We show that in the presence of the torsion tensor \, the quantum commutation relation for the four-momentum, traced over spinor indices, is given by \. In the Einstein–Cartan theory of gravity, in which torsion is coupled to spin of fermions, this relation in a coordinate frame reduces to a commutation relation of noncommutative momentum space, \, where U is a constant on the order of the squared inverse of the Planck mass. We propose that this relation (...) replaces the integration in the momentum space in Feynman diagrams with the summation over the discrete momentum eigenvalues. We derive a prescription for this summation that agrees with convergent integrals: \^s}\rightarrow 4\pi U^{s-2}\sum _{l=1}^\infty \int _0^{\pi /2} d\phi \frac{\sin ^4\phi \,n^{s-3}}{[\sin \phi +U\varDelta n]^s}\), where \}\) and \ does not depend on p. We show that this prescription regularizes ultraviolet-divergent integrals in loop diagrams. We extend this prescription to tensor integrals. We derive a finite, gauge-invariant vacuum polarization tensor and a finite running coupling. Including loops from all charged fermions, we find a finite value for the bare electric charge of an electron: \. This torsional regularization may therefore provide a realistic, physical mechanism for eliminating infinities in quantum field theory and making renormalization finite. (shrink)

The electric field of an orbiting charge or electron observed in the rotating frame takes on a circular trajectory with a maximum radius of \. The resultant extended electromagnetic structure is used to derive the spin–orbit energy of the orbiting electron. A surprising result of the derived expression is that the orbital velocity has a specific value ) in close agreement ) with the experimentally determined value for the fine structure constant ). Furthermore, the derived spin–orbit expression does not include (...) a g-factor ) which means that the Larmor and Thomas precessions are equal and opposite, resulting in zero net precession in the lab frame. These results suggest that the quantised fine structure constant and by extension Planck’s constant, are a natural extension of classical electromagnetism and conservation of energy in a rotating frame. (shrink)

In this fascinating autobiography from the foremost genius of twentieth-century physics, Max Planck tells the story of his life, his aims, and his thinking. Published posthumously, the papers in this volume were written for the general reader and make accessible his scientific theories as well as his philosophical ideals, including his thoughts on ethics and morals. Max (Karl Ernst Ludwig) Planck was a German physicist and philosopher known for his quantum theory, for which he won the Nobel Prize (...) in Physics in 1918. Planck was born in Kiel, Germany, in 1858 to an academic family, and he valued education from a young age. He attended the Universities of Munich and Berlin to study physics under the great scientific leaders Kirchhoff and Helmholtz. His early work mainly focused on the study of thermodynamics, and in 1900 he published a paper on his quantum theory that would change the face of modern physics. Planck worked as a professor at Berlin University his entire life, and he also served as the president of the Kaiser Wilhelm Society for the Promotion of Science. During World War II, Planck experienced great hardships while he remained in Germany but openly opposed the Nazi regime. One of his two sons was executed during this time for an unsuccessful attempt on Hitler's life, and Planck's home in Berlin was eventually bombed. He continued to write on physics and philosophy until his death in 1947. (shrink)

Penseur et philosophe, Max Planck a dominé par sa personnalité toute la science moderne. Pour Albert Einstein, il a " doté le monde d'une grande idée créatrice " dont la découverte deviendrait " la base de toute la recherche en physique au XXe siècle ". C'est dans le domaine de la thermodynamique que fit irruption sa découverte révolutionnaire, en 1900, alors qu'il s'intéressait au rayonnement émis par les corps qu'on échauffe et aux propriétés de la matière avec laquelle ce (...) rayonnement interagit: contrairement à ce que supposait la physique classique, les échanges d'énergie entre le rayonnement et la matière ne peuvent se faire que par paquets discontinus, les quanta. Une hypothèse de quantification vis-à-vis de laquelle Planck lui-même exprima la plus extrême réticence mais qui signa l'acte de naissance de la physique quantique. Au terme de sa vie, à l'âge de quatre-vingt-sept ans, l'illustre savant revient une dernière fois sur son oeuvre et nous livre la démarche même de son esprit au travail. Un témoignage inestimable, suivi de quatre grandes conférences, qui furent aussi ses derniers écrits : " Les faux problèmes de la science ", " La signification et les limites de la science ", " Le concept de la causalité en physique " et, tel un testament spirituel, " Science et religion ". (shrink)

"...wenn wir etwas näher zusehen und den Aufbau der exakten Wissenschaft einer genaueren Prüfung unterziehen, dann werden wir sehr bald gewahr, daß das Gebäude eine gefährlich schwache Stelle besitzt, und diese Stelle ist das Fundament. Dem Bau fehlt eine von vornherein nach allen Richtungen hin gesicherte, von äußeren Stürmen nicht zu erschütternde Grundlage, oder mit anderen Worten: es gibt für exakte Wissenschaft kein Prinzip von so allgemeiner Gültigkeit und zugleich von so bedeutsamem Inhalt, daß es ihr als ausreichende Unterlage dienen (...) kann. Wohl rechnet sie allenthalben mit Maß und Zahl und trägt daher mit vollem Recht ihren stolzen Namen; denn die Gesetze der Logik und der Mathematik müssen wir ohne Zweifel als zuverlässig betrachten. Aber auch die schärfste Logik und die genaueste mathematische Rechnung können kein einziges fruchtbares Ergebnis zeitigen, wenn es an einer sicher zutreffenden Voraussetzung fehlt. Aus nichts läßt sich nichts folgern." (Max Planck, S. 5 f. in diesem Buch) Der deutsche Physiker Max Planck (* 23. April 1858 in Kiel, † 4. Oktober 1947 in Göttingen) gilt als Begründer der Quantenphysik. Im Jahr 1919 wurde ihm der Nobelpreis für Physik für das Jahr 1918 verliehen. 1941 hielt Planck einen vielbeachteten Vortrag über das Fundament der "exakten" Wissenschaften, zu denen auch die Pysik gezählt wird. Lange vergriffen liegt sein Vortrag "Sinn und Grenzen der exakten Wissenschaft" nun in einer ungekürzten Neuausgabe, ergänzt um einen illustrierten Anhang, wieder als Einzelpublikation vor. Max Planck. Sinn und Grenzen der exakten Wissenschaft. Vortrag gehalten im November 1941. Erstdruck: Johann Ambrosius Barth – Verlag, Leipzig 1942. Durchgesehener Neusatz, der Text dieser Ausgabe folgt der siebenten Auflage, Johann Ambrosius Barth – Verlag, Leipzig 1965. Für die Neuausgabe 2021 mit sieben Illustrationen versehen. Gebundene Ausgabe - Hardcover - mit Lesebändchen. Neuausgabe, LIWI Verlag, Göttingen 2021. LIWI Literatur- und Wissenschaftsverlag. (shrink)

This paper begins by asking a simple question: can a farmer own and fully utilise precisely five tractors and precisely six tractors at the same time? Of course not. He can own five or he can own six but he cannot own five and six at the same. The answer to this simple question eventually led this author to Alfred Marshall's historically-ignored, linguistically-depicted 'cardboard model' where my goal was to construct a picture based on his written words. More precisely, in (...) this paper the overall goal is to convert Marshall's ('three-dimensional') words into a three-dimensional picture so that the full import of his insight can be appreciated by all readers. After a brief digression necessary to introduce Euclidean three-dimensional space, plus a brief digression to illustrate the pictorial problem with extant theory, the paper turns to Marshall's historically- ignored words. Specifically, it slowly constructs a visual depiction of Marshall's 'cardboard model'. Unfortunately (for all purveyors of extant economic theory), this visual depiction suddenly opens the door to all manner of Copernican heresy. For example, it suddenly becomes obvious that we can join the lowest points on a firm's series of SRAC curves and thereby form its LRAC curve; it suddenly becomes obvious that the firm's series of SRAC curves only appear to intersect because mainstream theory has naively forced our three-dimensional economic reality into a two-dimensional economic sketch; and it suddenly becomes obvious that a two-dimensional sketch is analytically useless because the 'short run' (SR) never turns into the 'long run' (LR) no matter how long we wait. (shrink)

Ce texte a déjà paru le 26 octobre 2015 sur le site de la Max-Planck Gesellschaft. Nous remercions Jean-Paul Vignal de nous l'avoir signalé. Researchers at Max Planck Institute for Empirical Aesthetics in Frankfurt and of New York University have identified how brain rhythms are used to process music, a finding that also contributes to a better understanding of the auditory system. Furthermore, the study suggests that musical training can enhance the functional role of brain rhythms. The - (...) Sciences du vivant – Nouvel article. (shrink)

I propose an experiment that may be performed, with present low temperature and cryogenic technology, to reveal Wheeler’s quantum foam. It involves coupling an optical photon’s momentum to the center of mass motion of a macroscopic transparent block with parameters such that the latter is displaced in space by approximately a Planck length. I argue that such displacement is sensitive to quantum foam and will react back on the photon’s probability of transiting the block. This might allow determination (...) of the precise scale at which quantum fluctuations of space–time become large, and so differentiate between the brane-world and the traditional scenarios of spacetime. (shrink)

We consider the special and general relativistic extensions of the action principle behind the Schrödinger equation distinguishing classical and quantum contributions. Postulating a particular quantum correction to the source term in the classical Einstein equation we identify the conformal content of the above action and obtain classical gravitation for massive particles, but with a cosmological term representing off-mass-shell contribution to the energy–momentum tensor. In this scenario the—on the Planck scale surprisingly small—cosmological constant stems from quantum bound states having (...) a Bohr radius a as being \. (shrink)

The energetics controversy is understood variously as energy vs. atoms, thermodynamics vs. statistical mechanics, phenomenalism vs. realism, equations vs. pictures, and especially Ostwald vs. Boltzmann. It is generally thought that at Lübeck in 1895 Boltzmann and Planck demolished energetics, but while its momentum was slowed, energetics in one or more of the above senses still retained supporters as late as the great physics conference at the St. Louis World’s Fair in 1904. Indeed, after Ostwald himself abandoned it in (...) 1908, Ernst Mach began for the first time to defend it. The main emphasis in this paper, however, is on Georg Helm (1851–1923) who had been invited to Lübeck to be the main speaker on energetics. He had adopted his position earlier than Ostwald and his views avoided many of the errors and oversights in Ostwald’s approach. Indeed, Helm could be called the strongest defender of energetics, even if Ostwald was Boltzmann’s main target. Helm was largely Machist in philosophy at that time and did not reify energy. (shrink)

Superluminal particles are studied within the framework of the Extended Relativity theory in Clifford spaces (C-spaces). In the simplest scenario, it is found that it is the contribution of the Clifford scalar component π of the poly-vector-valued momentum which is responsible for the superluminal behavior in ordinary spacetime due to the fact that the effective mass $\mathcal{M} = \sqrt{ M^{2} - \pi^{2} }$ is imaginary (tachyonic). However, from the point of view of C-space, there is no superluminal (tachyonic) (...) behavior because the true physical mass still obeys M 2>0. Therefore, there are no violations of the Clifford-extended Lorentz invariance and the extended Relativity principle in C-spaces. It is also explained why the charged muons (leptons) are subluminal while its chargeless neutrinos may admit superluminal propagation. A Born’s Reciprocal Relativity theory in Phase Spaces leads to modified dispersion relations involving both coordinates and momenta, and whose truncations furnish Lorentz-violating dispersion relations which appear in Finsler Geometry, rainbow-metrics models and Double (deformed) Special Relativity. These models also admit superluminal particles. A numerical analysis based on the recent OPERA experimental findings on alleged superluminal muon neutrinos is made. For the average muon neutrino energy of 17 GeV, we find a value for the magnitude $|\mathcal{M } | = 119.7\mbox{~MeV}$ that, coincidentally, is close to the mass of the muon m μ =105.7 MeV. (shrink)

Particle physicists, over the last 50 years, have discovered several hundred strongly interacting “elementary” particles. The list of such particles begins with the proton and the p meson and goes up from there. We now understand that all of these particles are actually composites, formed from various combinations of quarks. Such particles are normally classified in two types. Mesons (the name implies medium weight) are particles with masses that go up from 140 MeV/c 2 and have an intrinsic angular (...) class='Hi'>momentum or “spin” that is an integer in units of ħ (Planck’s constant over p). Baryons (the name implies heavy weight) are particles with masses that go up from 938 MeV/c 2 and have half-integer spin. This column is about the discovery of the pentaquark, a brand new form of matter that represents a new particle species, neither meson nor baryon, but a combination of both. (shrink)

Recent advances on quantum foundations achieved the derivation of free quantum field theory from general principles, without referring to mechanical notions and relativistic invariance. From the aforementioned principles a quantum cellular automata theory follows, whose relativistic limit of small wave-vector provides the free dynamics of quantum field theory. The QCA theory can be regarded as an extended quantum field theory that describes in a unified way all scales ranging from an hypothetical discrete Planck scale up to the usual Fermi (...) scale. The present paper reviews the automaton theory for the Weyl field, and the composite automata for Dirac and Maxwell fields. We then give a simple analysis of the dynamics in the momentum space in terms of a dispersive differential equation for narrowband wave-packets. We then review the phenomenology of the free-field automaton and consider possible visible effects arising from the discreteness of the framework. We conclude introducing the consequences of the automaton dispersion relation, leading to a deformed Lorentz covariance and to possible effects on the thermodynamics of ideal gases. (shrink)

The Madelung equations map the non-relativistic time-dependent Schrödinger equation into hydrodynamic equations of a virtual fluid. While the von Neumann entropy remains constant, we demonstrate that an increase of the Shannon entropy, associated with this Madelung fluid, is proportional to the expectation value of its velocity divergence. Hence, the Shannon entropy may grow due to an expansion of the Madelung fluid. These effects result from the interference between solutions of the Schrödinger equation. Growth of the Shannon entropy due to expansion (...) is common in diffusive processes. However, in the latter the process is irreversible while the processes in the Madelung fluid are always reversible. The relations between interference, compressibility and variation of the Shannon entropy are then examined in several simple examples. Furthermore, we demonstrate that for classical diffusive processes, the “force” accelerating diffusion has the form of the positive gradient of the quantum Bohm potential. Expressing then the diffusion coefficient in terms of the Planck constant reveals the lower bound given by the Heisenberg uncertainty principle in terms of the product between the gas mean free path and the Brownian momentum. (shrink)