Science and Marxism

Newton: belief and contradiction

Copernicus’ theory led to fresh speculation about the nature of the universe. The modern concept of an infinite universe first began to emerge here, linked to religious expressions of an infinite god.

Copernicus’ theory led to fresh speculation about the nature of the universe. The modern concept of an infinite universe first began to emerge here, linked to religious expressions of an infinite god.

Newton did not prove but merely asserted that the world was infinite. The idea of an infinite universe was undoubtedly extrapolated at least in part from the belief that to the vast quantities of stars and space that Galileo saw through his telescope there must be added vast quantities more, without end, to the glory of god.

The universe, Woods writes,

was rapidly ‘expanded’ – in the minds of men – and… is now thought to measure tens of billions of light years across, and time will show that even the present calculations are nowhere near big enough. For the universe, as Nicolas of Cusa and others thought, is infinite. (p184)

Recent calculations suggest that the universe is at least 156 billion light-years wide. The German cardinal, Nicolas of Cusa (1401-1464), anticipated Copernicus (1473-1543) by nearly a century, proposing that the earth rotated and, as Woods rightly points out, argued that the universe was infinite.

Sir Isaac Newton (1643-1727)

In 2002, Woods appeared to have changed his estimation of the width of the universe. In his preface to the 2002 USA edition of Reason in Revolt, Woods offers his support to a mainstream re-working of the old speculative cyclical Big Bang theory. The idea that the universe goes through cycles consisting of a Big Bang followed billions of years later by a Big Crunch had been first suggested in the 1930s, soon after observation suggested our universe had a hot dense origin a few billion years ago. Woods embraces the theory advanced in 2002 by prominent physicists Paul Steinhardt and Neil Turok, or more correctly, Woods embraces the theory as reported in the popular media. Woods asserts that Steinhardt and Turok’s theory is fully compliant with dialectical materialism, subject to experimental proof, purely because these two physicists, at least in their popular presentation, talked about a universe infinite in time.

Steinhardt and Turok’s cyclical big bang theory proposes that the universe goes through a perpetual motion of Big Bangs followed by what they term “big splats” as the universe reaches the end of the cycle. Woods, in 2002, thus continues to defend an infinity of time, but not an infinity of space, which expands and contracts perpetually with each cycle, according to the model. Are we to conclude that Woods now concedes that dialectical materialism does not prescribe to the universe an infinity of space, as he originally asserted in 1995 when Reason in Revolt was published?

Nicolas of Cusa argued that the universe is infinite because god is infinite. Today the concept of an infinite god in infinite space is a commonplace concept. Nicolas of Cusa developed this concept from the ideas originating with the ancient Greek idealist philosopher Plato and the school of philosophy which Plato established. Cusa argued against the existing scholasticism based on the Aristotelian model of the finite universe, which the Catholic church embraced at that time.

Thomas Diggs (1546-95), an early supporter of Copernicus, was the first modern European astronomer to argue that the universe was infinite. He said it reflected the greatness of god, although the church at the time objected that an infinite universe left no room for heaven. This theme, that god was infinite and that the universe should reflect this, began to be adopted by the most far-sighted ‘theorists’ of the day, who had broken from Aristotle’s influence, although it was not until the end of the nineteenth century that it became an uncontested commonplace viewpoint.

William Shakespeare, a family friend of Diggs, reflected the conflicting views of the universe in many allusions (some quite obscure) in Hamlet. John Barrow cites, in The Infinite Book, a mention of the concept of infinite space in one of Hamlet’s declamations: “I could be bounded in a nutshell, and count myself a king of infinite space.”  (Hamlet, Act II, scene ii)

Speculation about an infinite universe lacked a basis in fact, but was linked to abstract religious considerations. The old concept that the universe consisted of concentric spheres began to break down. Giordano Bruno (1548-1600) was burned at the stake after refusing to recant his belief in an infinite universe. He claimed that there was no limit to the power of god and that god could have created an infinite universe.

Thus is the excellence of God magnified and the greatness of his kingdom made manifest; he is glorified not in one, but in countless suns; not in a single earth, a single world, but in a thousand thousand, I say in an infinity of worlds. (On the Infinite Universe and Worlds, 1584)

Bruno introduced many ideas that became commonplace in the later centuries, such as that space with its infinite worlds extends without limit in all directions and it has no central point. Bruno also suggested that life exists on other planets.

Bruno was a Neo-Platonist mystic with no understanding of astronomy, and today the concept of an infinite universe is often credited to Copernicus. What is called the Copernican principle – that the sun-centred solar system occupies no special place in the universe, and that the sun is one of many stars – is perhaps better credited to Bruno.

Among Newton’s influences was his contemporary, Henry More (1614–87). More was one of the leading philosophers of the influential group of philosophical ‘divines’, now known as the Cambridge Platonists, who broke with Aristotelian tradition. More believed (not unlike Hegel), that space was infinite, since infinite, immaterial space is analogous to god, who was an infinitely extended spirit.

In 1654, just a few years before Newton observed an apple fall and wondered whether the same attraction of the apple to the earth might keep the moon in tow, William Charleton wrote, in opposition to Aristotle, that time “flow[s] on eternally in the same calm and equal tenor” and is distinct from any measure of it. (Stanford University’s Stanford Encyclopaedia of Philosophy website: Newton’s Views on Space, Time and Motion) These views on time, once again, can be attributed to the influence of the thoroughly idealist philosopher Plato.

Newton’s infinite, absolute space and time

But it was Newton who most certainly set in motion what became our ‘common sense’ ideas about the universe, until the advent of Einstein’s theories and then the Big Bang cosmology. Newton’s general views on infinite time and space were essentially the same as these contemporaries. In the closing discussion in his Principia, Newton explains why he regards space and time to be infinite and absolute:

by existing always and every where, [god] constitutes duration and space. Since every particle of space is always, and every indivisible moment of duration is every where, certainly the Maker and Lord of all things cannot be never and no where. (Principia, book three, General Scholium, p1,158)

For Newton, infinite absolute space was a meaningful concept for these reasons. Gottfried Leibniz, the German philosopher and mathematician and one of the most prominent of Newton’s scientific contemporaries in Europe, opposed this view. There was a long-running, bitter dispute between the two. Newton must take most of the blame for the bitterness, but the debate extended over a wide range of issues and continued for decades among the most prominent scientists of Europe.

Woods cannot, in fact, distinguish between Newton and Einstein on these questions. Woods argues that “the greatness of Einstein” was to reveal the relative character of “the ‘absolute truths’ of classical Newtonian mechanics”, but adds that the “relative aspect of time, was, however, not new. It was thoroughly analysed by Hegel”. (p147) This view cannot be supported. The examples given have no bearing on the meaning of Einstein’s relativity in relation to time, the origin of which will be touched on very briefly in its proper historical context. Woods later gives examples such as: “A year on earth is not the same as a year on Jupiter” (p158), and so forth, in a series of irrelevant commonplaces, which never escape from Newtonian physics.

Contradictions in Newton’s beliefs: absolute space

In fact, Newton grasped these issues more profoundly, since he also understood Galileo’s principle that we experience space as relative and admitted that he had failed to provide evidence of his belief in absolute space.

In the opening Scholium, or discussion, of his Principia, Newton asserts: “Absolute space, in its own nature, without regard to anything external, remains always similar and immovable.” He also discusses relative space, which he assumes takes place in absolute unmovable space. “Relative space is some movable dimension or measure of absolute space.” But Newton admits that absolute space cannot be detected: “… the parts of that immovable [absolute] space, in which these motions are performed, do by no means come under the observation of our senses.” Newton ruminates that “the thing is not altogether desperate” and provides a range of arguments and suggests experiments that might detect absolute space.

But Newton’s absolute space is undetectable because the Newtonian concept of absolute space is false. It is relative space on which Newton’s laws of motion are based.

ScientistMotion UniverseInfinity
AristotleAbsoluteAbsoluteFiniteInfiniteDenied actual infinite
GalileoRelativeRelativeFinite (assumed)Infinite (assumed)Showed paradoxes of infinite
NewtonAbsoluteAbsoluteInfiniteInfiniteGod as infinite
Table 3. Schematic summary of Newton’s views added to table 2.

Aristotle: Denied the existence of space & time outside universe (= relative)

Newton: Newton’s Laws of motion were based on relative space & time; he assumed absolute space & time were real but undetected

Problems with Newton’s universal gravity

Newton admitted he had no idea what formed the basis of the mysterious “action at a distance” by which his universal gravity binds tiny planets in the vastness of space in their orbit round the sun. In his concluding General Scholium of his Principia, he famously says:

But hitherto I have not been able to discover the causes of those properties of gravity from the phenomena, and I frame no hypotheses.

  More frankly, in a letter to Richard Bentley in 1693, Newton writes that action at a distance is “so great an absurdity that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it”. (Quoted in Newton: Philosophical Writings, Cambridge University Press, p102) Woods falls into it.

Newton’s rival, Leibniz, argued that Newton’s universal gravityhad an “occult quality”. “The fundamental principle of reasoning”, Leibniz emphasised, “is, nothing is without cause,” yet Newton, “is admitting that no cause underlies the truth that a stone falls towards the Earth.” (Quoted by James Gleick, Issac Newton, p156)

In a damning letter Leibniz wrote:

“Thus the ancients and the moderns, who own that gravity is an occult quality, are in the right, if they mean by it that there is a certain mechanism unknown to them, whereby all bodies tend towards the centre of the earth.”

Referring specifically to Newton, Leibniz continues, “if they mean that the thing is performed without any mechanism by a simple primitive quality, or by a law of God, who produces that effect without using any intelligible means, it is an unreasonable occult quality, and so very occult, that it is impossible that it should ever be clear, though an angel, or God himself, should undertake to explain it. (Leibniz, Philosophical Writings, 112, quoted by Andrew Janiak in Newton as Philosopher, p7, footnote 14)

Newton did not necessarily disagree on this point, however vehemently he and his followers disputed with Leibniz. It is now widely recognised that Newton spent a great deal of time on what would now be classed as the occult, particularly alchemy. The economist John Maynard Keynes, who acquired many of Newton’s writings on alchemy, stated: “Newton was not the first of the age of reason: he was the last of the magicians.” (The Collected Writings of John Maynard Keynes, Volume X, pp 363-4) 

The reason he frames no hypotheses, Newton says, in the above quoted passage from his Principia, is because hypotheses, “whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy”. Science had not yet fully separated itself from alchemy, astrology and the occult. Newton rules out neither mechanical nor occult qualities to explain the action of gravity at a distance but he does rule out hypotheses. He was searching for proof, not hypotheses, and he was not able to discover any explanation for his universal gravitation, despite a considerable amount of investigation into the occult. Nevertheless, Keynes is not entirely correct. The Principia, more than any other work of the era, was defining the new ground of experimental physics and mathematical proof and, in addition, replacing an interventionist god with a god that designed the physical universe along rational and universal principles only at the moment of creation.

The mechanists of the period were “labouring to banish occult influences – mysterious action without contact,” James Gleick points out in his biography of Newton. Yet “Action at a distance, across the void, smacked of magic. Occult explanations were supposed to be forbidden.” (Issac Newton, p96, p142)  How did gravity mysteriously act on bodies completely remote from them, with no intervening substance? Hegel chides Newton for not developing laws which go beyond a mere description of the actual mechanics of gravity’s effects. “Even Newton’s proofs,” he says, somewhat stretching the point, are “nothing more than mere jugglery and window-dressing” (Science of Logic, p273), especially those which merely gave mathematical expression to the motion of the planets which Johannes Kepler had already discovered.

It was Einstein’s general theory of relativity that eventually resolved this paradox, by showing how space and time are bent (“warped”) by mass and energy. It is this warped path in space-time that the planets follow. There is no force acting at a distance through the void on the planets. The planets do not depart from Newton’s first law, which says that no object will depart from a straight path unless a force compels it to change direction. No force is acting on the planets to make them move from a straight path, but the space-time they inhabit is itself bent, as viewed from the perspective of the solar system, and all paths bend with it. In the dark vastness of space, the planets follow curved paths because space and time are bent by the sun’s gravitational effect. It is a stunning discovery, both mathematically and experimentally proven.

No longer could space and time, mass and energy, be treated as absolutely independent of one another. The sun’s great mass dimples the space-time around it so that the planets ploughing through space-time naturally follow the curvature of space-time around the sun. Thus Newton’s occult force which acts at a distance is replaced with a material effect. In scientific terminology, the Newtonian term ‘gravitational force’ is replaced with the term ‘gravitational effect’. Yet Woods disparages Einstein’s general theory of relativity and wants to return to Newton. To save science from mysticism, he wants to deliver it to the occult.

The near century that lies between Galileo’s discovery of the moons of Jupiter and Newton’s publication of the Principia is a remarkable period. Galileo demolished Aristotle and showed that there was corruption in the spheres – the universe must have had a beginning and an end. He further showed that space was relative and that the earth went round the sun, and stood on trial before the Inquisition. Eight decades later Newton reasserted that space and time were absolute and re-established a universe that was infinite in space and time, so long as god was the Prime Mover.

Problems of the infinite: starlight

Not all scientists in Newton’s time, however, accepted an infinity of space and time. Newton’s contemporary, Edmund Halley, who was the first to calculate the orbit of a comet using Newton’s laws, attempted to refute “the ancient notion, some have of late entertained, of the eternity of all things”. (Quoted in Stephen Jay Gould, Eight Little Piggies, p175)

This did not mean, as has been supposed, that Halley was a creationist. On the contrary, Halley refused to take The Bible literally. John Flamsteed, the Astronomer Royal of that time, opposed Halley’s appointment to a post at Oxford University, saying he would “corrupt the youth of the university”.

Halley required evidence, and there was neither evidence for the biblical creation, nor for an infinite universe. There was evidence against in both cases, however. Halley noted a serious contradiction in the concept of an infinite universe:

I have heard it urged that if the number of fixed stars were more than finite, the whole superficies of their apparent sphere would be luminous. (Quoted by John Barrow, The Infinite Book,p151)

In other words, if the universe was infinite and therefore populated with an infinity of stars, the night sky should be brilliantly illuminated, as if it were day. This contradiction was rediscovered by Wilhelm Olbers (1758-1840), and became known as Olbers’ paradox. Despite many attempts, no explanation of this paradox (such as interstellar dust, distance, etc), in the context of a universe infinite in space and time, has been successful.

Suppose you are in a deep forest with an infinite amount of trees. Every line of sight soon ends up at a tree. But if you are in a small wood with a finite amount of scattered trees, every line of sight does not end up at a tree. We live in a universe that has a finite amount of scattered stars and galaxies, with great voids where there are no stars or galaxies.

Problems of the infinite: gravitational collapse

Woods contrasts his version of infinite space with that of Einstein’s, which he says was “closed” and “static”. This is not true. Einstein’s theory allows for both an open and a closed universe, and makes no claims that the universe is static. It was Newton who developed a view of an infinite universe in a “static or a permanent state of equilibrium”, as Woods puts it.

If space is finite, Newton correctly argues, gravity would make stars move “towards all the matter on the inside and by consequence fall down to the middle of the whole space and there compose one great spherical mass.”

But, Newton reasons, in infinite space it might be possible to position each star so precisely that it is equally attracted by all on all sides. Then, argued Newton, the stars would not be able to fall into one another. But only a divine power could position the stars so exactly, as Newton explains:

but that there should be a Central particle so accurately placed in the middle as to be always equally attracted on all sides and thereby continue without motion, seems to me a supposition fully as hard as to make the sharpest needle stand upright on its point upon a looking glass. For if the very mathematical centre of the central particle be not accurately in the very mathematical centre of the attractive power of the whole mass, the particle will not be attracted equally on all sides…

Yet I grant it possible, at least by a divine power… they would continue in that posture without motion for ever, unless put into new motion by the same power. (Letters to Richard Bentley, 1692-3)

No scientific solution (as opposed to a spiritual one which invoked the hand of god to initially set things in motion) could be found to this apparent contradiction between the theory of gravity, Newton’s greatest scientific discovery, and an infinite universe, Newton’s unshakable belief.

Newton saw that the problem of gravitational collapse is posed for any system, finite or infinite, however dynamic or static, so long as it contains matter.

It makes no difference if there is a “continual process of movement and change, which involves periodic explosions, expansion and contraction, life and death”. (p189) Or whether, “Long periods of apparent equilibrium are interrupted by violent explosions.” (p215) Whichever scenario you choose, continual movement or interrupted equilibrium, neither scenario avoids the issue. Gravitational attraction between places of equilibrium, or expansion and contraction, would pull them together over a period of time that would be a blink of an eye compared to an infinity of time, as Newton foresaw.

What is the answer to the conundrum of gravitational collapse? Why has all the matter in space not collapsed in on itself in the universe?

Expansion of space

The definitive answer came in 1929-31 with Edwin Hubble’s earth-shaking discoveries. Hubble provided the first evidence that the universe is expanding. Using powerful telescopes, Hubble showed that galaxies are generally receding from one another and from us, not simply moving this way and that. Hubble also noticed another remarkable fact that was far more significant.

It appeared that space itself was expanding. Hubble’s results showed a universe expanding in such a way that clusters of galaxies move away from ours at a speed that increases with distance. Galaxies are not all receding from us at around 700 miles per second – 2.5 million miles per hour – as Woods nonchalantly says. (p155) In general, at 100 million light-years away, galaxy clusters are moving away from us at 5.5 million miles per hour, while those at 200 million light years are moving away at twice as fast, at 11 million miles an hour, and at 300 million lights years away, they are moving away three times as fast. (Brian Greene, The Fabric of the Cosmos, p229)

Why is this? If a “great explosion”, as Woods calls the Big Bang (p189), had torn apart some pre-existing primordial mass – the equivalent on a much larger scale of a star going supernova – then the speeds of the different objects observed would tend to be related to their masses, with the lightest pieces being thrown further with the greatest motion, compared to the heaviest. There would at least be a great variation in speeds. Hubble did not find this.

Instead, Hubble saw the universal orchestration of an orderly expansion. Hubble recognised that this could only be explained if what was expanding was space itself.

In the same way, when a cake stuffed with raisins rises in the oven, the raisins (the equivalent of galaxies) move apart from one another in a simple relationship determined by the surrounding cake mixture – in particular, the amount of self-raising flour in the mixture. If the cake explodes, one sees quite a different dynamic.

It is this expansion of space which is such a significant indication of a hot, dense origin of the universe and of space-time itself. The evidence is not consistent with what Woods calls a “great explosion” taking place in infinite space and time. (The term ‘Big Bang’ is a mischievous misnomer, which amuses astrophysicists but trips up Woods. Ironically, it was first coined by Fred Hoyle, who believed to the end of his life that the universe was infinite in space and time but was forced to admit that the Big Bang was the only existing satisfactory explanation for astronomical experimental data. Hoyle used the term derisively, and was perfectly aware of how misleading it was.)

Where gravity is strong enough to counteract it, it is thought that this expansion of space is halted. Within galaxies and some clusters of galaxies, for instance, this expansion of space is overcome and gravity has taken over. Nevertheless, as a whole, the universe is expanding and gravity has been unable to overcome this expansion, and thus has been unable to cause the entire universe to collapse into “one great spherical mass”.

By the end of the nineteenth century, so ingrained in common sense was the concept of an infinite universe (whether containing within it regions of expansion and contraction or equilibrium), that even Einstein, who seemed to question every common sense conception, did not at first question it, and tried to solve the problems which Newton pondered. Only hard scientific evidence provided by Hubble and reinforced by countless observations since, caused Einstein to abandon the concept of an infinite universe.

Woods does not seem to understand the nature of the problem: “The Achilles’ heel of Einstein’s static, closed universe is that it would inevitably collapse in on itself because of the force of gravity.” (p204) Woods does not seem to realise that this is also the Achilles’ heel of his universe where “Long periods of apparent equilibrium are interrupted by violent explosions.”

In his 1917 paper, Cosmological Considerations on the General Theory of Relativity, Einstein considers the problem, and ruminates that “if we really have to regard the universe as being of infinite spatial extent”, then, “It seems hardly possible to surmount these difficulties on the basis of the Newtonian theory.”  This is because Newton’s infinite universe suffers the same Achilles’ heel.

Einstein suggests that, “if it were possible to regard the universe as a continuum which is finite (closed) with respect to spatial dimensions”, a solution can be found, but only if there was a repulsive force, which he termed a cosmological constant, which could counteract gravity.

After learning that the universe was expanding so that gravity is currently being overcome by the expansion, Einstein called the addition of the cosmological constant to his general theory of relativity his “greatest mistake”. A cosmological constant could not in any case keep the universe in equilibrium, it was found. Recently, in a further twist, it has transpired that a repulsive force, or something akin to it, from an unknown source, appears to exist in the universe, since the universe’s expansion seems to be accelerating under its influence.

Why does Woods suggest that the problem of gravitational collapse affects only a closed universe? Is he obscuring from Reason in Revolt’s readers this significant and widely known contradiction: that a universe infinite in time and space would inevitably collapse under its own weight? Or is he simply unfamiliar with the science?

Next: Kant’s cosmology and Engels’ commentary