The transition from a paradigm in crisis to a new one is far from a cumulative process. Rather it is a reconstruction of the field from new fundamentals.
Thomas S. Kuhn, The Structure of Scientific Revolutions, pp. 84-85
In the article High Energy Physics and the Reciprocal System¹ we indicated that high energy physics is a field approaching a crisis, and therefore the Reciprocal System, originated by Dewey B. Larson, has greater chances of getting a hearing since it offers a truly general theoretical framework resolving long-standing problems. We believe that the dawning of a new century is particularly propitious for new ideasas it always has beenand the Reciprocal System, with its new paradigm of scalar motion as the sole content of the physical universe, has much to contribute. The need of the times is a good number of interface articles that could bring the knowledge of the Reciprocal System to the orthodoxy, or at least to the iconoclastic thinkers in its ranks.
The title of this article is adopted from that of an article² written by A. J. Leggett in the Indian journal of Current Science. I shall quote extensively from this article, giving the page numbers in parentheses. Prof. Leggett is well known in the field of condensed matter physics. He advances in the above article forceful arguments against the reductionist viewpoint in science. Reductionism implies that the behavior of macroscopic systems is in principle entirely determined by the behavior of their microscopic constituents. Leggett is not alone in drawing attention to the limitations of reductionism. Since the pioneering work of the celebrated thermodynamicist and Nobel laureate, Ilya Prigogine, there has been a growing awareness of the limited applicability of the reductionist viewpoint in the fields of physics and life sciences.
Epistemology of Reductionism
Leggett observes that the reductionist argument goes like this: We have analyzed the properties of macroscopic bodies in terms of those of atoms and molecules; these systems in turn behave as they do because of the properties of the electrons and nuclei; the behavior of the nuclei is determined by that of their constituent nucleons; and now we trace the properties of the nucleon itself to that of its constituent quarks. What could be more obvious than that the behavior at each level is determined by that of the constituents at the next level below? (p. 787).
He then tracks down that our experience of understanding how things work starts with mechanical devices made by other human beings, and that the most natural way of achieving such an understanding is precisely to take the device apart into its constituent parts, since these are what the maker started with. Does this experience subconsciously color our perception of what constitutes an explanation of natural phenomena as well as of human artifacts? (p. 787)
He questions that would it be really obvious that the behavior of complex bodies is entirely determined by that of their constituents (p. 792) were it not for this subconscious conditioning about what constitutes explanation. Reductionism is probably as deeply ingrained in the thinking of most of us as any single element in the whole of our scientific world view.(p. 792)
Who Put Reductionism in Nature?
Let us inquire, says Leggett, what most of the contemporary experimentalists and theorists in the field of high energy physics are involved in.
Most high-energy experimentalists are engaged in a single enterprise which, conceptually if not technically, has a very simple structure. Namely, they accelerate particle A and particle B so as to hit one another, and watch where they and/or particles C, D, E emerge, and with what energy and (sometimes) spin. In particular, the experiment is designed so that, as nearly as possible, the incoming beams are each described by quantum-mechanical pure states of definite momentum; and while the theory certainly predicts that, in certain cases at least, the outgoing states are not simple classical mixtures of products of plane wave states, but have built into them subtle quantum correlations of the type which are important in Bells theorem, the whole setup is designed precisely so that such subtleties can be neglected. (p. 787)
Now when the particle physicists claim that experiments show that Nature is actually simpler at higher energies, might it not be due, Leggett wonders, at least partly to the fact that we have chosen to ask her only questions, which by their very construction allow no subtlety in the answers? (p. 787)
Referring to the theoretical front he says: A few years ago, at least, there were high hopes (I am not clear how far those at the forefront of the field now share them) that in the super-string picture the constraints imposed by the need for self-consistency would be so severe that they would uniquely determine the parameters of the theory, including as outputs not only the masses and coupling constants of the known elementary particles but even the true dimensionality of space-time. (p. 788)
He then raises the genuine epistemological quandary: Can mathematicsa subject which is usually taken to be concerned with analytic truthreally put constraints on how Nature can behave? (p. 788)
The Whole is the Sum of the PartsOr is it?
Leggett now surveys the evidence for and against reductionism in science. He points out: So long as one is dealing with those phenomena, and only those, where we believe that the predictions of quantum mechanics are well approximated by those of classical physics, then the evidence for the reductionist point of view is very strong, and moreover there is absolutely no a priori, internal reason to challenge it.
For example, in a typical macroscopic quantum effect in the conventional sense, such as the Josephson effect, what we are actually seeing is the effect of a macroscopically large number of Cooper pairs behaving in identical fashion; the observed supercurrent is simply the sum of the supercurrents carried by the individual pairs of electrons. Similarly, in laser diffraction, we are simply seeing the coherent sum of the behavior of many individual photons. So long as we are dealing with the summed effectseven the summed quantum effectsof a large number of small groups, there seems no reason to doubt a reductionist approach. (p. 793)
He continues: It is only when we come to intrinsically quantum phenomena that we have a problem. First the positive evidence in favor of reductionism in this regime is much less strong than it looks at first sight and secondly, there are indications, which are intrinsic to the quantum formalism itself, that the reductionistic program not only might, but must eventually fail.
Let us start with the phenomenon usually known as the Aharonov-Bohm effect. In this, the current flowing through a region of metal which encloses a hole turns out to be affected by the magnetic flux through the hole, even though the magnetic field vanishes everywhere within the metal itself. In other words, the electrons carrying the current are sensitive to the conditions in a region which they never enter, but only enclose with their paths! This already demonstrates that quantum mechanics forces us to give up some of our classical notions about the locality of physical effects. (p. 793)
As the next example he considers Bells theorem and the related experiments: given that we make our normal assumptions about local causality in the sense of special relativity theory, and about the statistical properties of ensembles being determined entirely by the initial conditions, then what Bells theorem and the associated experiments show is that even though two regions of the universe may be spatially separated and physically noninteracting, we nevertheless cannot ascribe to each of them individual properties; any realization of properties takes place only at the level of the combined system.(p. 793)
What Bells theorem experiments have shown us is that, in the context of reductionism which implies that the behavior of macroscopic systems is entirely determined by that of their atomic-level constituents, we are not justified in assuming that the concept of constituent is necessarily associated with spatially localized region. So Leggett exclaims that the Bell's theorem experiments are a death-knell for reductionism. (p. 793)
The Quantum Measurement Paradox
There is one more feature of the current quantum mechanics world view to which Leggett draws attention, which gives us reason to doubt the validity of reductionismthe quantum measurement paradox.
Consider an ensemble of systems which can go from some initial to some final state by either of two paths B and C. At the microlevel, we believe that despite the fact that measurement of the path followed by any individual system will always show that it followed either B or C, the quantum formalism must nevertheless be interpreted as in some sense saying that if no measurement was made, it simply is not the case that one (unknown) possibility out of B and C was realized; rather, both possibilities are in some sense represented in the correct description. as a matter of experimental fact, the properties of our actual ensemble are not identical to those which we would obtain from a combination of the two ensembles obtained by allowing only B and only C respectively; i.e., we verify, experimentally, the phenomenon of interference between the two paths. So it seems that the quantum formalism in some sense either ascribes reality to both the possibilities B and C, or ascribes it to neither. (p. 794)
"At the macrolevel the formalism of quantum mechanics remains exactly the same; but there is now no direct experimental evidence against the hypothesis that one of the possibilities B or C has been realized in each particular case.
We have here a case in which we have two maps of realitythe quantum-mechanical map which we apply to atomic phenomena, and the 'common-sense, classical map which we use for the macroscopic, everyday world. The problem is that they claim in principle to describe the same level of realitythe world of counters, cats etc.and yet no one has succeeded in showing that they are compatible. (p. 795)
Now, Leggetts penetrating insight into this enigma, which first fastened our attention onto his article, was the realization that under appropriate circumstances if we extrapolate [the quantum] formalism up from the microlevel to the macrolevel, there is no point at which any natural discontinuity occurs. (p. 794) [my emphasis]
He is unequivocal in his conclusion: My own belief is that the quantum measurement paradox can have no solution within our current reductionist world-view. (p. 795) He opines that the quantum field theory is only a half-way house, sure to be supplanted by a radically new picture of physical reality whose nature we cannot at present even guess. (p. 795) He adds: I for one intend to use my best efforts to hasten that day.
Enter the Reciprocal System
The Reciprocal System, with its new paradigm that (scalar) motion is the sole constituent of the physical universe, resolves all the difficulties. Larsons finding that space and time are discrete in nature and quantized answers the crucial question raised by Leggett above, that there is no point at which any natural discontinuity occurs. Such a natural discontinuity does occur at the boundary of the natural unit of space. We have explained in detail in a previous article how at the boundary between the time region (the region inside unit space) and the familiar³ three-dimensional spatial region a discontinuity occurs, and how the apparent directions of the forces applicable (the gravitation and the space-time progression) change from outward to inward and vice versa. We have shown that this gives rise to the solid, liquid and the gaseous states.
Larsons discovery that space and time are reciprocally related had been a crucially important finding. This led to the discovery of the existence of coordinate time analogous to the familiar coordinate space. We have shown³ that the phenomenon of spatial non-locality arises due to the switching from the spatial reference frame to the temporal reference frame on entering the time region. This makes for the equal possibility of all the alternative paths, at the microlevel. At the macrolevel, however, this is not the case since the interaction is no longer in the time region but is in the conventional spatial frame. We have further explained the concept of temporal non-locality which is responsible for producing the statistical pattern out of the independent microlevel events of an ensemble.
Larson pointed out the fact that correlated particleslike in the EPR experimentmaintain contiguity either in space (if separated in time) or in time (if separated in space).
We also note that in the Reciprocal System there are two kinds of time: the coordinate time and the clock time. These are respectively the reversible time, t, which occurs in the equations of classical physics and quantum mechanics, and the irreversible time, T, which is relevant to living processes and consciousness. This distinction arises naturally and logically in the Reciprocal System, whereas in the world view of the current science, as Prigogine finds, it is to be introduced as an ad hoc necessity. Analogous to coordinate time and clock time we also find that there are two kinds of space: the familiar coordinate space and what Larson terms clock space. The latter manifests itself to us as an irreversible and continual expansion, as is evidenced in the recession of the distant galaxies. In the Reciprocal System there is no need for the purely ad hoc assumption of the Big Bang to account for the galactic recession!
The Reciprocal System repudiates reductionism at the very outset. Larson finds the atom to be a unit of compound motion and without parts. The so-called sub-atomic particles turn out to be incomplete atoms and without parts. In the Reciprocal System there is no need for quarks and gluons, not even for nucleons. We can identify the cosmic ray decay particles and the exotic particles generated in the accelerators to be the transient apparitions of the atoms of the conjugate sector of the physical universe, which Larson refers to as the cosmic sector.¹ The cosmic sector is a complete duplicate of our material sector with the roles of space and time interchanged.
Larson was able to explain the characteristics peculiar to biological systems by the possibility of conjoining the structural units pertaining to the cosmic sector with the material structures. Remember that the structural units of the cosmic sector are not aggregates in space. Rather, they are aggregates in time, and hence their control on the cells, for example, appears totally nonlocal. This makes it possible for the logical inclusion of self-organization and creativity among other things.
All these insights about the quantum phenomena which the Reciprocal System is able to provide acquire even greater significance when we realize that its creator, Dewey Larson, had never explicitly thought out these aspects when he originally developed the theory. A perusal of his early correspondence with other students even reveals that he looked upon these quantum-mechanical phenomena, like the tunneling, with hesitation. (This, however, does not mean to underestimate his genius: he was so pre-occupied with the overall development of the theory so as to establish its generality, accuracy and cogency that he hardly ever had the time to go into the quantum subtleties. He used to do all his typing work himself, and imagine that his typewriter didn't even have the '+' key: he used to type '-', then backstep and overtype '/'.) Be that as it may, the actual fact is that the logical development of the Reciprocal System of theory comes up to match with the requirements to be satisfied by the new picture of physical reality we are looking for, and whose nature could not even be guessed by the scientists. The next question, therefore, is since such a theory did appear now, whether or not we can see the truth of this!