Science, Materialism, Mysticism

Einstein's Four-dimensional Continuum

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On April 18, 1955, passed away the most original scientific thinker the world has seen. A host of exceptionally revolutionary ideas were let loose by him from the beginning of his scientific career in the early years of this century up to the very end of his life: it is not more than a couple of years since he propounded his last version of what he called the Unified Field Theory, the fullest expansion of the relativity theory with which his name burst on us in 1904. Perhaps the most notable contribution by his work to the world of thought is the concept of a four-dimensional continuum of space-time to replace Newton's of a three-dimensional space and a one- dimensional time. But the exact significance of it is seldom realised. It is worthwhile glancing at it from several sides.

There are thinkers who tell us: "The new concept has so revolutionised the view of reality in physics that science would do well to look in a direction beyond materialism." Others say: "It is indeed revolutionary, but its revolutionariness is confined to physics and has no bearing on a philosophical view of reality. By itself it has neither a materialistic nor a non-materialistic implication." A third group declares: "The question of any implication is idle, for the concept stands for no reality at all, not even a physical one. It is simply a geometrico-mathematical picture, an abstract symbolic representation of the connection between phenomena of space and time as they figure revolutionarily in Einstein's physics. It is a mere convenience or device for calculation." A fourth school brings another sort of damper: "It is a revolution, yet not quite a radical one. Physics always recognised four-dimensionality when it took four co-ordinates - three of space and one of time - to specify an event. Relativity theory has added some important details of far-reaching usefulness, but the general framework is still the same."

To strike on the true significance of the new concept we

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should follow briefly the development of relativity theory by which a revolution was effected in Newton's physics. Newton had held that though every known material mass is in motion and therefore no motion of matter can be measured against any material mass at rest, we are not confined to merely relative measurements among moving masses: there is a motion absolute and not relative, for there is a universal space which is at absolute and not relative rest and which can serve as a frame of reference for measuring absolute motion. Further, if absolute motion is a valid concept, we can know what moment can be regarded as being the same moment at different points of space. For, it is by signals from point to point that time at different points can be expressed and even the fastest signal - light - takes a finite time to travel and, with the possibility of measuring the absolute speed of light against static space, we can allow in an absolute manner for the time-lag between the sending of a light signal from one point and the receiving of it at another. Calculating the various time-lags we can calculate what moment anywhere is simultaneous with a moment here: simultaneity throughout the universe is a valid concept. That is to say, time can be thought of as uniform everywhere. Absolute time follows from absolute motion and absolute space.

Soon after Newton's life a substance called the ether filling all space was considered inevitable for the explanation of the wavelike movement of light. Because of certain astronomical observations it was also considered as fixed in space. For all practical purposes the ether and absolute space became synonyms. So an opportunity was provided in a concrete form to measure motion against a frame absolutely 3t rest. A most delicate experiment, repeatedly performed, to "measure earth's motion through the ether in the direction of its own orbit showed that somehow the absolute measurement always evaded us. This null result of the Michelson- Morley experiment Lorentz and Fitzgerald sought to explain "Y calculating that physical changes always take place in our measuring instrument in such a way that they constitute a

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minus quantity compensating for and cancelling the plug quantity necessary for the absolute measurement. Thus the static ether and through it absolute space were saved for physics.

Einstein launched a double attack on this interpretation. He said that if no absolute measurement can ever be obtained, then whatever be the reason for the failure the Newtonian concept of motion and space is quite gratuitous and serves no useful purpose in physics. Further, if absolute motion cannot be measured, the same moment at different points of space can never be absolutely ascertained. Universal simultaneity is an "unobservable". The concept of absolute time is metaphysics and has no useful place in physics. In addition to the practical in utility, Einstein proved the logical in utility of the three absolutes. He said that the situation of a minus quantity exactly compensating for and cancelling the required plus quantity would arise even if we made measurements against a body moving relatively to another body but acceptable for convenience's sake as at rest relatively to our own motion. So if any compensation or cancellation is taking place, it will not uniquely distinguish an absolutely static frame from a relatively static one. To suppose that the compensation or cancellation conceals an absolute ether or space is logically unwarranted. Again, since in all relativities of motion between two bodies the mathematical terms are not altered by our taking the first body to be at rest and the second to be moving or vice versa, the compensation or cancellation can be thought of as happening on either body and does not indicate which of the two bodies is having its motion measured in reference to a static space or ether. This ambiguity leaves us no logical ground for talking of a space-absolute in reference to which the positive quantity of a body's absolute motion is somehow precisely compensated for or cancelled by a negative quantity. And, of course, once absolute motion and absolute space are logically superfluous, absolute time also logically fades out of the picture.

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Measurements of space and time were proved by Einstein to differ with the rates of relative motion. No more can we speak of motion occurring within an unaffected space and time: no more are space and time universal uniform receptacles in which matter in motion exists. There are as many spaces and times as there are relative rates of matter's motion. The sole bond between them is a transformation-rule formulated by Lorentz when he tried to co-ordinate the compensating or cancelling factors proposed by him before Einstein's appearance. The new relativistic interpretation which did not deny those factors but dispensed with their implications of an absolute Newtonian background took over Lorentz's rule as a means of passing correctly from one relative reading to another. It also, by the way, threw light on a somewhat obscure term in Lorentz's rule. The rule allowed for a change in the instrument of measuring space, the shortening of a rod's length in the direction of its motion, but could not explain a corresponding change which appeared to apply to the instrument of measuring time, the slowing down of the rhythm of a clock during its motion. Einstein legitimised the changing time-term since he clearly brought out the relativity of time no less than of space.

The first or restricted theory of relativity stopped here. It did not offer any new absolute or absolutes in place of the Newtonian ones. And those who regard as a mere mathematical device or convenience the four-dimensional continuum or space-time which was later suggested to be the appropriate Einsteinian absolute are evidently of the belief that only relativities really exist. The sole real revolution effected by Einstein is for them the joint difference which space- measurements and the time-measurement undergo according to the difference in motion-rate. Inasmuch as space and time together undergo this difference, unlike in Newton's system, these quantities figure revolutionarily in the system of Einstein, but space is space and time is time and no amount of hyphenating them can be anything save a purely formal affair: there can be no actual fusion of them. The so-

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called fusing is a useful picture or symbol of the Lorentz transformations which tell us how the space-numbers and the time-number vary with different co-ordinate systems and how the variations are mutually related.

The implication of this "formalist" view of the four- dimensional continuum is that though the Newtonian absolutes of space and time are abolished the relative space and time of Einstein are in fundamental nature the same as Newton's: Newton too was aware that at different stand- points different quantities are obtained for space and time and if he believed that the difference could be adjusted and a uniformity calculated in terms of absolute space and time it was because he did not know of the greater variations introduced by varied standpoints, but this cannot stop space and time from fundamentally differing from each other or involve their fusion.

The exponents of the "formalist" view, in further elaborating their thesis, exploit for their own ends the argument which is properly of the fourth school of interpretation. They inform us: "In a certain sense space and time have always constituted a four-dimensional continuum. Our experience in common life is that nothing happens at any place except at a particular time and nothing happens at any time except at a particular place: space and time are co-existent and inseparable. Similarly, science uses four numbers to describe events in nature. Positions are characterised by three numbers and the instant of an event is the fourth number. Four definite numbers correspond to every event: ergo, the world of events forms a four-dimensional continuum. Even the old physics never denied this. In the new physics the numbers undergo some interesting changes and we have to deal with them more jointly than before, but there is no four-dimensional continuum in a fundamentally different sense than before - a different sense which blurs our common experience that space is space and time is time. Relativity theory, studying them more penetratively and dealing with them more jointly than before, does not involve the equivalence of the space-

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co-ordinates with the time-co-ordinate. The former co-ordinates are defined physically wholly differently from the latter: a rod is used in the one case and a clock in the other."

Well, it is indeed true that the physical operations by which the numbers for space and time are obtained are entirely distinct and never fuse, but the rest of the "formal" view has little substance and when we understand its hollowness we shall learn to see this distinction in a proper light. To start with: it is illogical to say that Einstein's space and time are in fundamental nature the same as Newton's. Newton could pass to his absolutes because whatever relativities he acknowledged were of a certain sort: if for Einstein his own relativities did not differ from Newton's in a fundamental way he could have no ground for rejecting those absolutes: some mathematical adjustment would be possible. He could not pass to those absolutes because his relativities were different in fundamental nature. If they were thus different his space and time must also be so. The formalists recognise as much when they emphasise, though mistakenly, that in Einstein's physics as at first propounded there is no real absolute and that, unlike in Newton's physics, only relativities really exist here. But they deny a real Einsteinian absolute on account of missing the important point which emerged when Einstein stated his relativities and stopped short of any absolute.

Einstein stopped short not because any absolute was bound to be really inexistent: he did so because his own immediate aim was limited and he never looked in the direction of an absolute. However, one point emerged suggestively. If the relativities were not ultimate and if anything absolute could be found, it would not be in terms of motion, space and time as commonly understood. Another mode of putting this is: the absolute, if any, would not just raise, as those of Newton did, commonly understood motion, space and time to a universal plane of conception. And it would not for a simple reason: the relativities them- selves do not involve motion, space and time as commonly

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understood. They are more radical than Newton thought and the three terms in each relativity are knit together in a way utterly beyond Newton's thinking. To say that there are as many spaces and times as there are relative rates of motion does not merely abolish Newton's idea of space and time as universal uniform receptacles in which matter in motion exists. Over and above finding measurements of space and time to be variables of motion, it implies that the space and time of each frame of reference differ with motion in a close co-operation between themselves: when the space-numbers change, the time-number changes too and vice versa, as if space and time were quantities perfectly analogous though not of the same kind, instead of being as in Newton's physics non-analogous though never dissociated. Of course, for practical purposes the old division of the space-co-ordinates from the time-co-ordinate is valid: we can assign a la Newton relative space-co-ordinates but an absolute time-co-ordinate to any event within common experience. Only when the velocity of objects ceases to be small and comes close to that of light the time-co-ordinate no less than the space-co- ordinates are found relative and we have the observation of both space and time changing instead of the former alone doing so. But the joint change, though mostly unobserved, is always there as of two perfectly analogous quantities. In other words the two quantities depend on motion as if they were differentiations of one and the same quantity: the rod measuring space and the clock measuring time seem two distinguishable modes of measuring a single system of dimensions. Briefly, space and time appear to be somehow the same in spite of being dissimilar: they give the impression of being an identity-in-difference.

The revolution in physical concepts here is surely pro- founder than what the formalists make out. Although no absolute is yet on the scene, the relativities already suggest some kind of fusion in the nature of space and time. The suggestion, however, loomed a little remote until Minkowski put his mind to the relativities. And it loomed a little remote

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because no direct mathematical demonstration of the actual identity was present and because the fusion suggested in each set of space-number and time-number was not yet shown to be of any immediate utility in either mathematical practice or mathematical theory. Minkowski was the first to remedy these lacks by seeking in the suggested fusion an invariant behind the Lorentz-transformations connecting the variants that are the relativities - an invariant concealed like a thread on which the transformation-rule hung them like beads and taught us how to pass from one bead to another. He showed that the different observations of space and time about an event from frames of reference moving at different rates could yield a common invariant quantity, an absolute measurement of a non-Newtonian sort corresponding to the non-Newtonian relative measurements, if the time-measurement obtained within each frame of reference were subtracted from the space-measurement. Mathematically, this not only gave the invariant but also illuminated the nature of space and time. For, it is a platitude in mathematics that we cannot add one quantity to or subtract it from another without the two quantities being of the same kind. We can multiply one kind of quantity by another, as mass by velocity to give momentum. We can divide one kind of quantity by another, as energy by time to give horse-power. But we cannot add mass to velocity or subtract energy from time to give any physical quantity unless they are somehow identical. Similarly we cannot add inches to seconds or subtract seconds from inches unless we mean to imply that somehow the same entity is measured partly by a rod and partly by a clock.

The suggestion emerging from relativity theory that in a certain sense a single system of dimensions rather than two associated systems was being measured came to a clear focus in Minkowski's description of this system as a four-dimensional continuum in which space and time ceased to be separate and fused into one fundamental absolute: space- time. The single entity, space-time, could be split into two

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systems of dimensions by taking cross-sections, as it were, of it and the various ways in which we make the cross-section give the Einsteinian relativities. If we imagine a geometrical graph of the four-dimensional continuum, then the influence of the different rates of motion on the measurements of space and time will be shown in that the three axes or co-ordinates x, y, z of space and the one axis or co-ordinate t of time will be differently orientated. And the relations between these different sets of axes will be those contained in the Lorentz equations.

Minkowski's space-time is the inevitable background of the Einsteinian relativities. Einstein himself acknowledged it and later developed the concept of it geometrically far beyond Minkowski. We are not concerned at the moment with the development. Suffice it to say here that space-time is inherently implied by the relativities and is just as real or unreal as they. Even, in the sense that the invariant, the quantity on which there is agreement from all standpoints, is more real than the variants or the quantities about which there is disagreement from all standpoints, the universal quantity that is space-time has a greater reality than the space and time that figure in the relative readings.

Having demonstrated that the hyphenating of space and time is no purely formal affair we should exhibit in a proper light the undeniable distinction between them as proved by the wholly different manner in which the numbers for space and for time are obtained. The fact is that the hyphenating does not slur over the distinction. It is a mistake to turn the hyphenating to mean that a fourth dimension of space is welded on to the three known to us. Only if such a welding is signified the distinction may be said to suffer a slurring over. Unfortunately this significance is liable to be caught from the final form in which Minkowski stated his description of the four-dimensional continuum. There by a couple of mathematical operations he altered to a plus sign the minus sign between the space-numbers and the time-number and substituted the number of miles light travels in one second - a

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constant 186,000 in all frames of reference - for the one second itself, thus making the time-dimension equivalent to

space-dimension. The justification of these operations is that thus alone the four-dimensional continuum becomes the absolute of Einstein's relativities in the simplest form possible and best explains the facts of scientific observation and experiment. The operations are a brilliant act of analytic insight into the truth of physical nature and, together with the original formula of subtracting the time-measurement from the space-measurement, constitute one of the peak performances of mathematical genius in our day. But they do not really add a fourth space-dimension to the other three. The very need of those mathematical operations which brought about an "isotropy" (or similarity in all directions) is proof enough of a certain difference between the three components and the one component in spite of their fusion. A true fourth dimension of space would require no such strange treatment. The treatment is administered just because space-time is an irregular and not a regular four- dimensional continuum or, rather, because it is a four- dimensional continuum irregularly regular. To employ a phrase already used by us, it is by all tokens an identity-in- difference. The criticism that Minkowski overlooked the distinction between a rod and a clock would hold only if the fourth dimension were a regular one - that is to say, spatial.

But, we must add, the irregular element makes no odds to the revolutionary character of this four-dimensionality. It is erroneous to protest as the fourth school of interpreters do, that after all science always recognised four-dimensionality when it took four co-ordinates - three of space and one of time - to specify an event and that we have nothing quite radically revolutionary now. No doubt, the actual basic four- dimensionality of nature is the same in the day of Einstein and Minkowski as it was in that of Newton; but science's recognition of it in the past never took it for a fusion of space and time. Now alone we know what exactly should be meant by our regarding the world we live in as basically a four-

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dimensional continuum that figures in our immediate measurements as spatial and temporal quantities changing in a joint interdependent manner; for now alone can we speak of this continuum as being not of space and time but of space-time. The general framework is not at all still the same.

The fourth school of interpreters, no less than the third Or "formalist" group, is off the mark. Space-time is not only real: it is also a radically revolutionary reality.

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If Einstein's four-dimensional continuum of space-time is, as we have shown, a reality and a revolutionary one at that because of the actual fusion of space and time in it, is the revolution introduced by it confined to physics, with no bearing on a philosophical view of the world, or does it call for a look by us in a direction beyond materialism?

The actual fusion does not, of course, reduce time to a space-dimension: time is still time, but it acquires the proper­ties of space. A fourth dimension of space would break the limitations of the three space-dimensions: for instance, if one had a fourth space-dimension to move in, one would not be limited by being enclosed in a room covered in the directions of length, breadth and height, for one more direction would remain without any cover and one could enter the room from it. But the time-element would not be changed in any basic sense: time would continue to be a movement from past to present to future just as much as it is now in our normal vision of it. When the dimension of time enters into a four dimensional continuum and is welded on to space in the way in which within space itself the three dimensions of length, breadth and height are welded to one another, then it is not the spatial limitations of these dimensions that are broken. What are broken are the limitations of time itself for those dimensions - limitations due to time's being a separate dimension from them. If time is fused with space in the continuum whose mathematical structure is specified by

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Minkowski's elucidation of the background of Einstein's relativities, time without ceasing to be time gets spatialised. To put it more concretely: just as all points of space are co­existent, all instants of time are co-existent - the past and present and future of spatial points co-exist as if they them- selves were spread out in space. .

Our heads are bound to grow dizzy with this import. But that is no test of its not being the truth. Nor can truth stop being truth when our heads grow dizzier still on our under­standing what the scientific concept of causality and deter­minism becomes in connection with this import. Strict causality and determinism are there in the sense of an unseverable hanging together: the very word "continuum" ensures unbroken ness. But pre-relativity physics took cau­sality and determinism to be working from past to present to future. In the four-dimensional continuum of actually fused space and time, where the three times co-exist, there is evidently no one such unique direction for causality and determinism to work in. So the scientific use of causality and determinism may be considered as representing for practical purposes the truth only if the experience which leads us to this use is the sole one or the predominant one. It certainly is not the sole one. We have the experience in which we feel a sense of freewill: there we appear to be to some extent unbound by the past and creative of the future and able to re­create the past by depriving it of the effect the scientific use of causality and determinism would ascribe to it as inevitable. We have also the experience in which we feel a sense of goals or ends, of a purpose that seeks realisation as if from a future through the present and which, by causing the present, determines also the past which the present constantly becomes. The whole time-flow then seems in the direction opposite to that which is assumed by science. But, inasmuch as the latter is also never absent in our experience even when We have a sense of freewill and a sense of pre-existing and purpose-realising future and inasmuch as there has been no sure ground for not regarding the future as still to be born

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rather than as something already real and for regarding the present as co-existent with the past no less than with the future, we have allowed the experience leading to the scientific use of causality and determinism to bulk in our minds above any other. We have let this experience cast on the others a colour of unreality or lesser reality, things to be somehow brought into line with it. With the concept of the four-dimensional continuum we find that there is no reason to give that experience any predominance. So the direction dictated by that experience to causality and determinism can have only a certain degree of truth. Degrees of truth are possessed also by the directions suggested by our sense of freewill and our sense of pre-existing and purpose-realising future.

Perhaps the greatest degree of truth is given by what is actually our time-experience. What we know as time is a continuous present with projections into both the past and the future, projections concealed in the one case except in the form of memory and in the other except in the form of imaginative or predictive anticipation. The primary datum is the present, from which past and future are arrived at by means of theoretical constructions. If this is so, then in view of the impartiality of the four-dimensional continuum, our sense of limited freewill which is associated with the present may be taken by us as the truth predominantly supported by the absolute arrived at in Einsteinian physics.

We may even say that the four-dimensional continuum is precisely such as predominantly must support this truth in the world of threefold time-experience that is ours. For, what do we mean by a co-existence of past and present and future? Do we not mean an all-comprehensive Now, with no succes­sion of events - a Now of which our continuous present is a faint inkling?

And taking a cue from our own limited Now and its sense of freewill we may surmise that the comprehensive Now of the ordered totality of events in all the three times is an immense multiple creativity. Such a conception does full

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justice to both the truths involved in the irregular regularity ~f the four-dimensional continuum: the truth of space by which points stand together and the truth of time by which instants succeed each other - a co-existence coupled with dynamism so that the spread-out events of the three times are the signs of an ordering creativity immense and multiple though non-successive.

It is difficult not to think this creativity the physical counterpart or expression of the freewill of a cosmic con­sciousness. We have definitely to look beyond materialism if we accept Minkowski's fusion of space and time to be actual. And Einstein's general relativity theory, which came ten years after his special or restricted one, does not in the least forbid us to do so. What that theory does is just to link up material masses with the four-dimensional continuum: it establishes a certain relation between these masses and space-time in the sense that the amount of material mass is proportional to a degree of geometrical structure of space-time and that the accelerations of the masses can be calculated according to the overall space-time structure answering to the comparatively larger or smaller mass-amounts neigh­bouring one another. Thus the movements of the planets around the sun are said to be in accordance with the more dominating structure in space-time answering to the sun's greater mass than the one answering to the smaller masses of the planets. Newton's force of gravitation which was sup­posed to act directly from mass to mass is dispensed with and an entirely new notion comes in by which the state of space-time between the disproportionate masses explains their mutual "gravitational" behaviour - a new notion which has passed some crucial tests in which Newton's calculations proved wrong.

The state of space-time involved is called in technical mathematical language "curvature". Newton had considered space to be "flat": just as on a flat surface the natural motion, as well as the shortest line between two points, is straight, so also in flat space the natural motion is straight and a straight

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line is the "geodesic" or shortest distance between two points. Space thus considered is known as Euclidian. Al­though some geometricians in the nineteenth century had evolved non-Euclidian geometries of space, nobody ever imagined that these could correspond to reality. But when, as we saw, Minkowski set up the formula of an irregularly regular four-dimensional continuum, the minus sign of the fourth dimension prevented the geometrical properties from being quite Euclidian as they would have been if no irregular feature had been there. His geometry was semi-Euclidian or hyperbolic rather than non-Euclidian. However, it opened Einstein's eyes to further possibilities and, when he attempted to bring into his scheme the accelerated motion characteristic of "gravitational" effect, he applied to the four-dimensional continuum the spherical geometry of Riemann, the geometry which Riemann had extended to space of three or more dimensions from a curved surface instead of the Euclidian geometry which had been extended to space from a flat surface. Einstein discovered that in space-time the sim­plest analogue of the quantity which for a curved surface is termed "curvature" solved his problem if he made the curvature proportional in a certain manner to the amount of material mass present. The curvature of space-time calcu­lated in the region of the sun's neighbourhood gave in space the exact orbits of the planets and in time the exact change of speed-rhythm which the planets exhibit as they move nearer or farther from the sun in their various ellipses.

What bearing have the several features of the general relativity theory on the beyond-materialism interpretation? First, if the continuum is capable of geometrical structure, it must be "substantial" in some sense: the ordering, immense and multiple though non-successive, would represent not only a cosmic consciousness but also a cosmic being. The pointer away from materialism seems strengthened. Second­ly, the material masses by being brought into relation with the "substantial" continuum may themselves be thought not only integrated with it in one whole but also identical with

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certain characteristics of it and appearing otherwise by simply being a certain manifestation of it. Of course, until all the characteristics of matter, particularly its atomicity, are explicable in terms of space-time structure, we cannot affirm this last possibility. Signs, however, are not lacking to persuade us that we are on the right track. They are noticeable in connection with the invariant "interval" in space-time which is the absolute of the relative distances and durations.

Sullivan, in his Aspects of Science (Second Series) puts the case very well. "From this relation, the interval," he writes, "various complicated mathematical expressions may be built up by purely mathematical analysis. At a certain stage in this process we reach expressions which obey exactly the same equations as density, stress, momentum etc. Now these latter quantities, density and so on, form what a physicist means by a piece of matter. But the mathematical expressions derived from the interval refer to geometrical properties of the continuum - to its curvature, for example. What is the meaning of the fact that certain geometrical properties of the four-dimensional continuum and certain physical quantities, characteristic of matter, obey the same equations? The suggestion is that the physical quantities and the geometrical properties are the same thing ... "

Their being the same and yet seeming different is ex­plained by Sullivan in the immediately next phrase in terms that are a little doubtful. He states the above suggestion in other words as "that what we call matter is, indeed, only the way in which our minds perceive the existence of these geometrical peculiarities of the four-dimensional conti­nuum." No doubt, the human mind has a good deal of say in the perceptual experience that it has of reality; but the more balanced view would appear to be that the world of matter and of relative space and time is itself an actual manifestation of the four-dimensional continuum and certain aspects of this manifestation are discovered and interpreted by the human mind rather than completely created by it in response

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to that hidden reality. That reality and this manifestation have both of them the look of a physical counterpart or expression of a Conscious Being at work; so the granting of an "objective" status to the world of matter and of relative space and time does not diminish the primacy of Conscious­ness and what the human mind does in its perceptual experience is just to get into a particular sort of commu­nication with the ultimate Consciousness. All is play of Consciousness, but a complex multifold play. And part of the play is the actual existence of Sullivan's "matter" and of scientifically measured space and time as differentiations of one and the same quantity, differentiations which seem distinctions as of two quantities so long as an event is studied in reference to a frame in relative motion at a rate very far from that of light but which reveal their true nature as soon as velocities nearing that of light are met with. The world or perceptual experience is very different really from our older pre-Einsteinian picture of it, yet it still remains objective in a certain valid sense so far as the human mind is concerned.

But, objective or no, the main point stands that material properties appear to be basically identical with space-time structure. And we may add that the whole implication of Einstein's repeated effort to create a "unified field theory" taking into its sweep electro-magnetism no less than gravita­tion and accounting for the particle-nature of matter is this very point. So the curving that the general relativity theory gave to space-time has brought in its train a many-sided accession of strength to the interpreters who feel drawn by the special relativity theory beyond the confines of physics and beyond a materialistic world-view.

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