Planck, the Quantum, and the Historians

In late 1900, the German theoretical physicist Max Planck derived an expression for the spectrum of black-body radiation. That derivation was the first step in the introduction of quantum concepts into physics. But how did Planck think about his result in the early years of the twentieth century? Did he assume that his derivation was consistent with the continuous energies inherent in Maxwellian electrodynamics and Newtonian mechanics? Or did he see the beginnings, however tentative and uncertain, of the quantum revolution to come? Historians of physics have debated this question for over twenty years. In this article, I review that debate and, at the same time, present Planck's achievement in its historical context.     

Color,flavor, duality,and the pomeron

AtN _c /N _f =∞ such that quark loops are absent the Harari-Freund (HF)P+f model of diffraction can be motivated through the identification Pomeron ≈ glueball,f≈leading planar trajectory. AtN _c =3, the presence of confinement-related mass scales introduced by quark loops is a basic complication that can easily change this situation to, e.g., a dominantP?f identity structure. Aurenche and Gonzales Mestres (AGM) have argued that diffraction is essentially identical atN _c /N _f =∞ and atN _c =3. They further claim to have generated the HF scheme directly atN _c =3 through the novel mechanism of a multiperipheral iteration of daughters that becomes theP. We respond to these arguments. We give a general qualitative discussion of changes expected in theN _c /N _f =∞ toN _c =3 transition. Important hadron scattering quantities like particle multiplicities are very different in dynamics dominated by glue and atN _c =3, unlike other quantities like resonance width to mass ratios. We argue that the weak coupling dual model is not a reliable guide toN _c =3 dynamics. We criticize AGM's “daughter generated Pomeron”, and we close with a brief summary of other attempts to generate theP+f model.     

Surmounting the Cartesian Cut Through Philosophy, Physics, Logic, Cybernetics, and Geometry: Self-reference, Torsion, the Klein Bottle, the Time Operator, Multivalued Logics and Quantum Mechanics

In this transdisciplinary article which stems from philosophical considerations (that depart from phenomenology??after Merleau-Ponty, Heidegger and Rosen??and Hegelian dialectics), we develop a conception based on topological (the Moebius surface and the Klein bottle) and geometrical considerations (based on torsion and non-orientability of manifolds), and multivalued logics which we develop into a unified world conception that surmounts the Cartesian cut and Aristotelian logic. The role of torsion appears in a self-referential construction of space and time, which will be further related to the commutator of the True and False operators of matrix logic, still with a quantum superposed state related to a Moebius surface, and as the physical field at the basis of Spencer-Brown??s primitive distinction in the protologic of the calculus of distinction. In this setting, paradox, self-reference, depth, time and space, higher-order non-dual logic, perception, spin and a time operator, the Klein bottle, hypernumbers due to Musès which include non-trivial square roots of ±1 and in particular non-trivial nilpotents, quantum field operators, the transformation of cognition to spin for two-state quantum systems, are found to be keenly interwoven in a world conception compatible with the philosophical approach taken for basis of this article. The Klein bottle is found not only to be the topological in-formation for self-reference and paradox whose logical counterpart in the calculus of indications are the paradoxical imaginary time waves, but also a classical-quantum transformer (Hadamard??s gate in quantum computation) which is indispensable to be able to obtain a complete multivalued logical system, and still to generate the matrix extension of classical connective Boolean logic. We further find that the multivalued logic that stems from considering the paradoxical equation in the calculus of distinctions, and in particular, the imaginary solutions to this equation, generates the matrix logic which supersedes the classical logic of connectives and which has for particular subtheories fuzzy and quantum logics. Thus, from a primitive distinction in the vacuum plane and the axioms of the calculus of distinction, we can derive by incorporating paradox, the world conception succinctly described above.     

Steering, entanglement, nonlocality, and the Einstein-Podolsky-Rosen paradox

The concept of steering was introduced by Schr?dinger in 1935 as a generalization of the Einstein-Podolsky-Rosen paradox for arbitrary pure bipartite entangled states and arbitrary measurements by one party. Until now, it has never been rigorously defined, so it has not been known (for example) what mixed states are steerable (that is, can be used to exhibit steering). We provide an operational definition, from which we prove (by considering Werner states and isotropic states) that steerable states are a strict subset of the entangled states, and a strict superset of the states that can exhibit Bell nonlocality. For arbitrary bipartite Gaussian states we derive a linear matrix inequality that decides the question of steerability via Gaussian measurements, and we relate this to the original Einstein-Podolsky-Rosen paradox.     

Formal structures,the concepts of covariance,invariance, equivalent reference frames,and the principle Relativity

In this paper a given spacetime theoryT is characterized as the theory of a certainspecies of structure in the sense of Bourbaki [1]. It is then possible to clarify in a rigorous way the concepts ofpassive andactive covariance ofT under the action of the manifold mapping groupG _M . For eachT, we define also aninvariance groupG _I T and, in general,G _I T ≠G _M . This group is defined once we realize that, for eachτ ∈ModT, each explicit geometrical object defining the structure can be classified as absolute or dynamical [2]. All spacetime theories possess alsoimplicit geometrical objects that do not appear explicitly in the structure. These implicit objects are not absolute nor dynamical. Among them there are thereference frame fields, i.e., “timelike” vector fieldsX ∈TU, \(U \subseteq M\) M, whereM is a manifold which is part ofST, a substructure for eachτ ∈ModT, called spacetime. We give a physically motivated definition of equivalent reference frames and introduce the concept of theequivalence group of a class of reference frames of kind X according to T, G _X T. We define thatT admits aweak principle of relativity (WPR) only ifG _X T ≠ identity for someX. IfG _X T =G _I T for someX, we say thatT admits a strong principle of relativity (PR). The results of this paper generalize and clarify several results obtained by Anderson [2], Scheibe [3], Hiskes [4], Recami and Rodrigues [5], Friedman [6], Fock [7], and Scanavini [8]. Among the novelties here, there is the realization that the definitions ofG _I T andG _X T can be given only when certain boundary conditions for the equations of motion ofT can be physically realizable in the domainU \(U \subseteq M\) M, where a given reference frame is defined. The existence ofphysically realizable boundary conditions for eachτ ∈ModT (in ?U), in contrast with the mathematically possible boundary condition, is then seen to be essential for the validity of a principle of relativity forT. The methodology of the present paper has been applied to several topics of spacetime physics with very interesting results. Here we mention:

1. The Newtonian concepts of absolute space and absolute time can be presented in a very elegant way as “species of structure”. One of the surprising results is that we succeeded in finding a Lorentzian structure [9] in Newtonian spacetime without introducing any new explict geometrical object in the original structure. The Newtonian spacetime structure and its relation to the relativistic spacetime structure and to the structure of the spacetime of the so-called Lorentz aether theories [11,12] is fully discussed in [13].
2. It is possible to present in a novel and unified way the question concerning experiments designed to detect a possible breakdown of Lorentz invariance, a subject we already dedicated attention to in Rodrigues and Tiomno [11,12] and Rodrigues [14,15]. A full account of this subject will be published elsewhere.
3. In Rodrigues and Scanavini [16], we proved that there are models of General Relativity that contain a canonical privileged locally inertial reference frame that can be physically distinguished from any other frame by experiments doneinside the frame.

Although the formalism of this paper may at first sight look very abstract, actually it is easy to aplly it to specific theories. We present an example at the end of the paper which is sufficiently general to show “in action” almost all concepts introduced in this paper.     

Antimatter, the SME, and gravity

A general field-theoretic framework for the analysis of CPT and Lorentz violation is provided by the Standard-Model Extension (SME). This work discusses a number SME-based proposals for tests of CPT and Lorentz symmetry, including antihydrogen spectroscopy and antimatter gravity tests.     

Mass, energy, and the electron

The two-component solutions of the Dirac equation currently in use are not separately a particle equation or an antiparticle equation. We present a unitary transformation that uncouples the four-component, force-free Dirac equation to yield a two-component spinor equation for the force-free motion of a relativistic particle and a corresponding two-component, time-reversed equation for an antiparticle. The particle-antiparticle nature of the two equations is established by applying to the solutions of these two-component equations criteria analogous to those applied for establishing the four-component particle and antiparticle solutions of the four-component Dirac equation. Wave function solutions of our two-component particle equation describe both a right and a left circularly polarized particle. Interesting characteristics of our solutions include spatial distributions that are confined in extent along directions perpendicular to the motion, without the artifice of wave packets, and an intrinsic chirality (handedness) that replaces the usual definition of chirality for particles without mass. Our solutions demonstrate that both the rest mass and the relativistic increase in mass with velocity of the force-free electron are due to an increase in the rate of Zitterbewegung with velocity. We extend this result to a bound electron, in which case the loss of energy due to binding is shown to decrease the rate of Zitterbewegung.     

ICP-AES同时测定铝合金中Fe,Si,Cu,Mg,Mn,Ni,Zn,Ti,Cr,Sr等杂质元素

本文通过基体干扰和操作条件的试验研究，分别用基体匹配法和干扰系数法校正基体干扰和待测元素间的干扰，建立了以氢氧化钠溶样，ICP－AES同时测定铝合金中铁、锰、铜、锌、镁、钛、硅、镍、铬、锶等杂质元素的方法。方法快速、简便、可靠，回收率93％－102％，适用于进出口铝合金的快速检验。     

Stability of bipolarons, electron-electron correlations, the variational principle, and the virial theorem

For bipolaron states, a relation is established between the variational principle and the virial theorem optimizing the electronic wave functions. It is shown that a bipolaron one-center state is unstable under any conditions that do not violate basic physical principles. It is established that a stage-by-stage increase in the flexibility of the electronic wave function due to the electron-electron correlations does not stabilize a one-center bipolaron. It is argued that the results of calculations based on the one-center bipolaron model are incorrect.     

Decoherence,the Density Matrix,the Thermal State and the Classical World

Decoherence has been the basis for understanding the emergence of the classical world from its quantum underpinnings. Unfortunately the calculations establishing decoherence overshoot and, based on assumptions that break down, predict that with the passage of time the off-diagonal elements of the density matrix become arbitrarily small. It has been recognized by some authors that the thermal state, assumed to hold for systems in equilibrium, places a bound on off diagonal terms. In this article we establish—preserving the conservation of energy, as is not the case for previous work—that indeed the thermal state is an attractor under scattering. Moreover, the bound on the off-diagonal terms present in the thermal state does not contradict everyday experience.     

Torsion,wormholes, and the problem of the Cosmological constant

We consider the effect of torsion in the early universe to see if it is possible to explain the small value (if not zero) of the Cosmological constant at the present time. For the gauge-theoretic formulation of the Einstein-Cartan theory, we find a wormhole instanton solution which has a minimum (baby universe) radius of the Planck length. The basic difficulty with the wormhole approach is stressed. Finally, we give an explicit calculation from the expression for the evolution of the scale factor, which shows that the spin-dominated interaction term in the very early universe can cancel the Cosmological constant term at that epoch.     

Neutrinos,supernovae, and the origin of the heavy elements

Stars of～8-100 M_⊙end their lives as core-collapse supernovae(SNe). In the process they emit a powerful burst of neutrinos,produce a variety of elements, and leave behind either a neutron star or a black hole. The wide mass range for SN progenitors results in diverse neutrino signals, explosion energies, and nucleosynthesis products. A major mechanism to produce nuclei heavier than iron is rapid neutron capture, or the r process. This process may be connected to SNe in several ways. A brief review is presented on current understanding of neutrino emission, explosion, and nucleosynthesis of SNe.     

Onsager,ice, biomembranes,dimer models and the F-model

Personal recollections give a sampling of some of Onsager's later interests in ice and biomembranes. The author's involvement in these topics led to modeling a particular biomembrane phase transition using dimer models. Recent work is described for a particularly rich dimer model which is isomorphic to the F-model in three kinds of fields (direct, staggered, and quarter). New results for the full three-dimensional phase diagram show (1) how the anomalous OK multicritical point is destroyed by a direct field, and (2) how a new line of critical points must be added to the phase diagram in direct and staggered fields obtained previously by Baxter, due to diverging susceptibilities in the quarter field.     

Edward Teller, the Hungarian, American and Jew, too

As explained on p. 57 of George Marx’ comprehensive treatiseThe Voice of the Martians [1] (a pun on Leo Szilárd’sVoice of the Dolphins [2]), the titleThe Martians refers to another Szilárd joke, namely to his reply to a question of Fermi’s. In end-of-the-Century parlance, Fermi’s question would be formulated as follows: —With the galaxy presumably full of planetary systems, thereby also of life and thus of intelligence, where are all those extraterrestrials? [3] — to which Szilárd answered —They are among us, but they call themselves Hungarian… — One of these individuals of high intellectual stature, is (“let him be distinguished by a long life” as we would add in such cases by Jewish custom)Edward Teller.     

Objectivity,nonlocality, and the Bell inequalities

It is argued that the Bell inequalities are not a specific feature of local hidden variables theories, but obtain both for local and nonlocal theories that are objectivistic. A nonobjectivistic theory is constructed reproducing the quantum mechanical correlations obtained in realisations of the Einstein-Podolsky-Rosen-Bohm experiment.     

Unitarity,phenomenology, and the bare Pomeron

The possibility of utilizing the multifireball expansion and a bare Pomeron at $\text{α}\text{?}{}_{\mathrm{o}}\text{=0.85}$ as an approximation to a solution of the s-channel unitarity equations explicitly connecting 2-body and inelastic phenomenology is discussed. A scale for Pomeron renormalization effects is inferred.