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The Infinite Universe

Remarks on Davison's Apeiron Article


A.  A. Faraj

In the January-July-2000 issue and the subsequent issue of the Montreal-based journal, Apeiron, C. J. Davison argues, convincingly, in my view, for the superiority of the notion of 'Infinite Universe' over the idea of 'Finite Cosmos' [Davison, 2000].

Without doubt, he is logically and philosophically on the right track. The contradictions of 'Finite Universe' are appalling, to say the least. Who cannot see the glaring absurdities of this form of  'Medieval Cosmos', called the ‘Big Bang’?

As you know, the Ptolemaic idea of 'Finite Cosmos' has been resurrected in the early Twentieth Century, under the heading: Finite-but-Unbounded Universe. Whether it's bounded or unbounded, the whole notion of 'Finite Universe' is, as it was in the Middle Ages, unrealistic and plainly untenable. No argument, on scientific, epistemological, or aesthetic grounds, could be persuasively advanced, in its favor.

After the demise of the 'Ptolemaic Cosmos' on the hands of Copernicus, Kepler, Galileo, and Newton, who could have guessed its resurrection in the 20th century? But that is exactly what happened.

It all started with Einstein's General Theory of Relativity. Initially, it was advanced as a resolution of the conflict between his Special Relativity and Newtonian mechanics. After a decade or so of half-baked ideas, Einstein, in the end, sided unequivocally with G. Leibniz in his well-known clash with Isaac Newton, during the 17th century.

As his published letters reveal, Leibniz in that debate was very convinced of the cogency of his argument against Absolute Space, as an integral part of physical reality, on kinematic grounds. That is because, Stellar Aberration (the strongest kinematic evidence for Absolute Space) was unknown at that time. But when the debate shifted from kinematics to dynamics, Leibnitz started to stumble and to waver. Rotating Pails, Equatorial Bulges, and many other dynamical effects of Rotating Earth are too obvious and too simple to be denied. They all point to a simple fact: Absolute Space is real. In the end, he wrote to S. Clarke:

"I grant there is a difference between an absolute motion of a Body, and a mere relative change in its situation with respect to another Body. For when the immediate cause of the change is in the Body, that Body is truly in motion; and then the situation of other Bodies with respect to it, will be changed consequently, though the cause of that change be not in them" [Jammer, 1969].

Unlike Leibniz, Einstein, however, thought otherwise. In his opinion, dynamical proofs of Absolute Space, such as Coriolis Force, Foucault-Pendulum Inertiality, etc., can be transformed away by simply changing the frames of reference.

The procedure is, in the final analysis, a futile manouevre. No change in frames of reference could possibly transform away such dynamical phenomena. For this reason, Einstein and his followers have taken refuge in the 'Infinitesimals'.

If, for instance, you decide to use a gradiometer to find out whether your system is freely-falling under the effect of gravity, or moving inertially in a straight line, then Einsteinians will tell you: Make the spatial dimensions in your measurements infinitely small. In this case, and in this case only, your gradiometer does not work. In short, they are hiding behind experimentally-inaccessible Infinitesimals. SEE [Ciufolini et al, 1987].

It's, thus, very hard to disagree with Bishop Berkeley's statement:"Infinitesimals are the ghosts of the departed quantities". You may call them: 'the graveyard of the departed theories'!

Briefly, the following points can be made, regarding the fundamental irrationality of the hypothesis of 'Finite Universe' and its detrimental influence on the development of the physical sciences:

I. A pure void expands and curves on itself without any physical mechanism or even a rational mental image.

The supposition of 'Finite Void' is untenable. In fact, it's absurd, and hence it has been utilized, since Antiquity, in proving its opposite. The universe, by definition, is the sum of all things in existence. That is the starting point of T. L. C. Lucretius' famous proof. It runs as follows:

"Now since we must admit that there is nothing outside the sum, it has no outside, and therefore is without end and limit. And it matters not in which of its regions you take your stand; so invariably, whatever position any one has taken up, he leaves the universe just as infinite as before in all directions. Again, if for the moment all existing space be held to be bounded, supposing a man runs forward to its outside borders and stands on the utmost verge and then throws a winged javelin, do you choose that when hurled with vigorous force it shall advance to the point to which it has been sent and fly to a distance, or do you decide that something can get in its way and stop it? For you must admit and adopt one of the two suppositions; either of which shuts you out from all escape and compels you to grant that the universe stretches without end" [Jammer, 1969].

This argument works even better against Riemann's Hypothesis of 'Finite-and-Unbounded Void'. If the void is held to be finite and unbounded, then every path must eventually return to its starting point. What if every point on every path is taken as an origin for a new Gaussian co-ordinate system? Either you prohibit the use of the Third Dimension in your co-ordinate systems, or they will extend to Infinity. For you must adopt one of these two suppositions, either of which shuts you out from all escape and compels you to grant that Space is infinite.

II. An entire universe is reduced to the size of the atom and beyond. 'Dancing angles on a pinhead' is more rational.

The current hypothesis of 'Finite Cosmos' reduces the entire universe, at a moment, not very far in the past, to the size of the hydrogen atom and beyond. Not even an out-of-his-mind shaman could have dreamt up anything like this 'Cosmic Egg'. Nonetheless, a sheer repetition has made the 'Big Bang', for some time now, quite popular among cosmologists.

In some sense, the Big-Bang hypothesis is a simple but very crude projection of the image of the 'Nuclear Bomb' on the Cosmos at large. Cosmologists, as a matter of fact, were very fascinated by the Herculean rocking of the Nuclear Baby. So, like the ancient Sumerians, who had filled their universe with harrows and ploughs, the cosmologists of the 20th century embarked on creating a cosmos out of gigantic explosions and mushroom clouds.

The Big-Bangers claim that their theory is a result of a direct extrapolation towards the past. The relevant observations, however, can be explained away in 1001 ways, which are more rational and more plausible than the Big Bang. Even without a viable alternative, it's much easier to live with unexplained red shifts and microwaves, than having to live with the unmitigated foolishness of the Big Bang.

III. Black holes and White holes swallow and spew everything except their own gravity.

In addition to the Big-Bang, Einstein's Theory of General Relativity has filled the Cosmos with Black holes and White holes, which literally swallow up and spit out every thing except, according to this theory, their own gravity.

Those hypothetical entities are presented by their proponents as glorious predictions of the theory. In reality, they signal a catastrophic breakdown in the very fabric of this unrealistic theory. That is why Einstein was horrified by them, in the first place. Black holes, in particular, are the immediate consequence of decreeing velocity of light as the upper limit for all velocities of ponderable bodies, regardless of their actual momentums and kinetic energies.

The Field Equations of Einstein's General Relativity are solvable only in very few idealized cases. Even then, many arbitrary assumptions and approximations must be made. Nonetheless, it's clear that under certain conditions, the theory leads to gravitational collapse.

It should be mentioned, in this regard, that Oppenheimer's Black Hole is very different from Laplace's Black Star. There is no limiting velocity in Newtonian mechanics. Given enough kinetic energy, through collision, matter can escape from the Laplace Star, at any time.

In Newtonian mechanics, gravitational singularities, simply, cannot exist. That is because all linear momentums and kinetic energies gained under the effect of gravity, must be removed from the system. Otherwise, the various parts of the system will continue to oscillate between their initial and final positions forever. But that removal requires an infinite amount of escaping materials. Such a requirement is clearly unrealistic.

From the Black Hole, on the other hand, only gravity can escape. That is curious. How can gravitation escape from the Black Hole? No convincing answer could be given to this question. Furthermore, the escaping gravity leads to a ganging-up by Einstein's two theories (the General & the Special) to produce a paradox: 'the Infinite-Mass Paradox'.

According to the General Theory, if a ponderable body falls into a black hole, from whatever distance, its velocity approaches that of light indefinitely. That is because its potential energy at any distance from the centre is infinite. On the other hand, according to the Special Theory, the Relativistic Mass of a falling object, in this case, approaches Infinity.

The strength of its gravitational field, therefore, must be approaching Infinity as well. A powerful gravitational field of this kind, should have dragged and pulled every ponderable thing in the universe into the Black Hole, long time ago. It never happened. Thus, either the Special Theory or the General Theory, at least, is false, or gravitation cannot escape from the Black Hole. Either one of these two suppositions shuts you out from all escape and compels you to grant that the Conventional Theory of 'Black Holes' must be absolutely false.

IV. Dark Matter lurks everywhere. That is, perhaps, the apparition of the Old Aether.

The universe has been, theoretically, filled with 'Hypothetical Dark Matter', which has all of the notorious characteristics and properties of the Old Aether, except the ability to transmit electromagnetic waves and being gravitationally-neutral.

This ugly monster of today cosmology, presents a colossal breakdown at the very bottom of the adopted theories. Totally-ad-hoc assumptions have placed severe limitations on exploiting the enormous explanatory power of kinematics, in modern astronomy.

Many kinematic manifestations are treated as if they were true dynamical phenomena. As a result, the laws of dynamics have been stretched far beyond their proper limits. Their total failure, therefore, is not altogether unexpected.

V. The Second Law of thermodynamics is on the loose, wreaking havoc on the end, on the middle, on the beginning, and perhaps even on the beginning of the beginning of the Finite Cosmos.

A finite universe is, obviously, a 'Sitting Duck' (from its incomprehensible start to its miserable end) for all the ravages of the Second Law of thermodynamics. It's ephemeral, gloomy, and pointless. Some kind of Aristotelian 'Prime Mover' may come to the rescue.

But, then, to call that 'moved thing' a universe is an overstatement. That is because, in this case, all the sufficient causes and all the essential properties of a 'Stand-Alone Universe' must be banished collectively from the universe and assigned to its 'Prime Mover'.

Besides, why should, in this case, the Prime Mover reveal the Blueprint of the Universe to our cosmologists? After all, they are armed only with a Tensor Notation. It's highly compact but rarely solvable and largely useless.

Proposals founded on chaos and indeterminism have been put forward by I. Prigogine and others, in order to avoid the Thermodynamic Catastrophe. But as far as the Relativistic Cosmologies are concerned, those attempts are doomed to failure right from the start. That is because Einstein's Relativity has blocked their way to the only two available sources of infinite energy in Newtonian mechanics. On one hand, its 'Fundamental Locality' has denied them the access to the infinitely large in extent. On the other hand, its 'Black holes' have shut out the infinite energy of gravitational coalescence of 'finite amount' of matter, from all escape beyond their Event Horizons. In brief, the Thermodynamic Death of the Relativistic Cosmos is pre-ordained and inevitable.

VI. In a finite cosmos, no real compromise between Freedom and Necessity could be made.

Only under the aegis of Infinity, Free will and Determinism can be successfully reconciled. The importance of these two concepts cannot be overstated. Freewill is the basis for the laws of Society. Determinism is the basis for the laws of Science.

To oversee, steer, control, or change the outcome of a specific set of causes, Free will must rely on the unlimited supply of potential causes. Free will, through this, and only through this, can overcome the constrains of the Status Quo and transcend itself indefinitely.

VII. Cult mentality is getting hold and widespread.

That is inevitable. Myths beget myths. Superstitious beliefs and irrational hypotheses can only lead to superstitious mentalities and irrational attitudes. It's as simple as that.

VIII. Grant committees and project administrators, abound, are as fair and just as the little despots of the Middle East.

In particular, they are notoriously addicted to rewarding their cronies and punishing their opposition, without regard to anything else.

IX. Many professional journals are as committed to free exchange of ideas and real debate, today , as the Soviet newspapers of yesterday.

They are monotonous, lopsided, dogmatic, and obscenely totalitarian. Even Einstein, himself, had felt the sting of this modern form of Inquisition.

Would you believe it? Albert Einstein, at the height of his career, had received a rejection slip from the journal of Physical Review! He co-authored a paper on some part of his theory. He sent it from Princeton to Phys. Rev. And it was rejected!

Einstein was furious. Who can blame him? He vowed he would never ever submit a paper to that journal, as long as he lived. I believe, he kept his promise.

X. Collective monolithic nonsense is held as the hallmark of good research.

The Hypothesis of 'Finite Universe' is untenable. Untenable ideas, by their own very nature, can be raised to prominence only by shunning out any competition, and through the continuous employment of a reward-punishment system and censorship. Consequently, many promising research projects and programmes have been rejected, for one simple reason: They are not in accord with the current dogmas.

Accomplished researchers have been demoted and ostracized, simply, for discovering or attempting to discover disconcerting anomalies. The case of the astronomer, Hilton Arp, is a stark example. His use of the 'Locality of Quasars' as a working hypothesis, was non-conforming enough for the narrowed-minded Establishment to shun him out and to strip him of the small privileges of a professional astronomer: His telescope was taken away. That was , really, a very shameful act, on the part of the Establishment. Even the Inquisition of the 17th century didn't try to strip Galileo of his telescope.

XI. Zealous professionals and amateurs never get tired of battling the flat-earthers and the writers of the horoscopes. At the same time, they are unaware that, they themselves, have swallowed a 'Dead Rat' up to its tail.

For instance, consider their silly reaction towards Dr. Velikovsky. He honestly believed that Venus had been born out of Jupiter's head. So committed Big-Bangists stood at once and threatened to organize a general boycott to kill his book: Worlds in Collision.

One amazing aspect of this foolish row is that it had been led by some people, in my opinion, of good judgment. If this proves anything, it proves that personal integrity plays no significant role in Orthodox reaction. That is because Orthodoxy, in every field, is like a boa constrictor. When it goes downhill, it always goes head first.

XII. Physics is in a shambles.

It has been infiltrated by absurd theories, and infested by worthless hypotheses, from top to bottom. Einstein's theories are only the top of the iceberg. Hence it requires a revolution to set it right. It is not the kind of revolution, the Establishment is always talking about, but an Ockham's razor: a revolution of the Copernican type.

Having that out of our way, I believe C. J. must be aware of his old compatriot's argument against Infinity. I mean "Dear Lord" Sir Eddington. To reiterate his objection, we must first point out that an infinite universe implies an infinite chain of causality as well. That is exactly what Eddington attacked, in addition to Infinite Past. He wrote:

"The difficulty of an infinite past is appalling. It is inconceivable that we are the heirs of an infinite time of preparation; it is not less inconceivable that was once a moment with no moment preceding it. The dilemma of the beginning of time would worry us more were it not shut by another overwhelming difficulty lying between us and the infinite past" [Eddington, 1929].

At first sight, the Infinite-Past argument appears startling and powerful. Of course, he did not invent it. It had been mentioned time and time again in Medieval Philosophy. The philosophers of the Renaissance however, launched full-scale assault on this and the other arguments that favor a finite universe.

The Italian, G. Bruno for example, had used successfully the idea of Eternity to demolish these medieval objections to Infinity. His exact words are too long to be quoted in this context. But his main point is this. You cannot single out a particular point in an infinite space and say this is the centre of the Universe. In the same way, you cannot pick a certain moment of time and say this is the central moment of Eternity.

Time is a homogeneous continuum. It consists of all rates, from the infinitely small to the infinitely large, all at once. Thus, Eternity is a special case of this universal continuum. It's defined as a time whose rate of flow is equal to zero, and hence its duration is infinite. Therefore, it is a mistake in logic, to use a different rate of time flow for describing Absolute Existence, which is conceivable only under Eternity.

More importantly, the chain of causality runs in Eternity, not by Eternity. This moment is as good as the moment of your birth. Yet you cannot go back. Not because it is the arrow of time, but because it is the arrow of causality.

Ah, we almost forget. When A. Einstein declared time relative, it was hilarious. There was excitement and sweet anticipation in the air. Behold! Wild Time was about to be tamed! Fountains of Youth would flow all over the Planet, at last. Needless to say it was a disappointment. Now that sweet illusion is almost gone. Weinberg's airplane meditations had spoiled everything. It is causality not time. Anyone with conquistadorean dreams must find the way to biochemistry. Biology is a good choice.

Eternity is also important in other respects. The three major laws of human thinking: A is A, A or -A, and the excluded middle cannot be held absolutely true in the absence of Eternity. And when these are not valid, every aspect of human thinking, qualitatively and quantitatively, is false. That is precisely what Ultimate Skepticism had aimed at, in attacking both the infinite universe and non-infinite universe.

The argument goes something like this. Suppose Reality physical and otherwise is a very big dream. Imagine being a pure ego, skull, brain ball, or anything insignificant in Blaise Pascal's infinite spaces. Then how can you prove that you did not create all this wonderful stuff by your own imagination, in your own imagination, simply to entertain yourself?

Rene Descartes had examined this principle of Absolute Skepticism. He found it to be good in every case he could think of, except one: "I think then I exist". The Ultimate Skeptic can doubt the reality of every single thing, and deny the truth of every single fact, except the fact of his own existence. And if the principle of Ultimate Skepticism is not true in this single case, then there is no reason to believe it will not be violated in the rest.

I had mentioned Blaise Pascal. He had written some tearful and moving stuff about his fear and loneliness in the infinite spaces of Newtonian mechanics. It is not very clear why anyone should be afraid of Infinity. It is wonderful. It is the ultimate freedom. Perhaps, it is all a matter of psychology. If the psychologists are right, then there are two kinds of people: Those who love closed places and dislike Infinity. And those who like open places and love Infinity. But this diagnosis has nothing to say about the Absolute Skeptic who dislikes both of them.

I should mention one more point. An infinite chain of causality is such in two possible ways. It could be infinite because the last result in the chain produces the first cause. So Infinity here is just a repetition, as in the Cyclic Return of Oriental Philosophies, the so-called Maxwell-Daemon Hypothesis, and Poincare's Cyclicity. The other is the Eternal Return adopted by the son of Aristotle and F.W. Nietzsche.

Eternal Return simply means we were born in this world and we shall never get cast out of it. It is not because the last generates the first. It is because there is an infinite number of chains of causality in various stages of progress. This implies that there is an infinite number of exact replicas of every thing, not just only in time, but also in space at the same time, as well.

Eternal Return, is, undeniably, one of the most sweeping hypotheses of Absolute Existence, ever invented. Only 'being in the same place at the same time' remains as the Absolute Identifier of Uniqueness, which cannot, under this hypothesis, be duplicated in any way.

I am not quite sure which of these two options, C. J. Davison has chosen. As for me, in this particular case, I prefer to follow Nietzsche. The reasons are simple. Eternal Return may include Cyclic Return. The reverse is false. Pascal's gamble in this case is good. Last, but it is not the least. Cyclic Return spoils the grace and the beauty of Causality marching ahead for Eternity, in Eternity, the whole Eternity.


Arp, H. C. (1987). Quasars, Redshifts, and Controversies. Berkeley CA: Interstellar Media.

Ciufolini, I. & J. A. Wheeler. (1995). Gravitation and Inertia. Princeton: Princeton University Press.

Descartes, Rene. (1955). The Philosophical Works. New York: Dover.

Davison, C. J. (2000). "The Universe: Finite or Infinite", Apeiron, Vol. 7, No. 1-2.

Davison, H. M. (1983). Blaise Pascal. Boston: Twayne.

Eddington, A. S. (1929). The Nature of the Physical World. London: Cambridge University Press.

Glendenning, N. K. (2000). Compact Stars. New York: Springer.

Gatti, H. (1999). Giurdano Bruno and Renaissance Science. Ithaca: Cornell University Press.

Jammer, M. (1969). Concepts of Space. Massachusetts: Harvard University Press.

Lerner, E. (1991). The Big Bang Never Happened. New York: Random House.

Maor, E. (1987). Infinity and Beyond. Boston: Birkhauser.

Nietzsche, F. W. (c1969). Thus Spoke Zarathustra. New York: Penguin Books.