appears to be indefinitely compressible, as is
demonstrated by its extreme expansion4 – it is observed to seem
indefinitely decompressible. So, any reference by the FE to a “ground”
having mass density, ρ or rho, and a pressure, p5, must indeed refer
to a system comprised of a putative ideal gas because this sub-floor would then
meet the definition. This is especially so in the absence of any qualifier. Inadequate
as it may be, there simply is no alternate interpretation.
Semantic
arguments will not fix the flaws in the inherent, fully explicit complete definitions
of the FE/FLRW. The ideal gas model also presumes that this system is bounded
and it must be at equilibrium. It presumes it is bounded because, if it is not,
it is cannot be at equilibrium. The ideal gas law and its corollaries simply do
not apply to any system that is not “stationary”. So, the equilibrium condition
is prerequisite. Then, indeed, the universe must also be timeless.
As
mentioned above, this ideal gas must be frictionless: it must be an explicitly
defined superfluid6. Altogether, on the surface, the ideal gas model
seems not to be such a terribly bad approximation since the vast majority of
the volume of the universe is filled with hydrogen with a little helium thrown
in7, all embedded in superfluid spacetime. Assuming we can mix the spacetime continuum and its
“content” this way, as if the content is separate and apart, this mixture
exists at an extremely low pressure, which would facilitate the ideal gas
approximation. The average density of the universe is thought to be only about
6 atoms or molecules per cubic meter8.
In
an expanding universe, stars, galaxies, nebulae, planets and people may be
considered to be just along for the ride because according to the
approximations made - strictly for the sake of computational tractability -
they are not supposed to comprise a significant new condensed phase9.
That
condensed or more highly compressed phases are supposed to constitute an
insignificant contribution to the nature and properties of the universe is
summarized by the so-called “Cosmological Principle” (CP). The total density of
the universe may be considered identical with an average density, as if the
condensed matter is all smeared out evenly over the whole volume. In other
words, the CP approximation says that there really are no such things as stars,
galaxies, nebulae, planets or people. And, in effect, this approximation
imputes mass to the continuum. This might have useful implications, but it is
not part of the general theory of relativity, having no experimental basis.
Moreover,
CP says that everywhere one looks, in any direction, from any location in the
universe, in this homogeneous rarified soup of mainly hydrogen and helium
embedded in a relativistic spacetime matrix, the view is exactly the same. In
reality, the universe may be very lumpy and heterogeneous, but this detail is
handled separately by the “new standard model of precision cosmology” as an
ugly ad hoc add-on. In other words, a
lumpy bumpy model is superimposed upon the smooth and creamy model to make a
sort of stack of pancakes - with butter and maple syrup too, no doubt.
“In
a strictly FLRW model, there are no clusters of galaxies, stars or people,
since these are objects much denser than a typical part of the universe.
Nonetheless, the FE-FLRW model is used as a first approximation for the
evolution of the real, lumpy universe because it is simple to calculate, and
models which calculate the lumpiness in the universe are added onto the FLRW
model as extensions.” from Wikipedia, The FLRW Metric10.
Needless
to say, there are a few problems with these approximations and assumptions. The most severe problem is that the
“consensus” of cosmologists (and Wikipedia editors too) does not recognize any
of the problems. Conventional wisdom among astrophysicists and such amateurs
alike does not accord the FE-FLRW “standard model” with nearly enough
skepticism.
The Trouble with All
“Models”
Models
are always designed to simplify and sometimes even to oversimplify. Otherwise,
they would be called “ab initio”
exact descriptions. At best, this model is indeed a “first approximation”. The
math is unsolvable if the lumpiness of the real universe is included, so this
“detail” is left out when computing numerical properties of the universe like
density, pressure and even the interpretation of redshifts. So, nobody should
be surprised when queer circular conclusions are reached such as an
accelerating expansion rate and “dark energy”.
One
trouble is that the condensed or relatively compressed or compact matter in the
universe constitutes new phases which, over the billions of years that the
universe has existed, must be expected to behave as if they had a vapor
pressure. They are not inert.
They
are not degenerate either. So, a mixture containing a gas and these
other more compact phases cannot be treated like a pure virgin gas. Any amount
of an active compact or condensed phase, no matter how small, a physical
chemist will say, will upset pressure and density calculations for any kind of a
putative gas11.
Plus, any physicist will
aver that a dispersed suspension within any kind of fluid containing more than
one phase is expected to have altered bulk properties like the way it transmits
light and other energy. This will be true even if these other phases are indeed
actually otherwise inert. In the universe, the percentage of additional phases
may be very small, but the effects that are to be detected are also very small.
This should be of concern to “modern precision cosmologists”.
Using
the ideal gas law does indeed require one to presume that the system is at a
stationary timeless condition of equilibrium. But, the universe is demonstrably
not at equilibrium. This fact not only upsets the direct mathematical
approximations, but it seriously upsets any indirect theoretical physics of all
such oversimplified models that presuppose the ideal gas law, like the
Friedmann equations.
Equilibrium
The
FE/FLRW model indeed requires one to presume that the fluid system, regardless
of type, must be truly at equilibrium, including uniform constant temperature,
because it refers the system to a “state” variable, w. Therefore, since the
universe must always be in some particular state, a value for an equilibrium
constant, K(eq), may be defined.
Repeating,
the universe is demonstrably not at equilibrium. Also, if it is insisted, for
the sake of argument, that the universe is really held to be at equilibrium at
all times, strictly speaking, then its
processes must be held to be thermodynamically reversible. This is huge:
the real, practical and eschatological thermodynamic implications of this are
stunning. If it is held, for the sake of argument, that these auxiliary
implications simply do not apply, then this constitutes another colossal set of
assumptions.
Equilibrium
also means that the magnitude of the equilibrium constant points to whether the
system proceeds toward completion of the implied process or “reaction”, that
is, toward the final yield of “products”. Or else, it stays close to the
initial stage composed mainly of beginning substances, phases or “reactants”.
Thus
M0(s) ↔ M0(g) .
In
other words, according to Alan Guth’s inflationary scenario, the “inflaton”, a
potentially huge parcel or domain of greatly excited false vacuum, an
infinitely dense solid clot of pure energy that must arise probabilistically,
call it M0(s), must ultimately decay to its final ground state, a true vacuum,
labeled M0(g). At the finish, the ground state comprises nothing else but the
simple vacuum except, perhaps, a stray degenerate photon.
The
equilibrium constant would then be written
K(eq) = [M0(g)] / [ M0(s)]
,
where
the brackets denote concentration, partial pressure or partial density.
With
the bracketed quantities in natural units, a vast volume containing a unit
“quantity” of the true vacuum denotes the final product “density” or concentration,
[M0(g)]. This is divided by a unit quantity of matter, [ M0(s)], as the clot of
pure energy from Guth’s super dense, ultra intense solid energy “inflaton”
point particle. This is expressed as
K(eq) = 1/1 = 1 .
By
its intermediate magnitude alone, a
process physicist or physical chemist would know, this nonzero low value neatly
admits or allows that the evolution of the universe should obviously still be
continuing. The implication is that it will take a long time to reach
equilibrium. So, both the stated and hidden FE/FLRW assumptions actually will
be met only at such time as this equilibrium condition becomes a reality,
perhaps more than 2 trillion years hence. By their own definitions, the hidden assumptions
can neither pertain to our real universe at this moment nor at any time in the
near future.
Eternal
Homogeneity
Universe homogeneity is part
of the so-called “Cosmological Principle” (CP). The CP approximation says that
there really are no such things as stars, galaxies or people; there are no
relative concentrations of matter. Another unstated presumption is that this
condition must have persisted throughout time - since the beginning ‑ or
else the other affected assumptions will never have had a chance to initialize.
That is to say, crucial characters most typical of the deep past cannot
possibly obey the implications of CP because the expansion process itself must
interfere.
That is, CP homogeneity
maintains that such characters should be considered to typify, help or
epitomize the universe’s evolution, but cannot have evolved themselves. Yet,
the crucial features of the universe really do evolve. This is what cosmology
is all about! So, as another contradiction in terms, eternal homogeneity is
impossible.
The so called “perfect” timeless
CP is not different from the true and complete definition of the putatively less
stringent CP because whenever we look at distant celestial objects, we look far
back in time. Any statement of the CP must assume this as a sort of
“timelessness”. We deal with spacetime, after all, when we make astronomical
observations. The ideal gas model also assumes the same sort of timelessness
and so does not constitute a dynamic model at all. Far from it. It treats a
dynamic process as if it was static, another hidden postulate.
So,
homogeneity, as here discussed, is not a property of the universe. The universe
simply is not homogeneous. This assumption is totally bogus. Why should it be
relevant that the universe could be considered to be homogeneous on scales of
more than 100 megaparsecs? What has scale got to do with it? Whatever the
answer, we must “Prove it.”
Prove it, consistent with
the scientific method, with explicit falsifiable premises and without a trace
of circular logic. This cannot be done. The universe is either homogeneous or
it is not, there is no middle ground.
Plus,
there are structures in the universe that are larger than 100 megaparsecs, such
as several “great walls” or “sheets” of galaxy clusters and superclusters12.
Furthermore, every spiral galaxy has a supermassive black-hole in its core that
possesses an hyperbolic gravitational potential around it. This is due to the
relativistic nature of black-holes which are supposed to exist as gravitational
or spacetime singularities.
Because
of this detail of its relativistic geometrical nature, a gravitational
singularity must possess an hyperbolic gravity field. Hyperbolic gravitational
potentials (proportional to 1/r) do not fall off very rapidly, nearer to zero,
like the normal parabolic potentials of Newton’s
Law (proportional to 1/r2). Hyperbolic supermassive black-hole
potentials extend to infinity, or at least to a lot farther than 100
megaparsecs. They could actually explain “dark matter” (DM) because the
presence of the galactic disc means that the potential falls off very slowly
indeed (as 1/r + 1/r2). These debate points mean that the universe
is actually as heterogeneous as Swiss cheese.
Furthermore,
if it is seen that DM is a result of this hyperbolic field, it would confirm
that black-holes really are relativistic singularities. Some of the competitors
to Einstein’s theory might thus be eliminated. So, we would not need “M theory”
or “Supersymmetry”. It would be so sad if there is no such thing as an
ultra-massive Higgs boson or a DM particle. Astrophysicists may be so willing
to uncritically accept the FE/FLRW model and DE with DM because so many of
their colleagues’ whole careers depend on it.
Isotropism
And,
we cannot assume that the universe is isotropic either. George Ellis has repeatedly
maintained and others have also pointed out that, since we cannot observe the
universe in the direction of the plane of our galaxy, we cannot be sure that it
is isotropic. Even if we could observe in that direction, our light horizon may
not extend far enough to confirm that we are not inside a huge cosmic void.
Interpolation to fill in the blocked zone must use all sorts of assumptions
that subvert what we would be trying to define. If we are in a void, redshift
measurements at very large distances will be skewed to appear as if the
universe’s expansion rate is accelerating13.
Saul Perlmutter and
Adam Riess
Saul
Perlmutter and Adam Riess each claim to head up independent teams of
researchers that have both uncovered evidence for accelerating expansion and
dark energy. But, their efforts were not independent but were a concerted
collaboration14.
But,
this observation of acceleration, made by Saul Perlmutter15 et al.
and Adam Riess16 et al. is the result of assuming yet another item.
They presume that the Hubble constant is, ever will be and surely always has
been truly constant. Because they insist on this unstated premise, they
multiplied the magnitude modulus versus redshift data for nearer or not so old
type Ia supernovae by a fudge factor to bring this data into line with data got
for much more distant and older data. This produces a nice straight line and
irons out the kink that embarrassingly shows between segments of a simultaneous
plot of the two data sets. Then the slope of the straight line is artificially
made constant, like data for a well behaved Hubble diagram should be. It does
not matter to either of them that this kink in the straight line between the linked
data sets could just as well denote an unresolved systematic error.
In
an exercise of pure faith, this fudge factor alone, all by itself, is said to
indicate acceleration17 because its sign is positive.
Yet,
one could just as well apply a fudge factor to the more “ancient” supernova
data and bring this segment of the curve into alignment with that of the “younger”
SNe Ia data. Then, the fudge factor would say that the universe is
decelerating, not accelerating. That the whole argument for acceleration
depends on the arbitrary application of a manufactured fudge factor is very disturbing.
It
is another case of intellectual recklessness within the debate. And the media,
including Wikipedia editors, go for this bait.
With
amazing hubris, both Perlmutter and Riess claim that theirs is the only good
Hubble constant data that has ever been obtained18. But, their
magnitude modulus versus redshift data for SNe Ia were
calibrated using data got from analysis of Cepheid variable stars. Earlier
modern Hubble constant determinations were also got by using Cepheid variable
stars. So, this data should be every bit as good. But, all previous
determinations show that Ho is not constant and
is decreasing with time, not increasing19.
Dark
Energy
Now, the FE/FLRW model
implicitly refers to the whole universe as if it is an homogeneous laboratory
subsystem. The FE must allow that energy or thermodynamic work, w, can be done
upon the universe and it can do work on its parent system. This presumption
that the universe must do work is used to conclude that a perceived
acceleration in the rate of expansion means that there is such a thing as “dark
energy” (DE). But, this system/subsystem implication is never mentioned by
anybody. It is yet another hidden presumption.
DE purportedly follows from
the idea that there must be a real discrete value for w. It must actually be
less than zero because the above mentioned pressure, p, is putatively
decreasing and has actually become negative in the recent epoch due to
“acceleration”.
Negative pressure always
implies external suction. Blatant explicit referral to an external influence
must be avoided, however, since even amateur cosmologists will hesitate to
infer that there is, in fact, an “outside” to the universe. So, “-p” must be
internalized by characterizing it as a result of some kind of DE, not really
externally applied w.
That is, the so called
“equation of state” (the stationary condition summary equation for this ideal
gas) of the universe is derived from a form of pv = nRT (the ideal
gas law) and basic thermodynamics. Simplifying the development of the idea, pv
= w (remember, w is work, a kind of energy and pv is the work that is done on
the gas or could be done by the gas if it got compressed or was allowed to expand
to or from nearest to zero pressure and nearest to infinite volume), and v = 1,
the current and ongoing value for the putative volume of the universe in
natural units.
That v = 1 at all times is a
gross distortion too. If v = 1 today, it cannot have been equal to 1 six or
eight billion years ago, but this is what such a simple timeless model must
assume. Some have called the FE/FLRW model a “dynamic” model. This must be some
kind of joke, for the FE are anything but dynamic in nature.
Time enters the FE/FLRW model
only as a so-called scale factor, “a” or “R”. The “scale factor”, in natural
units, is used only to compute a Hubble parameter, H, which is equal to 1 only
when time is equal to 1, meaning “the present”. H is used for ? So, time dependence is introduced despite the
contrary implication of timelessness in all the other hidden postulates,
unstated assumptions and given definitions. “Self‑consistent” is not an
adjective that can be used to describe the FE/FLRW model.
The scale factor concept is
said to follow from the approximations of homogeneity and isotropism inherent
in the CP. Nobody ever mentions exactly how it follows logically. They do not
dare because it certainly does not so follow without still more hidden
postulates and unstated assumptions. If more layers of approximations and
assumptions are not to be added, then it is really just another ad hoc add-on.
Now, if the expansion rate is
supposed to be accelerating, Ho is not constant and then
w =
-p ,
as if suction is being
applied to the universe.
But, since we must deem this
to be impossible, we cannot allow even any contribution to p to be negative,
then
w ≤ 0
,
which, by its sign and the definition
of w, says that this work energy (if there is any) must come from within the
universe. From whence does it issue?20
To satisfy the conservation
law, there must always have
been an untapped and invisible reservoir of such “dark” energy. So, it must
also have an impalpable, unmeasurable mass-equivalent. Except for the stack of
assumptions that have been accumulated, this is said to solve “the missing mass
problem”. Being unmeasurable is considered to be only a technicality.
But, technicalities are what
science is all about. To sidestep this problem, it has been seriously suggested
that the scientific method should literally be dumped21.
However, being not really this
simple, but purely as a debate point, one might insist that by telescopically observing
phenomena in the universe as far back in time as 8 to 10 billion years, for well
over its half-life from Hubble’s Law, this current latter phase is seen to have
taken quite a bit longer than the former. Yet, things are proven to have not
really changed that much since then. The whole process has clearly progressed
only marginally in over 8 billion years. Yet, up until more than 10 billion
years ago, the changes must have been dramatic. These earlier spectacular
changes took place in less than 4 billion years.
So, the whole process,
including the expansion rate, must actually be decelerating. This is pure
logic, an inescapable mathematical certainty. But, many cosmologists somehow
insist that the expansion rate is indeed currently accelerating due to DE.
Some
of these points may be contradicted by a good debater. But, any one of them
will demolish the FE/FLRW. All these critical points would have to be refuted
simultaneously in defense of the FE/FLRW and DE. This cannot be done without
self contradiction.
It
will be very bad for science if we have to backtrack again on such matters as
accelerating Hubble expansion and dark energy. Scientists should be absolutely
triple certain before they make even preliminary pronouncements to the Press.
But,
as Lev Landau, the Nobel laureate physicist, said: “Cosmologists are always
wrong, but never in doubt.”22
BIBLIOGRAPHY
1 The composition of the Friedmann Fluid is a
mixture of ideal gases that includes the
spacetime continuum. See Wikipedia, Friedmann
Equations – Mixtures, also http://en.wikipedia.org/wiki/Equation_of_state_%28cosmology%29 and references
therein.
2 Ideal Gas, see any good college or high
school chemistry text or Wikipedia or
3 Albert Einstein The Collected Papers, vol. 6, Princeton
University Press, 1997
The Foundation of the General Theory of
Relativity, DOC. 30
4 Hubble expansion, search “Hubble’s Law” or “Edwin
Hubble” or see Wikipedia –
5 Friedmann equations - variables p and rho,
see any detailed treatment of the FE or
see
Wikipedia
6 Spacetime as a superfluid – see ref. 3 and
The Perfect Relativistic Gas T. Y. Thomas
Proceedings
of the National Academy of Sciences of the United States of America, Vol. 51,
No. 3 (Mar. 15,
1964), pp. 363-367 (article
consists of 5 pages) Published
by: National Academy of Sciences
There
are literally thousands of internet search hits when a search is done on
spacetime superfluid, spacetime ideal fluid, spacetime perfect fluid, spacetime
ideal gas, etc.
7 Majority of sensible matter (by volume) in the universe is hydrogen, H,
or H2 and a
little He – search “composition of the
universe” – such as http://map.gsfc.nasa.gov/universe/uni_matter.html
8 Average matter density of the universe,
search or see
9 Cosmological Principle as an approximation –
almost any search on “critique of the
cosmological principle” will reveal statements
referencing this.
10 Ibid
11 “Gas laws” do not work in the presence of “condensed
phases” – search on these
phrases
– it is very difficult to find an explicit statement. However, if one searches
on “inhomogeneous or heterogeneous equilibrium” one may get better results. One
can write an equilibrium constant expression for the spacetime continuum and matter/energy
phases in the universe. Clearly, the ideal gas model makes no room for such an
addendum to its mathematical description of the universe. But, such an
equilibrium expression would itself be a huge approximation because the
universe is definitely not at equilibrium.
14 http://arxiv.org/abs/astro-ph/9804065
Snapshot Distances to Type Ia Supernovae -- All in “One” Night's Work Adam G. Riess, Peter Nugent, Alexei V.
Filippenko, Robert P. Kirshner, Saul Perlmutter
15 http://arxiv.org/abs/astro-ph/9901052
Constraining dark energy with SNe Ia
and
large-scale structure Saul Perlmutter (LBNL), Michael S. Turner
(Chicago/FNAL), Martin White (UIUC)
16 http://arxiv.org/abs/astro-ph/9807008
Results from the High-Z Supernova
Search Team
Alexei V. Filippenko, Adam G. Riess
17 Fudge factor or “adjustment” http://arxiv.org/abs/astro-ph/0201034
Michael Rowan‑Robinson
18 P&R “The best Hubble constant data to
date.” quote
19 http://www.lonetree-pictures.com/
The data for the diagram showing linear drop in
the universe expansion rate with time is got from numerous observations of the
Hubble constant obtained for various distances from earth. The data is
converted to natural units. The original data easily can be got by searching on
the term “Hubble diagram”.
20 Self contradiction is the
hallmark of the FE/FLRW model. On one hand, the ideal gas model requires that the universe be
bounded with variable volume and at equilibrium at all times. If there are to
be changes, they must occur in infinitesimally and immeasurably small
increments. The equivalent statement is that there must be no measurable
turbulence. The universe is changing only at measurably large increments and it
is notoriously turbulent.
On the other hand, for w to
be negative leaving p as a positive quantity, implies that the universe is
unbounded with a heretofore unrecognized internal or potential energy, contrary
to the model itself. So, if contradictions can be overlooked, this really means
that we must still be in a Guthian “false vacuum” state. Then, the whole
universe must be describable by reference to a time dependent Schroedinger-like
equation.
Physics will never accept
that we have been and continue to be part of a purely quantum object. Nor will
it accept that there are two, discrete equally valid sides to the coin of
reality; quantum and relativity theories. The Holy Grail of a grand unified
theory or a theory of everything must exist. It was Einstein’s dream, after
all. “M Theory” must be real, say theoretical physicists.
Physics will never just “let
it be”. Theoretical physicists will try to force relativity and quantum
theories to meld into a single great façade simply because they can, not
because it may afford us any higher degree of truth. It is mindless seeking for
seeking’s sake. Theories that are so much harder to understand and to use
really constitute no improvement. They simplify nothing while complicating
everything. This is not what science should be about. It is not what art is
about either. The essence of art is to know when to stop.
21 "The scientific method should be dumped" -
quote
22 Lev Landau quote from
