Writing the Biography of Hans Bethe: Contextual History and Paul Forman1

Some facets of the life of Hans Bethe after World War II are presented to illustrate how Paul Forman’s works, and in particular his various theses—on mathematics and physics in Wilhelmine and Weimar Germany, on physics in the immediate post-World War II period, and on postmodernity—have influenced my biography of Bethe. Some aspects of the history of post-World War II quantum field theory, of solid state/condensed matter physics, and of the development of neoliberalism—the commitment to the belief that the market knows best, to free trade, to enhanced privatization, and to a drastic reduction of the government’s role in regulating the economy—are reviewed in order to make some observations regarding certain “top-down” views in solid state physics in postmodernity, the economic and cultural condition of many Western societies since the 1980s, the decade in which many historians assume modernity to have ended.     

Empirical reality,empirical causality,and the measurement problem

Does physics describe anything that can meaningfully be called “independent reality,” or is it merely operational? Most physicists implicitly favor an intermediate standpoint, which takes quantum physics into account, but which nevertheless strongly holds fast to quite strictly realistic ideas about apparently “obvious facts” concerning the macro-objects. Part 1 of this article, which is a survey of recent measurement theories, shows that, when made explicit, the standpoint in question cannot be upheld. Part 2 brings forward a proposal for making minimal changes to this standpoint in such a way as to remove such objections. The “empirical reality” thus constructed is a notion that, to some extent,does ultimately refer to the human means of apprehension and of data processing. It nevertheless cannot be said that it reduces to a mere name just labelling a “set of recipes that never fail.” It is shown that our usual notion of macroscopic causality must be endowed with similar features.     

A categorical framework for quantum theory

Underlying any physical theory is a layer of conceptual frames. They connect the mathematical structures used in theoretical models with the phenomena, but they also constitute our fundamental assumptions about reality. Many of the discrepancies between quantum physics and classical physics (including Maxwell's electrodynamics and relativity) can be traced back to these categorical foundations. We argue that classical physics corresponds to the factual aspects of reality and requires a categorical framework which consists of four interdependent components: boolean logic, the linear‐sequential notion of time, the principle of sufficient reason, and the dichotomy between observer and observed. None of these can be dropped without affecting the others. However, quantum theory also addresses the “status nascendi” of facts, i.e., their coming into being. Therefore, quantum physics requires a different conceptual framework which will be elaborated in this article. It is shown that many of its components are already present in the standard formalisms of quantum physics, but in most cases they are highlighted not so much from a conceptual perspective but more from their mathematical structures. The categorical frame underlying quantum physics includes a profoundly different notion of time which encompasses a crucial role for the present. The article introduces the concept of a categorical apparatus (a framework of interdependent categories), explores the appropriate apparatus for classical and quantum theory, and elaborates in particular on the category of non‐sequential time and an extended present which seems to be relevant for a quantum theory of (space)‐time.     

Nuclear physics and ideas of quantum chaos

The field nowadays called “many-body quantum chaos” was started in 1939 with the article by I.I. Gurevich studying the regularities of nuclear spectra. The field has been extensively developed recently, both mathematically and in application to mesoscopic systems and quantum fields. We argue that nuclear physics and the theory of quantum chaos are mutually beneficial. Many ideas of quantum chaos grew up from the factual material of nuclear physics; this enrichment still continues to take place. On the other hand, many phenomena in nuclear structure and reactions, as well as the general problem of statistical physics of finite strongly interacting systems, can be understood much deeper with the help of ideas and methods borrowed from the field of quantum chaos. A brief review of the selected topics related to the recent development is presented.     

The Shelter Island Conferences Revisited: “Fundamental” Physics in the Decade 1975–1985

The focus of this broad historical overview of “the steady evolution of theoretical ideas” from Shelter Island I in 1947 to Shelter Island II in 1983 is some of the developments in “fundamental” physics after the establishment of the standard model, in particular, the adoption of the view that all present day field theories are “effective field theories” based on the gauge concept; taking seriously big bang cosmology, grand unified field theories (GUTs), and inflation; and the emergence of a new symbiosis of physics and mathematics.     

Conventions in Relativity Theory and Quantum Mechanics

The conventionalistic aspects of physical world perception are reviewed with an emphasis on the constancy of the speed of light in relativity theory and the irreversibility of measurements in quantum mechanics. An appendix contains a complete proof of Alexandrov's theorem using mainly methods of affine geometry.     

Theory of filters

We consider the following statistical problem: suppose we have a light beam and a collection of semi-transparent windows which can be placed in the way of the beam. Assume that we are colour blind and we do not possess any colour sensitive detector. The question is, whether by only measurements of the decrease in the beam intensity in various sequences of windows we can recognize which among our windows are light beam filters absorbing photons according to certain definite rules? To answer this question a definition of physical systems is formulated independent of “quantum logic” and lattice theory, and a new idea of quantization is proposed. An operational definition of filters is given: in the framework of this definition certain nonorthodox classes of filters are admissible with a geometry incompatible to that assumed in orthodox quantum mechanics. This leads to an extension of the existing quantum mechanical structure generalizing the schemes proposed by Ludwig [10] and the present author [13]. In the resulting theory, the quantum world of orthodox quantum mechanics is not the only possible but is a special member of a vast family of “quantum worlds” mathematically admissible. An approximate classification of these worlds is given, and their possible relation to the quantization of non-linear fields is discussed. It turns out to be obvious that the convex set theory has a similar significance for quantum physics as the Riemannian geometry for space-time physics.     

Is there a reality out there?

Joseph Bertrand's 1888 evidencing that assignment of a probability depends upon what one chooses to know or not and to control or not, congruent with Grad's 1961 evidencing that statistical entropy depends upon what one deems relevant or not in formalization and measurement, radically undermine common sense realism; mean values are symbols, but symbols of what? For that very reason, recent clever conceptualizations of the quantum measurement process via partial tracing do not restore realism: How could deliberate ignorance generate a reality? Beyond this, Born's and Jordan's quantal wavelike probability calculus, entailing algebraic nonseparability and spacetime nonlocality, blurs “reality” still more radically. Thus information stands out as the master word, with its two reciprocal aspects: knowledge and organization.     

Leibniz' principle,general relativity,and the observational dominance of euclidean geometry

Leibniz' principle and the observational dominance of Euclidean geometry suggest a huge cosmological constant in Einstein's field equations and a correspondingly huge negative “vacuum” density. This theory lends support to renormalization procedures in quantum electrodynamics and to the view that the interactions we “observe” are fluctuations of the “vacuum state” interpreted as a Fermi sea. Einstein's “preferred” equations, with A=0, are recovered. “Empty” space has no metric geometry at all.     

Semiclassical quantum gravity: statistics of combinatorial Riemannian geometries

This paper is a contribution to the development of a framework, to be used in the context of semiclassical canonical quantum gravity, in which to frame questions about the correspondence between discrete spacetime structures at “quantum scales” and continuum, classical geometries at large scales. Such a correspondence can be meaningfully established when one has a “semiclassical” state in the underlying quantum gravity theory, and the uncertainties in the correspondence arise both from quantum fluctuations in this state and from the kinematical procedure of matching a smooth geometry to a discrete one. We focus on the latter type of uncertainty, and suggest the use of statistical geometry as a way to quantify it. With a cell complex as an example of discrete structure, we discuss how to construct quantities that define a smooth geometry, and how to estimate the associated uncertainties. We also comment briefly on how to combine our results with uncertainties in the underlying quantum state, and on their use when considering phenomenological aspects of quantum gravity.     

Sinn und Möglichkeiten der Theoretischen Physik. Zum 300. Jahrestag von Newtons „Philosophiae Naturalis Principia Mathematica”︁

The Meaning and Abilities of Theoretical Physics The Newtonean principles and — derived from them — the congnition of the exixtence of elementary constants according to Planck, Einstein and Bohr increasingly prove to be a strong base not only of physics and its apllication in technology but also of each kind of “exact” sciences in the broadest sense of the word. Since Newton the clarification of concepts with regard so their physical takes place in close connection with the development of mathematical methods. This combination proves to be further productive and ensures the progress of physics an of the “exact” sciences. Most likely all problems which may be of importance in the realm of life can be treated successfully — adequate expenditure taken for granted — with the existing fund of knowledge and methods. The connection between law and accident resting on reality proves to be a relation of complementarity (“there is no absolute accident”). This becomes evident in all branches in all branches of physics, not only in thermodynamics and quantum physics, and can be treated already on the level of the Newtonean principles and elementary constants. Theoretical physics as initiated by newton was designed to comprise all parts of nature. About that there is no contrast between classical physics and quantum physics. It is only a matter of differentiation with regard to the different physical contents and the appropriate mathematical methods, dependent of course on the choice problems. Theoretical physics represents a generally available concentration of the reliable knowledge of physics, which is at the same time the foundation of the “exact” sciences. In this way theoretical physics is the means of communication within the cooperation necessary for the solution of the great complex tasks of science and technology.     

A note on measurement

Grounded on the quantum measurement riddle, a general argument against the universal validity of the superposition principle was recently put forward by Bassi and Ghirardi (Phys. Lett. A 275 (2000) 373). It is pointed out that this argument is valid only within the realm of the philosophy of “objectivistic realism” which is not a necessary part of the foundations of physics, and that recent developments including decoherence theory do account for the appearance of macroscopic objects without resorting to a break of the principle.     

Finite groups and quantum physics

Concepts of quantum theory are considered from the constructive “finite” point of view. The introduction of a continuum or other actual infinities in physics destroys constructiveness without any need for them in describing empirical observations. It is shown that quantum behavior is a natural consequence of symmetries of dynamical systems. The underlying reason is that it is impossible in principle to trace the identity of indistinguishable objects in their evolution—only information about invariant statements and values concerning such objects is available. General mathematical arguments indicate that any quantum dynamics is reducible to a sequence of permutations. Quantum phenomena, such as interference, arise in invariant subspaces of permutation representations of the symmetry group of a dynamical system. Observable quantities can be expressed in terms of permutation invariants. It is shown that nonconstructive number systems, such as complex numbers, are not needed for describing quantum phenomena. It is sufficient to employ cyclotomic numbers—a minimal extension of natural numbers that is appropriate for quantum mechanics. The use of finite groups in physics, which underlies the present approach, has an additional motivation. Numerous experiments and observations in the particle physics suggest the importance of finite groups of relatively small orders in some fundamental processes. The origin of these groups is unclear within the currently accepted theories—in particular, within the Standard Model.     

An exactly soluble model of a shallow double well

Shallow one-dimensional double-well potentials appear in atomic and molecular physics and other fields. Unlike the “deep” wells of macroscopic quantum coherent systems, shallow double wells need not present low-lying two-level systems. We argue that this feature, the absence of a low-lying two-level system in certain shallow double wells, may allow the finding of new test grounds for quantum mechanics in mesoscopic systems. We illustrate the above ideas with a family of shallow double wells obtained from reflectionless potentials through the Darboux–Bäcklund transform.