Lecture IX. Relativity
XLI. Spatial Frames. XLII. A Space-time Frame. XLIII. Classical Treatment. XLIV. Special and General Relativity. XLV. Relativity subject to Projicience.
§ XLI. Spatial Frames.
The burden of my contention in the foregoing lecture may be expressed under two clauses:
(1) That contact-treatment affords an avenue leading to acknowledgment of such intrinsic qualities as are exemplified by the proper figure and the size of a thing i.e. the spatial relatedness within it; and
(2) That projicient reference under vision founded on Sir Charles Sherrington's treatment of distance-receptors is a better policy for the interpretation of apparent shape and of colour than is direct apprehension under the alternative doctrine of vision.
In approaching the difficult topic of this lecture we have first to distinguish in some way relativity from relatedness. The concepts are not coterminous. Relatedness embraces more than the relativity we have now to consider. May one say:
(a) That relativity characterises a feature of extrinsic relatedness;
(b) That it deals with the relation of some record to events which are thereby recorded; and
(c) That what is chiefly on the tapis of recent discussion is some visual record; or some optical record which gives so to speak vision at second hand?
Thus Professor Einstein predicts what will be given in the optical record of certain events which will occur during a solar eclipse.
One must try to lead up through instances of what Mr. Einstein calls the “principle of relativity” to the special and the general “theory of relativity.” Let us revert then to the glass cube in our room which has already been used for purposes of illustration. Positions as terms in intrinsic spatial relatedness were then tacitly and should now be explicitly regarded as occupied—let us say by events. The cube is not only an orderly set of purely geometric relations of purely spatial terms; it is an orderly cluster of events which go together within the boundaries of this figure.
It is unnecessary to enter more than a reminder here that in dealing with the figure of a cube or other contemplated thing a special construct has classical sanction. A frame of three planes perpendicular to each other is erected within the spatial system under consideration. These three planes of events within the system are selected under device of method as a frame of reference for other events therein. The assigned place of any event will be given by the lengths of three Cartesian co-ordinates (x y z) dropped from that place on to the three selected planes. This scheme and its Euclidean implications will be familiar to all who are likely to read these pages.
Thus a 3-dimensional frame may be constructed within the cube as an aid to the determination of its own proper figure and the assigned positions of events within it. But the cube is also in extrinsic relatedness to other acknowledged things beyond its confines. And when we go outside the cube and install ourselves in the larger system in which it is set-and this is what we do in reflective thought—we need something more than the cube's own frame. Suppose for example we see it turned about or set a spinning. We then perhaps say that it rotates in “space.” What from the common-sense standpoint do we mean by this? We mean I suppose primarily that it rotates in the room. So we think of the room which as we say contains the cube (and much else including ourselves) and construct it on its 3-dimensional frame. The interpretation of the observed facts may then run thus: The cube with its frame (which after all is only a selected part of its intrinsic structure) rotates relatively to the room with its bigger frame. The fact that it is bigger does not much matter. The more important point is that the room with its frame is taken by common-sense as fixed in orientation so that we speak of the rotation of the cube as relative to the unchanging frame of the room.
But is this more than a prejudice due to our naturally taking our own “point of view” as we sit pretty securely attached to the floor of the room? What about that of the cube? Imaginatively I install myself within it. Pro hac vice I am it. There occurs some strange convulsion of nature. Looking out through my glass walls I exclaim: How that room is whirling round! Projicient vision will objectively locate the spinning motion in that which I see from a point of view extrinsic to it. If I identify myself with the frame of the room (which I commonly do since I am sitting in it) I am recording the spin of the glass cube. But if I identify myself with the cube (and imaginatively sit in it) I record a spinning of the room. In each case I can do no otherwise. It is the evolutionary nature of projicience in its primitive and unreflective form to refer from the record which we are actually or imaginatively to that which gives the record.
Which then is right-projicient reference from the room as record; or projicient reference from the cube as record? The essential and indubitable fact is just relative spin. That is given in each record. Can we so long as we just keep to this fact then and there immediately in evidence-without straying into extraneous considerations regarding other natural facts-can we get beyond and behind this basal fact of relativity? We can never I think do so through the avenue of vision only.
Note here in passing that we can in a measure wipe conscious vision as directly concerned off the slate. Let the cube and the room be fitted with suitable sensitised plates in suitable photographic cameras so as to record what takes place during let us say one-tenth of a second. Each will record so to speak a streak of relative movement of some point in the other more or less in focus. Neither can afford evidence of aught but relative motion.
On this understanding then let us frankly accept the relativity which is inalienable from vision and from optical records. And let us revert to the question: Which “really” spins cube or room? Common-sense still clinging to an interpretation based on classical treatment (the foundations of which are not only visual) may regard as the saner view that the room records an acknowledged spinning of the cube rather than that the cube records a “real” spinning of the room. If adequately instructed the “plain man” may pertinently ask whether in the person installed another kind of record-that of receptors in the “semi-circular canals”—might not forthwith decide the question. That person who had such a receptor-record would be the one who was “really” in motion. That person who had no such receptor-record would be really at rest so far as rotation is in question. It is worth noting again in passing:
(1) That the data afforded by such a receptor-record are naturally and naïvely referred to the rotation of oneself as the person who has them and
(2) That a curious and interesting touch of relativity comes in here. Seated in a closed cupboard (so as to exclude all view of surroundings) on a turn-table running quite smoothly on ball-bearings one is rotated let us say clockwise. One feels the turn quite distinctly. But so long as rotation continues at that rate one is quite insensible to its continuance. It feels as if one were at rest. Quicken speed. One feels an added turn clockwise; but is again insensible to continued rotation at that speed. But now let the speed be slackened by an operator in control. What one feels is an anti-clockwise turn. So long as that diminished speed is maintained one is not sensible of any rotary movement. But slacken speed again. One feels a further anti-clockwise turn. And so on. What one feels then on the data afforded by the receptor-record in the semi-circular canals is relative change of rotary motion. And though the movement in rotation is felt as one's own it is in us at least subject to projicient meaning. If one assume the most unreflective attitude possible to a being so reflective as to participate in such enquiries still one cannot (or I cannot) get rid of and annul all reference to a context of a surrounding world in extrinsic relation to which I am turned this way or that. Projicience on our interpretation is always the outcome of individual experience in a world which is for us predominantly objective through vision. And it is relative to that world that the modes of experience I have briefly described take definite form.
But this kind of thing may perhaps be regarded by the physicist as mere psychological whimsy and nihil ad rem. Let us then return to our main theme. There the point is that if we rely on visual or on optical data only then in taking the room as stable and the cube as spinning we yield to natural prejudice or we accept an “as if” based on other considerations than those which are strictly in evidence.
Even so is this good enough? Common-sense still under the sway of classical treatment quite realises that the room is part of the earth-system which is in rotation and revolves in its orbit. It is quite prepared to admit that we require for adequate interpretation a greater natural system (though its size does not much matter) and a frame of things more stable in orientation (the more essential feature). On astronomical grounds it is commonly assumed that within this more stable frame the lesser system of the room with its frame spins just as does the cube within the room. The pole-star (nearly) marks the direction which determines the setting of the frame with reference to which events in our solar system run their course. What we speak of as “in space” is comprehensively within this “larger room.” But if we mean by “space” a specific mode of relatedness named “spatial” it is clear that no system small or great is strictly “in space”; nay rather “space” (i.e. spatial relatedness) is in the system. Space as a limitless receptacle or container has I take it been relegated to the limbo of discarded notions.
Now if we could only be sure that the pole-star is an ultimate fixture we could construct an absolute frame of spatial relatedness with known orientation—that to which all subordinate positions are referable. But we cannot; for we are assured that the polestar is not fixed “in space.” What then are we to do? We want to get a 3-dimensional frame in which the three selected planes are absolutely and ultimately determinate with immutable axes. And that it seems is just what (even on the basis of an a-device) we cannot get. There is no use in whining about it; and it is scarcely worth while to boast of our incompetence. We must be content to accept the position.
§ XLII. A Space-time Frame.
Thus far we have taken “time” more or less for granted. We must do so no longer. We have in some way to link up spatial and temporal relatedness within one constructive scheme.
Consider how far it may be said that from the evolutionary point of view it is with the advent of distance receptors at a fairly high level of development that the chief data are afforded from which are derived the twin concepts of objective space and time. Picture a lowly organism-amoeba or the like-moving sluggishly over the surface with which it is in contact. There are touch-data here and there on the surface of the organism. In this respect neither passage of events from a distance nor location of events at a distance comes within its ken. In this respect for its almost inconceivably primitive mind (if such it may be called) there would be no “space” beyond the surface of actual contact common to it and that over which it moves. Space as objective and beyond the range of contact would be unknown. If we grant a kind of memory there would be duration within it-what M. Bergson would call “lived time.” There would be little or no “projection” of time into an external world beyond its surface; and such is the time we have now to consider.
This is not the occasion to elaborate the thesis thus adumbrated or to qualify a statement admittedly crude. Nor is it necessary. It suffices to emphasise the view that what one may speak of as external time-M. Bergson would say spatialised time as distinguished from duration-is in large measure projective. I use the word “projection” in this temporal sense as distinguished from “projicience” in its spatial reference where such a distinction may serve to make my meaning clearer. The point of emphasis in our present context is that in visual events both temporal projection and spatial projicience demand careful consideration.
Let us here pause to note that since the velocity of light is finite the starting-time of the effluent event is never simultaneous with the arrival-time at which the influence reaches the distance-receptors. Mr. Russell says (cf. p. 210) that two places are associated with every “sense-datum”; that at which it is and that from which it is perceived. Similarly two times have to be considered in respect of every optical event; that at which effluence starts and that at which influence is received. There are two occurrences in temporal relatedness-say one in Nova Persei and the other in someone's retina on our earth. Which occurrence then is to be called the “sense-datum”? Mr. Russell may say: That in Nova; the biologist may say: That in the distance-receptors. In any case no visual “sensedatum” in the one sense is ever simultaneous with that in the other sense.
To proceed. The classical doctrine with which we are at present concerned presupposes the uniform flow of external time (at any rate Newton did so) under the passage of which things either persist without sensible alteration or undergo change in some respect. The kind of change of predominant classical interest is motion. Uniform flow of time it was assumed has continued and will continue always and everywhere i.e. in all that happens within some absolute space-frame. Mr. Alexander bases his world-interpretation on the hypothesis that time is fluent.
Another line of interpretation still following classical tradition but with a difference might be roughly but inaccurately expressed by saying that it may be a better policy to regard events as flowing through time than to regard time itself as fluent. This however lends colour to the notion that time is a special sort of container of events which are thus said to be “in time” as well as “in space” the other sort of container. That is unsatisfactory; for temporal no less than spatial relatedness is in events. Both sorts of container must be relegated to the limbo of discarded notions.
Some method of treatment must therefore be devised which shall afford a yet better policy. We must bear in mind:
(1) That just as positions (places contracted almost to vanishing-point) are terms in spatial “here-there” relatedness so too are instants (durations likewise contracted) terms in temporal “now-then” relatedness; and
(2) That although temporal relatedness (for which the word “time” is shorthand) is for classical treatment utterly different from spatial relatedness (for which the word “space” is shorthand) yet both kinds of relatedness inseparably co-exist in all events and in every event.
Hence the aim of fruitful method should be to treat these two co-existent and co-related kinds of relatedness on quite similar lines and within one comprehensive construct of conceptual thought. Such a construct is the 4-dimensional continuum with x y z t as co-ordinates. To whom the first suggestion of such a world-scheme in which there is provision for indicating the time at which any given event occurs and the place which it then occupies I do not know. But a personal reminiscence may here be of interest.
Some half-century ago in the early seventies W. K. Clifford with what seemed to a young student extraordinary brilliance and clarity was discussing 4-dimensional space. He paused; and said with emphasis: “Mind you; I'm talking of a purely imaginary space of four dimensions. Our actual world may well be regarded as 4-dimensional with time as the fourth dimension”—or words to that effect. I was puzzled and afterwards asked Frederick Guthrie (who was present when Clifford spoke and under whom I was then working) what it meant. “Well” he said “something like this. Just as in the conventional space-time diagram one so arranges matters as to take the space-factor in one dimension and plots in time in the second dimension on the plane of one's paper so can a man like Clifford conceive though even he cannot picture or make a model of a sort of mental scheme in which all three spatial dimensions and a fourth time-dimension are so combined as to enable him to deal mathematically with the space-and-time course of anything in motion.”
A point for special notice is that one can neither picture nor make a model of a 4-dimensional continuum-for all picturing and modelling are 3-dimensional. If however one is dealing with two spatial dimensions only i.e. with events on one spatial plane and introduces time as a third dimension one can picture or make a model of that mental scheme. One just spatialises time as replacing one of the three spatial dimensions of our ordinary world. Suppose for example a mouse pursues a sinuous path as a flatlander along the floor of my room. Of course as a 3-dimensional thing the mouse is not “really” a flatlander; but one may legitimately discount this. Then one gets rid of all vertical here-there relatedness “in space” and one can substitute the now-then relatedness “in time.” In our model of the space-time frame of what happens the mouse will be at different levels from its spatial floor at successive instants. My room thus becomes a space-time model of the mouse's line of advance “in space and time.” If he be so far above the spatial floor that will mean so much time-interval from his start. The scales of space and time will need conventional adjustment. A purely natural scale has been suggested and may be worked out; but like the vertical and horizontal scales on a map some conventional adjustment is in most cases more profitable.
Now if snapshot records be made from the four corners of the spatial floor of our model all will be different. Each record gives appearances from selected “points of view” and some of them will be foreshortened in perspective. This foreshortening will be projiciently referred to the mouse's sinuous course.
Furthermore since the velocity of light is finite there are differences between times projective from the record-the times of appearance-and the “real” time of the events recorded. Moreover the projective times-so-called “local times”—are not the same from different recording standpoints. Time-intervals are subject to projective foreshortening. Two pulses of influence on the record are “now” and “then” with a time-interval irrespective of the distance of their effluent sources. But if the “now” and “then” be projectively referred to effluent events m and n at different distances the time-interval between departure of effluence from m and from n is not the same as that between the arrival of influence from them on the record. Events are warped for visual appearances—spatially under projicience temporally under projection. Even the space-time frame itself constructed four-square or Euclidian to fit the “real facts” for classical treatment may seem to require some non-Euclidian distortion and some borrowing so to speak from “space” or from “time” to fit the no less real facts for visual appearance viewed through the record.
In ordinary events projective time-distortion is negligible. Still there is always some difference; and in events of more than ordinary velocity it ceases to be negligible.
§ XLIII. Classical Treatment.
Let us now introduce time-relatedness into our picture in what is perhaps a simpler and more elementary way. Let us take two systems or bodies in relative motion as the one moving and the other (relatively of course) at rest. Each has its 3-dimensional space-frame which is in relative motion as a whole. It travels with its system or body. We are to observe one system from the other. Under device of method one may so arrange matters that the direction of motion to be dealt with is in one dimension only say x. This means that a measured length along y or z as observed from the other system is not affected by the relative motion of either system. And we will assume under classical tradition that the time-relatedness of events is uniform and common to both systems. In the two systems then y of the one and y1 of the other z and z1 remain constant for the observer. That leaves us to deal only with x and x1.
What we want to get at is this: How can an observer on one of the two systems so bring the length x1 into relation to x that he can pass from one to the other with assurance. Those who have solved this little problem show that (to allow for relative motion) we must here take into consideration velocity v (say in feet per second) during so many seconds as a value of t. In other words one has to use a “classical” (Newtonian or Galilean) transformation thus expressed x1 = x − vt. This is discussed and justified in the classical text-books. It works well in all cases of moderate velocity up to and a good way beyond that of the earth in its orbital sweep.
On this elementary plane of more or less familiar experience a long-ago recognised form of relativity comes in where there is cross-reference to different records as registered in different frames. Take the illustration with which Professor Einstein and others have made us at home. A stone is dropped from the window of a train in motion. It participates in the onward movement of the carriage and there is no relative motion as between stone and train in that direction. The relative motion is entirely downwards with increasing velocity as the stone falls. And this will be recorded visually or optically in the train.
But let there be also an optical record secured by someone on the platform which the train passes. Relatively to its frame the “stone-motion-record” is quite different-namely a parabolic curve on a suitable plate on the platform. Its parabolic form betokens acceleration in fall. Similarly the fall of a stone on the platform is relatively to its frame wholly downwards as records will there show. But the record thereof on a suitable photographic plate attached to the train will be a parabolic curve. The stress therefore is on different frames of reference. May one then say:
(1) That optical and visual records will under suitable precautions give correspondent results within any given frame whether relatively at rest or in motion;
(2) That records in one frame of what occurs in another frame give results different from those obtained under (1) when the two frames are in relative motion;
(3) That this relative motion—e.g. of “train” and “earth-rail-platform” will be inferable from optical records of what is seen or as Mr. Einstein so often says “judged” to occur in the one from the standpoint of the other; and
(4) That which “really” moves-train-system or earth-system-cannot be determined if visual or optical observations be restricted to just these two systems in relative motion. In all this “classical treatment” suffices.
If therefore one who is still under the sway of classical tradition be asked: which then is really in motion? How will he reply? He might I take it say: You know the order of nature which men of science have worked out not wholly without success; our earth rotating on its axis and revolving in its orbit round the sun; trains running over its surface; stones falling towards its centre and the rest. Does not this-stated perhaps with added refinement-give a sufficient answer to your question? Or do you want more? Do you seek to know what on our view is the absolute frame of reference how it is oriented and what is the motion say of the stone in reference to it? I do not know what may be the orientation of an absolute frame of reference and I frankly say so. But if you will kindly supply me with sundry data-such as compass-direction latitude time of year and a few more-I can give you a closely approximate answer in reference to a provisional pole-star frame subject to the universal uniformity of time-relations which we accept as a policy or (if you will) as part of our classical creed.
§ XLIV. Special and General Relativity.
α. Special Theory.
In the special theory of relativity there is much that need not concern us notwithstanding its great value and its splendid achievements. One must try to get at the gist of a difficult matter bristling with technicalities only so far as it affects our evolutionary interpretation.
The chief point for emphasis is that when the physicist has to deal under vision or in optical records (and he can deal no otherwise) with uniform velocities of translation approaching that of light (some 300000 kilometres per second iin vacuo) classical treatment does not work. His task therefore is to find a transformation formula that does work.
The position I take it is something like this. Given uniform translation at velocities from say 3 to 30 (or even 300) kilometres per second the Newtonian or classical transformation gives by calculation results which accord with observation. But given velocities from say 300000 down to 30000 kilometres per second that transformation formula does not give results which are accordant with observation. The problem therefore is to find a formula that does give accordant results.
Now the steps by which the call for a new formula was rendered imperative and the way in which it was suggested as the outcome of electro-magnetic research form a most interesting chapter in the recent history of physical science. But its recital does not fall within my province. Is it not told in many books and papers by those who have the requisite knowledge-and unfortunately by some who have not? For us here the essential point is that under certain special circumstances the classical transformation does not work. For records dealing with uniform velocities approaching more or less closely to that of light (c) a more complex transformation (Lorentzian) is required. In place of the x − vt of the classical equation one must write
(x − vt)⁄√(1 − v2⁄c2)
Then all goes well under the restricted or special theory of relativity—i.e. that which quite legitimately disregards or abstracts from fields of acceleration.
Does this mean that at some critical velocity there is a jump from the classical to the Lorentzian equation? Surely not. Under this special mode of treatment dealing say with optical records the Lorentzian formula admits no exceptions. But for moderate velocities the √(1 − v2⁄c2)—may for all practical purposes be expunged. Since its value then very closely approximates to 1 it makes no appreciable difference in the result-say one part in 200000000 even in the case in which the earth's orbital velocity of some 30 kilometres per second comes into the reckoning. Is it surprising that the old classical folk were unaware of its existence? Should one say in strictness or in fairness that Galileo or Newton have now been proved to be wrong?
Whatever then may be its calculable value great or small negligible or not the Lorentzian factor is there in the visual or the optical record and is thence on our view projicient as an acquired property of that which makes the record. Revert to the illustration of the train and the platform. It follows from Lorentzian treatment that the length of a metre-rod as measured in the train is judged through the record on the platform to be less than a metre but for the trains of our daily and current experience less by a very minute and quite negligible amount. Conceive however an ideal train travelling at 100000 kilometres per second. Then apply if you have this moderate amount of training the Lorentzian transformation to the length of a metre in that train as judged from the platform; or the length of a metre on the platform as judged from a record in that train; and make a note of how much shorter it is judged to be. Work out just a few examples. Then you will appreciate Mr. Einstein's statement that under such judgment “the rigid rod is shorter when in motion than when at rest and the more quickly it is moving the shorter is the rod” (T. R. p. 35).
But in accordance with Lorentzian treatment not only is an x—transformation required; a t—transformation is also required. This follows quite prettily. But here it must suffice to say that just as spatial distance is judged to be diminished so is time-interval judged to be greater. A time-interval of 5 minutes in the train is judged from the platform to be more than 5 minutes; and so much more in accordance with the speed of the ideal train. It follows that subject to judgment from the record “as a consequence of its motion the clock goes more slowly than when at rest” (p. 37).
β. General Theory.
In the special or restricted theory of relativity uniform motion in translation as given in optical records registered within a different frame is the subject-matter of discussion. Acceleration is left out of account under abstraction quite legitimate. In the general theory of relativity acceleration so conspicuous a feature in nature is deliberately brought into the picture and matters already complex enough are rendered very much more complex. I can only give a bare indication simplified by the omission of some important details of the kind of change which comes over the physical scene requiring for its treatment new modes of mathematical device.
If one conceive around a magnet a field of influence (i.e. something physically describable) varying in density or intensity with the distance from the magnet the observed motion of certain entities in that field can be interpreted in terms of that generalised “description” which science now employs. Similarly if one conceive around the earth a gravitative field (likewise describable) anything no matter what its so-called material substance-anything that has mass or inertia (which must here be identified cf. Einstein T. R. ch. xix.) exhibits accelerated motion within that field in accordance with the varying density of some given small area through which it moves. A de facto field of acceleration thus replaces a “force” supposed to be in some sense active. But many physicists have for fifty years and more dropped overboard any such notion of “force” as active or operative.
As we have seen the recorded behaviour of “clocks and measuring rods” as judged from the frame of reference of the optical recipient is such that the time-intervals in the swiftly-moving system appear to be lengthened and the space-intervals appear to be shortened in accordance with the Lorentzian formula. But in any field of acceleration matters are much more complicated.
In illustration Mr. Einstein (ch. XXXIII.) takes the field of acceleration in a rotating disc. The “density” of the field in this case is nil at the centre and increases with the distance therefrom as we proceed outwards. How about “clocks and measuring rods” at various positions on the disc as judged from a non-rotating reference-frame outside it? Clearly a clock near the periphery of the disc will be judged to go slower than one near the centre-all others at intervening positions will be judged to go at different rates each according to its station. Clearly too measuring rods placed tangentially to concentric circles will be judged to be shortened by an amount accordant with their several speeds in conformity to their distances from the centre; but those placed radially will appear unaffected. Hence the classical π of Euclidian geometry can have no status in respect to these judgments and must so far as they are concerned go by the board.
Well then (asks the somewhat bewildered “plain man”) what is to be done? Tell us I beseech you the gist of it. I think the gist of it is that just as classical treatment does not suffice where uniform velocities approaching that of light are in the record but must be replaced by Lorentzian transformation; so here where acceleration is in the picture this transformation is no longer good enough and must be supplemented by new methods of treatment based on “Gaussian co-ordinates” or on “tensor transformation” which perhaps a few score of mathematicians can securely wield.
§ XLV. Relativity Subject to Projicience.
That the modern doctrine of relativity should unreservedly be accepted as a policy no one is likely to deny. Splendid results stand to its credit in this respect. But whether it should be accepted as a philosophical creed is another matter. And this I contend turns on the acceptance of visual apprehension on the one hand or of projicience and projection on the other hand.
One must realise to how large an extent not only the special and the general theory of relativity but the relativist position at large in its modern development depends on vision and involves optical records. Two intertwined issues should be distinguished. Let me put the matter thus. First strike out from Mr. Einstein's masterly exposition (in T. R.) all that implies some optical analogue of the distance-receptors as a recording instrument and consider how much or how little remains. Secondly mark all such expressions as “judged from this or that frame of reference” and weigh carefully their exact import. Thirdly ask whether in those more direct statements where “judged from” is not explicitly inserted some such concept is not implicitly inferable though unexpressed. Thus when we read “the rigid rod is shorter when in motion than at rest” or “as a consequence of its motion the clock goes more slowly” (pp. 3 5 37) may we or may we not preface each statement with “as judged from another frame of reference” and still preserve the spirit of such statements? Fourthly if the question just asked be answered in the negative consider on what grounds the jump from “is judged to go more slowly” to “goes more slowly” is justified.
What then are the intertwined issues?
(1) That of recipient record in relation to some occurrence at a distance therefrom;
(2) That of “judgment” (to adopt Mr. Einstein's expression) having reference (in some sense) to the occurrence at a distance.
With regard to (1) the primary difficulty is that the only means of getting at what the occurrence at a distance intrinsically is apart from the record is through this record or other such records. To this I shall revert. With regard to (2) we must clear the ground a little. May we take the word “judged” as equivalent to “perceived” in the sense that what is so judged would be perceived had we organs of suitable refinement? That I think is partly what is meant in perhaps rather a metaphorical sense. But only in part. For I take it the aim of the physicist is to abstract from percipience as a mental event-in other words to deal with the whole matter irrespectively of the so-called relativity of knowledge-quite a different story. Unfortunately some writers introduce the words “objective” and “subjective” to trouble not a little the waters of exposition. Now all that is in any way perceived is objective at any rate as I have used this word; but my contention is that not all that is objective in that sense belongs of right to the thing which is said to be perceived. As to “subjective” unless the word be defined in some such way as Mr. Russell suggests (A. M. pp. 130–295) (which empties it of much of its usual connotation) it is better to eschew it altogether. In fact both words-objective and subjective-should be reserved for use under careful definition in connection with the special problem of the nature of the cognitive relation.
But can this relation be wholly ignored? Perhaps not. But it is open to the relativist to say “What may be the nature of this relation is no concern of mine. I leave that wholly on one side as what Mr. Whitehead calls a metaphysical question.” But does he leave it on one side? Nay rather he says “I loyally accept what is given as what veritably is. Thus it is given; thus must it be taken. What we deal with under the old and mistaken expression ‘physical objects’ are constructs of which ‘sense-data’visual “sense-data pre-eminently—are the given stuff and the only stuff with which we are acquainted. This is the realistic doctrine of direct apprehension and this is what I loyally accept in dealing with relativity.”
Thus we revert to the issue raised under (1) above. For the realist there is no difficulty about it. “The record” he says “just reveals or discloses the occurrence at a distance. Does not this suffice?” It amply suffices no doubt for the physicist as a policy. But as an evolutionary creed there is an alternative to visual apprehension in the theory of reference under visual projicience.
We want however so far as is possible to get rid of the part if any played by the mind in matters of physical relativity. Well and good. There is an occurrence in one system and an optical record thereof in another system at a distance. Let it be such a record on a photographic plate. The question then is: Does this optical record reveal or disclose the occurrence it registers without perspective distortion? One here gets back to the photographic record of the rotating coin. Does it reveal the acknowledged shape as it is disclosed through contact-treatment? Some of us are of opinion that it only accords therewith and then only so far as figure is concerned under certain specially selected conditions. All other revelations are distorted in perspective and attributed to the coin under projicience. What then says the realist? He may say that for the photographic plate the coin is just its world of perspectives and the only world to which it is in ad hoc relation. Any perspective record has therefore just as good a claim to reveal the true shape of the coin as any other. Selection of one rather than any other is just a convenient policy of interpretation which works well.
Now the record on the plate is the analogue of direct apprehension in vision. The pattern on the plate when we suitably examine it is correspondent to a retinal pattern. We may thus pass from the optical record through the correspondent retinal pattern to the visual apprehension which involves this eye-record. And the realist may claim that as Mr. Nunn puts it a thing “has” as many shapes as direct apprehension in vision discloses. It follows that a falling “stone has” as many trajectories represented by parabolic curves as are optically recorded or are visually apprehended by observers in a dozen or more aeroplanes flying at different speeds; it follows that under Lorentzian treatment a measuring rod or a clock “has” as many lengths or as many rates of going as are recorded in different frames of reference in relative motion and so on. If for “has” we substitute “appears to have under optical or visual treatment” all will agree. On these terms passing events in the Minkowski-Einstein world-frame are “warped” or non-Euclidian from the point of view of visual appearances or phenomena. Hence the exact determination of this warping is of prime scientific importance. This warp may well be a property of a gravitative field; that warp a property of an electro-magnetic field as judged from records of events therein.
Since then the whole problem turns on what appears from the record's perspective the validity of relativist policy for strictly scientific interpretation is unimpeachable. At the present juncture no other policy is admissible.
But if the relativist claim at the bar of philosophy not only that there are as many apparent lengths and times as there are frames of reference in relative motion; not only that scientific policy in this domain of research demands a universe of warped events; but that he thus takes us one step nearer to an interpretation of intrinsic reality in the world as it is apart from perspectives the grounds of his doctrine of direct apprehension or revelation through vision must be firmly established before any such conclusion can be accepted-I repeat at the bar of philosophy. According to those who accept some such alternative doctrine as that of projicience these grounds are open to criticism.
One must again urge that so far from being a primitive mode of acquaintance with the world vision is one of the least primitive modes of approach. Evolved as a premonitory guide to coming through behaviour into direct contact with things; acquiring step by step the pragmatic endorsement of working so well; affording to the full the extrinsic reality of appearances; supported in this by the verdict of relativity; it is from first to last subject always to that projicience which is on the one hand the secret of its success and on the other hand the condition of its failure to get into touch with intrinsic reality. Such is our evolutionary view—to be subjected of course to counter-criticism.
On its success as a guide to behaviour in a world which is for us so largely one of ever-changing perspectives it is needless to enlarge. But on its failure as such to give aught but appearance as a clue to that intrinsic reality which it is of itself incapable of reaching the evolutionist is bound to insist. As I look up from my desk in the corner of my room there is scarcely a thing whose apparent shape even approximately accords with the acknowledged configuration of that thing in its intrinsic spatial relatedness. In all save some specially selected instances of accord where what we may speak of as the plane of the retina is parallel with the plane of events recorded vision so distorts the thing it renders objective that it is unsafe to rely on judgment based only on optical records for knowledge of the intrinsic course of events in that system having visual depth which lies at a distance. The new relativity does but point the moral of this old tale.
May I now at the risk of some repetition be allowed to emphasise the contention that we must be careful to distinguish between a scientific policy and a philosophic creed? As a policy physical relativity is to be accepted at the present juncture with the most cordial sympathy. It has shed brilliant light on the interpretation of phenomena as revealed in optical records. It entails non-Euclidian reconstruction of the spatial frames in terms of which such phenomena must be interpreted if the policy of physical science is to be carried on to further stages of advance. It entails too a revised treatment of objective time as incorporated in 4–dimensional frames. There is assuredly nothing here to which the philosopher of any school if he have some tincture of wisdom should take exception.
But if it be said that this warping of the universal frame as revealed in optical records reveals also the intrinsic space and time plan of the universe; if it be said that temporal relatedness in events can no longer be distinguished in the nature of its being from spatial relatedness; if it be said that since thus are things given in the record thus also must they be given apart from the record; if in brief it be claimed that a successful policy must be the one true basis of an acceptable creed; then the whole position is different.
Those whose researches have lain in other departmental fields of science may ask whether the physicist has weighed with due care the biological and psychological evidence in matters of vision and of optical records as necessarily interpreted through vision; whether in view of the results obtained within this field of scientific enquiry new realists are quite sure that on the evolutionary evidence the policy of accepting direct apprehension at its face-value is the only policy and therefore the unambiguous platform of a creed; whether on broader lines they are fully satisfied that their epistemological foundations are secure.
It is I know the fashion among some new realists to relegate epistemology—the basal problem of knowledge—to a quite subordinate position. Mr. Whitehead I think would say that it is one for “metaphysics” and not for science to discuss. None the less a rather naïve solution of the problem is too often accepted without any serious discussion of its merits. If it be a problem for “metaphysics” let it be metaphysically discussed and let full references be given to such discussion so that it may be quite clear what reasons are assigned why this metaphysical solution and not another is to form the basis of scientific procedure. For us however the problem is not “metaphysical” in the sense intended. For us any definition of nature according to which mind and knowledge are other than natural is out of court. And if this be so the epistemological problem falls within and nowise outside the purview of scientific enquiry.
If it be said: Science has no concern whatever with what you are pleased to call a philosophic creed; then I must ask: If reference from the record casting a more or less warped shadow on to that which is thus recorded be a policy alternative to that of direct apprehension by the record of that which is intrinsic to physical nature; should not an interpretation based on the former policy receive serious consideration whether it be accepted or not?
But one of the claims of relativists is that the modern doctrine entails a thorough revision of out concept of the intrinsic structure of the physical universe. And this is hard to distinguish from what I have spoken of as a philosophic creed in respect thereof. Is it as a policy only that we are bidden to regard the inevitable warping of visual and optical constructs as revealing the actual course of events in nature itself? May we still subscribe to the essential tenets of the Newtonian creed? Many physicists will reply that we may no longer do so. We have to reckon with a new scientific creed.
In attempting to discuss—I hope without grave errors of presentation—a cardinal issue that is raised by modern physicists I have taken relativity on its own terms as concerned only with what new realists speak of as the non-mental. I have therefore said nothing on the further issue which idealists regard as foundational—the so-called relativity of knowledge. They urge that any sundering of the apprehended from apprehending is false and meaningless. Wedded in synthesis no analytic decree of divorce can separate them. Each is what it is in relation to the other. I regard this however as a matter that falls under relatedness rather than relativity. Furthermore so far as I can judge from much that has been written of late this further problem cannot profitably be discussed on the same platform as that on which the advocates of physical relativity take their stand.