Where does the Lake go, when the Geese fly to Canada?

 

to Dawn

There seems to be a love affair between the Vatican and Big Bang. "I was there when Abbe Georges Lemaitre proposed the theory of Big Bang for the first time,” said the physicist and Nobel laureate Hannes Alfven (1908 – 1995). “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.” In 1951, in a speech before the Pontifical Academy of Sciences, Pope Pius XII offered his enthusiastic endorsement: "It would seem that present-day science, with one stroke across the centuries, has succeeded in bearing witness to the august instant of the primordial Fiat Lux, when along with matter, there burst forth from nothing a sea of light and radiation, and the elements split and churned and formed into millions of galaxies." The Pope went on to conclude that Big Bang proved the existence of God: “Thus, with that concreteness which is characteristic of physical proofs, science has confirmed the contingency of the universe and also the well-founded deduction as to the epoch when the world came forth from the hands of the Creator. Hence, creation took place. We say: therefore, there is a Creator.” In 1978 the cosmologist Professor Stephen Hawking (*1942) visited the Vatican to receive the Pius XI Medal from the Pontifical Academy of Science.

In his book A History of Time, Hawking claims that Pope John Paul II tried to discourage him and other scientists from trying to figure out how the universe began. “I was glad then,” Hawking said, “that he did not know the subject of the talk I had just given at the conference – the possibility that space-time was finite but had no boundary, which means that it had no beginning, no moment of creation.''

In that alleged lecture, Stephen Hawking brought forward the scenario of a universe expanding from Big Bang towards a maximum and then falling back into the “big crunch” without actually doing either. Instead of a linear progression, he proposed a permanent one-off where the whole process is laid out and suspended in a dimension of simultaneous occurrences beyond our cognitive categories of time and space. “The quantum theory of gravity has opened up a new possibility,” he argued, “in which there would be no boundary to space-time and so there would be no need to specify the behavior at the boundary. One could say: ‘The boundary condition of the universe is that it has no boundary.’ The universe would be completely self-contained and not affected by anything outside itself. It would neither be created nor destroyed. It would just be.” It was the first time that I read something remotely appealing about this ugly idea of Big Bang. In Hawking’s analogy the Universe expands from the pole – symbolizing Big Bang – towards the equator, and further on shrinks back to the point of collapse at the other pole. Yet we continue on our travel, reach again the equator and then the opposite pole, and so on, indefinitely.

There is no beginning and no end. “If the laws of physics could break down at the beginning of the universe, why couldn’t they break down anywhere? To admit a singularity is to deny a universal predictability to physics, and, hence ultimately, to reject the competency of science to understand the universe.” That is an interesting statement by the very man who made a career out of the research of black holes, which are physical singularities by definition. The Universe “if completely self-contained, having no boundary or edge,” would have “neither beginning nor end: what place, then, for a creator.”

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I think it was Meister Eckhard (1260 – 1328), who was the first to suggest a world where every event is laid out simultaneously in time-withdrawn permanence. Yet when Professor Hawking is saying that space-time has no boundary he didn’t, however, mean to say the Universe is infinite; to me at least, the idea that a hamster can run in his wheel forever without ever hitting an obstacle has nothing to do with infinity, the real thing, as explained to us by Georg Cantor (1845 – 1918). Cantor made us understand that infinite sets possess an actual, albeit infinite number of members and that various infinite sets can vary in size. Any section out of an infinite set – for instance the prime numbers – has as many members as the collection as a whole. Infinite sets are as complete as any set of finite integers and yet as "countable" as is every set that can be put in a one to one correspondence with other sets of integers.

In other words, “infinity” is not an ever-growing progression. It is an immediate presence.

I am not a physicist. I grew up with the contention of Immanuel Kant (1724 ­­– 1804) that our spatial intuitions and the true nature of time and space are two different things. The empirical world beyond our senses, does not know of “order” and “chaos.”

These terms are purely cognitive categories. Kant postulated that the human mind is as much the originator as it is the passive recipient of our perceptions. Immanuel Kant took particular pride in his table of cognitive categories. His critics mocked the idea as a "glittering palace," but Kant saw it as the key to his philosophy. The American philosopher Charles Sanders Peirce (1839 – 1914) adopted this view, with the important correction, that these categories actually are laying at the bottom of our linguistic toolbox.

Our instincts about time and space, finality and infinity, are the offshoot of the operational logic that enables us to cogitate perceptions. The information filtering in from our senses can only be processed as a string of stimuli; therefore we map out the images and words as a sequence stretching through time and space. It is the way our semantic memory is compelling us “a priory” to assemble the items gathered in our episodic memory. This doesn’t necessarily put a limit on our understanding, but it stands to illustrate Kant’s contention that in actual fact we are incapable of intuitively comprehending the true nature of the phenomenon. Not that our senses are lying to us, the prey wouldn’t survive the chase if it didn’t spot the predator, but “space,” Kant explained, “is merely a form of intuition for the external, but not a real object in itself; it is not a correlate of phenomena, it is the form, our faculty of perception uses, to present phenomena to our understanding.“ Even our mathematical tools are drawn a priory from our capacity to work out categorizations, before we use them as mental receptacles for the empirical data at hand. Yet even without the support of empirical evidence, an idea may still be ontologically valid. Descartes observed that we can know everything there is to know about triangles, but this doesn’t guarantee the occurrence of any real life triangle out there. Should there be, however, real life triangles, they will be as “predicted” by the geometries of Euclid and Karl Friedrich Gauss (1777 – 1855).

We know of course exactly how old the Universe is. According to Johannes Kepler (1571 – 1630) the Old Potter opened for business on Sunday, the 27th of April in 3877 BC, at 11.00 am, central European time. Drinks were on the house.

Who knows, this Universe could be the latest model from a whole assembly line of discarded prototypes! This world – complete with the light reaching us from the galaxies in the Virgo cluster apparently after billions of years, with fossils of dinosaurs hidden in the rocks, with Professor Hawking lecturing the Vatican on a Universe without origin, and with me typing at this essay and recalling that only yesterday I’d arrived in Singapore after twelve hours on the plane – could have sprung into existence five seconds ago, and we wouldn’t be any the wiser for it.

Opinions remain divided whether the Old Potter merely dropped the ball for the kickoff and then withdrew to the terraces for tea and scones, or actually remained on the grounds for a spot of umpiring.

These “grounds” seem to cover an awful lot of empty space; in the larger scheme of things, all our ingenious string theories and quantum mechanics are a mere glitch, barely a blip on the scale. Yet even “empty” space is a mathematical manifold with intrinsic metrics. The physical properties of mass, charge and velocity of objects in space correlate with these metrical values. Ptolemy (87 – 150 AD) – yes that Ptolemy, the one who placed Earth at the center of the Universe – understood already that space is not an entity separate from matter. Based on this, Albert Einstein (1879 – 1955) postulated that the element of time has to be included too, and referred to what is out there as the “Space-Time-Continuum” or “space-time.” A continuum that seems to expand! In 1929, Edwin Hubble (1889 – 1953) had noticed a uniform shift towards red in the light-signature of galaxies and clusters at extreme cosmic distances. Since the light arriving from an object moving through deep space is either shifted towards blue when it approaches – like the Andromeda galaxy – or towards red when it hurries away, the likely explanation seems a universal motion away from the observer.

The more distant the object, the more the escape velocity seems to increase. The factor of this increase is called the Hubble constant. When it was discovered "in 1926, it had a value of 500 kilometers per second per mega-parsec” (Halton Arp). Which prompted the astronomer 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” (Halton Arp, 'Extragalactic Astronomy', Science, 17 Dec. 1971, vol. 174, p. 1189). That sounds absurd, yet we may be sitting at the center of this apparent “expansion,” for a good reason, but it is not a reason supporting Big Bang.

As long as the boundaries of the Universe exceed the observer’s horizon, any observer’s horizon, no matter where he is located, whether here or in one of the Sloan Galaxies, such observer occupies the center of his observational horizon. There is no preference of one observer over the other; all observers are equal in that they occupy the center of their observational horizon.

In a very much larger Universe, let alone in an infinite Universe, the tidal force from “outside” on every point along every observer’s horizon must by far exceed the gravitational pull from “inside.” In other words, the light-signature of objects closer to the observational horizon should be uniformly shifted towards red, and the Hubble constant rather stands for the value of gravitational pull from the observational horizon’s outside, than for an inert escape velocity. 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 distance from Earth. If this were to indicate an expansion, the Universe would be rapidly dispersing into an ever-thinner cloud of nothing, leaving behind merely the debris of microwaves.

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. It is a requirement by the second law of thermodynamics. Physicists use the term “entropy” to categorize the irretrievable consumption of energy. In their parlance, they have a loose way to identify the degree of entropy with a state of order or disorder. Yet what really happens is that energy is burned whether we wage war or build a palace; the result is exactly the same: an increase in entropy. Entropy is quantified in units of energy per units of temperature. In a locomotive the steam pushes a piston until the energy from the fuel heating the water in the boiler is consumed. There is no viable way to reclaim the residual heat dispersed into the environment after the steam has done its work. Entropy has increased. Energy spent is spent for good. The entropy of the entire Universe is moving towards “a maximum" (Rudolf Clausius, 1822 – 1888). So in every conceivable scenario, there always have to be microwaves in the background, 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 should put a question mark on Big Bang.

No matter into what direction we look, the background temperature is pretty much the same everywhere, roughly 3º Kelvin with very minor fluctuations, but if we go by the assumption that some thirteen billion years ago a big bang actually had occurred, then just not enough time has elapsed since this event for radiation to zip across the Universe and level out at the same universal average.

An affirmation of Big Bang would also require the Universe to look different in the past. There should be noticeably fewer heavy elements in the spectrum of ancient stars. Yet 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 shift in the spectrum is of a very similar composition than our cosmic neighborhood. The observed superabundance of deuterium, helium-3, helium-4, and lithium-7, may have been the product of a more “local” collision between regions of matter and antimatter each exceeding the size of the observed Universe. According to the Nobel laureate Hannes Alfven this would create a superheated state and a rapid expansion of the debris into the space surrounding the area of annihilation, giving cause to the observed nuclear synthesis. The model does not invoke any exotic physics and employs well-understood electromagnetic forces and gravity. (When I hear the term “dark matter” I feel a sensation of smelling burning flesh.) Among the cosmologists of the past – Epicurus, Lucretius, Bruno – Sir Isaac Newton (1642 – 1727) was the first real scientist taking the notion of infinity seriously.

In his private notes Newton had anticipated much of Albert Einstein: "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 a man from a century with horse manure piling up in every corner. In his publications however, he placed his reputation on Kepler's three laws of planetary motion. Newton’s resulting law of gravity suggested to him a world ultimately destined to collapse. So to prevent this from happening, Newton’s celestial mechanics require a homogeneous Universe stretching into infinity. Professor Hawking in his book has brushed this aside, claiming, that even so all matter would ultimately coalesce and collapse into one dense mass. An example for Homer caught napping. After all, it was Professor Hawking himself, who had proven that even black holes eventually must evaporate, in other words, have a limited lifespan – which in an infinite Universe can only mean that some may not make the distance towards the crunch point. The imperial astrologer Johannes Kepler thought he had a better argument against infinity; it became later known as “Olber’s Paradox.”

In his novel Conversations with the Starry Messenger from 1610, the first piece of SF fiction known to history, Kepler wrote: “In an infinite Universe every line of vision must end on the surface of a star. Would this not make the whole celestial vault as luminous as the Sun?"

Kepler was as bright as Newton or Professor Hawking. Still writing by candlelight, it must have occurred to him that even an infinite number of candles do not burn all the time. In 1676 Ole Roemer (1644 – 1710) calculated a good approximation for 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 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. 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. Even with all eternity available, in order 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. Of all possible explanations why and how in an infinite Universe the sky is dark at night – there are several I am aware of – this is the one with the fewest theoretical assumptions. Therefore “there is no rational reason to doubt that the universe has existed for an infinite time. Only myths attempt to say how the universe came about, either 4,000 or twenty billion years ago,” says Hannes Alfven.

It is a world where the number of transcendental numbers – values such as pi and e – is very much larger than the total of integers and the values of rare constants stand out from the chaos of random numbers like the nodes marking the intervals on a musical string instrument.

So what is really out there? I mean, what is out there when nobody is looking and trying to make sense of what his senses communicate to his instincts and ideas?

The mathematician Kurt Gödel (1906 – 1978) is best known for his theorem of incompleteness: “For any consistent formal theory that proves arithmetic truths, there is an arithmetical statement that is true, but not provable by the theory.” Gödel liked to think that “the world in which we live is not the only one in which we shall live or have lived.” I’ve heard the same thing from an elderly lady waiting for her train on platform four of Waterloo Station. In 1949, Kurt Gödel proposed a spinning Universe with no singularities but allowing for time travel. The proposition is based on a fudge factor in Einstein's field equations, the “cosmological constant” λ (lambda). The actual value of this constant is still everybody’s guess and, depending which value we prefer, allows for multiple solutions of the equations.

Since there is no “outside” to the Universe, nobody “inside,” for lack of a point of reference, will ever notice the spin. Except we consider the inert effects of gravity. For instance on Earth the rotational velocity increases from zero at the poles to a speed of 1,500 km per hour on the equator, slightly pulling the planet out of its spherical shape. On a cosmic scale, this means that the rotational velocity at the "cosmic pole" has to be zero as well, while the increase towards the "equator" must affect the overall distribution of matter, very similar to the distribution of the bands of cloud formations and of weather systems on Jupiter. There are tantalizing clues right before our telescopes. The huge void of the “WMAP Cold Spot” could very well be the equivalent of a “cosmic pole,” only it isn’t actually that void. Recent long-range surveys from the Hubble telescope have been pinpointed at apparently void regions in the most distant expanses. These long exposures reveal the existence of a crowded world of galactic clusters too far away to be picked up in a normal sweep even by Hubble. Closer to the equator, matter should accumulate, stretching in bands along the latitudes. The “cosmic walls” in our telescopes – galaxies and clusters of galaxies, strung out a billion light-years across and streaming along at velocities that approach 1,000 kilometers per second may just fit the description. Some 150 to 250 million light-years away, there is the “Great Attractor,” a gravity anomaly within the range of the Centaurus Supercluster revealing the existence of a localized concentration of mass equivalent to tens of thousands of Milky Ways. It is observable by its effect on the motion of galaxies and their associated clusters over a region hundreds of millions of light years across. In 2003, a survey by the ROSAT x-ray satellite revealed another concentration of matter some twelve billion light years end to end. Who is to say this could not be the effect of a cosmic spin? And since in a spinning Universe the velocity of every region along one of the "cosmic latitudes" must vary from the other regions above and below, traveling at angles to other worlds along the cosmic longitudes should enable us to tunnel through time which is spinning forward along the latitudes even without the assistance of exotic physics and wormholes; yet this was not what Gödel was after. "If one can travel to other worlds of a different time," Gödel asked, "how can time be the passage from a no longer existing past to a not yet existing future, when the physics of a spinning Universe require a form of “eternalism,” where the future is a foregone affair and the past embedded in the present because all points in time are equally valid frames of reference – or equally real." In Gödel’s Universe this has consequences for the entropy of matter and perhaps even for the second law of thermodynamics; in fact the implications may go much further: instead of going from the past into the future in a straight line, past and future are rolled together in a closed time-like curve (CTC) tying together every event in space-time, past present and future simultaneously. For Gödel this anomaly was the crucial point of his suggestion, and whatever it meant to Gödel himself, he arguably succeeded in proving that Einstein's equations of space-time are not consistent with what we intuitively understand time to be.

Einstein was generous enough to acknowledge that his friend had raised new and disturbing questions about the nature of time. Since then physicists have tried without success to challenge Gödel's physics or at least find a missing element in relativity itself that would rule out the applicability of Gödel's results. The apparently increasing red-shift of distant objects can also be explained as the effect of increased rotational velocities nearer to the “equator” of the Universe. In this case we would know that our own position in the Cosmos is somewhat removed from the cosmic equator.

© – 7/11/2009 – by michael sympson, 4,000 words, all rights reserved