The Infinite Universe

 

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

Proprietary Notice: © – 04/10/2003 – by michael sympson. Text may be downloaded for personal use, provided all copies retain the copyright and proprietary notices. No material may be modified, edited or taken out of context. Any commercial use in advertising or publicity requires permission in writing by the author’s estate.