Reference: The Book of Physics
Note: The original text is provided below.
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Summary
It is difficult to answer any question about space unless we understand what space is. According to Einstein’s theory, space is “finite but unbounded.” But, that still does not define space. It just ties the space up with geometry, or some abstract shape. The features of space which we discover by experiment are extensions, i.e. lengths and distances. So space is like a network of distances.
Eddington says, “Distances are linkages whose intrinsic nature is inscrutable.” But distances are measured on some substance. Therefore, distances are comprehensible only in the context of substance. They have no meaning in themselves. If the surface of an object is curved it would affect the distance accordingly.
Eddington is defining space in terms of linkages between mathematical points. In reality, we have solid particles instead of mathematical points. As we cut these particles into smaller and smaller particles they ultimately reduce to a field of force without any particles. This field of force at first appears as the thick electronic field around the nucleus of an atom. As this thickness (consistency) of the field reduces it appears like an energy field, such as, light. As the consistency reduces further it appears as a field of thought. Volume increases as consistency decreases. The largest volume will be for the field of thought. Beyond thought there shall be a lack of substance, and, therefore, a lack of awareness.
Eddington is defining time as the view through a small window of a moving train. One sees sequence of events passing with a before and after. But if one climbs on the roof of the train, one sees the whole terrain laid out before one, with different elements having different durations. Science always uses a broad, universal viewpoint. From this viewpoint, time reduces to duration of substance. The duration of the substance decreases as its consistency decreases. The least duration shall be for the field of thought. Beyond thought there is no substance; therefore, there is no awareness of duration or time.
All confusion arises because the definitions of substance, space and time are not stated with scientific precision. The universe, as a whole, may have a certain volume and a certain duration, which defines the limits of its space and time. Beyond those limits there is no substance and no awareness. The universe may cycle through awareness and non-awareness.
Eddington says, “Travelling backwards into the past we find a world with more and more organisation.” That is just what appears in consciousness from a narrow viewpoint. That is not the case when one is looking from a universal viewpoint (see the train example above). From the universal viewpoint one sees a universe made up of matter, energy and thought, each with its different volume and duration. The substance has a spectrum, and so does space and time. It is a complex affair in a certain state of an overall equilibrium. That state of equilibrium is itself evolving. The subject of physics is an outcome of the evolution of thought. The current shortcoming of Physics is that it has yet to include thought as a substance in its considerations.
Materialism is a matter-centric viewpoint. This viewpoint is represented by the subject of physics as it stands today. There is a crack in this viewpoint as Einstein’s theory introduces energy as a substance. According to this theory, matter de-condenses into energy. Eddington is not happy with the idea that the universe started with a bang, but he doesn’t see that the idea of “Creator” alludes to thought being treated as a substance too, if physics has to gain a universal viewpoint.
The second law of thermodynamic seems to be limited as it does not include the influence of thought. Much still needs to be learned about thought as a substance. Ultimately, the conservation as well as the equilibrium of substance must include thought too. It is thought that must provide the counter-process by which radiation collects in space, evolves into electrons and protons, and begins star-building all over again.
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Comments
Space is defined by shape, or geometry as in mathematics. It is the shape of some substance. Similarly, Time is the duration of some substance. Both space and time have no relevance in the absence of substance. Without substance, there is no awareness either. Presence of space and time implies the presence of substance; and the presence of substance implies the presence of awareness.
Space and time are primary sensations that extend from the presence of substance. They make up the sense of awareness. As we look at substance as something substantial enough to be sensed, we discover that matter is not the only substance. Einstein extended the definition of substance to include energy. Now we are looking at the inclusion of thought as substance as well.
Once we do that we discover the spectrum of substance from matter to energy to thought that has wonderful implications as expressed in the summary above. We also discover that gravity is but the tendency of substance to align itself with surrounding substance according to its relative consistency.
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Original Text
I suppose that everyone has at some time plagued his imagination with the question, Is there an end to space? If space comes to an end, what is beyond the end? On the other hand the idea that there is no end, but space beyond space for ever, is inconceivable. And so the imagination is tossed to and fro in a dilemma. Prior to the relativity theory the orthodox view was that space is infinite. No one can conceive infinite space; we had to be content to admit in the physical world an inconceivable conception—disquieting but not necessarily illogical. Einstein’s theory now offers a way out of the dilemma. Is space infinite, or does it come to an end? Neither. Space is finite but it has no end; “finite but unbounded” is the usual phrase.
Infinite space cannot be conceived by anybody; finite but unbounded space is difficult to conceive but not impossible. I shall not expect you to conceive it; but you can try. Think first of a circle; or, rather, not the circle, but the line forming its circumference. This is a finite but endless line. Next think of a sphere—the surface of a sphere—that also is a region which is finite but unbounded. The surface of this earth never comes to a boundary; there is always some country beyond the point you have reached; all the same there is not an infinite amount of room on the earth. Now go one dimension more; circle, sphere—the next thing. Got that? Now for the real difficulty. Keep a tight hold of the skin of this hypersphere and imagine that the inside is not there at all—that the skin exists without the inside. That is finite but unbounded space.
No; I don’t think you have quite kept hold of the conception. You overbalanced just at the end. It was not the adding of one more dimension that was the real difficulty; it was the final taking away of a dimension that did it. I will tell you what is stopping you. You are using a conception of space which must have originated many million years ago and has become rather firmly embedded in human thought. But the space of physics ought not to be dominated by this creation of the dawning mind of an enterprising ape. Space is not necessarily like this conception; it is like—whatever we find from experiment it is like. Now the features of space which we discover by experiment are extensions, i.e. lengths and distances. So space is like a network of distances. Distances are linkages whose intrinsic nature is inscrutable; we do not deny the inscrutability when we apply measure numbers to them—2 yards, 5 miles, etc.—as a kind of code distinction. We cannot predict out of our inner consciousness the laws by which code-numbers are distributed among the different linkages of the network, any more than we can predict how the code-numbers for electromagnetic force are distributed. Both are a matter for experiment.
If we go a very long way to a point A in one direction through the universe and a very long way to a point B in the opposite direction, it is believed that between A and B there exists a linkage of the kind indicated by a very small code-number; in other words these points reached by travelling vast distances in opposite directions would be found experimentally to be close together. Why not? This happens when we travel east and west on the earth. It is true that our traditional inflexible conception of space refuses to admit it; but there was once a traditional conception of the earth which refused to admit circumnavigation. In our approach to the conception of spherical space the difficult part was to destroy the inside of the hypersphere leaving only its three-dimensional surface existing. I do not think that is so difficult when we conceive space as a network of distances. The network over the surface constitutes a self-supporting system of linkage which can be contemplated without reference to extraneous linkages. We can knock away the constructional scaffolding which helped us to approach the conception of this kind of network of distances without endangering the conception.
We must realise that a scheme of distribution of inscrutable relations linking points to one another is not bound to follow any particular preconceived plan, so that there can be no obstacle to the acceptance of any scheme indicated by experiment.
We do not yet know what is the radius of spherical space; it must, of course, be exceedingly great compared with ordinary standards. On rather insecure evidence it has been estimated to be not many times greater than the distance of the furthest known nebulae. But the boundlessness has nothing to do with the bigness. Space is boundless by re-entrant form not by great extension. That which is is a shell floating in the infinitude of that which is not. We say with Hamlet, “I could be bounded in a nutshell and count myself a king of infinite space”.
But the nightmare of infinity still arises in regard to time. The world is closed in its space dimensions like a sphere, but it is open at both ends in the time dimension. There is a bending round by which East ultimately becomes West, but no bending by which Before ultimately becomes After.
I am not sure that I am logical but I cannot feel the difficulty of an infinite future time very seriously. The difficulty about A.D. ∞ will not happen until we reach A.D. ∞, and presumably in order to reach A.D. ∞ the difficulty must first have been surmounted. It should also be noted that according to the second law of thermodynamics the whole universe will reach thermodynamical equilibrium at a not infinitely remote date in the future. Time’s arrow will then be lost altogether and the whole conception of progress towards a future fades away.
But the difficulty of an infinite past is appalling. It is inconceivable that we are the heirs of an infinite time of preparation; it is not less inconceivable that there was once a moment with no moment preceding it.
This dilemma of the beginning of time would worry us more were it not shut out by another overwhelming difficulty lying between us and the infinite past. We have been studying the running-down of the universe; if our views are right, somewhere between the beginning of time and the present day we must place the winding up of the universe.
Travelling backwards into the past we find a world with more and more organisation. If there is no barrier to stop us earlier we must reach a moment when the energy of the world was wholly organised with none of the random element in it. It is impossible to go back any further under the present system of natural law. I do not think the phrase “wholly organised” begs the question. The organisation, we are concerned with is exactly definable, and there is a limit at which it becomes perfect. There is not an infinite series of states of higher and still higher organisation; nor, I think, is the limit one which is ultimately approached more and more slowly. Complete organisation does not tend to be more immune from loss than incomplete organisation.
There is no doubt that the scheme of physics as it has stood for the last three-quarters of a century postulates a date at which either the entities of the universe were created in a state of high organisation, or preexisting entities were endowed with that organisation which they have been squandering ever since. Moreover, this organisation is admittedly the antithesis of chance. It is something which could not occur fortuitously.
This has long been used as an argument against a too aggressive materialism. It has been quoted as scientific proof of the intervention of the Creator at a time not infinitely remote from to-day. But I am not advocating that we drew any hasty conclusions from it. Scientists and theologians alike must regard as somewhat crude the naive theological doctrine which (suitably disguised) is at present to be found in every textbook of thermodynamics, namely that some billions of years ago God wound up the material universe and has left it to chance ever since. This should be regarded as the working-hypothesis of thermodynamics rather than its declaration of faith. It is one of those conclusions from which we can see no logical escape—only it suffers from the drawback that it is incredible. As a scientist I simply do not believe that the present order of things started off with a bang; unscientifically I feel equally unwilling to accept the implied discontinuity in the divine nature. But I can make no suggestion to evade the deadlock.
Turning again to the other end of time, there is one school of thought which finds very repugnant the idea of a wearing out of the world. This school is attracted by various theories of rejuvenescence. Its mascot is the Phoenix. Stars grow cold and die out. May not two dead stars collide, and be turned by the energy of the shock into fiery vapour from which a new sun—with planets and with life—is born? This theory very prevalent in the last century is no longer contemplated seriously by astronomers. There is evidence that the present stars at any rate are products of one evolutionary process which swept across primordial matter and caused it to aggregate; they were not formed individually by haphazard collisions having no particular time connection with one another. But the Phoenix complex is still active. Matter, we believe, is gradually destroyed and its energy set free in radiation. Is there no counter-process by which radiation collects in space, evolves into electrons and protons, and begins star-building all over again? This is pure speculation and there is not much to be said on one side or the other as to its truth. But I would mildly criticise the mental outlook which wishes it to be true. However much we eliminate the minor extravagances of Nature, we do not by these theories stop the inexorable running-down of the world by loss of organisation and increase of the random element. Whoever wishes for a universe which can continue indefinitely in activity must lead a crusade against the second law of thermodynamics; the possibility of re-formation of matter from radiation is not crucial and we can await conclusions with some indifference.
At present we can see no way in which an attack on the second law of thermodynamics could possibly succeed, and I confess that personally I have no great desire that it should succeed in averting the final running-down of the universe. I am no Phoenix worshipper. This is a topic on which science is silent, and all that one can say is prejudice. But since prejudice in favour of a never-ending cycle of rebirth of matter and worlds is often vocal, I may perhaps give voice to the opposite prejudice. I would feel more content that the universe should accomplish some great scheme of evolution and, having achieved whatever may be achieved, lapse back into chaotic changelessness, than that its purpose should be banalised by continual repetition. I am an Evolutionist, not a Multiplicationist. It seems rather stupid to keep doing the same thing over and over again.
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