The Infinite Universe
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I think it
was Heraclitus who said that even in our sleep we labor to build the
world.
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Marcus Aurelius (121-180 AD.)
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We know exactly how old
the Universe is. According to
Johannes Kepler (1571 –
1630) God
opened for
business on a Sunday, the 27th of April in 3877 BC., at 11.00 am.
central
European time. As far as I know, buffet and drinks were free. Johannes
Kepler
also found himself obliged not to believe that God’s Universe is
infinite.
Since Cosmas
Indicopleustes’ Topographia from the 6th century –
the book was
written to debunk the spherical theories of the Hellenistic scientists
– it was
virtually dogma to think of the Universe as God’s little jewelry box, a
box in
the shape of Solomon’s temple. The Sistine Chapel is designed in its
image.
Begging to differ could get you a slow roasting at the stake, after
they broke
every bone in your feet and gagged you to prevent you from saying any
memorable
last words. The Inquisition interrogated even Kepler’s mother on
charges of
witchcraft. The astronomer had every reason to deviate only by
increments from
established wisdom. The discovery of the elliptic trajectory of Mars
was
already pushing the envelope, it could be construed as an affront to
the
“perfection” of the circular trajectories in Ptolemy’s and Copernicus’
cosmologies and it did spoil the “harmony” in Kepler’s own Harmonia
Mundi.
So we will never know
whether he really
meant it when Kepler wrote: “In an infinite Universe where every line of
vision must
end on the surface of a star, would the whole celestial vault not be as
luminous as the Sun?" (Kepler, Conversation with the
Starry
Messenger, 1610). This
argument became later known as "Olber's Paradox." Kepler was a bright
fellow, he still wrote by candle light, it therefore must have occurred
to him
that even an infinite number of candles doesn’t burn all the time. Then again
what could he
really know about the limited lifespan of a star? It is easy to become
dismissive here, but the scientific community of the period kept many
things to
themselves. We think of Black Holes as the latest in cosmological haute
couture; but muted ideas about the theoretical possibility circulated
as early
as the decade after the publication of Newton’s Principia. The Swiss mathematician
Euler (1707 –
1783) spoke
of them as the “dark lords
of the Universe.”
In 1676 Ole Roemer (1644
– 1710)
calculated a
good approximation to the speed of light, and in 1901 Lord Kelvin (1824 – 1907) made the crucial step of
expressing
distances to stars in terms of their light signature’s travel time. In
his
paper On Ether and Gravitational Matter through Infinite Space, Lord Kelvin picked up
on a
suggestion by the poet and writer Edgar Allen Poe, and pointed out that
a
star's lifetime is limited by it's available energy resources. As we
look out
into space, we also look back in time, to the darkness that existed
before the
birth of a luminous body and to the darkness that followed its
expiration. Of
all possible explanations why and how in an infinite Universe the sky
is dark
at night, this is the most parsimonious with the least amount of
theoretical
assumptions; but among cosmologists simple explanations are not
particularly
popular, they lack the potential to engage institutions and the public
to cough
up the puny billions needed to construct another supercollider.
The idea of an infinite
Universe is
of course not a novelty. Epicurus, the Stoics and the Roman poet
Lucretius
already had thought of it, Nicolaus Cusano (1401 – 1464) expressed his opinion in
guarded language and Giordano
Bruno (1548 –
1600) made it
an issue to get himself
burned for. But the first actual scientist to take the idea seriously,
was Sir
Isaac Newton (1642
–
1727).
In his private notes
Newton had
anticipated much of Albert Einstein (1879 – 1955): "Are not gross
Bodies and Light convertible into
one another, and may not Bodies receive much of the Activity from the
Particles
of Light which enter the Composition?" I don’t know about you,
but this is hitting pretty
close to Einstein’s E=mv2 (energy
equals mass by the square
power of
light velocity). Sir Isaac even speculated that "another force,
independent of gravity, magnetism, and electricity, might prevail only
at the
smallest distances."
A truly eerie insight for the world of the 17th century with piles of
horse
manure in every corner. In his publications however, Newton decided to
stake
his reputation on Johannes Kepler's three laws of planetary motion.
Newton’s
resulting laws of gravity suggest a world collapsing on itself. So to
prevent
this from happening, Newton’s celestial mechanics require a homogeneous
Universe stretching into infinity. Professor Hawking in his book
brushed this
aside in one sentence, claiming that over eternity all matter would
already
have coalesced and collapsed into one dense mass. Another example for
the
professor’s notorious propensity to rush his judgments. Even with
infinite time
to convene the most distant objects will never arrive at the crunch
point
before they expire and disperse as microwaves; in a manner of speaking,
there
is just too much universe.
Modern estimates of the
distance of
luminous bodies in the cosmic background give a value of 1023
light
years, meaning that in order to see a star’s emissions on every line of
sight,
such star must have been shining for at least 10 to the power of 23
years. But
the lifetime of a sun-like star is only 1010
years. In other
words
the answer to the question where all the starlight has gone is, that it
hasn't
reached us yet, and some never will before our own solar system has
expired.
Infinity has become again a possible cosmological proposition. It will
present
us with a number of curious features, Gregor Cantor (1845 – 1918) has made us understand
that
infinite sets or transfinite numbers are as complete as any set of
finite
integers, and possess an actual, albeit infinite number of members, he
proved
that it is not a contradiction that any section – for instance the
prime
numbers – of an infinite number has as many members as the collection
as a
whole and this class of integers will form a still infinite set,
(Cantor then
moved on to demonstrate that the number of transcendental numbers –
values such
as pi and e – were much larger than the number of integers), but “there
is
no rational reason to doubt that the universe has existed indefinitely,
for an
infinite time. It is only myth that attempts to say how the universe
came to
be, either four thousand or twenty billion years ago,” says the Nobel Laureate
Hannes
Alfven. Keeping in mind Cantor’s transfinite numbers this means that
“eternity”
is not simply an ever growing progression of time, but that it is
complete and
present right here and now. (I must admit: I am itching to ask the
pundits
whether there exists only one such “complete” set or several – or even
an
infinite number of such units. This is way beyond my understanding.) It
seems
there is a sound reason for the notions of a “Block Universe,” the idea
that
time and distance sprawl out in a hyper-dimension – don't ask me to
give it a
number – as the simultaneous features of a world suspended in the
eternal
present.
Then why is it so
unpopular with
present day cosmologists? “I was there when Abbe Georges Lemaitre
proposed
the theory of Big Bang for the first time,” says Hannes Alfven,
“Lemaitre was both a member of
the Catholic hierarchy and an accomplished scientist. He said in
private that
this theory was a way to reconcile science with St. Thomas Aquinas'
theological
dictum of creation out of nothing” (Hannes
Alfven). Lemaitre believed to
have an
excellent reason to think so, and this reason seems to have convinced
also many
scientists who don’t share Lemaitre's theological preoccupation.
In 1929, Edwin Hubble (1889 – 1953) noticed a uniformly
increasing red
shift in the spectrum of light from galaxies and clusters at extreme
cosmic
distances. Since the velocity of a stellar object moving through deep
space
either makes its light signature shift towards the blue spectrum when
it
approaches us, like the Andromeda galaxy, or towards the red spectrum
when it
hurries away from us, the likely explanation is an universal motion
away from
the observer. The more distant the object, the greater, it seems, the
velocity,
but we should understand that Hubble’s variable is not an expression
for the
“expansion of space.” The idea of an expanding Universe comes in two
forms:
either the medium of space is expanding itself while the virtually
stationary
astronomical objects are carried along, or the astronomical objects
disperse on
their own through space.
Only the latter will be observable in a shift towards red or blue in
the
object’s light-signature. "When the Hubble variable was discovered
in
1926 it had a value of 500 kilometers per second per mega-parsec” (Halton Arp).
However any value above sixty for Hubble’s constant “has the
embarrassing
feature of yielding an age for the Universe since Big Bang that is
exceeded by
the oldest stars in our Galaxy" (Riccardo
Giovanelli,
Less
Expansion, More Agreement, Nature, 8 July, 1999, pp. 111-2). Which prompted Halton
Arp to make
the sarcastic remark: “During the past half-century this variable
has
gradually declined to 50.3 kilometers per second per mega-parsec. The
radius of
the Universe is inversely proportional to the magnitude of this
variable.
Accordingly the Universe is expanding by a factor of 100 per century.
Dividing
this factor into the above ratio discloses that the expansion began
here on
Earth 961 years ago, or 1015 AD. during the dark ages. Obviously, western
cosmology
was born in the dark and has been there ever since” (Halton Arp, 'Extragalactic
Astronomy', Science, 17 Dec. 1971, vol.
174, p. 1189).
That may
be so; but there is a logical reason why we seem to sit at the center
of this
“expansion.” As long as the boundaries of the Universe exceed the
observer’s
horizon, any observer’s horizon, no matter where he is located, such
observer
occupies the center of his observations. There is no preference of one
observer
over the other, we are all equal in that we occupy the center of our
observational horizon whether here or in one of the Sloan Galaxies. So,
assuming a perfectly stationary but truly infinite Universe of an
overall even
distribution of matter, the tidal force from “outside” of every
observer’s
horizon must by far exceed the gravitational pull from “inside” the
horizon. In
other words, the light signature of objects closer to the observational
horizon
should be uniformly shifted towards red, regardless where the actual
observational “center” happens to be. (If the edge to the “outside” of
a finite
Universe would coincide with the observer’s horizon, the situation
should be
exactly the opposite, the tidal force from “insight” would cause
objects to
rush inward and show a blue-shifted light signature. But since there is
no
“outside” to the Universe, nobody will ever observe it.)
The current value for the
Hubble
constant is seventy kilometers per second per mega-parsec, “with an
uncertainty of ten percent.” This means that a
galaxy appears to be moving 160,000 miles per hour
faster for every 3.3 million light-years away from Earth. Apparently
the
Universe is rapidly dispersing into an ever thinner cloud of nothing.
This seems to be
supported by
elementary laws of nature. I am not sure what it means to address the
Universe,
especially an infinite Universe as a “closed system,” but the overall
amount of
energy is “constant,” even in an infinite Universe, and therefore
entropy,
according to the second law of thermodynamics, is on the move towards “a
maximum" (Rudolf Clausius, 1822 – 1888). Entropy is quantified
in units of
energy per units of temperature. In a steam engine fuel is burned to
heat the
boiler and water goes up in steam. The steam pushes a piston until the
amount
of energy from the fuel which initially had heated the water is
consumed. Since
the amount of available energy remains the same at any given time, it
means
that energy spent, is spent for good, and entropy has increased. So,
every star
and everything alive is on a one way trip to the future, towards the
end of its
resources, and no possibility of turning back.
Time proceeds at the pace
available
energy is consumed and therefore, according to the 2nd law of
thermodynamics,
can go but into one direction, and one direction only. The radiation
humming in
the cosmic background is the debris of consumed energy. Everybody
agrees on
this. The question is, in what manner was it consumed?
The theorists of Big Bang
like to
present this debris as the fossil signature of the initial bang. For
them it is
the clincher for their theory but it would be difficult to concoct any
alternative cosmology without some or other form of radiation in the
background. There always has to be a debris of microwaves, whether it
all
started at the blink of an eye or whether since eternity the Universe
is slowly
burning away from a source of infinite supply. In fact the very
presence of
this radiation does actually put a question-mark on Big Bang. No matter
in what
direction we look into the Universe, the background temperature is
pretty much
the same in every direction, roughly 3º Kelvin with very minor
fluctuations,
but if we go by the assumption that a big bang actually had occurred,
then not
enough time has elapsed since this event for radiation to zip across
the
Universe and level out at the same universal average. It sounds
innocuous and is
barely mentioned among the pundits, but so far, every attempt to
explain away
the horizon problem has landed us in one or other violation of natural
laws if
we don't make allowances for a much more ancient age of the Universe.
It is
true, the connection between theory and the cosmic background radiation
discovered by Penzias and Wilson was made because of Gamov's
suggestion.
However every other cosmological idea about cosmic radiation would have
done
the same service. It was the time when we just began to acquire a
better
understanding of radiation while still believing in a featureless
vacuum
between the stars.
Science is the story of
hunches and
ideas put to the test; the prove lies in the method of the testing. But
the
story how we stumble over our hunches and ideas is a messy affair and
riddled
with detours and one-way lanes and the pitfalls of ill applied logic.
Genuine
discoveries have been made because of false assumptions, assumptions
which
sometimes continue to cast their shadow on an otherwise perfectly valid
fact. I
am not much of a believer in anything, but as far as I am concerned
Occam’s
razor applies. The more complicated an explanation, the larger the
margin of
error.
An affirmation of Big
Bang would
require the Universe to look different in the past. There should be
noticeably
fewer heavy elements in the spectrum of ancient stars. Embarrassingly
for the
theory it doesn’t. Galaxies from twelve billion years ago show the
familiar
distribution of stellar ages and a similar spectrum of chemical
elements just
like our Milky Way. As recent as January 2004, the American
Astronomical
Society confirmed that the Universe of billions of years ago and in
distances
marked by high red-shifts in the spectrum is of a very similar
composition than
our immediate cosmological neighborhood. Not that this means a whole
lot.
99.999% of all matter in the Universe exists as plasma. Plasma is a
very thin
gas where the atoms are stripped of their electrons. This creates a
medium of
positively charged ions which respond to electric and magnetic fields
in
complex ways.
The electric force behind
these
events is a thousand trillion, trillion, trillion times stronger than
gravity!
Hannes Alfven (1908
–
1995) was the
first to
prove its existence: "Students using astrophysical textbooks remain
essentially ignorant of even the existence of plasma concepts, despite
the fact
that some of them have been known for half a century" (Hannes Alfven).
In
1965 this did lead
Hannes Alfven to postulate a cellular Universe that exists as a mixture
of
matter and antimatter which he called “ambiplasma.” When occasionally
two such
regions come in contact and annihilate each other, this creates a
superheated
state and rapid expansion into the space surrounding the area of
annihilation,
giving cause to nucleosynthesis and the observed superabundance of
deuterium,
helium-3, helium-4, and lithium-7. The Alfven model postulates that the
regions
of matter and anti-matter are larger than the presently observed
Universe and
are separated by double-layers in the plasma. A confident prediction,
backed up
by observed phenomena such as intergalactic Birkeland currents and
plasma
double-layers. The model does not invoke any exotic physics and employs
well
understood electromagnetic forces and gravity.
In
other words, what we
use to call “cosmology,” is restricted to the tiniest remnants of such
tempestuous collisions between matter and anti-matter, to solids,
liquids and
gases, the physics just of 0.001% of the Universe. In the larger scheme
of
things, all our ingenious string theories and quantum mechanics are a
mere
glitch, barely a blip on the scale.
Personally I have little
patience
with the B-grade substitute to proper infinity: "finite space
without
boundary,"
candy-wrapped into St. Augustine's old chestnut from 400 AD., that
before the
world had jumped into existence "out of nothing" there was just this –
nothing
– and therefore no time. Augustine was perhaps the first person to
think of
time as a physical property of matter itself, which was a big leap in
understanding. But running in circles is not my idea of infinity, and
terms
like "before" and "after" do not suddenly stop to make
sense when the allocated time is up.
In his book A History
of Time,
Professor Stephen Hawking, it
seems, must have felt the same way when he described the evolution of
the
Universe from Big Bang towards maximum expansion and then back into the
“big
crunch,” a singularity where all physical laws as we know them
“collapse.”
Instead of a linear progression through time he proposes the event to
be a
permanent one-off, as something suspended beyond our cognitive
categories of
time and space; Hawking's version of the Block Universe if you will. It
is not a
cycle of repeated expansions and collapses. In Hawking’s analogy – and
it is an
analogy, not a description – if one travels along the geodesics of
Earth the
longitudes will lead from the pole (symbolizing Big Bang) away to the
equator,
the area of maximum expansion, and further on to the other pole, the
point of
collapse, without actually stopping there. We continue on our travel,
reach
again the equator and then the other pole, and so on, infinitely.
“Time” in
this analogy, is something that affects only the traveler who traverses
the
distance from point “A” to point “B,” and it seems to make no
difference
whether we travel the latitudes or the longitudes. Of course what the
good
professor failed to mention is the traumatic nature of arriving at one
of the poles.
Traveling the longitude will lead straight into a singularity where all
laws of
physics break down and no way out of it.
When Albert Einstein
worked out his
field equations for General Relativity he introduced a fudge factor, a
“cosmological constant.” The actual value of this constant is still
everybody’s
guess and therefore allows for multiple solutions of the equations,
depending
on what value we prefer. Einstein himself would later denounce his
introduction
of lambda as the “biggest mistake of my life.” It did inspire the
mathematicians
Willem de Sitter (1872 –
1934) and
Kurt Gödel (1906 – 1978) to propose two highly
creative
solutions of Einstein’s equations.
De
Sitter, in
collaboration with Einstein himself, developed the model of an empty
Universe
with nothing “in it,” no stars and no matter, that nevertheless
exponentially
expands. An expansion of emptiness? It is not as nonsensical as it
sounds.
Since Gauss (1777 – 1855), Bolyai (1802 – 1860) and Riemann (1826 – 1866), empty space is
understood to be a
manifold with intrinsic metrics of its own. The question is, whether
space is
defined by the nature of the physical events that inhabit it – to which
our
physical constants and variables lend expression – or by the postulates
of
geometry. The mathematician will maintain that whatever the actual
value of a
physical constant might be, it goes with a class of correlating
geometrical
metrics. If this correlation is holding up to observation, then it must
be an
intrinsic property of physical space, even if this space appears to be
empty.
Maxwell (1831
– 1879),
Einstein, even Mercator (1512 – 1594) and Ptolemy (87 – 150 AD.) – yes the Ptolemy who
had placed
Earth at the center of the Universe – understood that space is not an
entity
separate from matter, rather a mere feature of the stuff that
constitutes the
world. There is a continuum between the state of low energy in a near
void
vacuum and the energy that is equivalent to the mass of material
objects in a
densely populated galaxy. This manifests itself in the curvature of
electromagnetic waves and gravitational geodesics. Even “empty” space
is never
absolutely void. De Sitter’s cosmology is a vision of almost mystical
purity
and clean mathematical logic. And given the average density of our
Universe,
which is extremely low, it may not even be so very far from the truth.
The solution of Kurt
Gödel is even
more intriguing.
To
the general public the
Austrian mathematician is better known for his two “incompleteness
theorems.”
In 1931 and only 25 years of age, Gödel conclusively proved that
for any system
of consistent axioms which propose the arithmetic of natural numbers,
there are
true propositions that cannot be proven from the axioms alone. The set
of
axioms therefore must be incomplete and intuitive mathematical concepts
can not
be completely described by formal mathematical systems of proof. (One
is
tempted to call it a typically Austrian solution. At some point even
the most
rigorous thinker cannot help but to compromise. In the k.u.k. monarchy
compromise
was a political necessity.) Later in his life, Gödel concerned
himself with
searching for a proof that death is not the end. From his private
papers, we
know he did. What he came up with is a solution to Einstein’s field
equations
that results in a spinning Universe with no singularities but allowing
for time
travel. Since there is no “outside” to the Universe nobody “inside,”
for lack
of a point of reference, will ever know whether it is spinning, except
we
consider the gravitational effects of such spin on the distribution of
matter.
It’s a bit like the atmosphere on the images of Jupiter, which along
the
latitudes is torn into bands of increasing velocity when we approach
Jupiter’s
equator. On our Earth the velocity at the pole is zero and increases to
1,500
km per hour at the equator. In deep space the velocities are far more
extreme.
In our telescopes we see “cosmic walls” of galaxies and clusters of
galaxies
strung out a billion light-years across and streaming along at
velocities that
approach one thousand kilometers per second. In 2003, a survey by the
ROSAT
x-ray satellite revealed another huge concentration of matter some
twelve
billion light years end to end. Who is to say this could not be
effected by a
cosmic spin? If true, it raises questions about the true age of these
“cosmic
walls.” In Hawking’s Block Universe the travel time along the longitude
is
equivalent to the travel time along the latitude. In a spinning
Universe where
the relativistic effect of the increasing rotational speed towards the
cosmic
equator is warping time, this is not possible.
My
math is woefully
inadequate to appreciate all the niceties in Gödel’s solution; I
hear it has
been dismissed because it doesn’t allow for expansion. But the supposed
telltale sign for expansion, the red-shift of distant objects, can also
be
explained as a tidal effect on objects nearer to the Universe’s
“equator” or
horizon.
© – 10/9/2008 – by
michael sympson,
4,050 words, all rights reserved