Is the universe expanding?
It can't since nature is not able to create
energy from nothing
W. Jim_Jastrzebski@yahoo.com, file 3269.htm, original issue
Feb 1985
Physicists who allow creation of energy from nothing (which
would be a necessity if the universe expanded) maintain that
the universe is expanding since the spectrum of light coming
from distant galaxies is shifted in the direction of red end
of spectrum in relation to the light generated by the same
source of light next to the observer (effect called
cosmological redshift).
The astronomers who accept the creation of energy decided that
this phenomenon results from Doppler effect caused by the
galaxies moving away from the Earth, and if galaxies do this
the universe has to expand.
Other astronomers (as Carl Sagan) assumed that the universe
always and everywhere looked approximately the same in
agreement with the Perfect Cosmological (Copernican)
Principle.
This paper presents a hypothesis that the universe is a
stationary Einstein's universe and the cosmological
redshift is caused by the time dilation (called here the
Hubble time dilation in the honor of its discoverer)
compensating for curvature of space such that the spacetime
is Minkowski:
The time dilation compensates the curvature of space so
that the proper time in other galaxies runs from the
point of view of any observer slower than in observer's
galaxy, testifying to fundamental relativity of time.
The above hypothesis is based on the interaction between
masses of unverse known as dynamical friction that
makes necessarily the metric of spacetime non symmetric as
proposed by Einstein in 1950.
It has been shown that this effect exists in relativistic
physics just in right amount to explain the cosmological
redshift, its apparent acceleration, 'anomalous'
acceleration of cosmic probes Pioneer 10 and 11, and
several other "puzzling" cosmic phenomena as e.g. quasars.
Phenomenon of dynamical friction comes from a fact that
everything in the universe interacts gravitationally with
everything else and while doing it on the average it has
to lose its kinetic energy, as if there was friction in space.
The "attracting body" begins to move the "attracted one" and
by this on average (since it depends on masses and
random directions of movements of interacting bodies) has to
give to the other body a part of its kinetic energy, wwhich
looks exactly as friction (it turns out to be indepenret of
velocity of "atracting body").
Of course the amount of this friction may be easily calculated
but astronomers, believing in the Big Bang Hypothesis decided
the calculation is not necessary and it made me the first guy
who did it in agreement with simple principles of relativistic
physics .
It turned out that the principle of conservation of energy
forces on the universe that the time in curved space
runs slower with the distance from the observer proportionally
to the square root of curvature of space slowing down
exponentially with the distance from the observer
(see eq. 7).
Of course it simplifies the qualitative explanation of many
phenomena.
The slower running time in distant galaxies slows down
everyting in them and so also the oscillations of photons that
one might consider being tiny clocks measuring the proper time
in those galaxies.
The illusion of accelerating expansion of universe comes just
from this effect of Einsteinian slowing of time in curved space.
The derivation of Hubble time dilation from the
principle of conservation of energy
Let's call speed of light c, Newtonian gravitational
constant G, density of Einstein's dust universe
ρ (while one dust particle corresponds to a galaxy)
and therefore RE2 =
c2 / (4πGρ), where
RE is radius of curvature of space of
Einstein's universe called Einstein's radius.
We name the gravitational energy acquired by the dust through
the gravitational interaction between dust and photons contained
in a ball of radius r,
Edust(r).
|
After photons of energy Eo got radiated out
from arbitrarily located center of coordinates called "point
zero" (point of radial coordinate r = 0)
the gravitational force at distance r from point zero,
acting on a single dust particle is equal according to Newton's
equation for gravitational force
| |
Fparticle = - Eparticle(r) /
dr = ( G / c2 )[ Eo -
Edust(r) ] m /
r2
| (1) |
where Eparticle(r) is energy of dust particle
at distance r from point zero and m is mass of a
particle of Einstein dust universe.
Integrating over all dust particles in a spherical layer of
radius r and thickness dr we get the mass of the
layer at distance r from "point zero" as
merging (1) and (2), the whole force that is the source of
gravitational energy of this dust layer
| |
Flayer(r) =
- Elayer(r) / dr =
( 4πGρ / c2 )
[ Eo - Edust(r) ]
dr
| (3) |
integrating over all layers betwen point zero and r,
and differentiating both sides with respect to r
to get rid of integral on the right side) we get
| |
- d2Edust(r) /
dr2 = ( 4πGρ / c2 )
[ Eo - Edust(r) ]
| (4) |
Substituting Edust(r) =
Eo - E(r) where E(r) the photon
energy at distance r from point zero and we get quation
| |
d2E(r) / dr2 =
E(r) / RE2
| (5) |
|
Solving this equation with initial conditions
E(r=0) = Eo and
( dE/dr )(r=0) =
- Eo / RE we get
| |
E / Eo = exp( - r /
RE )
| (6) |
Einsteinian interpretation of the above is obviously the time
running slower in a distance from an observer according to
relation
| |
dτ / dt = exp( - r /
RE )
| (7) |
where τ is the proper time of the observed place in
deep space and t is the proper time of observer.
This equation makes the "grand leap" from Newtonian math
expressed by (6) to Einsteinian physics expressed by (7).
The cosmological redshift produced by the effect is
| |
Z = exp( r / RE ) - 1
| (8) |
and it simulates the expansion of universe with Hubble
constant of this apparent expansion
The obvious application of this effect is calculation of radius
of curvature of space and the density of space of universe from
the observed value of Hubble constant.
Hubble constant Ho =
70 km/s/Mpc implies density of space
ρ = 6×10 -27
kg/m3 with only twice smaller relative
accuracy than Hubble constant since
Ho2 ~ ρ.
Another application may be calculation of density and the size
of dust clouds surrounding quasars from the redshifts of quasars.
After splitting Hubble "constant" into Taylor series around
r = 0 the acceleration of apparent expansion
of universe becomes
and it has been observed with accuracy of one sigma already in
1998 by Supernova Cosmology Project and therefore
predicted by Einstein's gravitation over 80 years earlier.
Since Einstein's graviatio can't be falsified as it predicts
the principle of conservation of energy (still not
falsified), predicts Einstein's universe and
Einstein's radius of this universe (still not
falsified), and other (still not falsified) observational
results with accuracy to one σ (which in astronomy
corresponds to perfect agreement with the theory) it
looks like we may suggest that the metric tensor of spacetime
is not only non symmetric as Einstein figured out in 1950 but
also singular (which means its determinant is zero).
It turns out that such metric tensor produces quite decent
metric of spacetime
| |
dτ2 =
exp(- 2 r / RE ) dt2 +
2sinh( 2 r / RE ) dtdr / c -
exp( 2 r / RE ) dr2 /
c2
| (11) |
shown above for one spatial direction since it is isotropic.
It is easy to noticed that for r <<
RE it approximates to Minkowski's
| |
dτ2 =
dt2 - dr2 / c2
| (12) |
The only problem seems to be that assuming the full validity
of Einstein's gravitation might ruin a lot of PhDs and other
scientific degrees made on the Big Bang hypothesis.
It seems to be a minor problem though considering the gain for
science from explanation of the reason for the apparent
"creation of matter from nothing" (which might upset
creationists, but sorry guys, we can't stop science just to
make you happy), the apparent "accelerating expansion of the
universe", "quasars", "dark energy", and ohter things that
existed only in imagination of particular scientists such as
John Archibald Wheeler and others ...
Another gain for science would be the astrophysicists
concentrating on so far real problems as "dark matter", amount
of which we know thanks to Einstein's theory, the nature of
quasars, etc. since science seem to have a lot of stuff to be
discovered yet and it better does it if we want the inteligent
life ever to show up on this planet or anywhere in the universe.
And the science might be better prepared to do it while not
tight up by religious wars and prejudices of particular
scientists.
Otherwise one day a visitor from another civilization might
radio his base with the following message:
Beam me up Scotty.
There is no inteligent life here.
They still believe in miracles.