Delign et al.: A phenomenological and a conceptual structure of physics results into different scales of classical and quantum theory

There is a phenomenological and a conceptual structure of physics, which are mutually dependent on each other. This results into regional disciplines of physics, where physics at large scale decouples from the physics at a smaller scale. In other words, theoretical physics is scale dependent and at each scale, there are different degrees of freedom and different dynamics:

In classical mechanics one deals with three scales according to its 3 basic measurements: distance D, time T, mass M. In non-relativistic quantum theory and classical relativity it has two scales: D & T resp. D & M (mass M can be expressed through T & D using the Planck constant resp. T can be expressed via D using the speed of light). In relativistic quantum theory there is only one scale: distance D, P. Delign et al., Quantum Fields and Strings: A Course for Mathematicians, Volume 1, p. 551.


Driesch: the law of the conservation of energy is a proposition which in spite of the poverty of its content enraptured all the natural sciences

Four circumstances fundamentally determined the character of all thought about nature, and indeed on many other problems, in the second half of the nineteenth century.

First of all, the rise of materialistic Metaphysic in express opposition to the idealistic identity-philosophy.

Then Darvinism, which explained how by throwing stones one could build houses of a typical style.

Thirdly, the discovery of the law of the Conservation of Energy by Robert Mayer – a proposition which in spite of the poverty of its content enraptured all the natural sciences.

Lastly, and particular importance in reference to Biology, the discovery and systematic investigation of the delicate structures of living beings with the help of improved optical instruments“, H. Driesch, The History & Theory of Vitalism, pp. 137-138.


North: Time asymmetry in thermodynamic phenomena is a theory of macroscopic phenomena

Time in thermodynamics or better: time asymmetry in thermodynamics. Better still: time asymmetry in thermodynamic phenomena. „Time in thermodynamics“ misleadingly suggests that thermodynamics will tell us about the fundamental nature of time. But we don’t think that thermodynamics is a fundamental theory. It is a theory of macroscopic behavior, often called a „phenomenological science“. And to the extend that physics can tell us abot fundamental features of the world, including such things as the nature of time, we generally think that only fundamental physics can. On its own, a science like thermodynamics won’t be able to tell us about time per se. But the theory will have much to say about everyday processes that occur in time, and in particular, the apparrent asymmetry of those processes. The pressing question of time in this context of thermodynamics is about the asymmetry of thing in time, not the asymmetry of time, to paraphrase Price (1996, 16), C. Callender, The Oxford Handbook of Philosophy of Time, p. 312.


Sklar: Time in classical dynamics serves as a paradigmatic example of a kind of „conceptual refinement“ in the historical evolution of physics

It starts with Newton in his famous „Scholium to the Definitions“ of the Principia. … Now this is the same „Scholium“ that takes up absolute space and our empirical ability to determine at least some kinds of motion, accelerations, relative to „space itself“ by means of the consequent inertial forces such absolute accelerations engender. And with that comes the still ongoing debate about the appropriate metaphysics of space or spacetime – in particular substantivalisms of various sorts versus relationisms of equally varied sorts. Parallel to that debate there has to be a metaphysical dispute about time. Here notion of time as „substance“ seems even more peculiar that it does in the case of space as substance – and even Newton thought that peculiar enough. In the ligth of relativistic spacetimes it seems as though the two metaphysical issues become inseparably interwined. But one can put these metaphysical quandries to the side and still explore a very important way in which the place of time in classical mechanics serves as a paradigmatic example of a kind of „conceptual refinement“ that appears again and again in the historical evolution of physics, C. Callender, The Oxford Handbook of Philosophy of Time, p. 571.


Kneser: das Prinzip des kleinsten Aufwandes für jedes Erscheinungsbild meßbarer Vorgänge

Die Leibnizische Teleologie, auf die Physik meßbarer Vorgänge angewandt, drückt also das Vertrauen aus, daß für jedes einzelne Erscheinungsgebiet ein solches Aufwandsprinzip gefunden werden kann, aus dem sich die wirklich vor sich gehende Bewegung mittels rein mathematischer Methoden erschliessen läßt; diese Methoden gehören der Disziplin der Variationsrechnung an, einer Disziplin deren Wesen schon Leibniz bekannt war; …. Der Planet befindet sich in einer Anfangslage mit einer gewissen Anfangsgeschwindigkeit; seine Lage wird durch das Gravitationsgesetz gegeben für jede spätere Zeit; die Zukunft wird durch Vegangenheit und Gegenwart bestimmt. Bei Verwendung des Integralprinzips wird die Gegenwart durch Vergangenheit und Zukunft bestimmt; hierin liegt das teleologische, eine entfernte Erinnerung an das Handeln mit vorbestimmtem Zweck, A. Kneser, Das Prinzip der kleinsten Wirkung von Leibniz bis zur Gegenwart, S. 1/3.


Schrödinger: The usual way accounting for the conservation laws in non-relativistic theories

Compatibity and the conservation laws are automatically fulfilled if they are based on a variational principle (p. 87). In case of the metric of Special Relativity the most spectacular event is that the three components of momentum are at the same time those of the flux of energy. … The deeper significants  is that energy and mass is the same thing. Momentum, in its original conception mass x velocity, is a stream of  mass, and thus energy, (p. 90). Conservation laws follow from a variatinonal principle in classical (pre-relativistic) thories. All Hamiltonian derivatives must vanish. This lead to four equations of the „conservation-type“. Note three things: (i)  they are consequences of the Euler equations, (ii)  they require severally that the Hamiltonian function H shall not explicitly depend on the x(i) in question, (iii) the brackets are not necessarily symmetric in i and k.  In non-relativistic theories this was the usual way accounting for the conservation laws, (p. 92), E. Schrödinger, Space-Time Structure.


Schrödinger: General Relativity itself entails conservation laws – and that not as consequences of field equations, but as identities

In General Relativity things are changed. General Relativity itself entails conservation laws – and that not as consequences of field equations, but as identities. If you contemplate an integral I = Int ( R dx) in which R is now definitely assumed to be an invariant density, then from the mere fact of general invariance of this integral follow four identical relations between the Hamiltonian derivatives of R, relations of the type of conservation laws; identities, as I said; not, as before, equations which results from putting the Hamiltonian derivatives equal to zero; four relations between the Hamiltonian derivatives will be shown to hold whether or not these derivatives themselves are zero; indeed if they are, the relations become trivial,  E. Schrödinger, Space-Time Structure, p. 93.


Schrödinger: In statistical thermodynamics the given amount of energy E over N identical systems is the sum of the „private“ energies of those systems, which is a constant of the motion

There is, essentially, only one problem in statistical thermodynamics: the distribution of a given amount of energy  over  identical systems. Or perhaps better: to determine the distribution of an assembly of  identical systems over the possible states in which this assembly can find itself, given that the energy of the assembly is a constant . The idea is that there is weak interaction between them, so weak that one can speak of the „private“ energy of every one of them and that the sum of their „private“ energies has to be equal E. The distinguished role of the energy is, therefore, simply that it is a constant of the motion – the one that always exists, and, in general, the only one. The generalization to the case, that there are others besides (momenta, moments of momenta), is obvious; it has occasionally been contemplated, but in terrestrial, as opposed to astrophysical, thermodynamics it has hitherto not acquired any importance, E. Schrödinger, Statistical Thermodynamics, pp. 1-2.


Lorentz: The principle of relativity and the motion of the speed of light

Lorentz regarded the transformation equations as a first approximation. An object moving through a fluid of some kind would be squeezed and therefore shortened (because of various kinds of ether pressures), and the first approximation would be the Lorentz contraction. He thought there would be corrections to higher powers of v/c, and that experimental techniques would eventually become pricise enough to detect differences in the velocity of light. It was Einstein who said this is really a law of physics, a principle, as he declared Maxwell’s equations in a vacuum as a law of physics, L. Susskind, Special Relativity and Classical Fieeld Theory, p. 62.


Unzicker: All known tests of the general relativity theory can be explained by a variable speed of light

In 1960, an article appeared in the Annals of Physics by the physicists Dehnen, Hönl, and Westphal, Dehnen being a former chair of theoretical physics at the University of Constance. Under the title "A Heuristic Approach to General Relativity," the authors considered a series of physical quantities that changed in accordance with a variable speed of light. ... Yet, the article does no less than explain all known tests of the theory with a variable speed of light!, A. Unzicker, Einstein's lost key, p. 142.


Shu: The plasma dynamic Landau damping phenomenon and the capability of stars to organize themselves in a stable arrangement

In its purest form, Landau damping represents a phase-space behavior peculiar to collisionless systems. Analogs to Landau damping exist, for example, in the interactions of stars in a galaxy at the Lindblad resonances of a spiral downsity wave. Such resonances in an inhomogeneous medium can produce wave absorption (in space rather than in time), which does not usually happen in fluid systems in the absence of dissipative forces (an exception in the behavior of corotation resonances for density waves in a gaseous medium), F. H. Shu, The Physics of Astrophysics, Vol. II, p. 402.


Binney/Tremaine: Stellar dynamics is the study of the motion of a large number of point masses orbiting under the influence of their mutual self-gravity

Always majestic, often spectacularly beautiful, galaxies are the fundamental building blocks of the universe. The inquiring mind cannot help asking how they formed, how they function, and what will become of them in the stellar distant future. The principle tool used in answering these questions is stellar dynamics, the study of the motion of a large number of point masses orbiting under the influence of their mutual self-gravity, J. Binney, S. Tremaine, Galactic Dynamics, xiii.


Sanders: Dark matter perceived to be a pervasive fluid filling the Universe  

The reconciliation of astronomical observations with Newtonian dynamics is also the original motivation for the modern hypothesis of dark matter. But, as it has developed, this new form of dark matter is perceived to be a pervasive fluid filling the Universe and comprising the dominant component of bound astronomical systems like galaxies or clusters of galaxies, detectable only by its gravitational influence in these systems, R. H. Sanders, The Dark Matter Problem, A Historical Perspective, p. 12.


Robitaille: Blackbody radiation and its loss of universality

The extension of the Planck’s blackbody equation to other materials may yield apparent temperatures, which do not have any physical meaning relative to the usual temperature scales. Real temperatures are exclusively obtained from objects which are known solids, or which are enclosed within, or in equilibrium with, a perfect absorber. For this reason, the currently accepted temperature of the microwave background must be viewed as an apparent temperature. Rectifying this situation, while respecting real temperatures, involves a reexamination of Boltzman’s constant. In so doing, the latter is deprived of its universal nature and, in fact, acts as a temperature dependent variable. In its revised form, Planck’s equation becomes temperature insensitive near 300 K, when applied to the microwave background, (RoP1).


Robitaille: Water, Hydrogen Bonding, and the Microwave Background

Though liquid water has a fleeting structure, it displays an astonishingly stable network of hydrogen bonds. Thus, even as a liquid, water possesses a local lattice with short range order. The presence of hydroxyl and hydrogen bonds within water, indicate that it can simultaneously maintain two separate energy systems. These can be viewed as two very different temperatures. … it is shown that hydrogen bonds within water should be able to produce thermal spectra in the far infrared and microwave regions of the electromagnetic spectrum. This simple analysis reveals that the oceans have a physical mechanism at their disposal, which is capable of generating the microwave background, (RoP2).


Schrödinger: The subject-matter of physics and anorganic chemistry

Inorganic matter  - the subject-matter – by definition, of physics and chemistry – is an abstraction which, unless by special arrangement, we actually encounter scarely anywhere, or at any rate extremely seldom. If we consider our earthly environment, it consists almost exclusively of the living or dead bodies of plants and animals. This is certain as regards a great part of the earth’s crust. Hence one might well feel tempted to doubt the accuracy of the common view that everything start from inorganic, and wonder whether it is standing the actual situation on its head, E. Schrödinger, My View of the World, p. 41.


Schrödinger: „Organic“ and „inorganic“ as characteristics of our point of view

What does „organic“ mean? - excluding such simple answers as „protein“ or „protoplasm“.  Fixing our attension on a somewhat wider concept than this, we arrive at the criterion of metabolism. Thus Schopenhauer’s line of demarcation may be regarded as highly suitable, when he says that in inorganic being „the essential and permanent element, the basis of identity and integrity, is a material, the matter, the inessential and mutable element being the form. In organic being the reverse is true; for its life, that is, its existence as an organic being, consists precisely in a constant change of matter while the form persits.“ Bit it depends entirely on the observer what he chooses to regard as essential and what as inessential in a thing. Pr se everything is equally essential. This would turn „organic“ and „inorganic“ into characteristics, not so much of the object as of our point of view or the direction of our attention, E. Schrödinger, My View of the World, p. 42.


Weyl: The gap between organic and inorganic matter has been bridged to a certain extent by the discovery of virusses

One of the profoundest enigmas of nature is the contrast of dead and living matter. … The gap between organic and inorganic matter has been bridged to a certain extent by the discovery of virusses. … A virus is clearly something like a naked gene, H. Weyl, Philosophy of Mathematics and Natural Science, p. 276.


Schrödinger: Metaphysics in general

Metaphysics turns into physics in the course of its development - but not of course in the sense in which it might have seemed to do so before Kant. Never, that is, by a gradual establishing of initially uncertain opinions, but always through a clarification of, and change in, the philosophical point of view, E. Schrödinger, My View of the World, p. 5.


Schrödinger: The imperfection of understanding

On this ground alone exact science is never really possible, E. Schrödinger, My View of the World, p. 83.


Kant: A priori gegebene Stoffe zum Weltsystem

Lehrsatz: Die uranfängliche bewegende Materien setzen einen den ganzen Weltraum durchdringend erfüllenden Stoff voraus als Bedingung der Möglichkeit der Erfahrung der bewegenden Krafte in diesem Raume welcher Urstoff nicht als hypothetischer zur Erklärung der Phänomene ausgedachter sondern categorisch a priori erweislicher Stoff für die Vernunft im Übergange von den metaphysischen Anfangsgründen der Naturwissenschaft zur Physik identisch enthalten ist, E. Kant, Opus posthumum, II. Conv, VII. Bogen, 4. Seite.


Kant: Time, space, and causality are nothing but forms of our knowledge

Time, space, and causality are not determinations of the thing-in-itself, but belong only to its phenomenon, since they are nothing but forms of our knowledge. Now as all plurality and all arising and passing away are possible only through time, space, and causality, it follows that they too adhere only to the phenomenon, and by no means to the thing-initself. But since our knowledge is conditioned by these forms, the whole of experience is only knowledge of the phenomenon, not of the thing-in-itself; hence also its laws cannot be made valid for the thing-in-itself. What has been said extends even to our own ego, and we know that only as phenomenon, not according to what it may be in itself; A. Schopenhauer, The World as Will and Representation, Volume I, § 31.


Kant/Schopenhauer/Schrödinger: This one thing – mind or world – may well be capable of other forms of appearance that we cannot grasp and that do not imply the notions of space and time

However, the supreme importance of Kant’s statement does not consist in justly distributing the roles of the mind and its object  - the world – between them in the process of „mind forming an idea of the world“, because, as I just pointed out, it is hardly possible to discriminate the two. The great thing was to form the idea that this one thing – mind or world – may well be capable of other forms of appearance that we cannot grasp and that do not imply the notions of space and time. This means an imposing liberation from our inveterate prejudice. There probaby are other orders of appearance than the space-time-like. It was, so I believe, Schopenhauer who first read this from Kant, E. Schrödinger, What is Life?, p. 145.


Asmus: Das Verhältnis der allgemeinen Form zum einzelnen Inhalt, somit des Denkens zum Sein

Die Identität des Subjects und Objects – abstract ausgedrückt des Denkens und Seins – hat bekanntlich die gröbsten Missdeutungen erfahren. Der Grund davon liegt fast immer darin, dass man darunter die Identität eines bestimmten Subjects and bestimmten Objects verstanden hat. Aber eine Identität des Subjects und Objects überhaupt wird von jedem vorausgesetzt, der die Möglichkeit des Erkennens zugibt. Glauben wir die wirklichen Dinge zu erkennen, glauben wir, dass wir die Wahrheit des Objects, sein Ansich begreifend zu erfassen vermögen, so haben wir eben damit eine Identität des wirklichen Seins und unserer Subjectivität angenommen. …. So zeigt sich uns das Ich als Einheit der allgemeinen Form und des einzelnen Inhaltes.  … Damit haben wir den Sinn unserer obigen Behauptung dargethan, das Verhältnis der allgemeinen Form zum einzelnen Inhalt und somit des Denkens zum Sein erörtert, P. Asmus, Das Ich und das Ding an sich, S. 4 u.11.


Schopenhauer: Bringing the knowledge of the inner nature of the world into reflection is the only business of the philosophy

For here also is seen the great distinction between intuitive and abstract knowledge, a distinction of such importance and of general application in the whole of our discussion, and one which hitherto has received too little notice. Between the two is a wide gulf; and, in regard to knowledge of the inner nature of the world, this gulf can be crossed only by philosophy. Intuitively, or in concreto, every man is really conscious of all philosophical truths; but to bring them into his abstract knowledge, into reflection, is the business of the philosopher, who neither ought to nor can do more than this, A. Schopenhauer, The World as Will and Representation, Volume I, § 68.


Schopenhauer: On knowledge a priori; the entire content of the law of causality

Every change in the material world can appear only in so far as another change has immediately preceded it; this is the true and entire content of the law of causality, A. Schopenhauer, The World as Will and Representation, Volume II, chapter IV.


Schopenhauer: On the doctrine of knowledge of reason; the concept (BEGRIFF) as the most important instrument of intelligence

The outer impression on the senses, together with the mood that it alone and by itself evokes in us, vanishes with the presence of things. Therefore these two cannot themselves constitute experience proper, whose teaching is to guide our conduct for the future. The image of that impression preserved by the imagination is already weaker than the impression itself; day by day it grows weaker still, and in time becomes completely extinct. There is only one thing, the concept (DER BEGRIFF, term, notion, idea, universal), which is not subject either to that instantaneous vanishing of the impression, or to the gradual disappearance of its image, and consequently is free from the power of time. Therefore in the concept the teaching of experience must be stored up, and it alone is suitable as a safe guide for our steps in life. Therefore Seneca rightly says: Si vis tibi amnia sub jicere, to subjice rationi (Ep. 37).1 And I add that, to be superior (ÜBERLEGEN) to others in real life, (überlegt seyn, d.h. nach Begriffen verfahren) the indispensable condition is to be thoughtful and deliberate (lüberlegt), in other words, to set to work in accordance with concepts. So important an instrument of intelligence as the concept (BEGRIFF) obviously cannot be identical with the word, that mere sound, which as a sense-impression passes away with the present moment, or as a phantasm of hearing will die away with time. But the concept is a representation, whose distinct consciousness and preservation are tied to the word. Therefore the Greeks called word, concept (BEGRIFF), relation, thought, idea, and reason (Vernunft) by the name of the first, δ λογοζ. Yet the concept (BEGRIFF) is entirely different not only from the word to which it is tied, but also from the perceptions from which it originates. It is of a nature entirely different from these sense-impressions; yet it is able to take up into itself all the results of perception, in order to give them back again unchanged and undiminished even after the longest period of time; only in this way does experience arise. But the concept does not preserve what is perceived or what is felt; rather it preserves what is essential thereof in an entirely altered form, yet as an adequate representative of those results, A. Schopenhauer, The World as Will and Representation, Volume II, chapter VI.


Steiner: Die verwickelsten wissenschaftlichen Forschungen ruhen auf den beiden Grundsäulen unseres Geistes, Beobachtung und Denken

Beobachtung und Denken sind die beiden Ausgangspunkte für alles geistige Streben des Menschen, insofern er sich eines solchen bewußt ist. Die Verrichtungen des gemeinen Menschenverstandes und die verwickelsten wissenschaftlichen Forschungen ruhen auf diesen beiden Grundsäulen unseres Geistes. Die Philosophen sind von verschiednen Urgegensätzen ausgegangen: Idee und Wirklichkeit, Subjekt und Objekt, Erscheinung und Ding an sich, Ich und Nicht-Ich, Idee und Wille, Begriff und Materie, Kraft und Stoff, Bewusstes und Unbewusstes. Es lässt sich aber leicht zeigen, dass allen diesen Gegensätzen der von Beobachtung und Denken, als der für den Menschen wichtigste, vorangehen muss. Was für ein Prinzip wir auch aufstellen mögen: Wir müssen es irgendwo als von uns beobachtet nachweisen, oder in Form eines klaren Gedankens, der von jedem anderen nachgedacht werden kann, aussprechen, R. Steiner, Die Philosophie der Freiheit, Grundzüge einer moderne Weltanschauung, S. 43/44.


Einstein: Mein Weltbild; Religion und Wissenschaft; Furcht-Religion, moralische Religion, kosmische Religion

… an der Wiege des religiösen Denkens und Erlebens stehen die verschiedensten Gefühle. Beim Primitiven ist es in erster Linie die Furcht, die religiöse Vorstellungen hervorruft. … Man denkt nun, die Gesinnung jener Wesen sich günstig zu stimmen, indem man Handlungen begeht und Opfer bringt, welche nach dem Geschlecht zu Geschlecht überlieferten Glauben jene Wesen besänftigen bzw. dem Menschen geneigt machen. Ich spreche in diesem Sinne von Furcht-Religionen. … Die Sehnsucht nach Führung, Liebe und Stütze gibt den Anstoß zur Bildung des sozialen bzw. des moralischen Gottesbegriffes. … Dies ist der moralische Gottesbegriff. … All diesen Typen gemeinsam ist der antropomorphe Charakter der Gottesidee. … Bei allen aber gibt es noch eine dritte Stufe religiösen Erlebens, wenn auch nur selten in reiner Ausprägung; ich will sie als kosmische Religiosität bezeichnen. .. Ansätze zur kosmischen Reliösität finden sich bereits auf früher Entwicklungsstufe, z.B. in manchen Psalmen Davids sowie religiösen Propheten. Viel stärker ist die Komponente kosmischer Religiosität im Buddhismus, was uns besonders Schopenhauers wunderbare Schriften gelehrt haben. …Es kann daher auch keine Kirche geben, deren hauptsächlicher Lehrinhalt sich auf kosmische Religiosität gründet. … So kommen wir zu einer Auffassung von der Beziehung der Wissenschaft zur Religion, die recht verschieden ist von der üblichen. … Die Furcht-Religion hat bei ihm keinen Platz, aber ebensowenig die soziale bzw. moralische Religion.  … Es ist also verständlich, daß die Kirchen die Wissenschaft von jeher bekämpft und ihre Anhänger verfolgt haben. Andererseits aber behaupte ich, daß die kosmische Religiosität die stärkste und edelste Triebfeder wissenschaftlicher Forschung ist. … Es ist die kosmische Religiosität, die solche Kräfte spendet. Ein Zeitgenosse hat nicht mit Unrecht gesagt, daß ernsthafte Forscher in unserer im allgemeinen materialistisch eingestellten Welt die einzigen tief religiösen Menschen sind, A. Einstein, Mein Weltbild, S. 21/22.


Einstein: The world as I see it; The Religiousness of Science

You will hardly find one among the profounder sort of scientific minds without a peculiar religious feeling of his own. But it is different from the religion of the naive man. For the latter God is a being from whose care one hopes to benefit and whose punishment one fears; a sublimation of a feeling similar to that of a child for its father, a being to whom one stands to some extent in a personal relation, however deeply it may be tinged with awe. But the scientist is possessed by the sense of universal causation. The future, to him, is every whit as necessary and determined as the past. There is nothing divine about morality, it is a purely human affair. His religious feeling takes the form of a rapturous amazement at the harmony of natural law, which reveals an intelligence of such superiority that, compared with it, all the systematic thinking and acting of human beings is an utterly insignificant reflection. This feeling is the guiding principle of his life and work, in so far as he succeeds in keeping himself from the shackles of selfish desire. It is beyond question closely akin to that which has possessed the religious geniuses of all ages, A. Einstein, The world as I see it, p. 22.