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‘Cooled’ light as a static
space-time interpretation of the Hubble redshift relation
The Big Bang: Is light simply cooling down?
Susie Wheatcroft, Derby, Derbyshire, U.K.
sw81245 + @ + yahoo.co.uk
Abstract
Cosmological redshifts
have as their interpretation expanding space coupled with Doppler
recession. This interpretation stems back to the confusion of cosmologists
in the 1920s on being confronted with the centre-of-the-universe
position that the Hubble redshift relation indicated. Unable to
find a suitable static-redshift explanation, they embraced Friedmann
and Lemaitre’s work, which combined Einstein’s general
relativity and explained the redshift as a consequence of space
expansion, eliminating an idea of preferred position.
It was only in 1965 that
the CMBR with its temperature of 2.7k was discovered.
Light is so physical,
it can be seen… Everything known to us that is physical, can
be cooled. By considering light as a ‘plasma’ of photons
emitted by hot stars and cooled out in space, it can be shown that
Hubble’s redshift relation finds no contradictions with a
static space-time in agreement with the Cosmological Principle.
Keywords: Hubble, cosmology,
big bang, redshift, cooling, expansion
Contents
1. Introduction
2. Brief critique of big-bang theory
3. Background physics
4. The redshift attributed to cooling
5. Conclusion
Acknowledgments
References
1. Introduction
In 1929, Hubble discovered
that galactic redshifts increased in proportion to their distance
[1]. This challenged Einstein’s 1917 static space-time general
theory of relativity, which he had adapted for cosmology by introducing
a cosmological constant to ensure the static condition of the universe
[2]. If Hubble’s results were interpreted as Doppler shifts,
they implied a centre to the universe near our galaxy, a fact Hubble
as well as others found unacceptable [3]. Being unaware of any static
space-time redshift interpretation, cosmologists were in a quandary
until they discovered the expanding space-time solutions of the
Einstein field equations thought out by Friedmann [4] and Lemaitre
[5] in the mid 1920’s. A uniform space-time expansion would
cause photons everywhere to experience in-flight wavelength expansion
proportional to the expansion itself. So was born the idea of space-time
expansion redshifts
2. Brief critique of big-bang theory
The cornerstone postulates
of the big-bang theory are these Friedmann-Lemaitre (F-L) solutions
and the Cosmological Principle, which states that viewed on sufficiently
large distance scales, there are no preferred directions or preferred
places in the universe. The Hubble redshift relation (z
= Hr/c) can be derived from both the space-time expansion
theory and the Doppler shift theory. In 1965 radio astronomers found
the universe to be filled with a background microwave radiation
having a thermal spectrum consistent with that of a radiating black
body cooled. This Cosmic Microwave Background Radiation (CMBR) coupled
with the observed Hubble redshift relation interpreted as Doppler
shifts for nearby galaxies and expansion shifts based on a universe
governed by expanding space-time general relativity for distant
galaxies, are generally considered as proof of the big bang.
Crucially, the important
expansion scale factor a(t)=a0/a1
where a1 and a0
are the magnitudes of the F-L space-time expansion factors at emission
and observation, have never been experimentally verified. The expansion
redshift is given by zexp=a0/a–1
and is assumed to be identical with zobs=(λ0–λ1)/λ1)
the observed redshift of distant galaxies because Hubble’s
redshift relation z = Hr/c can be derived from the space-time expansion
theory as a result. MTW uses this assumption to associate quasar
redshifts with expansion redshifts rather than Doppler shifts [6].
Confusion is rife as to how to interpret the redshift whether as
a Doppler effect or as the result of space expansion particularly
since no method has been found to measure the scale factor or even
verify it exists. There is no quantitative evidence to support the
hypothesized in-flight stretching as a verified physical phenomenon.
This means that unlike in all other theories in physics, big-bang
cosmology is dependent on assumption rather than measurement, the
critical assumption being that for high redshifts, this expansion
redshift is identical with the observed redshift. Intuitively, it
is understood that there is a problem with the idea of objects travelling
at the relativistic and even superluminal speeds away from us as
indicated by their high redshifts (at z>3, recession
is considered to be superluminal). In fact, since ‘nothing
can travel faster than the speed of light’ is a postulate
of modern physics, these considerations highlight flaws in the theory
[7].
The pennies-on-the-balloon
expansion illustration depicts the assumption that the universe
is governed by the F-L space-time expansion. The pennies (galaxies)
do not expand but the space between them does. The expansion is
apparently unable to cause galaxies themselves to increase in size
even though the gravitational attraction within them is smaller
than between clusters. A continuous uniform expansion of all matter
would not have allowed galaxies to form in the first place. The
balloon illustration is often presented as justification for the
ideas of an expanding space-time but there are no equations given
to back this depiction. There are no experimental test results that
confirm that the relativistic structure of the universe is consistent
with the F-L expanding space-time solution [7].
Hubble understood that
redshifts, by increasing their wavelengths must lose energy and
that an interpretation of the redshift must account for this [8].
Radiation, gases and freely moving particles lose energy in an expanding
universe and the big-bang theory does not account for this violation
of energy conservation, an inconceivably large loss when considering
the expansion redshift of CMBR photons. Gravitational fields affect
photons, but just as electrons when deflected by a magnetic field,
leave the scene with their kinetic energy intact, no exchange of
energy occurs when a photon passes through a gravitational potential
gradient. So the energy loss caused by expansion cannot be attributed
to such an energy exchange. This fact has been experimentally confirmed
by the operation of GPS [7].
Other contradictions include
the fact that stars 30 billion light years away can be seen even
though the universe is estimated to be only 10 billion years old,
the value of Hubble’s constant is bigger than the inverse
of the estimated age of the universe when it should be the same
and no Population III stars have yet been identified even though
the big-bang’s primordial nucleosynthesis postulate predicts
the existence of vast numbers [10], [11], [12], And speaking as
a layman, where’s it all going anyway?
3. Background Physics
The reason for accepting
an idea of space expansion in the first place lay in the fact that
no static space-time interpretation for the redshift had been found.
Neither had the CMBR been discovered.
According to Einstein,
the energy of a photon, or ‘particle’ of the EM wave,
is directly proportional to the frequency of its associated EM wave
(E = hf), Higher energy photons are the counterpart
of higher frequency waves. Since a redshift is simply a decrease
in frequency of the original wave, a lower energy wave could simply
be a higher energy wave redshifted. Now this is the basis of current
‘tired’ light theories. A photon’s energy is degraded,
decreasing its momentum, causing the wave to redshift.
In current physics, light
is presumed to have no mass. To make the equations balance, its
particle properties are described in terms of momentum. Now a photon’s
momentum is directly proportional to its energy {(E/c)2=|p|2}.
Indeed light escaping from a black hole will redshift. Just like
a ball escaping gravity, light loses momentum as it moves away from
the black hole and this energy is translated from say kinetic into
potential energy. Looked at more closely, the speed of light remains
the same but the wavelength lengthens to account for the loss of
kinetic energy in the photons. Momentum cannot escape its classical
association with mass and light acts as if it has mass i.e. a gravitational
field affects it, causing a change in energy, manifested in a frequency
shift rather than a velocity loss (as of mass). Light can also exert
a pressure. To summarize, with light one can consider momentum and
frequency shift as with matter one considers mass and velocity change.
A large mass (e.g. star)
curves space-time and as a result, light that travels in a straight
line, will bend around the star (general relativity). Conversely,
from Newtonian physics, light is acting as if it has mass and since
mass attracts mass, this is why it bends. Light has no mass however
and so to describe the observation, general relativity applies.
In fact the theory was created with this paradox in mind. It was
Schwarzschild who found a static space-time solution to Einstein’s
field equations that could be used to describe a static universe
incorporating general relativity.
A star that is ‘hot’
emits a high frequency blue light. The cooler the star is, the more
the emitted light is of a lower (redder) frequency. From this simple
evidence alone, a relationship is stated between temperature and
the energy ‘entrapped’ within the photons. In fact,
thermal spectra graphs illustrate this fact clearly. Since the frequency
of light emitted from a star is determined by temperature, the question
is, can the light be ‘cooled’ once it has left the star?
Reactions happen faster
when the constituents are heated because the molecules gain energy
and this is converted to kinetic energy. Electrons are quantum mechanical
entities and a plasma of electrons with the same average kinetic
energy as a sea of gas molecules, has the same average temperature.
De Broglie showed that a relationship existed between the particle
and wave properties of the electron. The wavelength of the wave
is inversely proportional to the momentum of the electron (p=h/λ).
So the faster the electron moves, the higher the frequency of its
associated wave and ‘warming’ electrons increases their
energy, manifested as kinetic, which increases the frequency of
the waves associated with them. Consequently ‘cooling’
electrons results in a redshift in their quantum mechanical wave
natures, a clear indication that a similar phenomenon could be expected
in the quantum mechanical wave nature of photons. A ray of light
from a star can be thought of as a ‘plasma’ of photons.
Inverse Compton scattering demonstrates the interaction between
photons and relativistic electrons – like wave billiard balls
- in which photons lose energy to electrons. Collectively these
electrons would experience a change in temperature as a result and
by consequence so must the photons. Since this interaction takes
place, it suggests that thermodynamic concepts can indeed be applied
to a ‘plasma’ of photons just as they can to a plasma
of electrons.
Pupils at school learn
that in space, the temperature is very cold (3K). Each point, like
each drop of water in the ocean, has this temperature associated
with it, broadly speaking. Planets furthest from the Sun are colder
than those nearest, and rockets travelling in space cool. They ‘radiate’
heat. Apparently they radiate photons but how can these be exchanged
with other matter if the rocket travels in a vacuum? Yet the rocket
still cools so why not the photon? In fact everything known to us
that is physical can be cooled. Light is so physical that it can
even be seen…. The only acknowledgement to date that light
loses energy on its path to us is the idea of ‘tired’
light. Surely it is illogical to assume that there is no energy
loss at all in its passage lasting for so many years. Yet this is
not accounted for in current physics. Space is a vacuum we are told,
and so there is nothing with which the light can exchange energy.
The redshift is purely the result of the wave stretching.
Mass when cooled loses
mass (E=mc2) and so momentum. Equivalently
light when cooled must also lose momentum. In fact, are not particles
and waves just different forms of the same physical entity, energy,
only at opposite extremes? Is temperature exchange just an osmosis
of energy when there are large gradients and so applicable to anything
that can be considered ‘energy’? Arguments such as the
speed of light must remain the same and this is why is cannot happen
are not sufficient. When redshifted from a black hole, physicists
do not attack the idea of light changing speed.
In modern theory, the
universe is expanding as if it is a balloon and just like the action
of a balloon, the further away it is, the more slowly it is expanding
(implying a central position in fact?) [13]. The idea of a balloon
supports the fact that the position of galaxies in relation to each
other stays the same. An explosion would send particles off at different
speeds and their relative positions would be seen to change over
time. Since the ‘balloon’ idea is accepted, it seems
likely that astronomers have not perceived such a relative change
in galaxies far away. Ancient astronomers saw Orion, The Bear, The
Pleiades etc constellations in our solar system just as we do and
although these are in our galaxy and so not so applicable to this
discussion, this fact emphasises the lack of change in relative
position over time, a signal that what is close to us indicates
the nature of what is far away and that every part of space resembles
that part known to us as presumed by the Cosmological Principle.
Has it been observed that galaxies further away are getting dimmer
to the telescopic eye? It has not been pointed out in any literature.
In fact, the result of a supernova (star exploding at end of its
life) is in some cases, a rapidly rotating neutron star that can
be observed many years later as a radio pulsar. With the high redshifts
with which they are usually observed, this must be a contradiction.
Such a ballooning explosion is not a realistic one as known to us
in our world and so is to be regarded with suspicion.
4. The redshift attributed to cooling
According to Newton’s
law of cooling, the rate of loss of heat from a body is proportional
to the excess temperature of the body over the temperature of its
surroundings.
dE/dt
is proportional to – (T1 – T0)
(1)
where E, the energy is proportional to the heat of a body, t = time,
and T0 = 3k which can be approximated to 0. Consider the body to
be the photon, and the excess temperature to be the difference between
the temperature of the star and the temperature in space (3K). Since
the frequency of the emitted light and thus its energy is directly
related to the temperature of the star, we can say that T is proportional
to E.
dE/dt
is proportional to – E so E0
= E1exp(-εt) (2)
Now this relationship
is that of a simple exponential. In fact, several physical quantities
such as voltage and current sometimes decrease in an exponential
fashion and that temperature is one of these is well known. The
temperature difference between that of the star and space is vastly
superior to that between adjacent light frequencies and so temperature
exchange between the latter would be negligible. The way in which
photons lose their energy may lead to a blurring of distant objects
but simply a uniform loss in momentum should not.
The redshift (z) is defined
as the change in frequency divided by the original frequency z
= -Δf/f0 where Δ is Δ (Delta)
and the relativistic Doppler Shift formula is given by:
f0=
f1√{ (1 – v/c) / (1 + v/c)} (3)
where f0= freq. of observed light, f1
= freq. of emitted light and v = relative velocity
of the two bodies). So:
z
= (λ0 –λ1)/λ1
definition
of redshift
=
(f1–f0)/f0 ( = -Δf/f0
where Δf=f0–f1)
=
f1/f0 - 1
=
√ { (1 + v/c) / (1 - v/c)} - 1
Using binomial series
expansions where -1< v/c < or =1 ie the speed
of light is not exceeded, and applying the Hubble relation v=Hr
gives for small r (so to speak), the usual first
order accepted redshift relation z = Hr/c and for
relatively greater distances to the fourth order:
z = Hr/c + 1/2{Hr/c}2 + 1/2{Hr/c}3
+ 3/8{Hr/c}4
(4)
H
≈ 2 x 10-18s
Using
the accepted Einstein energy relation E=hf together
with the exponential relationship derived above from consideration
of a temperature loss, gives not just to first but to second order
also, exactly the same result, where the exponential decay constant
(ε) is in fact Hubble’s constant H!
ΔE=E1–E0
= E1(1-exp(-εt)) where
E0=E1exp(-εt)
(from (2))
z
= -Δf/f0 = -hΔf/hf0
=
ΔE/E0
=
E1(1-exp(-εt)/E0
=
exp(-εt){1 - exp(-εt)} = exp(-εt)–1
=
εt + (εt)2/2! + (εt)3/3!
+ ......
To first order, for small
εt, that is for short distances
z
≈ εr/c
Identifying ε
with H gives the well accepted redshift relation
for closer distances
z
= Hr/c
Where distances are far
enough away for second and further order terms to apply:
z
= Hr/c + 1/2{Hr/c}2 + 1/6{Hr/c}3 + 1/24{Hr/c}4
(5)
Notice that the dimensions
of ε which are {1/Time}, ensure that the
exponential factor is dimensionless as it should be.
So using either the Doppler
shift relationship or the temperature exponential relationship,
gives exactly the same result to second order. The relativistic
Doppler shift relationship however only applies to speeds less than
the speed of light or it breaks its own rules. The temperature exponential
relationship however places no such constraints. Large redshifts
are perfectly acceptable and do not violate the speed of light rule.
The expansion of the universe
is known to be ‘decelerating’ [13]. If this deceleration
is calculated with respect to the Doppler Shift expression, it can
be seen by comparing the two expressions above that for larger distances,
the exponential redshift has a lower value than the Doppler redshift.
This mirrors the observation that redshifts are not as large as
expected at large distances, giving the impression that expansion
is decelerating.
In some cosmology courses
[10], it is stated that if the universe were the same at all times,
with Hubble’s constant staying constant, the scale factor
would vary in an exponential manner as a(t) = exp(H(t0-t)).
Observation and estimation must be behind this assumption, which
is in complete agreement with the temperature exponential.
5. Conclusion
For some, the existence
of the CMBR is not unquestionable evidence to support the explosion
coupled with the expansion to cool the temperature. It could be
more easily understood as the limiting temperature of space heated
by starlight than as the remnant of a fiery explosion. However,
it proves that photons are everywhere with which other photons can
exchange energy in a natural exponential way and a black body spectrum
indicates that space can be considered as a ‘body’ with
which to exchange heat. Our ignorance as to its operation does not
preclude that operation. It can be stated that one cannot apply
thermodynamic concepts to quantum mechanical entities but what is
the evidence to support this statement when it is known that a ‘plasma’
of electrons with a specified average K.E. has a particular temperature
associated with it and that scattering with photons can alter that
kinetic energy?
The redshift could merely
be an energy loss that results from a ‘heat’ loss in
the photon. That it can be described mathematically using an idea
of temperature loss rather than receding motion or expanding space
with Hubble’s constant remaining as the determining constant
makes this theory very sound. The redshift may not essentially be
a Doppler effect coupled with space expansion but rather a momentum
loss caused by cooling. Since a ‘ballooning’ expansion
is currently accepted, it implies that distant galaxies are staying
in the same relative positions, just as they would if the universe
were not expanding at all. The idea of deceleration, consistent
with ideas of today, can neatly be accounted for mathematically
by comparing further terms between the very natural, exponential
relationship that describes the temperature exchange and the applied
redshift relationship calculated using the relativistic Doppler
shift expression.
How many of the problems
of current theory would be resolved if light indeed were simply
being cooled? No longer would there be the problem of superluminal
velocities; stars at large redshifts do not disappear because they
are not travelling at fantastic speeds away from us; the theory
behind the origin of galaxies would not begin with contradictions
nor need the existence of dark matter to explain their glue; the
age of globular clusters would not appear older than the age of
the universe; energy would be conserved since it is only a local
exchange of heat energy that is taking place; the Cosmological Principle
would be affirmed; no dark energy would be needed to explain the
expansion and Schwarzschild’s static space-time solution to
Einstein’s field equations would replace the Friedmann-Lemaitre
expansion space-time solution in the description of the universe,
in accordance with Einstein’s general relativity.
Many observations can
be fitted to a defective theory, a fact well known. A good theory
will produce such inconsistencies. Just as it has taken years to
build predictions and apply observations, so it is not the place
here to explain why many observations appear to fit the big-bang
theory, which was after all a derivation of Einstein’s work.
Outlined above is a simple solution to the redshift problem that
could be coupled with Schwarzschild’s solution to explain
a different physical situation in our universe. The fact that it
explains so many of the problems that the big-bang theory presents
and appeals to common sense makes it highly suitable for consideration.
Acknowledgements
An invaluable aid to this
letter has been the clear, in-depth, insightful critique of the
big-bang theory by Robert V. Gentry.
References
[1] E. P. Hubble, Proc. Nat. Acad. Sci. 15, 168 (1929).
[2] A. Einstein, Preuss. Akad. Wiss. Berlin, Sitsber. 142 (1917).
English reprint in The Principle of Relativity, (Dover Publications),
pp. 177- 198.
[3] Edwin Hubble, The Observational Approach to Cosmology (Oxford,
The Clarendon Press,1937) pp. 50-51, 54, 59.
[4] A. Friedmann, Z. Phys. 10, 377 (1922). English reprint in A
Sourcebook in Astronomy and Astrophysics, Eds. K. R. Lang and Owen
Gingerich, (Harvard University Press 1979), pp. 838-843.
[5] G. Lemaitre, Annales Societe Scientifique Bruxelles A47, 49
(1927). English reprint in A Sourcebook in Astronomy and Astrophysics,
Eds. K. R. Lang and O. Gingerich, (Harvard University Press 1979),
pp. 844-848.
[6] C. W. Misner, K. S. Thorne, and J. A. Wheeler, Gravitation,
(W. H. Freeman & Company, 1973)
[7] Robert V. Gentry, arXiv:physics/0102092 - 0102096, arXiv:physics/0102101
[8] Edwin Hubble, The Realm of the Nebulae (Yale University Press,
1936) p. 121.
[9] C. O. Alley, Proper Time Experiments in Gravitational Fields
with Atomic Clocks, Aircraft, and Laser Light Pulses, in Quantum
Optics, Experimental Gravity, and Measurement Theory, eds. P. Meystre
and M. O. Scully (Plenum Press, New York, 1981), pp. 363-427
[10] http://www.astro.ucla.edu/~wright/intro.html Professor Edward
L. (Ned) Wright (30th Jan 2006)
[11] R. Cayrel, Astron Astrophys. Rev. 7, 217 (1996).
[12] Timothy C. Beers, arXiv:astro-ph/9911171
[13] Open University Space, Time and Cosmology Block 4 (1997 The
Open University) Unit 14 Section 5
© Susie Wheatcroft 2006
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