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Bridging the gap between quanta and the rest of physics a thorough awareness of the following errors in judgment of contemporary interpretive schemes is a sine qua none. The first error was and is a totally unfounded assumption that Schroedinger's Ψ function might be describing a single quantum system; all other errors are contingent on this one. The second error became concocting a nonclassical statistics as a futile attempt at covering up Bohm's hidden variables as conceivably accounting for any changes in statistics. The third error is a related existence of an ever-present statistics of quantum uncertainty postulated by Heisenberg. It was derivable from Schroedinger's equation thus logically forcing: The fourth error is an ensuing endowment of Schroedinger's equation with an unwarranted first principle status. These four epistemic errors are avoided by replacing the single system by an ensemble of identical systems subject to a perfectly classical correlation statistics. Schroedinger's Ψ now deals with optimal ensemble randomness of minimal correlation reflecting the state of its spectral sources. Without the man-made, ever-present, non-classical statistics, a pre-statistical quantum order can now be resuscitated. It calls for tools capable of probing topological order. Avoiding injecting prejudicial information, its tools need to be topological invariant assessing global order. The Aharonov-Bohm integral and its two- and three-dimensional companions indeed meet those requirements. They are here discussed and tested by resolving a persistent thirty year old quantum Hall dichotomy.

1. The early Days of Quantum Recipes
2. The Heisenberg-Schroedinger eigen-values
3. Classic Ψ Statistics casts Light on Popper Ensemble
4. The Ordered quantum Alternatives of the Sixties
5. Quantization as a pre-metric Experience
6. The pre-statistic pre-metric Integrals
7. Gen. Covariance separates Apples and Oranges
8. Conclusion and the QH dichotomy

This paper attempts to improve the logical and conceptual relations between the Bohr Condition, the Quantum Hall Effect, Copenhagen Views and de Rham Theory.

We learn too much and understand too little,
Yet understanding comes from learning
So strive using the latter to enhance the first

What motivates the majority of scientists to accept the Copenhagen doctrine of quantum mechanics, when superior alternatives have existed since de Rham and before? This paper assesses what's really going on.

Global quantization reinstates basic quanta counting. It covers increasing numbers of experimental results in the pre-statistic realm. The ensuing 2-tear quantum aspect opens up a topological venue for highly ordered quantum structures while calling for abandoning the non-classical statistics of Copenhagen Doctrine.

Arguments of Cooper type screening and Bohr's angular momentum quantization yields a joint expression for integer and fractional Quantum Hall effect while confirming the Doll-Fairbank flux quantum h/2e over h/e.

The Copenhagen views developed in the late Twenties as an attempt at understanding of what Hermann Weil called Schroedinger's favor of fortune. Decades later Aharonov and Bohm presented their cyclic line integral of the four-vector potential [1] as equating multiples of flux quanta h/e. It uniquely describes a quantum interferometer experiment also devised by the same duo. A couple of years later Deaver-Fairbanks [2] and Doll-Naebauer [3] confirmed the existence flux quanta, yet of size h/2e not h/e.

The AB integral is, however, pre-statistical whereas Schroedinger's process is statistical; be it of a perhaps strange non-classical species. Early on Copenhagen claimed quantum mechanics as inherently statistical, thus dismissing any pre-statistic manifestation. Experimental reality clearly says otherwise. Yet inferring a non-statistical AB integral from a statistical Schroedinger tool took AB intuitive genius.

However, unbeknown to most physicists but known to a number of mathematicians, de Rham [4] formulated in the early Thirties an existence theorem in the realm of differential topology that permits a derivation of the AB integral from first principles. Translated in the space-time language of electromagnetism, it says:

It follows from global flux conservation (Faraday's law) that there exists a field A such that dA= F and depending on the contour c, the loop integral of A then equals a multiple of a smallest topologically invariant residue r; contour c everywhere resides in domains where F=0. The Fairbanks-Doll experiments [2,3] now show r = h/2e; which, if you will, is in fact an experimental confirmation of this application of de Rham's theorem.

This completes the proof how the Aharonov-Bohm law has its own first principles confirming its independence of Schroedinger's process. It restores options of carrying on causal argument by placing AB's law first and Schroedinger as derived. In fact Schroedinger's original variational derivation of his equation can be restored in that vein.

AB's double residue [1] can now be understood from an angle of residue integration for particles moving in external E, B fields. Particles having a field-free interior trace their own field-free path; the twin space-and time trajectories now double h/2e in h/e.

It can hardly be denied that the AB integral emerges as an experimentally confirmed winner of primary quantization. The Schroedinger equation derives by injecting the AB law as replacing conditions of single valuedness. It restores Schroedinger's original derivation of his equation that was somewhat silently discarded by Copenhagen.

All this completely uproots traditional Copenhagen views. A preliminary outline of the ensuing interpretive change [5] has been delineated in BSPS volume 181. Ironically, methods of approach were commented on in reviews but interestingly not the central message of interpretive reprogramming. Since there has not been much evidence of bringing an end to this scandalous AB-Copenhagen standoff, this letter is meant to invite mature opinion on the current use of de Rham theory as doing exactly that. In fact the same theorem, applied to the D,H, field reproduces Gauss' theorem of electrostatics as well as a discreteness of the quantum of charge; anybody questioning that?

1. Y. Aharonov & D. Bohm, Phys, Rev. 115. 489 (1959).
2. B. S. Deaver & W. M. Fairbank, Phys. Rev. Lett. 7, 43 (1961).
3. R. Doll & M. Neubauer, Phys. Rev. Lett. 7, 51 (1961).
4. G. de Rham, Vari?t?s Differentiables (Paris 1955).
5. E. J. Post, Quantum Reprogramming (Kluwer 1995; Springer 2005).

The vast majority of attempts at describing how the two quantum Hall effects fit existing theory have started out by viewing the phonemena in a Copenhagen-Schroedinger perspective. In the course of time extraneous adaptations had to be made ranging from fractional charge, composite fermions all the way to a Chern-Simmons 3-forms invoking strings. Yet this step of entering the field now reveals a structural topology not conveyable by statistical Schr?dinger methods. Ironically, the 1- and 2-form components of a physical 3-form used by Kiehn unify integer and fractional effects. More ironic is that this option had already been reported in ref.12 prior to the announced discovery of the fractional effect in 1982.

The paper is an interpretive adjustment of quantum fundamentals. Early days have been marked by too freely taken refuge in non-classical concepts that have not led to substantiation. While Schr?dinger's mathematical structure is not affected, incisive interpretive changes are called for. Its applicability now strictly covers only ensembles subject to classical statistics. Nonclassical statistics are in-complete temporary escapes. The pre-statistical processes of Aharonov-Bohm and Gauss Amp?re, have been extended by Kiehn into a de Rham cohomology, applying to single systems. Metric independence secures macro and micro applicability. The pre-1925 quantum methods are so recast into probes of single system topological structue. Unlike the deep-freeze nonclasical statistics, a classical statistics permits disorder-order transitions e.g., Bose-Einstein condensation. These transitions help in understanding a range of related phe-nomena. The  function so becomes a correlation statistics describing mutual phase and orientation behavior in the ensemble; this re-places the current Copenhagen's probability density of presence.

U of H Seminar.  The following is a critique of the Copenhagen single syetem interpretation of quantum mechanics, which can be advantageously replaced by an ensemble view obeying a perfectly classical statistics.

This title refers to the concept or conceivable existence of a nonclassical psi function statistics. At least two counter examples exist, which show there is no compelling need whatsoever to take recourse to this nonclassical measure. The concept of a nonclassical psi function statistics must be considered as logically flawed, and should be neither admissible in mathematics nor in physics. Preliminary delineations about this have been in the public domain for some time, yet there is great reluctance to confront this situation by having an all encompassing topical conference solely devoted to this predicament.

This paper is aka "Physics? Biggest Conceptual BooBoo in the 20th Century"

This essay is an unapologetic proposal for incisive changes in the traditional Copenhagen interpretation of quantum mechanics. Instead of a single system, the Schroedinger ? describes an ensemble of identical systems obeying a classical statistics. Since the Schroedinger equation is now to be taken as solely describing randomized ensembles, it can no longer be regarded, and should no longer be used, as a method of primary quantization such as might be associated with single systems. The variational argument used by Schroedinger for obtaining his equation now graduates to a derivation from pre-1925 propositions of quantization. Following Kiehn [9], pre-1925 quantizations are recognized as part of a mathematical system of period (residue) integrals describing global topological structure of single systems. Since these single system tools operate in a pre-statistical realm, it follows Heisenberg uncertainty, which derives from Schroedinger?s equation, now conveys limitations of observation associated with ensemble randomness. Following Planck, this randomness is maintained by the zeropoint energy. For mathematical details of these conceptual alternatives the reader is referred to ref.5.

Assessments of the quantum Hall effect by wave function procedures are compared with a global assessment using Aharanov-Bohm and Ampere-Gauss period integrals for flux and charge quanta.

This paper was also published in the Proceedings of the NPA, V1, N1, pp. 85-88 (2004).

This paper is a carefully-documented proposition to discontinue currently still standard references to the conceptual images of the Copenhagen interpretation, because they are at variance with the reality presently confronting the world of physics.  The Aharonov-Bohm and Ampere-Gauss integrals of quantum interferometry frame now gain an independent fundamental image in light of their potential to assume period integral status. The ensuing two-tier aspect of quantum theory then grants a conceptual perspective that permits dispensing with some of the non-classical wages of sin of standard one-tier presentations.  The suggested changes interfere little with standard mathematical procedures of operation, but they do affect decisions as to when to use Schrodinger-Dirac tools pertaining to randomized ensembles versus period integral tools for single systems or ordered ensembles thereof behaving as single systems.

There is in physics a sentiment and trust that the more perfect logical structure of mathematics can save the day for some of the not so logical conceptual leaps of modern physics. This investigation aims at a better logical balance between the two, wherever this is possible. The present account emerged in part from experiences in crystal physics, which long ago required a closer relation between physics and its mathematical description. For crystals the demands go well beyond standard needs in physics, in fact they end up gibing with those needed in differential geometry. Physics and mathematics are so close, because the language of modern physics is primarily one of mathematics. As a result physics has developed near-magic confidence in a never ending potential of some contemporary procedures for bringing in new harvests of results. Even after diminishing returns, more magic is attempted, yet oddly, ?magic? handwritings on the wall warning about overreaching goals are not always heeded. As a result man feels as if Nature has been leading him astray. Since no proof exists of Nature taking delight in intentionally misleading its students, it may well be closer to the truth if students of Nature were to admit to misleading one another. So, the following has become an unearthing of clues about marginal situations between physics and mathematics. Since this is not a pursuit of a specific physics problem with lengthy calculations, no equations are displayed in this paper. They are mentioned by name instead, which is more than adequate, because all of them are well known items in contemporary physics. Without equations and long extended deductions, more attention can be given to conceptual aspects. Since equations referred to here all have reputations of great effectiveness in modern physics, one would be reluctant to see them change. The hard earned experiences of numerous workers in past and present plead against undue tinkering with the intrinsic structure of well established tools. Yet everything else, specifically what exactly the tools stand for, is open to further probing. Let it be said, though, intrinsic structure may manifest itself better in suitable mathematical garb revealing its virtues. So, while leaving the tools intact, definition domains and realms of applicability are due for major reassessments. Readers drawn to a romantic sentiment in modern physics with its pronounced element of nonclassical mystique may well be in for an anticlimactic experience. The conceptual reassessment, as here delineated, largely does away with the many nonclassical metaphors of contemporary physics. After all, let us face the reality of life, the task of physics always was one of resolving mysteries, not adding to them.

The pre-1925 quantum prescriptions of Planck, Einstein, Bohr, Sommerfeld and recently Aharonov-Bohm permit a recasting as part of a complete set of electromagnetic residue integrals such as used in a mathematical discipline known as de Rham cohomology. The ensuing spacetime topological reorganization of early quantum aspects seems well supported by Josephson- and quantum Hall effects. This reversal of priorities demands a physical readjustment of standard nonclassical Copenhagen pronouncements. The Schroedinger equation becomes a tool solely applicable to ensembles consisting of single systems of random phase and - orientation. This reorganization is a return to the ensemble initiatives of the Thirties by Slater, Popper, Kemble and others, which now can be given a compelling form by identifying long standing classical counter-examples to Copenhagen?s nonclassical propositions. Heisenberg uncertainty and zero-point energy have to yield their pedestal of universal absolute status. They now become manifestations governing order-disorder transitions in ensembles.

Many people have been questioning whether the so-called Big Bang theory of the Universe is a physically realistic proposition or a product of man's apocalyptic disposition. The following discussion weighs this explosive Big-Bang proposition against the less spectacular tired-light hypothesis by focusing on global options of Universe structure compatible with Mach's Principle.

The following is an attempt at starting a dialogue on desirable changes in the traditional views of quantum mechanics, in the hope of improving the understanding of an underlying structure. Since the technicalities of these changes have been extensively discussed elsewhere, these arguments seek a delineation with a perspective on history.

Is Public Relation in Physics Prevailing over Academic Evaluation?

Many of those working in physics have had some thoughts about the question posed in the title. Yet it is hard to be specific as to what extent it is true and how much of it is part of a scheme to dominate. Large organizations have an edge in the PR game, yet how often do they use this advantage unfairly?

Most people are inclined to give them the benefit of the doubt, because there always are malcontents claiming, or imagining, they have been wronged by steam roller tactics of the high and mighty. If it is a clear judicial situation, the standard argument is let them bring suit if they are serious about what they say.

The manifold of space and time in which physical events evolve permits a subdivision of laws dependent or independent of a universal metric in the form of a metric tensor. Dimensional analysis and geometric transformation theory shed light on this aspect if the mass unit is replaced by an action unit. One so obtains a systematic separation between geometric and physical units of reference. These criteria permit the delineation of a subdivision of metric-free laws, especially a category of metric-free global relations culminating in a set of 1,2 and 3-dimensional residue integrals; the residues of which can be assessed as counting elementary flux, charge and action quanta. The charge counter is simply the Amp?re-Gauss law of Maxwell theory. The flux and action counters have traditionally been viewed as asymptotic byproducts of Schroedinger's equation. Since, the Amp?re-Gauss law is taken to have universal macro-micro validity, it is now reasonable to extend similar basic exactness also to the flux and action counters. The Schroedinger equation now emerges as a derived entity, applicable to ensembles of phase and orientation randomized identical systems. Schroedinger's own recipe for obtaining his wave equation then graduates to the level of a derivation; thus establishing its position as a tool for primeval ensembles while excluding single system applications.

This article discusses a selection of problems that ensue from (over-)using local description in inherently global situations. Two cases, discussed here, are Faraday's law of induction and the kinship of the Michelson-Morley and Sagnac interferometer experiments. Conceptual predicaments created by standard (local) approaches are first discussed in setting the stage for learning how to deal with the differentiation of integral expressions describing global situations. Once the results thereof have been secured, the business of repair begins. The global Faraday induction law gives rise to the source-free Maxwell equations as well as the Lorentz force law. The Michelson and Sagnac experiments end up in unified description, invoking minimal relativity precepts, here shared by special and general theory: i.e., constancy of the speed of light. The latter premise is valid for both, as long as gravity profiles remain "flat" on an astronomical scale. All of which brings us to the local concept of the Weber potential, which, after the revision by Phipps, is not only compatible with, but a sine qua non for a relativity view of E&M theory. Its application improves the logic and precision of the Sommerfeld-Dirac view of hydrogen fine structure. These efforts at conceptual integration make the Lorentz group a much more abstract item than hitherto perceived.

The developments of theoretical physics in this century can be subdivided in four major separate time intervals, each taking roughly twenty five years to come to fruition or the lack thereof. The first two quartiles maintain close relations to already existing theory, whereas the last two quartiles are becoming more divorced from existing concepts of understanding. Unlike the highlights of experimental discoveries, theory in those same years reveals a strange recurrence of doctrines that have proven ineffective.

A closed physical space, in conjunction with scalar versus pseudo scalar distinctions, and an accordingly adapted Gauss theorem, reveal unexpected perspectives on Mach's principle, the mass-energy theorem, and a bonus insight into the nature of the solutions of the Einstein field equations of gravity.

Annalen der Physik of July or August ?99.

This essay presents conclusive evidence of the impermissibility of Copenhagen's single system interpretation of the Schroedinger process. The latter needs to be viewed as a tool exclusively describing phase and orientation randomized ensembles and is not to be used for isolated single systems. Asymptotic closeness of single system and ensemble behavior and the rare nature of true single system manifestations have prevented a definitive identification of this Copenhagen deficiency over the past three quarter century. Quantum uncertainty so becomes a basic trade mark of phase and orientation disordered ensembles. The ensuing void of usable single system tools opens a new inquiry for tools without statistical connotations. Three, in part already known, period integrals here identified as flux, charge and action counters emerge as diffeo-4 invariant tools fully compatible with the demands of the general theory of relativity. The discovery of the quantum Hall effect has been instrumental in forcing a distinction between ensemble disorder as in the normal Hall effect versus ensemble order in the plateau states. Since the order of the latter permits a view of the plateau states as a macro- or meso-scopic single system, the period integral description applies, yielding a straightforward unified description of integer and fractional quantum Hall effects.

In British Society for the Philosophy of Science: Proceedings of London meeting 11-14 Sept 1998 Supplementary papers, pp. 147-149.

In British Society for the Philosophy of Science: Proceedings of London meeting 11-14 Sept 1998 Supplementary papers, pp. 141-146.

In British Society for the Philosophy of Science: Proceedings of London meeting 6-9 Sept, 1996, pp. 348-351. The non-classical paradigms of modern quantum physics are shown to be consequences of overextending the realm of applicability of the Schr?dinger equation. Suspicions of this kind have been abound ever since Hermann Weyl decided to refer to the Schr?dinger process, and its associated Hilbert spaces, as ?a favor of fortune for physics?. Yet, whenever fortune strikes, there is an added danger of adversely affecting, or even blinding, good judgment. It is reported that a restriction of the Schr?dinger process to phase and orientation randomized ensembles obviates the need for non-classical paradigms. So the non-classical paradigms, which for decades have challenged a common sense reality in physics, were designed to help us believe in an applicability realm that was much wider than Nature's favor of fortune had intended.

In British Society for the Philosophy of Science: Proceedings of London meeting 6-9 Sept, 1996, pp. 345-347. This essay is an attempt at a non-technical account of the interplay of concepts pertaining to the realms of relativity and quanta. An all-out global approach holds promise for a more compatible assessment of the two branches of physics. A re-evaluation of the traditionally central position presently held by the Schroedinger-Dirac process must be regarded as a natural consequence of such a change of strategy.

In British Society for the Philosophy of Science: Proceedings of London meeting 6-9 Sept, 1996, pp. 324-344.

Proceedings of a 1992 meeting at Columbia University on the Interpretation of Quantum Theory (Published by the Enciclopedia Italiana, Roma,1994) ed. Luigi Accardi, p. 229

Period integrals for single systems and Schroedinger process for ensembles.

A survey is presented of work that has preceded and followed the discovery of the quantum Hall effect (QHE). The inability of standard methods to cope with cooperative order is cited as a major cause of limitations. Difficulties manifest themselves especially for the fractional QHE. There is a tenuous applicability of Schr?dinger methods to highly ordered ensembles of systems. The latter are more appropriately described by methods predating modern quantum mechanics. Their mutual asymptotics is physical in origin and not to be regarded as an indication that one would be more exact than the other. Two totally independent, yet mutually supportive, methods describing integer and fractional QHE are presented as evidence to substantiate the need for a departure from the Schr?dinger method and its Copenhagen interpretation.

It is not possible to break out of the Copenhagen impasse with its limitations of indeterminacy unless the existing quantum formalism is identified and accepted as a description of an ensemble of single systems. The existence of, and need for an improved and more detailed pre-Copenhagen quantum mechanics is then implied. The present note is an assessment of fundamentals without undue technicalities.

(Rejects of the Past holding Promise for the Future)