Sample

Prologue

         Exploration, Theory and Reality

Some problems can be solved by systematically seeking a solution. There are other problems, however, that give us little choice but to wait for a solution to come and find us. The charting of an unknown continent resembles the first type of problem and will respond well to systematic searching. The rate of exploration of a continent is likely to be roughly proportional to the amount of time, money, and equipment consumed by the project. Scientific exploration, however, is more akin to the second type of problem and throwing resources at science does not necessarily solve its particular conundrums. Consequently, the lack of any proportionality relating scientific resources to the rate of scientific problem solving makes it impossible to put time scales on scientific objectives. This means, of course, that one cannot say by which year certain outstanding scientific issues will be resolved. In fact, there seems to be no a-priori reason why the cosmos should be organised so as to make it thoroughly amenable to scientific epistemology, and indeed some people have doubts about just how science friendly the Cosmos is:

         Physics appears to be a complicated subject, because the ideas of physics are difficult for us to understand. Our brains were designed to understand hunting and gathering, mating and child-rearing; a world of medium sized objects moving in three dimensions at moderate speeds. We are ill-equipped to comprehend the very small, the very large; things whose duration is measured in picaseconds or gigayears; particles that don't have position; forces and fields that we cannot see or touch, which we only know of only because they effect things that we can see and touch. 1

          Nevertheless, it would seem that scientific epistemology has been surprisingly successful in probing the things that this author says we are ill equipped to grasp, for we have been graced with at least a passable understanding of relativity and quantum mechanics. Whatever skills the necessities of genetic propagation have furnished us with, those skills have certainly proved to be portable enough to give us Einstein's equation and various Quantum equations, conceptual artifacts whose role in service of the immediate and pressing issues of survival is rather obscure. These seemingly unwarranted winnings give us the courage to keep plugging away, hoping that the organisation of our world and the chances generated by its complexity work in our favour, and that one day the long sought for solutions to our scientific problems will fall into our laps.

      There is an enormity in the scientific hope: A given theoretical problem in physics, for example, may be the subject of a prohibitive number of plausible hypotheses that can be used to explain the known facts. Theory making, therefore, may be not unlike one of those intractable combinatorial problems involving some kind of exponential tree search of the possibilities. When faced with such a problem, the linear stockpiling of resources in terms of human time, effort and sagaciousness are quickly overwhelmed, utterly dwarfed by the astronomical size of the search space. Even experiment may not be of much help in suggesting the right theoretical road to take, for it often has the rather negative role of providing some kind of evolutionary context in which weak theories can be weeded out. In this context generating a successful theory may seem about as likely as a successful biological mutation. Thus, as far as scientific endeavour is concerned we should not think of ourselves as pro-active protagonists with a planned programme of scientific conquest, systematically exhausting the space of possibilities. Instead we find ourselves to be opportunists waiting their chance, perhaps at most intellectual scavengers wandering around hoping to stumble across a solution. In fact, we may not even be as pro-active as this, for often in science there are those who find solutions to problems they haven't even been looking for. Scientific epistemology, in the matter of testing a given theory, may have some semblance of logicality and system, but the production of those theories in the first place is far from systematic. It may be best to think in terms of a reactive, opportunistic model, heavily reliant on the fortuitous. This could just as easily be interpreted as a providential rapport with the cosmos, even a kind of “winning streak” which means that we are primed against all odds to at least get it somewhere near right. In short, the success of our epistemology is the subject of such a complex of contingencies, conditions and chances that we have little choice but to trust to its integrity; those who do not will have little chance of reaping the rewards of success.

***

     I make these preliminary comments in an attempt to excuse the audacity of publishing the contents of this book. This book presents a theory of quantum gravity, no less. Let me say straight away this certainly doesn't mean that I think of myself as having, against all odds, got it somewhere near right; it's just that in the light of what I have said, I think there is a chance, albeit a small one, that I have got it right. The theory presented here does not come out of string theory, black hole thermodynamics, or loop quantum gravity, or any of the other current theoretical approaches. I shall be honest: I never went looking for a theory of quantum gravity. Much better, I thought, to leave it to the experts who are working in the fields I have already mentioned, fields that are way beyond my abilities. For now, let me just say this: in my wonderings and wanderings I just happened to stumble across one possible way to bring gravity and quantum mechanics together, and there seemed to be nothing to lose by giving it a try. Moreover, as I believe the issues surrounding the subject of gravity to impinge upon the meaning of life, the universe, and everything, the stakes are accordingly very high. With stakes as high as this and with limited choices and little to lose, there are few options but to be a gambler. Any chance, therefore, though it be small, is all one needs to get going – and, of course, a touch of crankiness helps. I am not cranky enough, however, to fail to realise that given my lack of background in gravitational theory, a direct assault by myself on the problem of quantum gravity in the hope of getting somewhere is an absurd notion; the basic ideas in this book were not arrived at through a motivation to solve this problem. Like many before me, my main interest has been in making philosophical sense of quantum mechanics. The results of this largely philosophical endeavour, itself a product of the fortuitous, is the subject of another work, but almost as a by-product of that work came, what seemed to me, a plausible theory of quantum gravity.

     If the problem of quantum gravity can be thought of as a riddle, then like all riddles it seems at first utterly opaque. It is often the case, however, that once given a solution to a riddle one is left wondering why one never thought of the solution before. In prospect riddles seem impossibly difficult, but in retrospect easy. The reason for this strange feature of riddles may be because of their “NP” like structure. That is, many riddles present an exponential problem and therefore a search space of myriads of spurious possibilities in which a few solutions are embedded. Nevertheless, once we are told the solution to a riddle it is a short task (i.e. one completed in polynomial time) to verify that we could have arrived at this solution from our starting point in n short steps where n is some relatively small number. This is why, once we know the solution, it seems easy: retrospectively we can see a short path from start to finish. Thus, if quantum gravity is a riddle, which I feel it is, then it was no surprise that once I fancied I had a possible solution, looking back it seemed an obvious solution. In fact, if I am right, the solution to the problem of quantum gravity has been there all along in quantum mechanics, staring us in the face, as I shall now try to explain. What now follows is not so much a bullet proof sequence of logic but rather the overall drift of the argument. I must also concede that the following line of thought is better appreciated by someone who has my own view of the meaning of quantum mechanics: briefly, this view is that the realities of our world are not particles but waves. The apparent existence of “particles” comes about because of the discontinuous changes of state of the wave function, chiefly in the form of “collapses” - which I take to be an actuality - from highly extended wave fronts to very localised wave packets, thus giving rise to the compact phenomenon we approximate as particles. In my view particles as vanishingly small points do not exist at all, only waves with varying degrees of localisation. In this book the approach sketched out below will be developed more rigorously, but in the meantime I hope the following will act as a prima facia case for directly linking quantum mechanics with space-time curvatures.

***

     According to Quantum Theory particles are a form of wave motion. The momentum of a particle and its consequent velocity is determined by its wave number, that is, the number of waves per unit length; in fact, the higher the wave number the greater the momentum and therefore the greater the velocity. Now, a wave is an entity extended in both space and time and as such it may have boundaries to that extension, or its wave number may vary from place to place or from time to time. Since the momentum and velocity of a particle is related to its wave number then it follows that that momentum and velocity may vary not only in time but also in space. This means there may be a variation of “particle” velocity within the volume filled by the body of the wave.

      Special relativity implies that when observed from a “stationary” frame the space “inside” the frame of a moving particle appears to “contract” in the direction of motion. Also, the time inside that frame “stretches” or dilates in a complementary relation with space contraction. But a “particle” is an extended wave-like entity with an associated “velocity” that may vary not only in time but also, because of possible spatial variations in wave number, may vary in space as well. Now here is the important but moot point: The possible variation of velocity within a wave field suggests to me that we somehow find a way to apply velocity dependent relativistic effects differentially across the region of this wave field. If we succeed in doing this then special relativistic effects will vary over the region of space the wave function occupies as a consequence of the variation in wave number. The details of the application of this rough and ready notion will be spelt out in the main body of the book. If we successfully apply this notion, then there will be a differential in space contraction and time dilation as it is applied over the wave field. If, then, a waveform has the effect of changing the contraction of space and the dilation of time within some region of space-time, this is very suggestive of a space-time curvature and it a is short step to the conclusion that quantum waves cause space-time curvatures, and therefore a kind of gravity

***

    If I am right about this close relation between quantum mechanics and gravity, it will not be the first time that a short link between what was already known and a deeper fundamental theory has been missed. For a long while Maxwell's equations stared scientists in the face, equations that were, in fact, an implicit witness to the Lorentz transformation of special relativity, but no one spotted it. However, whilst the argument in the foregoing paragraph suggests an immediate and obvious connection between quantum mechanics and gravity, it is a very sketchy argument and it needs quite a bit more added in order to make it work in detail. This book gives one construction of those details, but it carries the caveat that even though we might take this approach to quantum gravity seriously it does not necessarily mean that my particular implementation of it is correct. It is perhaps ironic that I did not arrive at my theory along the simple route suggested in the previous paragraph. The path I trod was much more convoluted and only in retrospect did I see that the connection between quantum mechanics and gravity can be made to appear so simple and obvious. My route involved an obscure and probably contentious philosophical take on quantum mechanics. These ideas lead to a theory from which special relativity seemed to be a consequence. Eventually it became apparent, however, that special relativity, with its space contractions and time dilations, could be applied differentially within a wave field, and the possibility of quantum wave induced space-time curvatures occurred to me immediately. But to implement the effect of this curvature requires other waves to be affected by these curvatures. This means that we lose the linearity of quantum mechanics. In my theory, quantum mechanics is not linear, and gravity is the evidence of that non-linearity. The linearity of quantum mechanics is not the only thing we lose; we also lose Einstein's hard won field covariance. The reason for this loss, according to the theory proposed in this book, is that gravitational fields are brought about by an atmosphere of highly attenuated quantum waves surrounding an object, thus constituting a kind of “atmospheric ether“ rather than some fundamental covariant principle of space-time. But having said that we need to understand here that the theory being proposed doesn't necessarily invalidate special relativity any more than the existence of atmospheres invalidates it; it all depends on what we identify as truly fundamental. Nevertheless, all this is no doubt a sad loss. The linearity of quantum mechanics and the covariance of Einstein's equation are two mathematical gems, the loss of which will probably count against the theory I am proposing.

***

     Even if the theory being proposed here is “right” it is certainly not “final”. If quantum theory can be said to deal with the microscopic, then the theory I am proposing hints that quantum mechanics itself issues from some deeper “sub-microscopic“ layer. My theory, however, does not probe in any detail into that layer and therefore it is a theory that has its limitations. It is certainly no grand unification - if such unification is possible. In keeping with the rationalist scientific tradition I view theories as not unlike computer programs which attempt to simulate reality. These simulations inevitably have their limits and therefore the question is not so much about whether a theory is “right” or “wrong” but whether or not it constitutes a good simulation on the basis of its succinctness and conceptual technique as well as its explanatory power and predictive value. Given this notion of theory construction, it becomes clear that there is latitude in the way a theory can be constructed in terms of the quality, elegance and nature of the concepts employed. This becomes very apparent when a growing list of experimental exceptions is patched into the body of an aging theory, increasing its shelf life, but making its construction untidy and complex. This eventually gives way to a complete rewrite of the theory so as to assimilate the same facts with a greater economy of principle. This reduction of the complexities of our world into the simplest possible principles constitutes a kind of data compression. But those complexities must be of a kind that admits compression in the first place, for there seems to be no a-priori reason why our world should yield to such compression. Parsimony of explanation is not always something to be found, and great theoretical unifications whereby skeins of facts are reduced to a few simple principles is not always guaranteed to work.

     In fact, in some cases the notion of explaining the complex in terms of the simple may actually be reversed. For example, elementary scene of crime clues may have complex underlying causes to do with the sociology and psychology of human beings. There may be things out there that are simply are not theoretically compressible, invalidating the sentiments of Occam's razor. If in fact there is such a thing as a creator God, then accounting for the complex in terms of the simple, as we are used to in physics, is turned on its head. But let us at least thank God that in physics providence has supplied the right balance of challenge enough to arouse our interest and yet fruit enough to support a faith that progress, if not grand unification, is possible. Even in physics there may be more than one technique of conceptually compressing a nexus of facts and theory making, like programming writing, is probably an art as much motivated by a sense of aesthetics as systematics. This does not mean that theoretical constructions are arbitrary or the “free creations” of the mind, for it is an art which must rise to the challenge of emulating an independent world. Anyone who has been involved with programming knows that programming is a bit like being given a construction kit of parts. All sorts of constructions can be imagined and contrived, but it is nevertheless clear that some constructions are neat and some of them clumsy, some work and some don't. Moreover, the problem domain itself may be intrinsically complex and difficult to represent and it may or may not admit elegant programmed solutions. Likewise, few would disagree that when it comes to simulating, and very importantly, anticipating the sensory aspects of our conscious perception, there are theories that work well and others that don't, theories that are clumsy and theories that excite our ascetic sense. But however beautiful, unifying and successful our theories may be they will ultimately face the contingency barrier, the limit beyond which elegant theoretical reduction can be taken no further. We will always be left with an irreducible, logically incompressible kernel of facts, whether those facts be boundary conditions, constants, or the form of physical law itself. It may be that only in the trackless infinities of God will logical necessity be found (if such can be found by finite beings) and the contingency problem ultimately solved. In short, as the theist insists, logical necessity is extrinsic, rather than intrinsic, to the Cosmos.

***

     Mind is thought to be composed of matter but this common sense view is challenged by a persuasive case for idealism; that is, that matter is composed of thought. The material of the cosmos is mathematically conceived as the interplay of complex loci in a Riemann space, but what actual reality does such abstraction have outside the mind? Is there anything beyond the stuff of minds corresponding to space-time loci? Can points and coordinates be anything other than cognita hosted by an advanced mind? In fact, is it even meaningful to make the “outside/inside mind” distinction given that the totality of our known world can only be that which impinges upon our minds? Even if we posit an independent “material world beyond the mind” we can only do so because it has been given to us to be able to conceive such a concept in the first place; the very idea of the “external” otherness of a material world must be constructed by the mind. We are therefore prompted to ask if there is any fundamental distinction between noumena and phenomena.

     Purely third person accounts of the nature of the conscious mind - that is, narratives instigated by other conscious observers who make conscious beings their object of study - are clearly possible. But what do these third person observers find? They find that much about their sentient objects of study resolve themselves into the theoretical abstractions the mind itself has conceived, e.g. as computation and information realised in chemistry and physics. Thus, the mind as the creator and translator of scientific narrative is itself paradoxically an object written in that self same narrative. Conscious cognition can be theoretically described in terms of its own conceptual artifacts. In effect neural theory is consciousness as it appears from the point of view of someone else's consciousness, and to claim consciousness is just the activity of neurons is to obscure the a-priori role of consciousness by admitting it through the back door of third person descriptions. Of course, it may be that a complete neural description of mind can not be made, but if it should, then it would amount to little more than a mathematical reduction; a telling of the story of consciousness in terms of logical cognita. This logical reductionism does not imply the strong ontological reductionism of the kind of materialism that imputes a primary metaphysical reality to “concrete” elementa, such as fundamental particles.

     For myself I have no problem with the concept of logical reductionism, for if God is a master mathematician then why not? Should this kind of mathematical reduction be possible it would constitute the ultimate elegant stroke of the whole rational coherent system we perceive the world to be: conscious cognition, like a software compiler that is written in the very language it compiles, can be described in its own terms. Those so called “objective” third person material concepts - neural computation, molecules and fields etc. - are none other than consciousness's view of consciousness, and are so bound up in a symbiotic relationship with mind as to make nonsense of the mind versus matter dichotomy. Our theoretical constructions have a holism about them in that they presuppose an up-a-running sentience in order that they can be perceived; they have a self-affirming circularity built into their very structure. The primary cosmic reality may be less some causative physical agency independent of sentience, but rather a kind of convoluted self-descriptive logic. Whether the structure of a good theory actually has a deep correspondence with some “hard material reality” beyond mind is really difficult to say. But the least we can say is this: our world presents such an integrated, consistent, seamless and coherent interface and is so thoroughly amenable to our simulations that sentience finds itself both subject and object. In this sense our world survives an in depth reality test and thereby fulfills a criterion of reality analogous to Turing's test for machine intelligence. The hard reality of our world exists at least in as much as it is capable of surviving the best test by which conscious cognition probes for that reality; namely, that this world comprehensively submits to theoretical simulation. We can ask for little more.

      The ontology of the cosmos may be one of appearance only, it may be more than one of appearance, but either way our experiences, our perceptions, and our theoretical apprehension of them jointly constitute a nexus that is so internally coherent and consistent as to be beyond the wit of finite beings to expose them as superficial fabrications. Like Turing's hypothetical intelligent machine, the logical depth of our world is such that it stands up to elaborate cross checking. Thus, as far as we are concerned the reality of our world is constituted in its ability to survive this in depth testing and cross-examination. It is this grand rationality which gives this world its touch and feel of reality, a reality to which a radical anthropocentric or nihilistic notion of ontology fails to do justice: We don't contrive our experiences; we don't even, in actual fact, consciously construct our theories; they assemble themselves from unconscious depths. The rationality of our world is not some arbitrary anthropocentric construction, for mind and experience, if we allow them, conspire together, independently of whim, to create the perception of a comprehensible world that can be rendered using theoretical logic. The intuition that the physical world has a life of its own, independent of the minds that perceive it, is therefore difficult to gainsay, although we must concede that this intuition is itself a resident of mind. It is very difficult to prove that the basis of this intuition goes further than a logical positivist’s take on the coherence and consistency of our perceptions. At the very least, however, our world is an elaborate logical construction, and its very faithfulness to the principles of coherence and consistency is perhaps a sign of a deeper integrity which means that it actually is what it purports to show.

***

     With the foregoing impressionist's sketch of the status of our theoretical constructions before us, it is possible to evaluate past theoretical projects in a way that does justice to them, else we may be tempted to concede that in the light of relativity and quantum mechanics Newton's theories have not only been superseded but are clearly completely wrong. This is rubbish, of course. Newtonianism was, and is, and will remain an excellent simulation of reality. Therefore by any reasonable standards, Newton was, is, and will remain right. There is something about the order of our world, an order imposed on our experiences, perceptions, and our mental tool kit, which makes Newtonian mechanics a good simulation. Of course, all simulations have their limits, and just as the 18th and 19th century physics of Newton, Faraday and Maxwell have, in the progress of time, been upstaged by the more sophisticated theoretical constructions of Einstein, Schroedinger and Heisenberg, the latter too, in the fullness of time, may well be upstaged. We cannot be sure how deep and wide the rational structure of our universe goes, and there are likely to be depths and breadths of structure, not covered by 20th century physics, yet to be plumbed and charted. That does not make this physics wrong; it just means that the level and extent of detail contained in the 20th century physics of Einstein and the quantum theorists have their limits. But it does no justice to the successes of 20th century physics to claim it will ultimately prove to be fundamentally flawed, and instead awaits some Kuhnian revolution that renders it obsolete. To a much higher intelligence than ourselves those theories may not be much more sophisticated than a child's representation of the human figure, constructed using simple lines and circles. But no parent, when he sees his child first drawing one of those crude stick men representations, declares them to be wrong - they are a step in the right direction and a sign of progressing perception and understanding. Concerned parents are not authoritarian minders of the child's perceptions but anxious and helpful bystanders who know the rational world will reward those who perceptions emulate it well and thereby find themselves in a reality that hangs together.

      In contrast the radical anthropcentrism and extreme scepticism typical of contemporary postmodernism has trashed the belief in intellectual progress toward integrated perception2. It is in cynical denial about the imperatives of a reality that hones successful ontologies and rewards those who possess them and punishes those who do not. Postmodernism attempts to shrink the perceived ontology of our world by caricaturing it as a fragmented, arbitrary and even fictitious transient construction. In order to make judgment and comment on postmodernism one can do little more than make recourse to the standards of one's experiences, perceptions, and theoretical extrapolations; the very things, in fact, extreme postmodernism calls into question. Thus, postmodern reductionism finds itself in a position not unlike that of someone declaring the whole universe to have shrunken in dimension, along with all the standards by which one might determine such a reduction has occurred, thereby making itself undetectable. Thus, quite apart from the fact that the extreme scepticism of postmodernism ultimately undermines itself in an unstable self referential loop there is, it seems, no observable content in postmodern scepticism; its notion of an arbitrarily and comprehensively shrunken world does little justice to the sheer coherence of experience and perception.

      The Kuhnian notion of successive scientific revolutions3 as a complete upheaval and discarding of what went before makes little sense, I believe, of the advance of science. The Kuhnian concepts involving confrontation, revolution, vested interest, rivalry etc. often describe the appealing human-interest aspects of the scientific drama. But the intellectual discontinuities we see in the activity of science are less the punctuation by revolutions than the articulations of a zigzagging path, which providence has so far graciously deemed to be a progressive course, or a drifting in the right direction. Whatever the cynical nihilistic postmodern ethos of contemporary times may suggest, our world, a world which includes ourselves, our society and our mental tool kit, is contrived to promote our perception that it makes sense, and, I believe, it will make more sense as time passes. But, I suspect, the structure of this world is deep and broad and our theoretical renderings of that world will not easily exhaust its subtlety and inherent cleverness. I am not at all convinced that the end of physics is near. In fact, my gut feelings on this subject are expressed well by Churchill: “It is not the end, it is not even the beginning of the end, but it might be the end of the beginning”.

    And there is hope, the enormity of the scientific hope; namely, that our universe is comprehensible and its organisation and chances are such that they conspire to construct our rational perception of it. Thus, science, if we believe in it and allow it, will continue to make progress. Newton and those who have followed him have shown us the way.

***

     The basics of differential calculus, a grasp of Shroedinger's equation, special relativity and the elements of general relativity are probably sufficient to understand the theory herein. The mathematics employed in this book is not specialised and therefore a wide audience who, like myself, have no training in the field of quantum gravity can apprehend the theory being proposed. During the course of the construction of this theory many “seat of the pants” decisions were made, anyone of which could be wrong, throwing the whole thing off course. Thus, the theory may not be “right” even in the sense that I allow Newton and his successors and the ideas contained here may be neither a “zig” nor “zag”. However, perhaps at the very least it might spark some interest as a curious piece of mathematics relating relativity to quantum mechanics, or maybe suggest some new routes into the problem of quantum gravity. That problem may be as difficult as cracking a convoluted cipher, but like all code crackers we only have a hope of progress whilst we believe ultimate meaning and sense to be hidden and waiting for us in the complexities that we confront: “It is the glory of God to conceal a matter; to search out a matter is the glory of kings” (Proverbs 25:2)

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