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Reference: The Nature of the Physical World

This paper presents Chapter VIII (section 3) from the book THE NATURE OF THE PHYSICAL WORLD by A. S. EDDINGTON. The contents of this book are based on the lectures that Eddington delivered at the University of Edinburgh in January to March 1927.

The paragraphs of original material are accompanied by brief comments in color, based on the present understanding.  Feedback on these comments is appreciated.

The heading below links to the original materials.

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Plurality of Worlds

I will here put together the present astronomical evidence as tQ the habitability of other worlds. The popular idea that an answer to this question is one of the main aims of the study of celestial objects is rather disconcerting to the astronomer. Anything that he has to contribute is of the nature of fragmentary hints picked up in the course of investigations with more practicable and commonplace purposes. Nevertheless, the mind is irresistibly drawn to play with the thought that somewhere in the universe there may be other beings “a little lower than the angels” whom Man may regard as his equals—or perhaps his superiors.

It is idle to guess the forms that life might take in conditions differing from those of our planet. If I have rightly understood the view of palaeontologists, mammalian life is the third terrestrial dynasty—Nature’s third attempt to evolve an order of life sufficiently flexible to changing conditions and fitted to dominate the earth. Minor details in the balance of circumstances must greatly affect the possibility of life and the type of organism destined to prevail. Some critical branch-point in the course of evolution must be negotiated before life can rise to the level of consciousness. All this is remote from the astronomer’s line of study. To avoid endless conjecture I shall assume that the required conditions of habitability are not unlike those on the earth, and that if such conditions obtain life will automatically make its appearance.

Science still needs to fill the gap between physics and biology.

We survey first the planets of the solar system; of these only Venus and Mars seem at all eligible. Venus, so far as we know, would be well adapted for life similar to ours. It is about the same size as the earth, nearer the sun but probably not warmer, and it possesses an atmosphere of satisfactory density. Spectroscopic observation has unexpectedly failed to give any indication of oxygen in the upper atmosphere and thus suggests a doubt as to whether free oxygen exists on the planet; but at present we hesitate to draw so definite an inference. If transplanted to Venus we might perhaps continue to live without much derangement of habit— except that I personally would have to find a new profession, since Venus is not a good place for astronomers. It is completely covered with cloud or mist. For this reason no definite surface markings can be made out, and it is still uncertain how fast it rotates on its axis and in which direction the axis lies. One curious theory may be mentioned though it should perhaps not be taken too seriously. It is thought by some that the great cavity occupied by the Pacific Ocean is a scar left by the moon when it was first disrupted from the earth. Evidently this cavity fulfils an important function in draining away superfluous water, and if it were filled up practically all the continental area would be submerged. Thus indirectly the existence of dry land is bound up with the existence of the moon. But Venus has no moon, and since it seems to be similar to the earth in other respects, it may perhaps be inferred that it is a world which is all ocean—where fishes are supreme. The suggestion at any rate serves to remind us that the destinies of organic life may be determined by what are at first sight irrelevant accidents.

The sun is an ordinary star and the earth is an ordinary planet, but the moon is not an ordinary satellite. No other known satellite is anything like so large in proportion to the planet which it attends. The moon contains about 1/80 part of the mass of the earth which seems a small ratio; but it is abnormally great compared with other satellites. The next highest ratio is found in the system of Saturn whose largest satellite Titan has 1/4000 of the planet’s mass. Very special circumstances must have occurred in the history of the earth to have led to the breaking away of so unusual a fraction of the mass. The explanation proposed by Sir George Darwin, which is still regarded as most probable, is that a resonance in period occurred between the solar tides and the natural free period of vibration of the globe of the earth. The tidal deformation of the earth thus grew to large amplitude, ending in a cataclysm which separated the great lump of material that formed the moon. Other planets escaped this dangerous coincidence of period, and their satellites separated by more normal development. If ever I meet a being who has lived in another world, I shall feel very humble in most respects, but I expect to be able to boast a little about the moon.

Mars is the only planet whose solid surface can be seen and studied; and it tempts us to consider the possibility of life in more detail. Its smaller size leads to considerably different conditions; but the two essentials, air and water, are both present though scanty. The Martian atmosphere is thinner than our own but it is perhaps adequate. It has been proved to contain oxygen. There is no ocean; the surface markings represent, not sea and land, but red desert and darker ground which is perhaps moist and fertile. A conspicuous feature is the white cap covering the pole which is clearly a deposit of snow; it must be quite shallow since it melts away completely in the summer. Photographs show from time to time indubitable clouds which blot out temporarily large areas of surface detail; clear weather, however, is more usual. The air, if cloudless, is slightly hazy. W. H. Wright has shown this very convincingly by comparing photographs taken with light of different wave-lengths. Light of short wave-length is much scattered by haze and accordingly the ordinary photographs are disappointingly blurry. Much sharper surface-detail is shown when visual yellow light is employed (a yellow screen being commonly used to adapt visual telescopes for photography) ; being of longer wave-length the visual rays penetrate the haze more easily.* Still clearer detail is obtained by photographing with the long infra-red waves.

* It seems to have been a fortunate circumstance that the pioneers of Martian photography had no suitable photographic telescopes and had to adapt visual telescopes—thus employing visual (yellow) light which, as it turned out, was essential for good results.

Great attention has lately been paid to the determination of the temperature of the surface of Mars; it is possible to find this by direct measurement of the heat radiated to us from different parts of the surface. The results, though in many respects informative, are scarcely accurate and accordant enough to give a definite idea of the climatology. Naturally the temperature varies a great deal between day and night and in different latitudes; but on the average the conditions are decidedly chilly. Even at the equator the temperature falls below freezing point at sunset. If we accepted the present determinations as definitive we should have some doubt as to whether life could endure the conditions.

In one of Huxley’s Essays there occurs the passage “Until human life is longer and the duties of the present press less heavily I do not think that wise men will occupy themselves with Jovian or Martian natural history.” To-day it would seem that Martian natural history is not altogether beyond the limits of serious science. At least the surface of Mars shows a seasonal change such as we might well imagine the forest-clad earth would show to an outside onlooker. This seasonal change of appearance is very conspicuous to the attentive observer. As the spring in one hemisphere advances (I mean, of course, the Martian spring), the darker areas, which are at first few and faint, extend and deepen in contrast. The same regions darken year after year at nearly the same date in the Martian calendar. It may be that there is an inorganic explanation; the spring rains moisten the surface and change its colour. But it is perhaps unlikely that there is enough rain to bring about this change as a direct effect. It is easier to believe that we are witnessing the annual awakening of vegetation so familiar on our own planet.

The existence of oxygen in the Martian atmosphere supplies another argument in support of the existence of vegetable life. Oxygen combines freely with many elements, and the rocks in the earth’s crust are thirsty for oxygen. They would in course of time bring about its complete disappearance from the air, were it not that the vegetation extracts it from the soil and sets it free again. If oxygen in the terrestrial atmosphere is maintained in this way, it would seem reasonable to assume that vegetable life is required to play the same part on Mars. Taking this in conjunction with the evidence of the seasonal changes of appearance, a rather strong case for the existence of vegetation seems to have been made out.

If vegetable life must be admitted, can we exclude animal life? I have come to the end of the astronomical data and can take no responsibility for anything further that you may infer. It is true that the late Prof. Lowell argued that certain more or less straight markings on the planet represent an artificial irrigation system and are the signs of an advanced civilisation; but this theory has not, I think, won much support. In justice to the author of this speculation it should be said that his own work and that of his observatory have made a magnificent contribution to our knowledge of Mars; but few would follow him all the way on the more picturesque side of his conclusions.* Finally we may stress one point. Mars has every appearance of being a planet long past its prime; and it is in any case improbable that two planets differing so much as Mars and the Earth would be in the zenith of biological development contemporaneously.

*Mars is not seen under favourable conditions except from low latitudes and high altitudes. Astronomers who have not these advantages are reluctant to form a decided opinion on the many controversial points that have arisen.

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 Reference: The Nature of the Physical World

This paper presents Chapter VIII (section 1) from the book THE NATURE OF THE PHYSICAL WORLD by A. S. EDDINGTON. The contents of this book are based on the lectures that Eddington delivered at the University of Edinburgh in January to March 1927.

The paragraphs of original material are accompanied by brief comments in color, based on the present understanding.  Feedback on these comments is appreciated.

The heading below links to the original materials.

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The Sidereal Universe

The largest telescopes reveal about a thousand million stars. Each increase in telescopic power adds to the number and we can scarcely set a limit to the multitude that must exist. Nevertheless there are signs of exhaustion, and it is clear that the distribution which surrounds us does not extend uniformly through infinite space. At first an increase in light-grasp by one magnitude brings into view three times as many stars; but the factor diminishes so that at the limit of faintness reached by the giant telescopes a gain of one magnitude multiplies the number of stars seen by only 1.8, and the ratio at that stage is rapidly decreasing. It is as though we are approaching a limit at which increase of power will not bring into view very many additional stars.

Attempts have been made to find the whole number of stars by a risky extrapolation of these counts, and totals ranging from 3000 to 30,000 millions are sometimes quoted. But the difficulty is that the part of the stellar universe which we mainly survey is a local condensation or star-cloud forming part of a much greater system. In certain directions in the sky our telescopes penetrate to the limits of the system, but in other directions the extent is too great for us to fathom. The Milky Way, which on a dark night forms a gleaming belt round the sky, shows the direction in which there lie stars behind stars until vision fails. This great flattened distribution is called the Galactic System. It forms a disc of thickness small compared to its areal extent. It is partly broken up into subordinate condensations, which are probably coiled in spiral form like the spiral nebulae which are observed in great numbers in the heavens. The centre of the galactic system lies somewhere in the direction of the constellation Sagittarius; it is hidden from us not only by great distance but also to some extent by tracts of obscuring matter (dark nebulosity) which cuts off the light of the stars behind.

We must distinguish then between our local star-cloud and the great galactic system of which it is a part. Mainly (but not exclusively) the star-counts relate to the local star-cloud, and it is this which the largest telescopes are beginning to exhaust. It too has a flattened form—flattened nearly in the same plane as the galactic system. If the galactic system is compared to a disc, the local star-cloud may be compared to a bun, its thickness being about one-third of its lateral extension. Its size is such that light takes at least 2000 years to cross from one side to the other; this measurement is necessarily rough because it relates to a vague condensation which is probably not sharply separated from other contiguous condensations. The extent of the whole spiral is of the order 100,000 light years. It can scarcely be doubted that the flattened form of the system is due to rapid rotation, and indeed there is direct evidence of strong rotational velocity; but it is one of the unexplained mysteries of evolution that nearly all celestial bodies have come to be endowed with fast rotation.

Amid this great population the sun is a humble unit. It is a very ordinary star about midway in the scale of brilliancy. We know of stars which give at least 10,000 times the light of the sun; we know also of stars which give 1/10,000 of its light. But those of inferior light greatly outnumber those of superior light. In mass, in surface temperature, in bulk, the sun belongs to a very common class of stars; its speed of motion is near the average; it shows none of the more conspicuous phenomena such as variability which excite the attention of astronomers. In the community of stars the sun corresponds to a respectable middle-class citizen. It happens to be quite near the centre of the local starcloud; but this apparently favoured position is discounted by the fact that the star-cloud itself is placed very eccentrically in relation to the galactic system, being in fact near the confines of it. We cannot claim to be at the hub of the universe.

The contemplation of the galaxy impresses us with the insignificance of our own little world; but we have to go still lower in the valley of humiliation. The galactic system is one among a million or more spiral nebulae. There seems now to be no doubt that, as has long been suspected, the spiral nebulae are “island universes” detached from our own. They too are great systems of stars—or systems in the process of developing into stars—built on the same disc-like plan. We see some of them edgeways and can appreciate the flatness of the disc; others are broadside on and show the arrangement of the condensations in the form of a double spiral. Many show the effects of dark nebulosity breaking into the regularity -and blotting out the starlight. In a few of the nearest spirals it is possible to detect the brightest of the stars individually; variable stars and novae (or “new stars”) are observed as in our own system. From the apparent magnitudes of the stars of recognisable character (especially the Cepheid variables) it is possible to judge the distance. The nearest spiral nebula is 850,000 light years away.

The galactic systems have disc-like structure because of a single axis of rotation. The atom may also have a single axis of rotation and a similar disc-like structure. In an atom the field-substance rotates forming a whirlpool. It becomes increasingly quantized as the center is approached.

From the small amount of data yet collected it would seem that our own nebula or galactic system is exceptionally large; it is even suggested that if the spiral nebulae are “islands” the galactic system is a “continent”. But we can scarcely venture to claim premier rank without much stronger evidence. At all events these other universes are aggregations of the order of 100 million stars.

Again the question raises itself, How far does this distribution extend? Not the stars this time but universes stretch one behind the other beyond sight. Does this distribution too come to an end? It may be that imagination must take another leap, envisaging super-systems which surpass the spiral nebulae as the spiral nebulae surpass the stars. But there is one feeble gleam of evidence that perhaps this time the summit of the hierarchy has been reached, and that the system of the spirals is actually the whole world. As has already been explained the modern view is that space is finite— finite though unbounded. In such a space light which has travelled an appreciable part of the way “round the world” is slowed down in its vibrations, with the result that all spectral lines are displaced towards the red. Ordinarily we interpret such a red displacement as signifying receding velocity in the line of sight. Now it is a striking fact that a great majority of the spirals which have been measured show large receding velocities often exceeding 1000 kilometres per second. There are only two serious exceptions, and these are the largest spirals which must be nearer to us than most of the others. On ordinary grounds it would be difficult to explain why these other universes should hurry away from us so fast and so unanimously. Why should they shun us like a plague? But the phenomenon is intelligible if what has really been observed is the slowing down of vibrations consequent on the light from these objects having travelled an appreciable part of the way round the world. On that theory the radius of space is of the order twenty times the average distance of the nebulae observed, or say 100 million light years. That leaves room for a few million spirals; but there is nothing beyond. There is no beyond—in spherical space “beyond” brings us back towards the earth from the opposite direction.*

*A very much larger radius of space (10¹¹ light years) has recently been proposed by Hubble; but the basis of his calculation, though concerned with spiral nebulae, is different and to my mind unacceptable. It rests on an earlier theory of closed space proposed by Einstein which has generally been regarded as superseded. The theory given above (due to W. de Sitter) is, of course, very speculative, but it is the only clue we possess as to the dimensions of space.

The space is finite because the field-substance has limits. Beyond field-substance there is no substance. There is only emptiness. In this emptiness there is no space or time either. It is a challenge to conceive of this emptiness.

Light is a form of field-substance. It is, therefore, limited. As light approaches the limit it descends to the bottom of the electromagnetic spectrum. It does not exist in emptiness.

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Reference: The Nature of the Physical World

This paper presents Chapter VII (section 4) from the book THE NATURE OF THE PHYSICAL WORLD by A. S. EDDINGTON. The contents of this book are based on the lectures that Eddington delivered at the University of Edinburgh in January to March 1927.

The paragraphs of original material are accompanied by brief comments in color, based on the present understanding.  Feedback on these comments is appreciated.

The heading below links to the original materials.

.

Non-Empty Space

The law that the directed radius is constant does not apply to space which is not completely empty. There is no longer any reason to expect it to hold. The statement that the region is not empty means that it has other characteristics besides metric, and the metre rod can then find other lengths besides curvatures to measure itself against. Referring to the earlier (sufficiently approximate) expression of the law, the ten principal coefficients of curvature are zero in empty space but have non-zero values in non-empty space. It is therefore natural to use these coefficients as a measure of the fullness of space.

There is material-space that characterizes the extent of material-substance. Then there is field-space that characterizes the extent of field-substance. There is no space without substance. Hence there is no such thing as empty space.

The measure of fullness of “field-space” comes from quantization of the field-substance. The vanishing ten principal coefficients of the general theory of relativity may then be applied to the field-substance because of the great variations in quantization that goes to zero. The inertia of material-substance remains pretty much finite and constant.

One of the coefficients corresponds to mass (or energy) and in most practical cases it outweighs the others in importance. The old definition of mass as “quantity of matter” associates it with a fullness of space. Three other coefficients make up the momentum—a directed quantity with three independent components. The remaining six coefficients of principal curvature make up the stress or pressure-system. Mass, momentum and stress accordingly represent the non-emptiness of a region in so far as it is able to disturb the usual surveying apparatus with which we explore space—clocks, scales, light-rays, etc. It should be added, however, that this is a summary description and not a full account of the non-emptiness, because we have other exploring apparatus—magnets, electroscopes, etc.—which provide further details. It is usually considered that when we use these we are exploring not space, but a field in space. The distinction thus created is a rather artificial one which is unlikely to be accepted permanently. It would seem that the results of exploring the world with a measuring scale and a magnetic compass respectively ought to be welded together into a unified description, just as we have welded together results of exploration with a scale and a clock. Some progress has been made towards this unification. There is, however, a real reason for admitting a partially separate treatment; the one mode of exploration determines the symmetrical properties and the other the antisymmetrical properties of the underlying world-structure (see p. 236).

There is material-space and field-space, but no “material in space” or “field in space”. That is where the “particles in void” perspective goes wrong. That perspective generates error with unnecessary concepts, such as, aether. Space is a general term for field-substance. We need to develop appropriate surveying apparatus to measure the quantization characteristic of space.

The curvature of the general theory of relativity represents the twisting of space. The ten coefficients, which describe this twisting of space are: mass (1 coefficient), momentum (3 coefficients) and stress (6 coefficients). We need to figure out how these coefficients may help us determine quantization.

Objection has often been taken, especially by philosophical writers, to the crudeness of Einstein’s initial requisitions, viz. a clock and a measuring scale. But the body of experimental knowledge of the world which Einstein’s theory seeks to set in order has not come into our minds as a heaven-sent inspiration; it is the result of a survey in which the clock and the scale have actually played the leading part. They may seem very gross instruments to those accustomed to the conceptions of atoms and electrons, but it is correspondingly gross knowledge that we have been discussing in the chapters concerned with Einstein’s theory. As the relativity theory develops, it is generally found desirable to replace the clock and scale by the moving particle and light-ray as the primary surveying appliances; these are test bodies of simpler structure. But they are still gross compared with atomic phenomena. The light-ray, for instance, is not applicable to measurements so refined that the diffraction of light must be taken into account. Our knowledge of the external world cannot be divorced from the nature of the appliances with which we have obtained the knowledge. The truth of the law of gravitation cannot be regarded as subsisting apart from the experimental procedure by which we have ascertained its truth.

Clock and scale as surveying apparatus apply to the measurement of material-time and material-space respectively. Using these, the theory of relativity discovered anomaly when light, which represents field-substance, was compared to material-substance. Einstein’s general theory of relativity, thus, sets the stage up for more refined explanations.

The conception of frames of space and time, and of the non-emptiness of the world described as energy, momentum, etc., is bound up with the survey by gross appliances. When they can no longer be supported by such a survey, the conceptions melt away into meaninglessness. In particular the interior of the atom could not conceivably be explored by a gross survey. We cannot put a clock or a scale into the interior of an atom. It cannot be too strongly insisted that the terms distance, period of time, mass, energy, momentum, etc., cannot be used in a description of an atom with the same meanings that they have in our gross experience. The atomic physicist who uses these terms must find his own meanings for them—must state the appliances which he requisitions when he imagines them to be measured. It is sometimes supposed that (in addition to electrical forces) there is a minute gravitational attraction between an atomic nucleus and the satellite electrons, obeying the same law as the gravitation between the sun and its planets. The supposition seems to me fantastic; but it is impossible to discuss it without any indication as to how the region within the atom is supposed to have been measured up. Apart from such measuring up the electron goes as it pleases “like the blessed gods”.

The concepts of distance, period of time, mass, energy, momentum, stress, etc., have been designed for material-substance. These concepts cannot be applied to space or, field-substance, without some modification. That modification requires knowledge of quantization of field-substance.

We have reached a point of great scientific and philosophic interest. The ten principal coefficients of curvature of the world are not strangers to us; they are already familiar in scientific discussion under other names (energy, momentum, stress). This is comparable with a famous turning-point in the development of electromagnetic theory. The progress of the subject led to the consideration of waves of electric and magnetic force travelling through the aether; then it flashed upon Maxwell that these waves were not strangers but were already familiar in our experience under the name of light. The method of identification is the same. It is calculated that electromagnetic waves will have just those properties which light is observed to have; so too it is calculated that the ten coefficients of curvature have just those properties which energy, momentum and stress are observed to have. We refer here to physical properties only. No physical theory is expected to explain why there is a particular kind of image in our minds associated with light, nor why a conception of substance has arisen in our minds in connection with those parts of the world containing mass.

We erroneously assign mass to field-particles, such as, electron, proton, neutron etc. They do not have mass (structured inertia); they have charge (unstructured quantization). Mass-energy equivalence really refers to the equivalence between mass and charge. Such equivalence does not mean that mass and charge can be interchanged.

The concepts, which were traditionally developed for material-substance, must be reviewed before they can be applied to field-substance.

This leads to a considerable simplification, because identity replaces causation. On the Newtonian theory no explanation of gravitation would be considered complete unless it described the mechanism by which a piece of matter gets a grip on the surrounding medium and makes it the carrier of the gravitational influence radiating from the matter. Nothing corresponding to this is required in the present theory. We do not ask how mass gets a grip on space-time and causes the curvature which our theory postulates. That would be as superfluous as to ask how light gets a grip on the electromagnetic medium so as to cause it to oscillate. The light is the oscillation; the mass is the curvature. There is no causal effect to be attributed to mass; still less is there any to be attributed to matter. The conception of matter, which we associate with these regions of unusual contortion, is a monument erected by the mind to mark the scene of conflict. When you visit the site of a battle, do you ever ask how the monument that commemorates it can have caused so much carnage?

The lines of force concept appropriately explains how a piece of matter gets a grip on the surrounding medium and makes it the carrier of the gravitational influence radiating from the matter. This brings Newtonian mechanics in consistency with the general theory of relativity when that theory is expressed in terms of quantization.

The philosophic outcome of this identification will occupy us considerably in later chapters. Before leaving the subject of gravitation I wish to say a little about the meaning of space-curvature and non-Euclidean geometry.

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