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Eddington 1927: The Scale of Time

September 11, 2018 – 2:17 PM
time-illusion

Reference: The Nature of the Physical World

This paper presents Chapter VIII (section 2) 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 Scale of Time

The corridor of time stretches back through the past. We can have no conception how it all began. But at some stage we imagine the void to have been filled with matter rarified beyond the most tenuous nebula. The atoms sparsely strewn move hither and thither in formless disorder.

Behold the throne
Of Chaos and his dark pavilion spread
Wide on the wasteful deep.

Then slowly the power of gravitation is felt. Centres of condensation begin to establish themselves and draw in other matter. The first partitions are the star-systems such as our galactic system; sub-condensations separate the star-clouds or clusters; these divide again to give the stars.

The power of gravitation leads to condensation. Condensation is increase in quantization and inertia. Gravitation accomplishes this by bringing substance together into equilibrium.

Evolution has not reached the same development in all parts. We observe nebulae and clusters in different stages of advance. Some stars are still highly diffuse; others are concentrated like the sun with density greater than water; others, still more advanced, have shrunk to unimaginable density. But no doubt can be entertained that the genesis of the stars is a single process of evolution which has passed and is passing over a primordial distribution. Formerly it was freely speculated that the birth of a star was an individual event like the birth of an animal. From time to time two long extinct stars would collide and be turned into vapour by the energy of the collision; condensation would follow and life as a luminous body would begin all over again. We can scarcely affirm that this will never occur and that the sun is not destined to have a second or third innings; but it is clear from the various relations traced among the stars that the present stage of existence of the sidereal universe is the first innings. Groups of stars are found which move across the sky with common proper motion; these must have had a single origin and cannot have been formed by casual collisions. Another abandoned speculation is that lucid stars may be the exception, and that there may exist thousands of dead stars for every one that is seen shining. There are ways of estimating the total mass in interstellar space by its gravitational effect on the average speed of the stars; it is found that the lucid stars account for something approaching the total mass admissible and the amount left over for dark stars is very limited.

Stars are formed through condensation of primordial material. The speed of the star depends on its inertia, but gravitational effects may contribute to some modification.  

Biologists and geologists carry back the history of the earth some thousand million years. Physical evidence based on the rate of transmutation of radioactive substances seems to leave no escape from the conclusion that the older (Archaean) rocks in the earth’s crust were laid down 1200 million years ago. The sun must have been burning still longer, living (we now think) on its own matter which dissolves bit by bit into radiation. According to the theoretical time-scale, which seems best supported by astronomical evidence, the beginning of the sun as a luminous star must be dated five billion (5 . 1012) years ago. The theory which assigns this date cannot be trusted confidently, but it seems a reasonably safe conclusion that the sun’s age does not exceed this limit. The future is not so restricted and the sun may continue as a star of increasing feebleness for 50 or 500 billion years. The theory of sub-atomic energy has prolonged the life of a star from millions to billions of years, and we may speculate on processes of rejuvenescence which might prolong the existence of the sidereal universe from billions to trillions of years. But unless we can circumvent the second law of thermodynamics—which is as much as to say unless we can find cause for time to run backwards —the ultimate decay draws surely nearer and the world will at the last come to a state of uniform changelessness.

Does this prodigality of matter, of space, of time, find its culmination in Man?

I doubt if the universe will decay to a state of ultimate changelessness. There will always be moving patterns obeying the universal laws.

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By vinaire | Tagged , | Comments (0)

Eddington 1927: The Sidereal Universe

September 11, 2018 – 10:28 AM

 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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By vinaire | Tagged | Comments (0)

Eddington 1927: Non-Euclidean Geometry

September 10, 2018 – 9:06 PM
non-Euclid

Reference: The Nature of the Physical World

This paper presents Chapter VII (section 5) 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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Non-Euclidean Geometry

I have been encouraging you to think of space-time as curved; but I have been careful to speak of this as a picture, not as a hypothesis. It is a graphical representation of the things we are talking about which supplies us with insight and guidance. What we glean from the picture can be expressed in a more non-committal way by saying that space-time has non-Euclidean geometry. The terms “curved space” and “non-Euclidean space” are used practically synonymously; but they suggest rather different points of view. When we were trying to conceive finite and unbounded space (p. 81) the difficult step was the getting rid of the inside and the outside of the hypersphere. There is a similar step in the transition from curved space to non-Euclidean space—the dropping of all relations to an external (and imaginary) scaffolding and the holding on to those relations which exist within the space itself.

If you ask what is the distance from Glasgow to New York there are two possible replies. One man will tell you the distance measured over the surface of the ocean; another will recollect that there is a still shorter distance by tunnel through the earth. The second man makes use of a dimension which the first had put out of mind. But if two men do not agree as to distances, they will not agree as to geometry; for geometry treats of the laws of distances. To forget or to be ignorant of a dimension lands us into a different geometry. Distances for the second man obey a Euclidean geometry of three dimensions; distances for the first man obey a non-Euclidean geometry of two dimensions. And so if you concentrate your attention on the earth’s surface so hard that you forget that there is an inside or an outside to it, you will say that it is a two-dimensional manifold with non-Euclidean geometry; but if you recollect that there is three-dimensional space all round which affords shorter ways of getting from point to point, you can fly back to Euclid after all. You will then “explain away” the non-Euclidean geometry by saying that what you at first took for distances were not the proper distances. This seems to be the easiest way of seeing how a non-Euclidean geometry can arise— through mislaying a dimension—but we must not infer that non-Euclidean geometry is impossible unless it arises from this cause.

Euclidean space is material-space; Euclidean geometry applies to material-substance. We would think of non-Euclidean space as the field-space; non-Euclidean geometry then applies to field-substance. The additional “dimension” that comes into play here is the dimension of quantization, which is “consistency” of energy as a substance, and not as a frequency of disturbance in some imaginary substance called aether.

NOTE: Consistency is a degree of density, firmness, viscosity, etc.

In our four-dimensional world pervaded by gravitation the distances obey a non-Euclidean geometry. Is this because we are concentrating attention wholly on its four dimensions and have missed the short cuts through regions beyond? By the aid of six extra dimensions we can return to Euclidean geometry; in that case our usual distances from point to point in the world are not the “true” distances, the latter taking shorter routes through an eighth or ninth dimension. To bend the world in a super-world of ten dimensions so as to provide these short cuts does, I think, help us to form an idea of the properties of its non-Euclidean geometry; at any rate the picture suggests a useful vocabulary for describing those properties. But we are not likely to accept these extra dimensions as a literal fact unless we regard non-Euclidean geometry as a thing which at all costs must be explained away.

Of the two alternatives—a curved manifold in a Euclidean space of ten dimensions or a manifold with non-Euclidean geometry and no extra dimensions— which is right? I would rather not attempt a direct answer, because I fear I should get lost in a fog of metaphysics. But I may say at once that I do not take the ten dimensions seriously; whereas I take the non- Euclidean geometry of the world very seriously, and I do not regard it as a thing which needs explaining away. The view, which some of us were taught at school, that the truth of Euclid’s axioms can be seen intuitively, is universally rejected nowadays. We can no more settle the laws of space by intuition than we can settle the laws of heredity. If intuition is ruled out, the appeal must be to experiment—genuine open-minded experiment unfettered by any preconception as to what the verdict ought to be. We must not afterwards go back on the experiments because they make out space to be very slightly non-Euclidean. It is quite true that a way out could be found. By inventing extra dimensions we can make the non-Euclidean geometry of the world depend on a Euclidean geometry of ten dimensions; had the world proved to be Euclidean we could, I believe, have made its geometry depend on a non-Euclidean geometry of ten dimensions. No one would treat the latter suggestion seriously, and no reason can be given for treating the former more seriously.

Energy is “field-substance” that is much less substantial than the material-substance.  The quantization levels are very distinct for field-substance. The ten coefficients of the general theory of relativity describe the twisting of the field-substance as it “moves” in the dimension of quantization.

I do not think that the six extra dimensions have any stalwart defenders; but we often meet with attempts to reimpose Euclidean geometry on the world in another way. The proposal, which is made quite unblushingly, is that since our measured lengths do not obey Euclidean geometry we must apply corrections to them—cook them —till they do. A closely related view often advocated is that space is neither Euclidean nor non-Euclidean; it is all a matter of convention and we are free to adopt any geometry we choose.*

* As a recent illustration of this attitude I may refer to Bertrand Russell’s Analysis of Matter, p. 78—a book with which I do not often seriously disagree. “Whereas Eddington seems to regard it as necessary to adopt Einstein’s variable space, Whitehead regards it as necessary to reject it. For my part, I do not see why we should agree with either view; the matter seems to be one of convenience in the interpretation of formulae.” Russell’s view is commended in a review by C. D. Broad. See also footnote, p. 142.

Naturally if we hold ourselves free to apply any correction we like to our experimental measures we can make them obey any law; but was it worth while saying this? The assertion that any kind of geometry is permissible could only be made on the assumption that lengths have no fixed value—that the physicist does not (or ought not to) mean anything in particular when he talks of length. I am afraid I shall have a difficulty in making my meaning clear to those who start from the assumption that my words mean nothing in particular; but for those who will accord them some meaning I will try to remove any possible doubt. The physicist is accustomed to state lengths to a great number of significant figures; to ascertain the significance of these lengths we must notice how they are derived; and we find that they are derived from a comparison with the extension of a standard of specified material constitution. (We may pause to notice that the extension of a standard material configuration may rightly be regarded as one of the earliest subjects of inquiry in a physical survey of our environment.) These lengths are a gateway through which knowledge of the world around us is sought. Whether or not they will remain prominent in the final picture of world-structure will transpire as the research proceeds; we do not prejudge that. Actually we soon find that space-lengths or time-lengths taken singly are relative, and only a combination of them could be expected to appear even in the humblest capacity in the ultimate world-structure. Meanwhile the first step through the gateway takes us to the geometry obeyed by these lengths—very nearly Euclidean, but actually non-Euclidean and, as we have seen, a distinctive type of non-Euclidean geometry in which the ten principal coefficients of curvature vanish. We have shown in this chapter that the limitation is not arbitrary; it is a necessary property of lengths expressed in terms of the extension of a material standard, though it might have been surprising if it had occurred in lengths defined otherwise. Must we stop to notice the interjection that if we had meant something different by length we should have found a different geometry? Certainly we should; and if we had meant something different by electric force we should have found equations different from Maxwell’s equations. Not only empirically but also by theoretical reasoning, we reach the geometry which we do because our lengths mean what they do.

The INERTIA is a measure of how substantial the material-substance is. As electromagnetic radiation has come to be recognized as field-substance, we use the term CONSISTENCY (quantization), to describe substantialness of field-substance. In this discussion, we shall use inertia to refer to the substantialness of substance in general.

The substance has natural motion which is balanced by its inertia. The object, thus balanced within itself, has a natural velocity. This velocity increases as the inertia decreases. Because inertia is absolute, so is this natural velocity. It then ascertains a certain combination of space and time for the object. We are not free to make our experimental measures obey any law.

Material-space has definite lengths that may be considered absolute. Any variation of length from one material to the next shall depend on the variation of inertia. However this variation happens to be insignificant in the material domain.

The variation becomes significant only in the field domain. But that is accounted for by consistency (quantization, substantialness). The ten principal coefficients of curvature vanish as the consistency approaches zero.

I have too long delayed dealing with the criticism of the pure mathematician who is under the impression that geometry is a subject that belongs entirely to him. Each branch of experimental knowledge tends to have associated with it a specialised body of mathematical investigations. The pure mathematician, at first called in as servant, presently likes to assert himself as master; the connexus of mathematical propositions becomes for him the main subject, and he does not ask permission from Nature when he wishes to vary or generalise the original premises. Thus he can arrive at a geometry unhampered by any restriction from actual space measures; a potential theory unhampered by any question as to how gravitational and electrical potentials really behave; a hydrodynamics of perfect fluids doing things which it would be contrary to the nature of any material fluid to do. But it seems to be only in geometry that he has forgotten that there ever was a physical subject of the same name, and even resents the application of the name to anything but his network of abstract mathematics. I do not think it can be disputed that, both etymologically and traditionally, geometry is the science of measurement of the space around us; and however much the mathematical superstructure may now overweigh the observational basis, it is properly speaking an experimental science. This is fully recognised in the “reformed” teaching of geometry in schools; boys are taught to verify by measurement that certain of the geometrical propositions are true or nearly true. No one questions the advantage of an unfettered development of geometry as a pure mathematical subject; but only in so far as this subject is linked to the quantities arising out of observation and measurement, will it find mention in a discussion of the Nature of the Physical World.

Any geometry is constrained by the consistency of substance it is representing. Geometry cannot be specified arbitrarily independent of substance. Geometry does not exist in the absence of substance.

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Final Comments

Euclidean space is material-space; Euclidean geometry applies to material-substance. We would think of non-Euclidean space as the field-space; non-Euclidean geometry then applies to field-substance or energy. The additional “dimension” that comes into play here is the dimension of quantization, or “consistency” of energy. We move away from the idea of energy being a disturbance in aether.

Energy is a substance that is much less substantial than the material substance. The consistency of energy increases as one moves up the energy spectrum. Matter appears at the upper end of this spectrum, while space appears at the lower end.

The INERTIA is a measure of how substantial the material-substance is. It becomes CONSISTENCY (quantization) at the level of energy. In this discussion, we shall use inertia to refer to the substantialness of substance in general.

The inertia expresses itself as resistance to motion and therefore, it marks the duration of the substance at a location. Thus relative inertia, in a sense, affects relative motion. The higher the inertia or consistency, the lesser would the substance appear to move by itself.

The object is thus balanced within itself, and therefore, seems ti possess a natural velocity. This velocity increases as the inertia decreases. Since the value of inertia for a substance may be determines absolute, so can be its natural velocity just like the velocity of light. It then ascertains that a certain combination of space and time goes along with the inertia or consistency of substance. We are not free to regulate the velocity of substance without also regulating its inertia.

Material-space has definite lengths whole units may be considered absolute. Any variation of the unit of length from one material to the next is likely to depend on the variation of its inertia. However this variation is insignificant in the material domain. It becomes significant only in the energy domain.

The ten coefficients of the general theory of relativity seems to describe the curvatures of energy in the dimension of inertia (consistency). These coefficients vanish as the inertia approaches zero.

Any geometry is constrained by the consistency of substance it is representing. Geometry cannot be specified arbitrarily independent of substance. Geometry does not exist in the absence of substance.

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By vinaire | Comments (1)

Eddington 1927: Non-Empty Space

September 10, 2018 – 4:31 PM
Space

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.

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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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Eddington 1927: Predictions from the Law

September 10, 2018 – 7:47 AM
Solar system

Reference: The Nature of the Physical World

This paper presents Chapter VII (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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Predictions from the Law

I suppose that it is at first rather staggering to find a law supposed to control the movements of stars and planets turned into a law finicking with the behaviour of measuring rods. But there is no prediction made by the law of gravitation in which the behaviour of measuring appliances does not play an essential part. A typical prediction from the law is that on a certain date 384,400,000 metre rods laid end to end would stretch from the earth to the moon. We may use more circumlocutory language, but that is what is meant. The fact that in testing the prediction we shall trust to indirect evidence, not carrying out the whole operation literally, is not relevant; the prophecy is made in good faith and not with the intention of taking advantage of our remissness in checking it.

We have condemned the law of gravitation as a put-up job. You will want to know how after such a discreditable exposure it can still claim to predict eclipses and other events which come off.

A famous philosopher has said—”The stars are not pulled this way and that by mechanical forces; theirs is a free motion. They go on their way, as the ancients said, like the blessed gods.” *

*Hegel, Werke (1842 Ed.), Bd. 7, Abt. 1, p. 97.

This sounds particularly foolish even for a philosopher; but I believe that there is a sense in which it is true.

The stars have natural motion balanced by their inertia. From space to the nucleus of the atoms, which make up the star, there is increasing quantization. Thus, there are lines of force extending outward from the star and thinning out into space, all around the star. The more massive and dense is the star, the more numerous are these lines of force. Here “force” refers to the gradient of quantization.

We have already had three versions of what the earth is trying to do when it describes its elliptic orbit around the sun.

  1. It is trying to go in a straight line but it is roughly pulled away by a tug emanating from the sun.
  2. It is taking the longest possible route through the curved space-time around the sun.
  3. It is accommodating its track so as to avoid causing any illegal kind of curvature in the empty space around it.

We now add a fourth version.

  1. (4) The earth goes anyhow it likes.

It is not a long step from the third version to the fourth now that we have seen that the mathematical picture of empty space containing “illegal” curvature is a sheer impossibility in a world surveyed from within. For if illegal curvature is a sheer impossibility the earth will not have to take any special precautions to avoid causing it, and can do anything it likes. And yet the non-occurrence of this impossible curvature is the law (of gravitation) by which we calculate the track of the earth!

There are lines of force extending out both from the earth and the sun, and they meet in between. There is a natural tendency to even out the gradient of quantization, and this draws the two bodies toward each other. However, the natural speed of earth is much greater than that of the sun because of its much lower inertia. As a result, the earth gets into an orbit around the sun.

The earth and the sun are keeping a balance between their inertia and the gradient of quantization in the intervening space. This is the law of gravitation.

The key to the paradox is that we ourselves, our conventions, the kind of thing that attracts our interest, are much more concerned than we realise in any account we give of how the objects of the physical world are behaving. And so an object which, viewed through our frame of conventions, may seem to be behaving in a very special and remarkable way may, viewed according to another set of conventions, be doing nothing to excite particular comment. This will be clearer if we consider a practical illustration, and at the same time defend version (4).

You will say that the earth must certainly get into the right position for the eclipse next June (1927); so it cannot be free to go anywhere it pleases. I can put that right. I hold to it that the earth goes anywhere it pleases. The next thing is that we must find out where it has been pleased to go. The important question for us is not where the earth has got to in the inscrutable absolute behind the phenomena, but where we shall locate it in our conventional background of space and time. We must take measurements of its position, for example, measurements of its distance from the sun. In Fig. 6, SS1 shows the ridge in the world which we recognise as the sun; I have drawn the earth’s ridge in duplicate (EE1} EE2 ) because I imagine it as still undecided which track it will take. If it takes EE1 we lay our measuring rods end to end down the ridges and across the valley from S1 to E1 , count up the number, and report the result as the earth’s distance from the sun. The measuring rods, you will remember, adjust their lengths proportionately to the radius of curvature of the world. The curvature along this contour is rather large and the radius of curvature small. The rods therefore are small, and there will be more of them in $1E1 than the picture would lead you to expect. If the earth chooses to go to E2 the curvature is less sharp; the greater radius of curvature implies greater length of the rods. The number needed to stretch from S± to E2 will not be so great as the diagram at first suggests; it will not be increased in anything like the proportion of S1E2 to S1E1 in the figure. We should not be surprised if the number turned out to be the same in both cases. If so, the surveyor will report the same distance of the earth from the sun whether the track is EE1 or EE2 . And the Superintendent of the Nautical Almanac who published this same distance some years in advance will claim that he correctly predicted where the earth would go.

And so you see that the earth can play truant to any extent but our measurements will still report it in the place assigned to it by the Nautical Almanac. The predictions of that authority pay no attention to the vagaries of the god-like earth; they are based on what will happen when we come to measure up the path that it has chosen. We shall measure it with rods that adjust themselves to the curvature of the world. The mathematical expression of this fact is the law of gravitation used in the predictions.

Perhaps you will object that astronomers do not in practice lay measuring rods end to end through interplanetary space in order to find out where the planets are. Actually the position is deduced from the light rays. But the light as it proceeds has to find out what course to take in order to go “straight”, in much the same way as the metre rod has to find out how far to extend. The metric or curvature is a sign-post for the light as it is a gauge for the rod. The light track is in fact controlled by the curvature in such a way that it is incapable of exposing the sham law of curvature. And so wherever the sun, moon and earth may have got to, the light will not give them away. If the law of curvature predicts an eclipse the light will take such a track that there is an eclipse. The law of gravitation is not a stern ruler controlling the heavenly bodies; it is a kindhearted accomplice who covers up their delinquencies.

I do not recommend you to try to verify from Fig. 6 that the number of rods in S1E1 (full line) and S1E2 (dotted line) is the same. There are two dimensions of space-time omitted in the picture besides the extra dimensions in which space-time must be supposed to be bent; moreover it is the spherical, not the cylindrical, curvature which is ,the gauge for the length. It might be an instructive, though very laborious, task to make this direct verification, but we know beforehand that the measured distance of the earth from the sun must be the same for either track. The law of gravitation, expressed mathematically by Gμν = λgμν means nothing more nor less than that the unit of length everywhere is a constant fraction of the directed radius of the world at that point. And as the astronomer who predicts the future position of the earth does not assume anything more about what the earth will choose to do than is expressed in the law Gμν = λgμν, so we shall find the same position of the earth, if we assume nothing more than that the practical unit of length involved in measurements of the position is a constant fraction of the directed radius. We do not need to decide whether the track is to be represented by EE1 or EE2 , and it would convey no information as to any observable phenomena if we knew the representation.

Eddington is basically saying that the distances are relative and the absolute scenario is impossible to know. This is the unscientific interpretation of the theory of relativity. In the scientific interpretation, the velocity of light is an absolute. It acts as absolute reference point from which to measure the values of inertia of the earth and the sun, and the quantization of the intervening space. The rest then follows.

I shall have to emphasise elsewhere that the whole of our physical knowledge is based on measures and that the physical world consists, so to speak, of measure-groups resting on a shadowy background that lies outside the scope of physics. Therefore in conceiving a world which had existence apart from the measurements that we make of it, I was trespassing outside the limits of what we call physical reality. I would not dissent from the view that a vagary which by its very nature could not be measurable has no claim to a physical existence. No one knows what is meant by such a vagary. I said that the earth might go anywhere it chose, but did not provide a “where” for it to choose; since our conception of “where” is based on space measurements which were at that stage excluded. But I do not think I have been illogical. I am urging that, do what it will, the earth cannot get out of the track laid down for it by the law of gravitation. In order to show this I must suppose that the earth has made the attempt and stolen nearer to the sun; then I show that our measures conspire quietly to locate it back in its proper orbit. I have to admit in the end that the earth never was out of its proper orbit;** I do not mind that, because meanwhile I have proved my point. The fact that a predictable path through space and time is laid down for the earth is not a genuine restriction on its conduct, but is imposed by the formal scheme in which we draw up our account of its conduct.

** Because I can attach no meaning to an orbit other than an orbit in space and time, i.e. as located by measures. But I could not assume that the alternative orbit would be meaningless (inconsistent with possible measures) until I tried it.

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