Man or Matter Part 27

After having replaced the customary concept of the light-bundle composed of single rays by the conception of two dynamically polar realms of s.p.a.ce bordering each other, we turn to the examination of what is going on dynamically inside these realms. This will help us to gain a proper concept of the propagation of light through s.p.a.ce.

In an age when the existence of a measurable light-velocity seems to belong to the realm of facts long since experimentally proved; when science has begun to measure the universe, using the magnitude of this velocity as a constant, valid for the whole cosmos; and when entire branches of science have been founded on results thus gained, it is not easy, and yet it cannot be avoided, to proclaim that neither has an actual velocity of light ever been measured, nor can light as such ever be made subject to such measurement by optical means - and that, moreover, light, by its very nature, forbids us to conceive of it as possessing any finite velocity.

With the last a.s.sertion we do not mean to say that there is nothing going on in connexion with the appearance of optical phenomena to which the concept of a finite velocity is applicable. Only, what is propagated in this way is not the ent.i.ty we comprise under the concept of 'light'. Our next task, therefore, will be to create a proper distinction between what moves and what does not move spatially when light is active in the physical world. Once more an historical retrospect will help us to establish our own standpoint with regard to the existing theories.

The first to think of light as possessing a finite velocity was Galileo, who also made the first, though unsuccessful, attempt to measure it. Equally unsuccessful were attempts of a similar nature made soon afterwards by members of the Accademia del Cimento. In both cases the obvious procedure was to produce regular flashes of light and to try to measure the time which elapsed between their production and their observation by some more or less distant observer. Still, the conviction of the existence of such a velocity was so deeply ingrained in the minds of men that, when later observations succeeded in establis.h.i.+ng a finite magnitude for what seemed to be the rate of the light's movement through s.p.a.ce, these observations were hailed much more as the quant.i.tative value of this movement than as proof of its existence, which was already taken for granted.

A clear indication of man's state of mind in regard to this question is given in the following pa.s.sage from Huygens's famous Traite de la Lumiere, by which the world was first made acquainted with the concept of light as a sort of undulatory movement.

'One cannot doubt that light consists in the movement of a certain substance. For if one considers its production one finds that here on the earth it is chiefly produced by fire and flame, which without doubt contain bodies in rapid motion, for they dissolve and melt numberless other bodies. Or, if one considers its effects, one sees that light collected, for instance, by a concave mirror has the power to heat like fire, i.e. to separate the parts of the bodies; this a.s.suredly points to movement, at least in true philosophy in which one traces all natural activity to mechanical causes. In my opinion one must do this, or quite give up all hope of ever grasping anything in physics.'

In these words of Huygens it must strike us how he first provides an explanation for a series of phenomena as if this explanation were induced from the phenomena themselves. After he has drawn quite definite conclusions from it, he then derives its necessity from quite other principles - namely, from a certain method of thinking, accepting this as it is, unquestioned and unalterably established. We are here confronted with an 'unlogic' characteristic of human thinking during its state of isolation from the dynamic substratum of the world of the senses, an unlogic which one encounters repeatedly in scientific argumentation once one has grown aware of it. In circles of modern thinkers where such awareness prevails (and they are growing rapidly to-day) the term 'proof of a foregone conclusion' has been coined to describe this fact.1

'Proof of a foregone conclusion' is indeed the verdict at which one arrives in respect of all the observations concerned with the velocity of light - whether of existing phenomena detectable in the sky or of terrestrial phenomena produced artificially - if one studies them with the att.i.tude of mind represented by the child in Hans Andersen's story.

In view of the seriousness of the matter it will not be out of place if we discuss them here as briefly as possible, one by one.2

The relevant observations fall into two categories: observations of certain astronomical facts from which the existence of a finite velocity of light and its magnitude as an absolute property of it has been inferred; and terrestrial experiments which permitted direct observation of a process of propagation connected with the establishment of light in s.p.a.ce resulting in the measurement of its speed. To the latter category belong the experiments of Fizeau (1849) and Foucault (1850) as well as the Michelson-Morley experiment with its implications for Einstein's Theory of Relativity. The former category is represented by Roemer's observations of certain apparent irregularities in the times of revolution of one of Jupiter's moons (1676), and by Bradley's investigation into the reason for the apparent rhythmic changes of the positions of the fixed stars (1728).

We shall start with the terrestrial observations, because in their case alone is the entire path of the light surveyable, and what is measured therefore is something appertaining with certainty to every point of the s.p.a.ce which spreads between the source of the light and the observer. For this reason textbooks quite rightly say that only the results drawn from these terrestrial observations have the value of empirically observed facts. (The interpretation given to these facts is another question.)

Now, it is a common feature of all these experiments that by necessity they are based on an arrangement whereby a light-beam can be made to appear and disappear alternately. In this respect there is no difference between the first primitive attempts made by Galileo and the Academicians, and the ingeniously devised experiments of the later observers, whether they operate with a toothed wheel or a rotating mirror. It is always a flash of light - and how could it be otherwise?

- which is produced at certain regular intervals and used for determining the speed of propagation.

Evidently what in all these cases is measured is the speed with which a beam of light establishes itself in s.p.a.ce. Of what happens within the beam, once it is established, these observations tell nothing at all.

The proof they are held to give of the existence of a finite speed of light, as such, is a 'proof of a foregone conclusion'. All they tell us is that the beam's front, at the moment when this beam is first established, travels through s.p.a.ce with a finite velocity and that the rate of this movement is such and such. And they tell us nothing at all about other regions of the cosmos.

That we have to do in these observations with the speed of the light-front only, and not of the light itself, is a fact fully acknowledged by modern physical optics. Since Lord Rayleigh first discussed this matter in the eighties of the last century, physicists have learnt to distinguish between the 'wave-velocity' of the light itself and the velocity of an 'impressed peculiarity', the so-called 'group-velocity', and it has been acknowledged that only the latter has been, and can be, directly measured. There is no possibility of inferring from it the value of the 'wave-velocity' unless one has a complete knowledge of the properties of the medium through which the 'groups' travel. Nevertheless, the modern mind allows itself to be convinced that light possesses a finite velocity and that this has been established by actual measurement. We feel reminded here of Eddington's comment on Newton's famous observations: 'Such is the glamour of a historical experiment.' (Chapter XIV.)3

Let us now turn to Roemer and Bradley. In a certain sense Roemer's observations and even those of Bradley rank together with the terrestrial measurements. For Roemer used as optical signals the appearance and disappearance of one of Jupiter's moons in the course of its revolution round the planet; thus he worked with light-flashes, as the experimental investigations do. Hence, also, his measurements were concerned - as optical science acknowledges - with group-velocity only.

In fact, even Bradley's observations, although he was the only one who operated with continuous light-phenomena, are exposed to the charge that they give information of the group-velocity of light, and not of its wave-velocity. However, we shall ignore these limitations in both cases, because there are quite other factors which invalidate the proofs they are held to give, and to gain a clear insight into these factors is of special importance for us.

Roemer observed a difference in the length of time during which a certain moon of Jupiter was occulted by the planet's body, and found that this difference underwent regular changes coincident with the changes in the earth's position in relation to Jupiter and the sun.

Seen from the sun, the earth is once a year in conjunction with Jupiter, once in opposition to it. It seemed obvious to explain the time-lag in the moon's reappearance, when the earth was on the far side of the sun, by the time the light from the moon needed to cover the distance marked by the two extreme positions of the earth - that is, a distance equal to the diameter of the earth's...o...b..t. On dividing the observed interval of time by the accepted value of this distance, Roemer obtained for the velocity of light a figure not far from the one found later by terrestrial measurements.

We can here leave out of account the fact that Roemer's reasoning is based on the a.s.sumption that the Copernican conception of the relative movements of the members of our solar system is the valid conception, an a.s.sumption which, as later considerations will show, cannot be upheld in a science which strives for a truly dynamic understanding of the world. For the change of aspect which becomes necessary in this way does not invalidate Roemer's observation as such; it rules out only the customary interpretation of it. Freed from all hypothetical by-thought, Roemer's observation tells us, first, that the time taken by a flash of light travelling from a cosmic light-source to reach the earth varies to a measurable extent, and, secondly, that this difference is bound up with the yearly changes of the earth's position in relation to the sun and the relevant planetary body.

We leave equally out of account the fact that our considerations of the nature of s.p.a.ce in Chapter XII render it impermissible to conceive of cosmic s.p.a.ce as something 'across' which light (or any other ent.i.ty) can be regarded as travelling this or that distance in this or that time. What matters to us here is the validity of the conclusions drawn from Roemer's discovery within the framework of thought in which they were made.

Boiled down to its purely empirical content, Roemer's observation tells us solely and simply that within the earth's cosmic orbit light-flashes travel with a certain measurable speed. To regard this information as automatically valid, firstly for light which is continuously present, and secondly for everywhere in the universe, rests again on nothing but a foregone conclusion.

Precisely the same criticism applies to Bradley's observation, and to an even higher degree. What Bradley discovered is the fact that the apparent direction in which we see a fixed star is dependent on the direction in which the earth moves relatively to the star, a phenomenon known under the name of 'aberration of light'. This phenomenon is frequently brought to students' understanding by means of the following or some similar a.n.a.logy.

Imagine that a machine-gun in a fixed position has sent its projectile right across a railway-carriage so that both the latter's walls are pierced. If the train is at rest, the position of the gun could be determined by sighting through the shot-holes made by the entrance and exit of the bullet. If, however, the train is moving at high speed, it will have advanced a certain distance during the time taken by the projectile to cross the carriage, and the point of exit will be nearer the rear of the carriage than in the previous case. Let us now think of an observer in the train who, while ignorant of the train's movement, undertook to determine the gun's position by considering the direction of the line connecting the two holes. He would necessarily locate the gun in a position which, compared with its true position, would seem to have s.h.i.+fted by some distance in the direction of the train's motion.

On the other hand, given the speed of the train, the angle which the line connecting the two holes forms with the true direction of the course of the projectile - the so-called angle of aberration - provides a measure of the speed of the projectile.

Under the foregone conclusion that light itself has a definite velocity, and that this velocity is the same throughout the universe, Bradley's observation of the aberration of the stars seemed indeed to make it possible to calculate this velocity from the knowledge of the earth's own speed and the angle of aberration. This angle could be established by comparing the different directions into which a telescope has to be turned at different times of the year in order to focus a particular star. But what does Bradley's observation tell us, once we exclude all foregone conclusions?

As the above a.n.a.logy helps towards an understanding of the concept of aberration, it will be helpful also to determine the limits up to which we are allowed to draw valid conclusions from the supposed occurrence itself. A mind which is free from all preconceived ideas will not ignore the fact that the projectile, by being forced to pierce the wall of the carriage, suffers a considerable diminution of its speed. The projectile, therefore, pa.s.ses through the carriage with a speed different from its speed outside. Since, however, it is the speed from hole to hole which determines the angle of aberration, no conclusion can be drawn from the latter as to the original velocity of the projectile. Let us a.s.sume the imaginary case that the projectile was shot forth from the gun with infinite velocity, and that the slowing-down effect of the wall was great enough to produce a finite speed of the usual magnitude, then the effect on the position of the exit hole would be precisely the same as if the projectile had moved all the time ' with this speed and not been slowed down at all.

Seeing things in this light, the scientific Andersen child in us is roused to exclaim: 'But all that Bradley's observation informs us of , with certainty is a finite velocity of the optical process going on inside the telescope!' Indeed, if someone should claim with good reason (as we shall do later on) that light's own velocity is infinite, and (as we shall not do) that the dynamic situation set up in the telescope had the effect of slowing down the light to the measured velocity - there is nothing in Bradley's observation which could disprove these a.s.sertions.

Having thus disposed of the false conclusions drawn by a kinematically orientated thinking from the various observations and measurements of the velocity which appears in connexion with light, we can carry on our own studies undisturbed. Two observations stand before us representing empirically established facts: one, that in so far as a finite velocity has been measured or calculated from other observations, nothing is known about the existence or magnitude of such a velocity except within the boundaries of the dynamic realm const.i.tuted by the earth's presence in the universe; the other, that this velocity is a 'group'-velocity, that is, the velocity of the front of a light-beam in process of establishment. Let us see what these two facts have to tell us when we regard them as letters of the 'word' which light inscribes into the phenomenal world as an indication of its own nature.

Taking the last-named fact first, we shall make use of the following comparison to help us realize how little we are justified in drawing from observations of the front speed of a light-beam any conclusions concerning the kinematic conditions prevailing in the interior of the beam itself. Imagine the process of constructing a tunnel, with all the efforts and time needed for cutting its pa.s.sage through the resisting rock. When the tunnel is finished the activities necessary to its production are at an end. Whereas these continue for a limited time only, they leave behind them permanent traces in the existence of the tunnel, which one can describe dynamically as a definite alteration in the local conditions of the earth's gravity. Now, it would occur to no one to ascribe to the tunnel itself, as a lasting quality, the speed with which it had been constructed. Yet something similar happens when, after observing the velocity required by light to lay hold on s.p.a.ce, this velocity is then attributed to the light as a quality of its own.

It was reserved for a mode of thought that could form no concept of the real dynamic of Light and Dark, to draw conclusions as to the qualities of light from experiences obtained through observing its original spreading out into s.p.a.ce.

To speak of an independently existing s.p.a.ce within which light could move forward like a physical body, is, after what we have learnt about s.p.a.ce, altogether forbidden. For s.p.a.ce in its relevant structure is itself but a result of a particular co-ordination of levity and gravity or, in other words, of Light and Dark. What we found earlier about the qualities of the two polar s.p.a.ces now leads us to conceive of them as representative of two limiting conditions of velocity: absolute contraction representing zero velocity; absolute expansion, infinite velocity (each in its own way a state of 'rest'). Thus any motion with finite velocity is a mean between these two extremes, and as such the result of a particular co-ordination of levity and gravity. This makes it evident that to speak of a velocity taking its course in s.p.a.ce, whether with reference to light or to a physical body in motion, is something entirely unreal.

Let us now see what we are really told by the number 186,000 miles a second, as the measure of the speed with which a light-impulse establishes itself spatially. In the preceding chapter we learnt that the earth's field of gravity offers a definite resistance to our visual ray. What is true for the inner light holds good equally for the outer light. Using an image from another dynamic stratum of nature we can say that light, while appearing within the field of gravity, 'rubs' itself on this. On the magnitude of this friction depends the velocity with which a light-impulse establishes itself in the medium of the resisting gravity. Whereas light itself as a manifestation of levity possesses infinite velocity, this is forced down to the known finite measure by the resistance of the earth's field of gravity. Thus the speed of light which has been measured by observers such as Fizeau and Foucault reveals itself as a function of the gravitational constant of the earth, and hence has validity for this sphere only.1 The same is true for Roemer's and Bradley's observations, none of which, after what we have stated earlier, contradicts this result. On the contrary, seen from this viewpoint, Roemer's discovery of the light's travelling with finite speed within the cosmic realm marked by the earth's...o...b..t provides an important insight into the dynamic conditions of this realm.

Among the experiments undertaken with the aim of establis.h.i.+ng the properties of the propagation of light by direct measurements, quoted earlier, we mentioned the Michelson-Morley experiment as having a special bearing on Einstein's conceptual edifice. It is the one which has formed the foundation of that (earlier) part of Einstein's theory which he himself called the Special Theory of Relativity. Let us see what becomes of this foundation - and with it the conceptual edifice erected upon it - when we examine it against the background of what we have found to be the true nature of the so-called velocity of light.

It is generally known that modern ideas of light seemed to call for something (Huygens's 'certain substance') to act as bearer of the movement attributed to light. This led to the conception of an imponderable agency capable of certain movements, and to denote this agency the Greek word ether was borrowed. (How this word can be used again to-day in conformity with its actual significance will be shown in the further course of our discussions.) Nevertheless, all endeavours to find in the existence of such an ether a means of explaining wide fields of natural phenomena were disappointed. For the more exact concepts one tried to form of the characteristics of this ether, the greater the contradictions became.

One such decisive contradiction arose when optical means were used to discover whether the ether was something absolutely at rest in s.p.a.ce, through which physical bodies moved freely, or whether it shared in their movement. Experiments made by Fizeau with running water seemed to prove the one view, those of Michelson and Morley, involving the movement of the earth, the other view. In the celebrated Michelson-Morley experiment the velocity of light was shown to be the same, in whatever direction, relative to the earth's own motion, it was measured. This apparent proof of the absolute constancy of light-velocity - which seemed, however, to contradict other observations - induced Einstein to do away with the whole a.s.sumption of a bearer of the movement underlying light, whether the bearer were supposed to be at rest or itself in motion. Instead, he divested the concepts of s.p.a.ce and time, from which that of velocity is usually derived, of the absoluteness. .h.i.therto attributed to them, with the result that in his theory time has come to be conceived as part of a four-dimensional 's.p.a.ce-time continuum'.

In reality the Michelson-Morley experiment presents no problem requiring such labours as those of Einstein for its solution. For by this experiment nothing is proved beyond what can in any event be known - namely, that the velocity of the propagation of a light-impulse is constant in all directions, so long as the measuring is confined to regions where the density of terrestrial s.p.a.ce is more or less the same. With the realization of this truth, however, Einstein's Special Theory loses its entire foundation. All that remains to be said about it is that it was a splendid endeavour to solve a problem which, rightly considered, does not exist.1

Now that we have realized that it is inadmissible to speak of light as consisting of single rays, or to ascribe to it a finite velocity, the concept of the refraction of light, as understood by optics to-day and employed for the explanation of the spectrum, also becomes untenable.

Let us find out what we must put in its place.

The phenomenon which led the onlooker-consciousness to form the idea of optical refraction has been known since early times. It

consists in the fact, surprising at first sight, that an object, such as a coin, which lies at the bottom of a vessel hidden from an observer by the rim, becomes visible when the vessel is filled with water.

Modern optics has explained this by a.s.suming that from the separate points of the floor of the vessel light-rays go out to all sides, one ray falling in the direction of the eye of the observer. Hence, because of the positions of eye and intercepting rim there are a number of points from which no rays can reach the eye. One such point is represented by the coin (P in Fig. 12a). Now if the vessel is filled with water, light-rays emerging from it are held to be refracted, so that rays from the points. .h.i.therto invisible also meet the eye, which is still in its original position. The eye itself is not conscious of this 'break' in the light-rays, because it is accustomed to 'project'

all light impressions rectilinearly out into s.p.a.ce (Fig. 12b.). Hence, it sees P in the position of P'. This is thought to be the origin of the impression that the whole bottom of the vessel is raised.

This kind of explanation is quite in line with the peculiarity of the onlooker-consciousness, noted earlier, to attribute an optical illusion to the eye's way of working, while charging the mind with the task of clearing up the illusion. In reality it is just the reverse. Since the intellect can form no other idea of the act of seeing than that this is a pa.s.sive process taking place solely within the eye, it falls, itself, into illusion. How great is this illusion we see from the fact that the intellect is finally obliged to make the eye somehow or other 'project'

into s.p.a.ce the impressions it receives - a process lacking any concrete dynamic content.

Once more, it is not our task to replace this way of 'explaining' the phenomenon by any other, but rather to combine the phenomenon given here with others of kindred nature so that the theory contained in them can be read from them direct. One other such phenomenon is that of so-called apparent optical depth, which an observer encounters when looking through transparent media of varying optical density. What connects the two is the fact that the rate of the alteration of depth, and the rate of change of the direction of light, are the same for the same media.

In present-day optics this phenomenon is explained with reference to the former. In proceeding like this, optical science makes the very mistake which Goethe condemned in Newton, saying that a complicated phenomenon was made the basis, and the simpler derived from the complex. For of these two phenomena, the simpler, since it is independent of any secondary condition, is the one showing that our experience of depth is dependent on the density of the optical medium.

The latter phenomenon we met once before, though without reference to its quant.i.tative side, when in looking at a landscape we found how our experiences of depth change in conformity with alterations in atmospheric conditions. This, then, served to make us aware that the way we apprehend things optically is the result of an interplay between our visual ray and the medium outside us which it meets.

It is exactly the same when we look through a vessel filled with water and see the bottom of it as if raised in level. This is in no sense an optical illusion; it is the result of what takes place objectively and dynamically within the medium, when our eye-ray pa.s.ses through it. Only our intellect is under an illusion when, in the case of the coin becoming visible at the bottom of the vessel, it deals with the coin as if it were a point from which an individual ray of light went out.. ..

etc., instead of conceiving the phenomenon of the raising of the vessel's bottom as one indivisible whole, wherein the coin serves only to link our attention to it.

Having thus cleared away the kinematic interpretation of the coin-in-the-bowl phenomenon, we may pa.s.s on to discuss the optical effect through which the so-called law of refraction was first established in science. Instead of picturing to ourselves, as is usually done, light-rays which are s.h.i.+fted away from or towards the perpendicular at the border-plane between two media of different optical properties, we shall rather build up the picture as light itself designs it into s.p.a.ce.

We have seen that our inner light, as well as the outer light, suffers a certain hindrance in pa.s.sing through a physical medium - even such as the earth's gravity-field. Whilst we may not describe this r.e.t.a.r.dation, as is usually done, in terms of a smaller velocity of light itself within the denser medium, we may rightly say that density has the effect of lessening the intensity of the light. (It is the time required for the initial establishment of a light-filled realm which is greater within such a medium than outside it.) Now by its very nature the intensity of light cannot be measured in spatial terms. Yet there is a phenomenon by which the decrease of the inner intensity of the light becomes spatially apparent and thus spatially measurable. It consists in the alteration undergone by the aperture of a cone of light when pa.s.sing from one optical medium to another.