There are good reasons to think there is a universal, fundamental length, specifically, at the order of the Planck length. If this holds, we then have an empirical answer for Zeno’s paradox of Achilles and the tortoise, a potential impasse in the second premise of the kalam cosmological argument, and creation ex nihilo. In this paper, I establish metaphysical, empirical, and epistemic reasons suggesting there is a universal, fundamental length. Along the way, I propose a “contingent (...) necessity” for such a notion. I then detail how a universal, fundamental length is a preferred solution for issues –. (shrink)

It is shown that the postulation of a minimum length for the horizons of a black hole leads to lower bounds for the electric charges and magnetic moments of elementary particles. If the minimum length has the order of the Planck scale, these bounds are given, respectively, by the electronic charge and by \. The latter implies that the masses of fundamental particles are bounded above by the Planck mass, and that the smallest non-zero neutrino mass (...) is \eV. A precise estimation in agreement to the area quantisation of Loop Quantum Gravity predicts a mass for the lightest massive state in concordance with flavor oscillation measurements, and a Barbero–Immirzi parameter in accordance to horizon entropy estimations. (shrink)

We propose that whatever quantity controls the Heisenberg uncertainty relations it should be identified with an effective Planck parameter. With this definition it is not difficult to find examples where the Planck parameter depends on the region under study, varies in time, and even depends on which pair of observables one focuses on. In quantum cosmology the effective Planck parameter depends on the size of the comoving region under study, and so depends on that chosen region and (...) on time. With this criterion, the classical limit is expected, not for regions larger than the Planck length, \, but for those larger than \^{1/3}\), where H is the Hubble parameter. In theories where the cosmological constant is dynamical, it is possible for the latter to remain quantum even in contexts where everything else is deemed classical. These results are derived from standard quantization methods, but we also include more speculative cases where ad hoc Planck parameters scale differently with the length scale under observation. Even more speculatively, we examine the possibility that similar complementary concepts affect thermodynamical variables, such as the temperature and the entropy of a black hole. (shrink)

It is argued that the `problem of time' in quantum gravity necessitates a refinement of the local inertial structure of the world, demanding a replacement of the usual Minkowski line element by a 4+2n dimensional pseudo-Euclidean line element, with the extra 2n being the number of internal phase space dimensions of the observed system. In the refined structure, the inverse of the Planck time takes over the role of observer-independent conversion factor usually played by the speed of light, which (...) now emerges as an invariant but derivative quantity. In the relativistic theory based on the refined structure, energies and momenta turn out to be invariantly bounded from above, and lengths and durations similarly bounded from below, by their respective Planck scale values. Along the external timelike world-lines, the theory naturally captures the `flow of time' as a genuinely structural attribute of the world. The theory also predicts expected deviations---suppressed quadratically by the Planck energy---from the dispersion relations for free fields in the vacuum. The deviations from the special relativistic Doppler shifts predicted by the theory are also suppressed quadratically by the Planck energy. Nonetheless, in order to estimate the precision required to distinguish the theory from special relativity, an experiment with a binary pulsar emitting TeV range gamma-rays is considered in the context of the predicted deviations from the second-order shifts. (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)

We construct the Extended Relativity Theory in Born-Clifford-Phase spaces with an upper R and lower length λ scales (infrared/ultraviolet cutoff). The invariance symmetry leads naturally to the real Clifford algebra Cl (2, 6, R) and complexified Clifford Cl C (4) algebra related to Twistors. A unified theory of all Noncommutative branes in Clifford-spaces is developed based on the Moyal-Yang star product deformation quantization whose deformation parameter involves the lower/upper scale $$(\hbar \lambda / R)$$. Previous work led us to show (...) from first principles why the observed value of the vacuum energy density (cosmological constant) is given by a geometric mean relationship $$\rho \sim L_{\rm Planck}^{-2}R^{-2} = L_{P}^{-4} (L_{\rm Planck} / R)^{2} \sim 10^{-122}M_{\rm Planck}^4$$, and can be obtained when the infrared scale R is set to be of the order of the present value of the Hubble radius. We proceed with an extensive review of Smith’s 8D model based on the Clifford algebra Cl (1, 7) that reproduces at low energies the physics of the Standard Model and Gravity, including the derivation of all the coupling constants, particle masses, mixing angles,....with high precision. Geometric actions are presented like the Clifford-Space extension of Maxwell’s Electrodynamics, and Brandt’s action related to the 8D spacetime tangent-bundle involving coordinates and velocities (Finsler geometries). Finally we outline the reasons why a Clifford-Space Geometric Unification of all forces is a very reasonable avenue to consider and propose an Einstein-Hilbert type action in Clifford-Phase spaces (associated with the 8D Phase space) as a Unified Field theory action candidate that should reproduce the physics of the Standard Model plus Gravity in the low energy limit. (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)

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)

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)

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)

Jede Zeit hat ihre eigene Vorstellung davon, nach welchen Grundsatzen ein Gemeinwesen verwaltet und auf welche Ziele dabei hingearbeitet werden sollte. In der Fruhen Neuzeit waren solche Leitbilder guter Verwaltung und Regierung unter dem Begriff der Guten Policey zusammengefasst. Die Lehre von der Guten Policey beinhaltete ein Ensemble von Strukturmerkmalen, die man fur ein wohlgeordnetes Gemeinwesen fur unerlasslich hielt. Daruber hinaus bot sie konkrete Anweisungen fur das Regierungs- und Verwaltungshandeln, mit denen man die Respublica an diese Strukturmerkmale heranfuhren konnte. Es (...) war die im Laufe des Hochmittelalters entstehende Literatur von der Politik, die jene Grundsatze einer guten Regierung ausformulierte und literarisch verarbeitete. Sie bildet die Quellengrundlage dieser Untersuchung, die den Wandel der politischen Leitvorstellungen im Laufe der Fruhen Neuzeit bis an die Schwelle der Moderne nachzuzeichnen sucht. Im Mittelpunkt steht dabei die Frage nach dem Hintergrund des rapide steigenden Steuerungsbedarfs, der sich in der stetig und rasch wachsenden Zahl policeylicher Normen niederschlagt, die durch die Gesetzgebung der fruhneuzeitlichen Territorien hervorgebracht wurden. Die Arbeit sucht den Zusammenhang zwischen der Veranderung der Steuerungsziele und dem standig steigenden Steuerungsbedarf zu ergrunden. (shrink)

Keywords: Planck, length, holographic, space, time, quantization, quantum, noise, gravity, wave, detector, GEO600 Published in the December-2008 issue of Analog Science Fiction & Fact Magazine ; This column was written and submitted 7/28/2008 and is copyrighted ©2008 by John G.

This paper investigates the significance of T-duality in string theory: the indistinguisha- bility with respect to all observables, of models attributing radically different radii to space – larger than the observable universe, or far smaller than the Planck length, say. Two interpretational branch points are identified and discussed. First, whether duals are physically equivalent or not: by considering a duality of the familiar simple harmonic oscillator, I argue that they are. Unlike the oscillator, there are no measurements ‘outside’ (...) string theory that could distinguish the duals. Second, whether duals agree or disagree on the radius of ‘target space’, the space in which strings evolve according to string theory. I argue for the latter position, because the alternative leaves it unknown what the radius is. Since duals are physically equivalent yet disagree on the radius of target space, it follows that the radius is indeterminate between them. Using an analysis of Brandenberger and Vafa (1989), I explain why – even so – space is observed to have a determinate, large radius. The conclusion is that observed, ‘phenomenal’ space is not target space, since a space cannot have both a determinate and indeterminate radius: instead phenomenal space must be a higher-level phenomenon, not fundamental. (shrink)