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After all, apart from all else, limits to knowledge do not liberate from law; and systematic limits give no licence to untested invention; whilst results of microcosmic action are not irrelevant to what is measured at macrocosmic levels.
If matter waves cohere about wave theories in pleasant and orderly fashion, while providing problems (in knowing the location of particles, when such appear) with the procedure of particulate appearance, what then ?
If quantification applies but form eludes, as to such particulate appearance, except statistically - then there is nothing which could coherently be called freedom there. If individual electrons in fact elected whether to do this or that (apart from the trifling consideration that no wherewithal for such works of liberty is perceptible in them), then there could be no quantifiability for forecast of the eventual outcomes. Irresponsible young scamps of electrons could be forever gliding hither or thither - out of sight, out of mind, to the considerable anguish of those wanting to see some continuity in the energic and quantifiable elements of the waves, with which they appear to interchange, from time to time. This however, they are spared.
If, then, short
of this, the identity is predictable, by mere humans, then it is
not free; and if it is free, then it is not predictable, under such qualifications.Predictable
macro-consequences would not occur on such micro-parameters as those.
Yet they do.
THE WORSHIP OF THE UNKNOWABLE NOUMENA
Where, moreover, one passes into the realm where one's measurements are systematically ... shall we say, 'restrained', as by the movement of the thing to be measured by the measuring instrument (however sophisticated may be the one and however small the other): then there is merely an escalation in the difficulties of obtaining data. Desire in its feeling for autonomy, may be dashed; but disorder is neither demonstrated nor indicated.
In such a case, nothing monumental has happened; it is obvious something monumental may have been prevented from happening however, at the theoretical level, some refinement of discovery, because of the restraint to so unusual a degree, on data. If, further, as here, the characteristics of matter waves, as theorist Ford (infra EXTENSION pp. 406 ff.) puts it, incorporate considerations which restrain our investigations; if they do not happen to yield to certain pre-conceived demands affecting their point-specifiability, then our theories may be further chastened, if not chastised.
If this be so, then what has happened ? Technology is shown as incapable of becoming God, as is the case; but then, this is no problem to those who see the systematic absurdity of any such thrust. There are limits to scientific knowledge; it is not able to have formulated for it, without limit, perceptible tools of foraging: it must rest content with the implications of what it knows and how it knows it. Truth is not invention.
The degree of continuity achievable in wave terms however is, as will be indicated, a representation at the outset that we are not in some new causeless chariot of events. Rather are we merely in one which exercises the intelligence and the imagination, to perhaps an unusual degree; one baulking the hypothesis-maker to a spectacular degree because of the measuring limits, and the deprivation (as if we had Ethiopian-famine style scientists here) of ability to gain ready knowledge of enough underlying units, or enough data on them, to play the role of system-maker.
This is an established principle of interpretation; and ground for its exclusion, rather than inclusion, in related thought areas would need to be - sought!
The concept, to take our simple ... and yet profound case of crystals, is one of characteristics relating not only to the ratios of various atoms of elements involved, to their absolute number, but also to their very spatial patterns.
This helps us understand why certain specific crystals are found for certain substances. Thus the underlying unit may give spectacular help where mere arid theorising is impotent. Where however minuteness, where measuring modes available prevent the penetration to those actual areas in terms of the minute, then conceptual limits are expected; and theoretical baulking is in effect predictable in the long run.
At the level noted for crystals, we are at least in part better able to measure, visualise, manipulate and formulate such underlying units and their modes of cohesion, their correlation and co-operation. Where this luxury is denied us, then, there is nothing new in the history of science, in our temporary baulking. What may be new, as Ford (EXTENSION, pp. 406 ff., infra) indicates, is the possibility that we may be coming to the ultimate (for us) in measurement, given what is supplied as means.
Available modes or measuring units are not illimitable. The concept of a limit to our examining prowess then has to be faced; but it has no metaphysical implications to this point. Our limits do not affect what is ... merely what we know of it. The known must be assessed with all its co-operative principles and implications.
This whole area, then, provides nothing for apologetic concern: except to give us reason to include the ensuing section in some more detail, in case the characteristics of matter waves, as Ford puts it, should come to be confused with something intrinsically different in the nature of causation, in an irrational manner.
This interference limit, owing to methods available, however, is not at all to be confused with non-causation (via the route of inoperative, precise predication of velocity and location to an electron simultaneously).
Not only, he notes, is it not scientifically possible to predict a physical event precisely, as noted earlier, because of measuring limits in all cases ... but geometrical proofs are viewed as rigorous, even though their data are not subjectible to precise interpretation in the physical world (that is, there is a limit to the exactitude of all our measurements in the physical world, which is not present in the geometrical model).
Failure to make precise prediction is then endemic, within limits, and persists here, within limits; and in each case the limits are inherent in the possible nature of approach to the subject matter. The necessity, for clarity, of defining an event as 'a certain merely intellectual process' is noted: It substitutes a new world in place of that given to us by the senses or by the measuring instruments which are used in order to aid the sense. This other world is the so-called physical world image; it is merely an intellectual structure ... It is a kind of model or idealization created in order to avoid the inaccuracy inherent in every measurement, and to facilitate exact definition.
Indeed Planck rigorously reasons, the validity of statistical laws is entirely compatible with strict causality.
The irregular impingement of gaseous molecules on a wall, in an enclosed container 'is entirely compatible with the admission that the impingement of any one molecule upon another or upon the wall is governed by law and hence is completely determined causally.'
Tracking methods, and limits to envisagement (*3) (dependent upon limits to measurement, and hence test and discernment of the subliminal world of causatively significant events) are merely a comment, then, on the non-divinity (*3) of man; not on the non-operation of causation. In no single instance has it been known to fail where adequate test is available; although man may fail because the domains are above the limits of his current - or here, perhaps, eventual scientific competence.
There is then nothing contradictory in determinable principle; what occurs is a humbling experience to the imagination, and this in precise accord with the history of science, always ennobled by discoveries it can make, and the coherence of what it does find when the implements available for measurement - after all ingenuity has been applied - are indeed adequate for factual knowledge and conceptual testing. There is, however, no inherent guarantee on the limitless sufficiency of these, for all things ... far less for even relevance, to that interface of action where the spiritual acted and and implemented in creation, or where it does uphold the physical.
As always, we come to terms with causality or face implicit extinction, uncreation, the sure sign that we have strayed from reality. In highway terms, wrong way, go back. You collide with unyielding reality.
For review and emphasis on the variety of causation, before we proceed to our particular cases, let us look at the field of causality briefly.
Neither a universe, a system nor a sub-section of a system is even analysable without the concept of causation operative; and as we have shown, neither reason nor language is applicable where it is not. Definition then dies; characteristics cease, even for reference : so it dies, being indistinguishable... from nothing.
True, different kinds of causes operate - a point Bloom is seen to adumbrate in an earlier part of this chapter; there is the directly material region, the analytically mental, the spiritually original and imaginative, and they operate on different grounds or bases, as shown. All this variety, however, is neither vapidly homogenisable, nor independently autonomous, but subject to system that is itself, the creation of God.
It is He who determines, by virtue of created criteria and characteristics (or by intervention, as a child may, stabilising by a touch the movements of his railway train on its circuit), the facility for mind to be delivered from body, for spirit to engage in will - past mind; and for degrees of interaction, or independence, ending in supernatural coverage, for His own purposes, from which it also began. An engineer may, in his own sphere of creativity, similarly superintend the design he made.
God indeed is the non-serial originator of the serial system of causes, and has absolute power to maintain at any level, any part of His design, to whatever it may be subjected. The causality-Creator, operative beyond serial causality, sanctions the laws, creates the systems and grants them their stature, status and kinds of inter-relations; and He conveys creatively with design ... the desired interfaces, interest and functionality - as is common with design; except that this design includes firstly, absolute creation, and together with that, spirit for man, as image-bearer of God (see Chapter 1 and *3, Part 1, Chapter 4 supra).
Those are, then, kinds of causes, systems and functions, for their operation; and within them, there is man, in God's image, spiritually, functionally; while beyond them, there is God, the Creator of serial causality. As seen, sense and system alike die when cause is denied (see pp. 264 ff., 'Mark II', relative to Hume, Chapter 3).
Any such 'place', where this is 'done', is then an arena of imagination, unformulable to thought, as also inexpressible in language, which of course immediately establishes the contradiction implied; just as the concept of any merely human creation of 'causing' or causation itself, is simple self-contradiction, using causation in order to get it, using sufficiency of reason in order to exclude it ... (For that matter, you could not even be the cause of its removal, if it were objectively invalid, for its absence would invalidate your action, just as only by its presence could you seek to 'account' for it. You need it to be rid of it! as to account for it, while it calmly looks on.)
You cannot validly exempt a part from the operation of principles necessary for any discourse at all: what you 'exempt' is thereby equatable with nothing. Accordingly, it makes no difference. Neither characteristic, nor form, nor any other variety of comprehensibility or coherence remains to it. Causality, itself similarly we can neither 'cause', create nor originate; nor quash, dispel and cancel: in principle; and therefore, in whole or in part of any system, scene or scenario. It has indispensable operation for those who do not wish to contradict themselves at the outset, so rendering their 'system' irrational... against which there is no law; it is just that it is then in the area of unreason, not subject to argument, not presentable with or for grounds.
'Being ridiculous' can be fun for a game; but life is not a game.
The first, that of Professor Hawking of Cambridge, though deterministic in a way that passes from his field, to others earlier shown to have diverse characteristics of their own and for which this approach is as irrelevant as it is inoperative (*4), still yields an interesting result for us in the relevant field. In fact, it adds a rather bizarre and chimerical, and indeed an almost Faustian feeling to the continual underlying appeal, that proceeds from the extraordinarily effective concept of precise material causation in the material domain.
The second approach, one already noted, will be seen in sequence with the above, and will occasion contemplation of the field. This approach is more composed than the first, though one showing perhaps no less determination... It is more discerningly limited to the field of investigation, the physical per se, being that of famed atomic physicist, Max Planck. Still, it has this in common with that of Hawking: he stresses strenuously the applicability, the propriety and the profit which comes from the theoretical and practical employment of strictly causal concepts in physics.
These preliminaries will allow us, with some preparation, to confront or construe the situation relative to waves and particles, with special attention to causation.
Before we embark on this multi-stage journey, however, it is apposite to notice three things. First, it is intriguing how philosophers (and physicists may unwittingly assume this role in passing) may find on this or that occasion, some element of what God makes so clear in the Bible... such as the manufactured look of molecules and components, so impressive to the famed creationist scientist L.E. Maxwell. This exposes the desperate drafting of such components, in their uniformity, into particularistic production (without the Creator) in the inadequacy of an imagined 'non-particular' universe ... the concepts collide! Moreover, it focusses the stringent operation of causation as distinct from that wryly humorous phenomenon, the magic of a materialist... and so on.
Second, it is just as arresting to find how some then, like sheep finding the gate attractive, but that to which they are thereby pointed and led less so, may stumble, even then! As illustration: causation changes, through false application, into determinism with a strangely odd backing of human determination to overcome the strangely inept basis. It is as if one idea had proved obsessive, and a survey with spiritual oversight and factual care, had become over-exacting. Extremes alternate ...
Third, it is fascinating how one may compare the perspectives of divergent thinkers, and yet find in them some crucial elements in common, a point of departure being individual and special to each, but a base shared.
Our first example, taken chiefly for the instructive light given to material causation, exhibits the phenomenon of causation becoming determinism (*4), with the help of determination, which might wish it had the sheer thrust of matter, which gets its thing done, miracles apart; but which, not being matter, lacks this property and is quite capable of showing our deliciously human weakness, the disjunction between purpose and ability, or between desire and design, or between intention and orientation, between the irrelevance and non-applicability of 'error', in some theory, and the facility to err in practice, in fact, in reality! (cf. pp. 23, 290, 315A ff. supra, 439 ff. infra). So does science die, and determination merely exhibit ... for science, the very error itself, with which determinism has no cohesion.
In The Australian Magazine, September 17/18 1988, he exposes something of his conviction of rigorous determinism, in his selected study area: physics.
He is confident in his field, of being able to predict - or of workers in this area being able to predict - in principle, all the events! He declares:
In principle we can predict everything from physics. But the calculations are much too complicated...Looking for a more advanced and unified set of physical theories then Einstein's, he sees intricate and complex equations in the interstices of matter.
In one way, this is refreshing: an eminent scholar seeking imaginatively for one more of those so numerous advances, by which science in physical matters has moved so far at the predictive level, with insights towards a greater rigour in the perception of the mathematical correlates to matter and motion. He is in the line that has proved both practical and progressive in the past. He is not throwing away in this matter a few thousand years of constantly confirming reason, where rigour has been, when applied, rewarded in the rigorous and material phase of the universe.
Like Maxwell, Faraday and Newton, Hawking expects rationality; like Planck, he pursues it with confidence, and is heartened.
Of course, it is what might appear an amiable defect, that he seeks to enclose in his expertise, like so many before him, areas in which he is not expert. This does not grossly reduce the force of what he does know, in its field; it does however in this case have fatal consequences for his thought, and for its fulfilment, where determination is no substitute for validity.
The erring - yes erring - mind that thinks, and the roving conceptual mind that soars, the willing spirit that breaks even its own perception of its own good for the glory of its own autonomy: these things are no more matters of equations than are the frequent conceptual misnomers which dash the intellect to humility so often. The latter may observed in the imaginative fixations which fly, imperceptive past the facts; or the broken tempers that defile the beauty of personality for the lust of success or the power of pride. This we have seen already, in some detail.
We have moreover, at some length, seen that deterministic bases omit the possibility of truth and hence destroy at the outset the possibility of the theory being so. Yet for all this, the principle of physical (*5) determinism is part of the beauty of a sub-structure - not divorced from miracle (*6), it is true - in which our spirits move. All of this, each component of matter, and all that to which it ministers, all of mind and spirit, God upholds (*7) by the word of His power.
The individual characteristics of matter, it is good from time to time to have people like Professor Hawking, like Planck, like L.E. Maxwell, declare. It is a sound antidote to that heedless and headstrong irrationalism which so contrarily and ridiculously argues for itself with its rejected instrument... of reason. (Cf. pp. 421 ff., infra.)However, blindness to the peculiarities of different parts of our bodies, or different parts of our universe is no ground for trying to use the hand as an eye; the mind as if matter; the will, which errs, as if matter, for which the concept is meaningless. These are mere chatters without reason, blindnesses without base, assumptions in the face of the criteria, self-contradictions in the light of the divergent phenomena to which the mind is directed, challenging in their richness, causal in their conduct, but in utterly different ways. (Cf. *13, pp. 882-884 infra - time.)
The various determinisms, of which this material case is merely one philosophic episode, tend in general simply, as if by a fateful and blind fascination, to demarcate the diverse and divergent character of so many of the components of our trilogy, our mind, matter and spirit. In this, they serve, if indirectly; for as the Bible indicates, God makes the angers of man to serve Him (Psalm 76:10). It is a misdirection of effort, the endeavour to absorb all things in one thing, as the early Greek philosophers strained to do in the cases of fire, of water, of earth; it does not go. It is one, but not a thing, to which reason inexorably thrusts our minds, as we have seen; and as we have also observed, the sheer irrationality of the efforts to homogenise all reality is eloquent, indeed elegant testimony to the spiritual disorder which occasions it, and thus to the Biblical analysis of man.
In particular, he deals with Ludwig Boltzmann, who found law behind the prima facie irregularity in gas molecules. Indeed, notes Planck, whether we look at gas molecules in a box, or waves' ripples on the sea, we have no reason whatever for postulating unreason. After all, multitudinous events do not destroy minute rationality, although as history exhibits, minds may boggle at their own incomplete powers, at some passing phase of history, to penetrate some domain of matter or other.
Planck majors on the fact that scientific theory is an intellectual construction not to be blithely identified with the reality; and within its own terms, it is a decisive and long tested instrument of discovery, prediction and progress. Indeed, he urges, even quite ordinary measurements are merely constructs. A lack of facility to measure is found everywhere - in degree - in science.
If this lack be systematic, as Ford (*8) urges, what then ? Is the case different because the measurement device, as far as can be seen, cannot perform the measurement ? What philosophic meander is to be used needlessly ?
We might say: If an electron limits, or indeed any other particle... the survey of any scene, or even the identification or inspection of any unit in the material universe, is this a philosophic enigma or a restraint of data ? The former is wholly unnecessary and unevidenced, as an opinion. It adds to known reality, and contradicts what is known. (See also pp. 288 ff. infra e.g.: for the inherent failure of the former possibility.)
Planck talks of his famed quantum as the limit of intelligence in this area, in the sense of the unit of oppression, the one which limits expression or discovery; but be this as it may, the principle is the same. There are limits; where they occur is relatively indifferent. This is a matter of data not dilemma, circumscription, not confusion (unless of course you want to avoid the circumscription; but then it is wilful confusion, not systematic confusion).
To quote Ford again, he finds the Heisenberg uncertainty principle much overworked. Planck puts it: material waves are the "elements of the new world image" (op.cit., p. 60). Their limits are the limits of inspection; their characteristics regulate meaningful enquiry; and Ford similarly urges that the peculiarities of matter waves are not a matter for assumed profundity, so much as notation (p. 1171 op. cit.). They have their characteristics, and are susceptible to this or that form of activity, not to that. Prescribing how their characteristics should occur is not descriptive but prescriptive science; and that, of course, is philosophy; here in collision with fact.
Certainly it is interesting that in the double slit diffraction case, it appears that the electron goes through the slits with two different modes, as Ford indicates; it does not go with one or the other, but both, which interfere. What a resourceful seeming object, if it becomes wave-like in transmissive antics and corpuscular in mission or reception at the other end.
A supersaturated chemical solution might, with similar amusement be personified: fancy, on the one hand there is the same substance in solution, spread out, diffuse, and then, in a moment it appears in one place (as a crystal) countable, discrete, and not diffuse. We know now some of the elements of the change; but without some background, it might appear to some to have the polymorphic performance characteristics (*9), which seem true of the electron now! It is fun (*10) to know that an electron or a photon can have such variety and such a facility; and no doubt if particles small enough for use in such scientific investigation, or other means, should be found, more may be determined. If so, the criteria of dynamic change and their specific mode of operation may be found as has happened through the history of science, typically, and as with crystalline and solution forms, increasingly.
Otherwise, we may have reached the discrete limit, and it may be merely indiscreet to seek what is technically, not logically (*11), a contradiction in terms; but more precisely, a contrast in forms. If this limit has been reached, the smallness of the probe growing too great for the minute character of what it touches: then investigation and consequent codification of the situation may be thrusts working in man, without the means to satisfy them... in some men, that is.
In fact, the time may come when the very production of (divine) maintaining power back of the elements of matter may be reached. Then, as with the scientific approach to the production of the universe, there may indeed be a systematic inability to go further.This limit does not constitute any failure of logic as we have noted above: it would simply indicate the failure of the human to be divine (*12). That, however, has been overwhelmingly indicated, long before this; though the lesson is far from always learned.
Analogically, it would resemble the effort to go beyond the author's book in seeking to interpret it... to the fingers and the brain; but in this case, that would be an unproductive creaturely enterprise. Within our limits, not of craft so much as creatureliness, we will remain, to whatever we may aspire (cf. Isaiah 14:13-15). All that we can discover, meanwhile, is filled with cause and flowing with effect; and limits appear both at the level of the mind, the spirit and matter.
Thus the competence of one creature wholly to know another resembles, in its limitations and constraints, the case of matter, so coherent in logic, so challenging to perception. Deity has in reserve, as it were, what we do not have in construction: exhaustive and constitutive knowledge of all things. The way it works remains.
It will be useful to put some of them together. On p. 1159, he notes that in quantum mechanics, "the wave function may be a vector quantity or a more complicated intellectual object" - thus giving yet more impetus to the thought of complex polymorphism, whether in a physical form or an intellectual model intimately related to it, for the matter under investigation. Obviously, where there is divergence and diversity of form and nature (in precisely the same multitudinous variety we have hinted at, and to a small degree illustrated in examples in nature elsewhere), there is challenge.
We must avoid trying to reconcile diverse alternative forms of matter with each other, as if the geometry or modes or phases of their different structures were to be reconcilable per se, when an intellectually programmed change, seen in or effected by law, re-fashions the raw material as to form, in ways not immediately envisaged before the event, but found as part of the creative aster of God, after it.
Where this is done, or such facile insistences are made: then there is confusion of mind, not in logic. That is why the expression: "or a more complicated mathematical object" is so fascinating. As with sulphur crystals, it is not a matter of this or that oddity or arbitrariness, but of minutely contrived, exquisite intricacy of form variation. Indeed, for interest, in the in the panorama of living and non-living nature, it is also fascinating to reflect on the nature of identity and variability in the developing elements of a frog from a tadpole. Obviously, the ultimate identity to the creature is the Design. The changes, accordingly, are governed. In this case, it is coded. The design? It is the series of chronologically disparate forms and relationships which are themselves parts of an overall integral plan. Part of that plan is the provision for the sequence, the code correlative to the forms, their sequence and their entire outcome physically. Such elements may be seen in measure, by studying the genetic design, with its almost endless programming specifications, or simply by watching the frog, large enough to be seen, come into adult life, having traced the stages.
Computer programmers now are gaining, with increasing 'power' the facility to make highly varied materials 'appear' with grave difficulties for anyone who does not know the purpose or the directions or the cohesive language which binds events to code and code to thought, both based in purpose, also expressible in language and engaging to imagination. If you know the language and the purpose, the diverse forms and the variety of performances which is caused by it, are readily discernible. Static formats, flowing forms and intellectually correlated sequences of different dimensions are not necessarily linked in one simple mode, but consequences of integral design, the form and format for which is a comparatively superficial correlative of the movement.
With matter, there may be sane simultaneity of forms for an identity. This is interesting, intriguing, but logically merely one more variety of actuality to ponder.
We must stop trying to play God and to set up an understanding of laws as if we were determining them. God determines them and we read them; His power implements them and we seek to discern the modes employed where these are set in physically or mathematically construable formats or formulae.
In terms of our poem analogy, the more compelling since language is now discerned in biological formats, the form of the words and their changes are part of a reservoir of forms which are symbolic, and which determine in different ways, the results of purpose. There is no common form or basic ground in form, for the changes of form; though they relate to a unity of purpose and a set of forms, correlative in comprehension, and more serially sequenced in procedure.
Law and language by their nature are not formally induced, but cognitively, the forms being symbols. As with computing machine code, there may be few who can understand this core, but many who can discern its consequences, for which, after all, it was written. In varying degrees, depending on the sharing of the author of the poem or program, as the case may be, and the insight or involvement of the viewer, aspects of the procedures may gain in clarity, or perspicuity, but at that, not necessarily all; and as noted, there are limits to what the writer may convey, in that much is personal beyond the exercise, or technical beyond the needs of the reader; or, conceivably, his capacity.
Of course, as Ford points out, it is intellectually satisfying when one can have not only the rules, but "a physical model that makes the rules seem reasonable, or even necessary." This, he indicates, p. 1157, was the case when the Bohr quantization rules in hydrogen were proposed. The de Broglie waves provided for the "Bohr orbits" a rationally construable model; whilst the Schrödinger wave theory of quantum mechanics refined this rationally helpful model.
So conceptualisation increased within the parameters of means for acquiring data, and divining correlative functions, at this level, or at that, in a phenomenon of many levels; as are, in their measure, some of our own creations.
On p. 1160, Ford refers to the case of a single slit diffraction for "electrons (or other particles)", and says: "In the act of detecting a particle, the wave becomes only a ghostly guide" for the position of a particle. Speaking of a double slit diffraction case, he notes "although easy to understand for waves, these facts strain our powers of visualisation for particles." He proceeds:
Because it is wave functions rather than probabilities that add, the combined state is an intimate combination of two states. The electron is in state 1 and state 2 ... (p. 1169, op.cit.).His point is that particle capacity for formulation is limited, and in terms of continuity, wave formulation covers the case; and that if particles are part of the forms devised for activity, this is not to be construed as a logical difficulty when the wave formulation is aptly embracive and covers the case overall (with "accurate equations that describe what happens in detail," to quote from Professor John McIntyre, cf. *9, infra). This would not seem difficult to follow. Indeed, we note on p. 1129 that "quantum mechanics is an unambiguous and quantitative theory."
In fact, on p. 1171, Ford expressly states:
The uncertainty principle when discussed by itself outside the framework of quantum mechanics (*13) is often assigned a profundity that is scarcely justified. It has obvious philosophic implications; and with those who wish to attack science it is especially popular because it shows that even the exact scientist is prohibited by nature from measuring things as exactly as he would like.It is important to notice the words - he is prohibited "by nature". There are limits to the presences of a particle, relative to its movement into waves, and these limits show us how foolish we are to lament and tear at logic when in fact we are dealing with the intellectually and geometrically polymorphic, and dimensional, not to say multi-purpose. Complexity is not a logical problem, merely a site for its application.
What remains at such a time as this, is the detective work of finding it out, where and if the minuteness of particles and waves permit it in terms of yet smaller measuring and manipulative equipment, provided that the relevant power and oversight is imparted into the visible realm. That is, both equipment and particles may need to be available for such measurement. The former may be beyond the ingenuity of men at any one time; and the latter may simply not exist, setting a permanent barrier to measurement by anything based on such means.
Dr Ford proceeds:
One may also argue that nature is shielding its innermost secrets by allowing man to proceed only so far and no farther in his downward quest. In truth, the uncertainty principle is fundamental and presents in capsule form an important part of the physical content of quantum mechanics. Nevertheless, it may be viewed as JUST ONE MORE ASPECT OF THE WAVE NATURE OF MATTER, in which case it seems considerably less mysterious (*14) (capitals added).Ford argues that wave characteristics not fitting into pre-determined desires for information, apt for something else, are not mysterious. There is a limit to the specification powers of man relative to certain physical objects or forces. This may at present be because the very act of detection of the place of a particle, by the means currently available and realised, may move that particle ; or it may indeed result from the assumption for its form being one which is simplistic relative to reality, in certain circumstances, one therefore requiring refinement. There may come a time, of course, when the measuring means to make any imaginative refinement to be evidentially verifiable, simply lack.
We must in any case await information from functional formats and their mathematical correlatives, if probing power develops, assuring conceptions and operational constructions of theory more in line with reality.
This then is not at all a matter of a limit to logic; but to characterisation, it would seem, of a polymorphic and multiply conceived scene of work (say a photon or electron - God's work) in terms prepared from prior preference: and not from intimate and adequate knowledge of just what is being measured, in what form, at what moment and in what circumstances, or with what results. All the time: measure, conceive, know, understand... are the crucial challenges which, when cut off at the commencement, cannot well proceed to the end, when it is a matter of man minding matter.
If, for example, certain waves have a peculiar cohesion and coherence in given conditions which, as a divine design designation precludes dispersion, segmentation or severance that is not correlative with the corpuscular, or which causes particulate correspondence in unexpected ways, we learn more laws, that is all: created laws.
Like kindergarten children, we can have real problems if preconceived ideas are used. To deal with a log as if a teddy, with water as if honey, with snow as if water and with steam as if air; indeed, to find the dog by lunging at it as if it could not move, or change its form: these may be the analogical problems of infancy, to teach us patience and imagination in age!
There is simply no logical problem; but whether as Ford suggests, we are being held at bay from further knowledge by a divine prohibition or a principle embedded in nature - whichever is his meaning - or not, there is a way to understand the limits of what we know. Unpredictability, in this conceptual domain, is far removed from unaccountability (see also *16 p. 421 infra).
Waves are not particles and some of the properties of the (simultaneously and variably ?) polymorphic entities in view, are not determinable quantitatively, except in terms of the overall wave concept, itself requiring consequences which may not, with our means, be broken down at all times, to predictive expression or known form in terms of the unit particle. How could they be, if the electron, or the photon is sallying forth as a wave with a necessary limit to any analogy of particle ? (Cf. p. 1128 - "We now know that even a single photon has wave properties"; and *10 infra, together with the construction of Dr John McIntyre).
Yet the wave background, or ghostly guidance which this format provides, or if you will, the overall structural limit, acting in ways not fully discerned (surprise, surprise!) leaves no option to the eventual form available for the expression of particulate consequence. Thus we read: "This discussion of wave superposition has demonstrated the essential point that the Heisenberg uncertainty principle is a consequence of the wave nature of particles. It is no more profound (*15)... than the de Broglie equation giving the wavelength of material particles. Uncertainty of measurement arises essentially from the non-localisability of waves."
Parameters suitable to one format may, in a sense, be proposed for some undergirding or aptitude for talking about them in another format. As the overall resultant situation for the particle detection, after diffraction, is determinate - or as Ford says, p. 1161, "the wave function gives quantitative expression to the idea of wave-particle duality" - so what is lacking is the capacity to localise absolutely the complex.
This, as we have shown, is a difficulty of desire not logic. Ford puts it (p. 1167): "The wave nature of matter explains why a particle can never have all its energy taken from it, and why it can never be localised in space. Were it otherwise, atoms might be inert nuggets 100,000 times smaller than they are . . ." Our powers of mathematical description are available for determinacy, in its place; but not for determining the complex to be simple, the dynamic to be static or the variable to be single.
Mathematical uncertainty in this area of determinacy of matter is simply this. It is the expression of the status of a desire to express what is (the actual reality before us in matter, with all its wonder and detail and variability), in terms of what is not (i.e. a simplistic figment manufactured in the mind for convenience); or of inability to measure adequately; or both. The device, the abstraction, the theoretical conception used for asking some of the questions may be useful, and dressed in terms of probability; but this device presents no problems logically for total material subjection to law, as a concept. Quantification applies where reality is aptly and adequately measured or measurable... and it is confirmed by the results that can be measured.
Past all this, symbolic forms are to be increasingly grasped in order to construe better the background machinations, imaginations, conceptions and codes, providing unity to diversity, point to variety and means for purpose.
All that is shown in the end is that man is not God. We must think His thoughts after Him, not prescribe them for Him. That (necessity) merely verifies His work - rationally, not rationalistically. It is the objective ground for the humility in observational science, proceeding by scientific method; and equally, the rational basis for the advance of science, when this has been its method.
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