Newton's Principia revisited: Volume 1: Meta- and protomechanics

By Michael Schmiechen

PROBLEM. The treatise is devoted to the reconstruction of our 'instinctive beliefs' in classical mechanics and to present them 'as much isolated and as free from irrelevant additions as possible'. The same motivation has driven many authors since the publication of Newton's Principia.

IMPORTANCE. Classical mechanics will remain the basic reference and tool for mechanics on terrestrial and planetary scale as well as the proto-theory of relativistic and quantum mechanics. But it can only serve its purpose if it is not considered as obsolete, but if its foundations and implications are understood and made 'absolutely' clear.

METHOD. Based on the 'instinctive belief' that the foundations of classical mechanics cannot be found and reconstructed within mechanics itself but only 'outside', classical mechanics is 'understood' by embedding it into an adequate theory of knowledge and adequate proto- and meta-theories in terms of the 'language of dynamics'. Evidence is produced that available philosophical expositions are not adequate for the purpose at hand.

Mechanics is treated as part of physics, not of mathematics. Not sophisticated mathematical artifacts, necessary for solving specific problems, but the intellectually satisfactory foundation of mechanics in general is subject and purpose of the exercise. The goal is reached using axiomatic systems as models.

SCOPE. Following an account of the unsatisfactory state of affairs the treatise covers the epistemological foundations, abstract proto-mechanics, i. e. the theories of time and space, meta-mechanics, i. e. the theories of state space models and of quantities proper, and, as an instance of the latter, abstract elementary mechanics, the theory of translational motions of 'small' solid bodies in three-dimensional Euclidean space, including classical general relativity. Subsequently the theory of classical kinematics is developed as basis for interpreted proto-mechanics and interpreted elementary mechanics. As an amusing interlude classical special relativity is treated in detail.

On the basis of a model of matter suggested by Newton's 'Definition IV' and d'Alembert's principle a theory of inertia and gravitation has been developed, which is in accordance with the standard model of nucleons and may be of interest to physicists. Gradients of the mass potential of physical space are considered as causes of momentum productions in bodies of ponderable matter. This point of view permits to avoid many problems so far unsolved.

Further, classical macroscopic mechanics is treated as continuum mechanics. Accordingly Cauchy's universal equation of motion is considered as the root of the healthy tree of classical mechanics. All its global branches including 'generalised' mechanics are shown to be 'nothing but' weighted integrals of the basic local momentum balance.

The final chapters deal with the theories of dynamics and kinematics of rigid bodies in vacuo and in fluids. The rational theories of motions and propulsion of bodies in fluids, developed by the author, demonstrate the power of the axiomatic approach. The treatise proper ends with a section on motions in wave media. The closing operations of evaluation, assessment and conclusions provide an executive summary, the assessment of the results so far and the decisions based on these results.

READERS. All teachers and students of physics and mechanics, theoretical and applied, as well as of didactics, philosophy and history of physics and mechanics, in fact everybody interested in understanding, in Goethe's sense, the world we live in.

• Language: English
• Publisher: Books on Demand
• Release date: Jan 4, 2011
• ISBN: 9783839160008

Michael Schmiechen

Until he retired in 1997 the author has been Deputy Director, Head of Research and Development at the Versuchsanstalt für Wasserbau und Schiffbau (VWS), the Berlin Model Basin, and apl. Professor for Hydromechanical Systems at the Institut für Schiffs- und Meerestechnik (ISM), Technische Universität Berlin (TUB). Ever since he continued to promote his ideas at lectures and conferences around the world. Details of his curriculum vitae and his personal background are to be found on his website www.m-schmiechen.de .

Book preview

Bibliografische Information der Deutschen Bibliothek:

Die Deutsche Bibliothek verzeichnet diese Publikation in der Deutschen National Bibliografie; detaillierte bibliografische Daten sind im Internet über http://dnb.ddb.de abrufbar.

Volume 1: ISBN 978-3-8391-6000-8

Volume 2: ISBN 978-3-8370-5308-1

Volume 3: ISBN 978-3-8370-5309-8

Dieses Werk ist urheberrechtlich geschützt. Die dadurch begründeten Rechte, insbesondere die der übersetzung, des Nachdrucks, des Vortrags, der Entnahme von Abbildungen und Tabellen, der Funksendung, der Mikroverfilmung oder der Vervielfältigung auf anderen Wegen und der Speicherung in Datenverarbeitungsanlagen, bleiben, auch bei nur auszugsweiser Verwertung, vorbehalten. Eine Vervielfältigung dieses Werkes oder von Teilen dieses Werkes ist auch im Einzelfall nur in den Grenzen der gesetzlichen Bestimmungen des Urheberrechtsgesetzes der Bundesrepublik Deutschland vom 9. September 1965 in der jeweils geltenden Fassung zulässig. Sie ist grundsätzlich vergütungspflichtig. Zuwiderhandlungen unterliegen den Strafbestimmungen des Urheberrechtsgesetzes.

The moral rights of Michael Schmiechen to be identified as the sole author of this work are asserted by him in accordance with the Copyright, Designs and Patents Act 1988.

© Michael Schmiechen Berlin 2009

Herstellung und Verlag

Books on Demand GmbH

Norderstedt near Hamburg

Germany

Printed on lasting paper.

"… absence of synonymy, clash of meanings, absurdity are desirable. Presence of synonymy, intuitive appeal, agreement with customary modes of speech, far from being the philosophical virtue, indicates that not much progress has been made and that the business of investigating what is commonly accepted has not even started."

Paul Feyerabend: How to be a good empiricist (1999/101 f).

PROBLEM

The present treatise is devoted to the task of philosophy on the most modest level, to reconstruct our 'instinctive beliefs' in classical mechanics and to present them 'as much isolated and as free from irrelevant additions as possible' as RussellB demanded in 1912. The same motivation drove many authors since the appearance of Newton's Principia, among them most prominently Hertz in constructing his 'Prinzipien der Mechanik', posthumously published in 1894.

IMPORTANCE

Classical mechanics will remain our basic reference and tool for mechanics on terrestrial and planetary scale as well as the proto-theory of 'relativistic' and quantum mechanics, as noted by Einstein 1919. It can only serve its purpose if it is not considered as obsolete, but if its foundations and implications are understood and made 'absolutely' clear.

The relation of the theory of general relativity to classical mechanics is similar to the relation of quantum theory to classical mechanics as claimed by Landau and Lifschitz in 1965, though that claim has never been substantiated (Laughlin 2007/58):

Sie enthält die klassische Mechanik als Grenzfall und bedarf gleichzeitig dieses Grenzfalls zu ihrer eigenen Begründung.

METHOD

Based on the instinctive belief that the foundations of classical mechanics cannot be found and reconstructed within mechanics itself but only 'outside', classical mechanics is 'understood' by embedding it into an adequate theory of knowledge and adequate proto- and meta-theories in terms of the 'language of dynamics' as demanded by Kant, Goethe and specifically by Maxwell in 1877. Evidence is produced that available philosophical expositions, provided they are sufficiently explicit, are not adequate for the purpose at hand.

Mechanics is part of physics, not of mathematics. Thus not the sophisticated mathematical artifacts, necessary for solving specific problems, but the intellectually satisfactory foundations of mechanics in general are subject and purpose of the present exercise. The goal is reached using axiomatic systems as models constituting representation spaces in accordance with Kant's Copernican turn and Poincaré's conventionalism.

Newton's Principia and related 'principles' revisited

Classical Dynamics reconstructed in the spirits of Goethe, Euler and Einstein

Elementary Mechanics from an advanced standpoint and vice versa

This simple minded contribution to mankind's unended quest is humbly dedicated to the Creator of the immeasurable Universe.

And it is gratefully dedicated to all, who made this work possible: to my wife Susanne, to our four children, and to the generations of my ancestors, of my teachers and of my colleagues, and, last but not least, of my students; and it is dedicated to all researchers, teachers, historians and philosophers of physics and mechanics.

In the spirit of Goethe and following Newton, Euler and Einstein a local model is being offered, embedded into a hierarchy of few, hopefully coherent and acceptable, yet instinctive beliefs, our 'principles', the mythical foundations of science, subject to superstition and fashion, and thus subject to change with further evolution of rationality.

Prof. Dr.-Ing. Michael Schmiechen

until his retirement on 31.03.1997

Deputy Director, Head of Research and Development,

   at the Versuchsanstalt für Wasserbau und Schiffbau (VWS),

      the Berlin Model Basin, and

  apl. Professor for Hydromechanical Systems

   at the Institut für Schiffs- und Meerestechnik (ISM)

      of Technische Universität Berlin (TUB)

Bartningallee 16, D-10557 Berlin (Tiergarten), Germany

Phone: [phone], E-mail: [e-mail]

Website: http://www.m-schmiechen.de

The website will be permanently archived by the Deutsche Nationalbibliothek at Leipzig in accordance with the DNB Law of July 22, 2006.

It contains links to all papers, presentations and worked examples of the author since about 1990, and hopefully in the near future to all prior work as well.

Covering

General subjects

Mechanics in general

Motions of vehicles

Propulsion in general

Ducted propulsors

Various materials

in sections

Recent additions

Papers annotated

Bibliographies

and further

Terms of usage

Letters (yet) unanswered

Fields of research

Biography of the author

Personal background (5.5.7)

Useful links

Die Physik ist nichts, als die Lehre von der Phantasie.

Novalis: Studienheft 1799 (1981/521).

Advertisement

From Newton's advertisements to the first two editions of his Opticks, (1952/CXXI ff):

Advertisement to the First Edition, April 1, 1704:

"Part of my ensuing Discourse about Mechanics was … put together out of scatter'd Papers. To avoid being engaged in Disputes about these Matters, I have hitherto delayed the printing, and should still have delayed it, had not the Importunity of Friends prevailed upon me. If any other Papers writ on this Subject are got out of my Hands they are imperfect, and were perhaps written before I had tried all the Ideas here set down, and fully satisfied my self about the Laws of Motion. I have here publish'd what I think proper to come abroa'd, wishing that it may not be translated into another Language without my Consent.

… The gravitation, I have endeavoured to give an Account of: but for want of sufficient Observations leave that Matter to be farther examined. Many Subjects I have also left imperfect, not having tried all the Considerations which I intended when I was about these Matters, nor repeated some of those which I did try, until I had satisfied my self about all their Circumstances. To communicate what I have tried, and leave the rest to others for farther Enquiry, is all my Design in publishing these Papers. …."

Italics: paraphrases*: MS.

* Different from the standard usage in the sense of 'rewording' the term 'paraphrase' is used for the 'result of an imitation' in the sense of 'parody, caricature, burlesque, travesty' throughout the whole treatise (Roget's Pocket Thesaurus. A Treasury of Synonyms and Antonyms. 1949).

Advertisement to the Second Edition, July 16, 1717:

… at the End … I have added some Questions. And to shew that I do not take Gravity for an essential Property of Bodies, I have added one Question concerning its Cause, chusing to propose it by way of a Question, because I am not yet satisfied about it for want of Experiments.

Note

Heutzutage will freilich niemand mehr etwas von Exposition wissen; die Wirkung, die man sonst im dritten Akt erwartete, will man jetzt schon in der ersten Szene haben, und man bedenkt nicht, daß es mit der Poesie wie mit dem Seefahren ist, wo man erst auf einer gewissen Höhe sein muß, bevor man mit vollen Segeln gehen kann.

Johann Wolfgang Goethe: 27.03.1831 (Eckermann, 1911/341).

Readers will find a number of 'cross-sections' worth noting before getting involved in the text. Right before the detailed table of 'Contents' the 'Survey' on the following page provides an overview of the material covered in three volumes. The 'Preface' is addressed to colleagues and friends, trying to catch their interest and asking them to join me in my continuing effort to clarify the foundations of classical mechanics and eventually jointly to arrive at an ISO standard meeting the current state of science and technology, hopefully offending nobodies instinctive beliefs.

At the end, in the 'Closing operations' the section 'Evaluation' provides an abstract, in parts a summary of the treatise. The appendices include the 'Acknowledgements', the 'Conventions' adopted, the 'References' and finally by the 'Indices'. For the convenience of readers the Preliminaries, including the overall 'Contents', the 'Preface' and the 'Bootstraps', as well as the 'Conventions', the overall 'References' and 'Indices', are repeated in all three volumes.

In plunging into the text readers are invited to follow their own curiosity as the author has done in his research. If the philosophy, the theory of theories, the protoand meta-mechanics are not to their tastes they may dive directly into the more technical sections of interest to them. These provide solutions for a number of fundamental problems, which have not been solved before due to the proud ignorance of the problems and of 'theory' and 'philosophy' still to be met among 'practicians' and 'theoreticians' as well.

Maybe these solutions motivate readers to go back and grasp, for their own advantage, the merits and power of the axiomatic method explained in detail and applied consistently. In view of the very many levels of discussion and the incredible confusion of issues and jargons a shorter text would not have served the purpose at this stage. Despite its scope and size the treatise is still unfinished, work in progress and Goethe has provided a good excuse for its publication (BA 11/300):

Eine solche Arbeit braucht nicht im höchsten Grade ausgeführt und vollendet zu sein; wenn sie gut gesehen, gedacht und fertig ist, so ist sie für den Liebhaber oft reizender als ein größeres, ausgeführtes Werk.

Survey

For the convenience of readers and, last but not least, in view of book production, the material conceived as a single coherent treatise is published in three separate paperbacks. The publication as an e-book is envisaged.

Preliminaries

Contents, Preface, Bootstraps

Part 1: Meta- and proto-mechanics

Prologue

Opening operations: Problems, Models, Goals

Related background: cultural, personal

Theory of theories: 'meta-physics' explicit

Proto-mechanics: abstract: time and space

Meta-mechanics: abstract: state space models

Part 2: Elementary and local mechanics

Meta-mechanics: ad hoc: balances of quantities

Elementary mechanics: abstract: dynamical relativity

Proto-mechanics: interpreted: physical measurements

Perspective, kinematical relativity: speed horizons

Elementary dynamics: concepts of 'force'

Elementary physics: inertia and gravitation

Meta-mechanics: local: balances of quantities

Local mechanics: continuum mechanics

Local mechanics: stress laws

Part 3: Global and propulsion mechanics

Global balances: elementary: weighted integrals

Global mechanics: abstract: partial energy balances

Rigid body mechanics: kinematics, dynamics

Rigid bodies in fluids: axiomatic approach

Propulsion mechanics: rational approach

Motions in wave media: various models

Closing operations: Evaluation Assessment, Conclusions

Epilogue, Post scriptum, Acknowledgements

Conventions, References, Indices

Contents

… I do not think 'The Rime of the Ancient Mariner' was for Coleridge an escape from reality: I think it was reality, I think he was on the ship and made the voyage and felt and knew it all.

Thomas Wolfe, 1932 (Coleridge, 1967/VI).

1 Preface

2 Bootstraps

2.1 Levels of problems

2.2 Solving problems

2.3 'Initial' problem

Part 1

Meta- and proto-mechanics

3 Prologue

3.1 Comprehending

3.1.1 Sufficient reasons

3.1.2 Language of dynamics

3.1.3 Exegesis of holy texts

3.1.4 Scientific 'systems'

3.1.5 Paradigm of paradigms

3.2 Coherent beliefs

3.2.1 Instinctive beliefs

3.2.2 Principle of coherence

3.2.3 Epistemic logics

3.2.4 Münchhausen's Trilemma

3.2.5 'Mythical' foundations

3.2.6 Knowledge and belief

3.2.7 Religious beliefs

3.3 Reconstruction

3.3.1 Intellectual problems

3.3.2 Interpretations

3.3.3 Scientific roots

3.3.4 Historical developments

3.3.5 'Methods' of research

3.3.6 'Against method'

3.3.7 Goethe's method

3.3.8 Guiding principle

3.4 Embedding

3.4.1 Basic idea

3.4.2 Modest goal

3.4.3 Meta-theories

3.4.4 Top-down approach

3.4.5 'Higher standpoint'

3.4.6 Other approaches

4 Opening operations

4.1 Classical expositions

4.1.1 Need for reconstruction

4.1.2 Limits of theory

4.1.3 Boscovich's Law

4.1.4 Dühring's assignment

4.1.5 Mach's concerns

4.1.6 Hertz' motivation

4.1.7 Boltzmann's 'Principe'

4.2 More recent expositions

4.2.1 Hamel's axioms

4.2.2 Lanczos' variations

4.2.3 'Axiomatic' approaches

4.2.4 'Mass points' et cetera

4.2.5 Hamel 'replaced'

4.2.6 Rational mechanics

4.2.7 Related efforts

4.3 Concepts of force

4.3.1 'Incredible' beliefs

4.3.2 Hopeless efforts

4.3.3 Euler's 'Naturlehre'

4.3.4 Non-trivial problem

4.3.5 Hopeless confusion

4.3.6 Much nonsense

4.3.7 Concepts of force: history

4.4 'Solutions' proposed

4.4.1 'Philosophical' approach

4.4.2 'Rational' approach

4.4.3 Elementary mechanics

4.4.4 Freely moving bodies

4.4.5 Constrained motions

4.4.6 Operational interpretation

4.4.7 Universes, reference molluscs

4.4.8 Theory of gravitation

4.4.9 'Zu Ende gekommen'

4.5 Model, Goal, Plan

4.5.1 Model of treatise

4.5.2 Goal of the treatise

4.5.3 'Engineering' philosophy

4.5.4 Proto- and meta-mechanics

4.5.5 Elementary and local dynamics

4.5.6 Global dynamics, 'principles'

4.5.7 Rigid bodies, in fluids

5 Related background

5.1 Historical aspects

5.1.1 Historical 'notes'

5.1.2 Various traditions

5.1.3 Newton's Principia

5.1.4 'Guide to the Principia'

5.1.5 Philosophical positions

5.1.6 History of mechanics

5.1.7 Unity of physics

5.1.8 Glasperlenspiel: a story

5.2 Philosophical aspects

5.2.1 'Mechanistic' thinking

5.2.2 Metaphysical views

5.2.3 'Non-existent' things

5.2.4 Weyl's apotheosis

5.2.5 'Bildung'

5.2.6 Third culture

5.2.7 'Fashionable nonsense'

5.3 Theoretical aspects

5.3.1 Home-made philosophy

5.3.2 Theories of science

5.3.3 Kant's Copernican turn

5.3.4 Concepts of truth

5.3.5 Objective truth

5.3.6 Mittelstaedt's grand survey

5.3.7 Serious doubts

5.4 Pragmatic aspects

5.4.1 Human nature

5.4.2 Social aspects

5.4.3 Various temperaments

5.4.4 Anschauung

5.4.5 Various languages

5.4.6 Various names

5.4.7 Various motivations

5.4.8 Various 'principles'

5.5 'Personal' aspects

5.5.1 'Stories'

5.5.2 Teachers and experts

5.5.3 Teaching

5.5.4 Pupils and students

5.5.5 Creativity

5.5.6 Psychological aspects

5.5.7 Personal background

6 Theory of theories

6.1 World model

6.1.1 Layers of the world

6.1.2 Ontology

6.1.3 Model of theories

6.1.4 Meta-theories

6.1.5 'Facta'

6.1.6 'Laws of nature'

6.1.7 General discussion

6.2 Axiomatic systems

6.2.1 Axiomatic systems: general

6.2.2 Axiomatic systems: usage

6.2.3 'In principio …'

6.2.4 Anschauen, Anschauung

6.2.5 Meta-'spaces'

6.2.6 Interpretation theories

6.2.7 Observation theories

6.3 Structures

6.3.1 Motivation

6.3.2 Basic structures

6.3.3 Derived structures

6.3.4 Fuzzy sets

6.3.5 Measurable magnitudes

6.3.6 Multi-dimensional magnitudes

6.3.7 Terminology, notation

6.3.8 Quantities: extensities

6.4 Theory of probability

6.4.1 Meta-probability

6.4.2 Derived probabilities

6.4.3 Other instantiations

6.4.4 Statistics

6.4.5 Estimation

6.4.6 Plausibility

6.4.7 Aggregate descriptions

6.4.8 Stochastic processes

6.5 Logics

6.5.1 Classical logics

6.5.2 Calculi of propositions

6.5.3 Calculi of predicates

6.5.4 Calculi of classes

6.5.5 Fuzzy logics, linguistics

6.5.6 Object orientation

6.6 'Ideal' objects

6.6.1 Linear equations

6.6.2 Fourier transforms

6.6.3 Laplace transforms

6.6.4 Sampled data

6.7 Real objects

6.7.1 'Reality'

6.7.2 Existence

6.7.3 Scepticism

6.7.4 Induction, falsification

7 Proto-mechanics: abstract

7.1 Meta-proto-theory

7.1.1 Need for proto-mechanics

7.1.2 Meta-proto-mechanics

7.1.3 'Euclidean' spaces

7.1.4 Carnap's 'Der Raum'

7.1.5 Hyperbolic planimetry

7.2 Curved spaces

7.2.1 Concept of curved space

7.2.2 Homogeneous spaces

7.2.3 Complex spheres

7.2.4 Transformations

7.2.5 Orthogonal frames

7.2.6 Normalisation

7.2.7 Circles: complex

7.3 Abstract chronometry

7.3.1 Concepts of time

7.3.2 Abstract time

7.3.3 Objectivity, causality, events

7.3.4 Curved time

7.3.5 'Theories' of time

7.4 Abstract stereometry

7.4.1 Concept of space

7.4.2 Abstract stereometry

7.4.3 Distances

7.4.4 'Freedom of choice'

7.4.5 Euclid's 'Elements'

7.4.6 Newton's stereometry

7.4.7 Philosophical problems

7.5 Complex time-space frames

7.5.1 Complex frames

7.5.2 Unitary transformations

7.5.3 Limited horizons

7.5.4 Unlimited horizons

7.5.5 Generic Lorentz 'rotation'

7.5.6 'Gleich-zeitig', 'gleich-ortig'

7.5.7 Minkowski frames

7.5.8 Generic hyperbolic 'rotation'

7.6 Concepts of matter

7.6.1 Concept of body

7.6.2 Concept of continuum

7.6.3 Quantity of matter

7.6.4 Structure of matter

7.6.5 Re-normalisation

7.6.6 'Dark' ages

7.7 Physical space

7.7.1 Transcendentals

7.7.2 Relativistic space

7.7.3 World geometry

7.7.4 Abstract versus physical space

7.7.5 'State of the art'

8 Meta-mechanics: abstract

8.1 State models: abstract

8.1.1 Black box models

8.1.2 State space models

8.1.3 Models of systems

8.1.4 Structures, parameters

8.1.5 Transformations

8.1.6 Models of processes

8.1.7 Discrete, continuous time

8.2 Interpreted state models

8.2.1 Operations

8.2.2 Interpretation of state

8.2.3 Aggregate models

8.2.4 Universal models

8.3 Linear state models

8.3.1 Convolution

8.3.2 Interpretation of state

8.3.3 Rational model

8.3.4 Equivalent models

8.3.5 Basic linear models

8.4 Systems identification

8.4.1 Purpose: simulation

8.4.2 Parameter identification

8.4.3 Principal solution

8.4.4 Feed back of noise

Part 2

Elementary and local mechanics

9 Meta-mechanics: ad hoc

9.1 Axiomatic meta-theory

9.1.1 'Logic' of science

9.1.2 Meta-concepts

9.1.3 First meta-axiom

9.1.4 Second meta-axiom

9.1.5 Third meta-axiom

9.1.6 Flow meta-axioms

9.1.7 Axiomatic meta-system

9.1.8 State space model

9.2 Meta-principles

9.2.1 Relativity, objectivity

9.2.2 Material invariance, equivalence

9.2.3 Material, immaterial production

9.2.4 Similarity

9.3 Meta-theorems

9.3.1 Steady states

9.3.2 'Isolated', 'free' systems

9.4 Quantity of matter

9.4.1 Balance of matter

9.4.2 Instances of balances: in general

9.5 Local balances

9.5.1 Densities, intensities

9.5.2 'Force' potentials

9.5.3 Energy equation

10 Elementary mechanics: abstract

10.1 Elementary axioms

10.1.1 Elementary primitives

10.1.2 Extensity of motion

10.1.3 Elementary momentum balance

10.1.4 Nature of forces

10.1.5 Momentum diffusion

10.1.6 Intensities of motion, of production

10.1.7 Elementary axiomatic system

10.2 Principles of relativity, objectivity

10.2.1 General relativity, objectivity

10.2.2 Theorem on steady motions

10.2.3 Theorem on body fixed spaces

10.2.4 Steady motions reviewed

10.3 Principles of materiality

10.3.1 Invariance of momentum diffusion

10.3.2 Components of momentum production

10.3.3 'Midwife buried'

10.3.4 d'Alembert's principle: derived

10.3.5 Concept of 'lost' forces

10.3.6 d'Alembert's principle: 'interpreted'

10.3.7 d'Alembert's principle: reviewed

10.3.8 General relativity 1889

10.3.9 Energy principle

10.4 Theorems on free motions

10.4.1 Unconstrained translations

10.4.2 'Basic bang': 'absolute' spaces

10.4.3 Motions in steady potentials

10.4.4 Motions in unsteady potentials

10.4.5 Principle of local equivalence

10.4.6 Equivalence misinterpreted

10.4.7 Forces 'expelled'

10.5 Elementary kinematics

10.5.1 Elementary kinematics: abstract

10.5.2 Paths: space curves

10.5.3 Arguments 'in free fall'

10.5.4 Mountains of potential

10.5.5 Complex 4D-space

10.5.6 'Inertial' spaces

10.5.7 Ridiculous caricature

10.6 ' kurzer Sinn'

10.6.1 Rigid body motion

10.6.2 'The simplest theory'

11 Proto-mechanics: time, space

11.1 Proto-mechanics interpreted

11.1.1 Time, space sensations

11.1.2 'Scales'

11.2 Chronometry

11.2.1 Interpreted time

11.2.2 Elementary clocks

11.2.3 Chronometers

11.3 Stereometry

11.3.1 Interpreted stereometry

11.3.2 Interpreted kinematics

11.3.3 Non-inertial spaces

11.4 Steady potentials: examples

11.4.1 Plane potentials

11.4.2 Twin 'paradox'

11.4.3 Inverse square potentials

11.5 Classical relativity

11.5.1 'Absolute' time, space

11.5.2 Basic relativity

11.5.3 Uniform potentials

11.5.4 Galilei transformation

11.5.5 Clocks in one space

11.5.6 Clocks in moving spaces

12 Perspective relativity

12.1 'Gleich-zeitige', 'gleich-ortige' events

12.1.1 Kinematics of messengers

12.1.2 'Gleich-zeitige' events

12.1.3 'Disturbing' effects

12.1.4 'Gleich-ortige' events

12.2 'Special' relativity

12.2.1 Einstein's experiment

12.2.2 Relativistic perspective

12.2.3 'Gleich-zeitige', general events

12.2.4 Slow speed approximation

12.2.5 Other derivations

12.3 Principle of relativity

12.3.1 Pseudo-twins

12.3.2 Twins in perspective

12.3.3 A 'proof'

12.3.4 Relativistic temperature?

12.4 Speed horizons

12.4.1 Objects identified

12.4.2 Speed 'limit'

12.4.3 Kinematical uncertainty

12.4.4 Horizons transcended

12.4.5 Pseudo-hyperbolic perspectives

12.5 'Quantum' description

12.5.1 Doppler effect, 'red shift'

12.5.2 Power spectra

12.5.3 'Wave'-corpuscle 'dualism'

12.5.4 Newton's Opticks

12.5.5 Acoustic quanta

12.6 Various notes

12.6.1 Apparent effects

12.6.2 Mis-'interpretations'

12.6.3 Standard material

12.6.4 Fizeau's experiment

12.6.5 Confusion of issues

13 Elementary dynamics

13.1 Concepts of force

13.1.1 'Nature of forces'

13.1.2 Surface forces

13.1.3 Body forces

13.1.4 'Force' fields

13.1.5 Historical notes

13.2 Weight and mass

13.2.1 Interpretations

13.2.2 Momentum production

13.2.3 Inertia interpreted

13.2.4 Principle of equivalence

13.2.5 Solid body model

13.3 Hylometry

13.3.1 Quantity of matter

13.3.2 Balance of mass

13.3.3 Abstract mass

13.3.4 Interpreted mass

13.4 'Prototypes', etalons

13.4.1 Mass prototypes

13.4.2 Etalons: basic units

13.4.3 Etalons: realisations

13.4.4 Mass etalon 're-newed'

13.4.5 'Watt scale'

13.5 Dynamometry

13.5.1 Abstract dynamometers

13.5.2 Ideal dynamometers: statics

13.5.3 Ideal dynamometers: kinetics

13.5.4 'Real' dynamometers

13.5.5 Usage of dynamometers

13.5.6 Mechanical impedances

13.5.7 Ideal Atwood machine

14 Elementary physics

14.1 Flow and production laws

14.1.1 Causes and effects

14.1.2 Local momentum balance

14.1.3 Diffusive momentum flow

14.1.4 Material momentum production

14.1.5 Concept of 'force' field

14.1.6 Concept of gravity field

14.2 Law of gravitation

14.2.1 Interaction of masses

14.2.2 Law of gravitation: invariant

14.2.3 'Subtle matter'

14.2.4 Einstein's 'general relativity'

14.2.5 Constant of gravitation

14.2.6 'Cosmic laziness'?

14.2.7 Lex tertia: gravitation

14.2.8 Law of conservation

14.3 'Gravitational' mass

14.3.1 'Active', 'passive' masses

14.3.2 'Equivalence principle'

14.3.3 'Common practice'

14.3.4 Experimental 'verification'

14.3.5 Total confusion

14.4 Concept of aether

14.4.1 Mach's principle

14.4.2 'It was to be otherwise …'

14.4.3 Void and aether

14.4.4 Spinning buckets

14.4.5 'Gravity' potential

14.4.6 Mass potential

14.5 Mass potentials

14.5.1 Mass potential

14.5.2 Rotating spaces

14.5.3 Spherical bodies

14.5.4 General potentials

14.5.5 'Hollow' universe

14.6 Model of matter

14.6.1 Global production model

14.6.2 Theory of gravity

14.6.3 'Identity' versus 'equivalence'

14.6.4 'Local' production models

14.6.5 Standard model of nucleons

14.6.6 Earlier models of matter

14.6.7 Historical theories

14.6.8 Recent speculations

14.7 Quantum theory

14.7.1 'Quantum mechanics'

14.7.2 Quantum gravity

14.7.3 Non-commutative geometry

14.7.4 'New physics'

14.7.5 Wave-body 'dualism'

14.7.6 Uncertainty principles

14.8 Cosmologies

14.8.1 Current cosmologies

14.8.2 The big bang

14.8.3 Historical cosmologies

14.8.4 Theories of relativity

14.8.5 'General' relativity

14.8.6 'Universes floating around'

15 Meta-mechanics: local

15.1 Abstract theory of meta-continua

15.1.1 Density fields

15.1.2 Meta-velocity field

15.1.3 Continuity of meta-mass

15.1.4 Specific magnitudes: intensities

15.1.5 Motions of continua

15.2 Motions of ideal meta-continua

15.2.1 Equation of meta-motion

15.2.2 Potential meta-flows

15.2.3 Analytical distribution function

15.2.4 'Wave' equation et cetera

15.2.5 'Classical' quantum mechanics

15.2.6 'Proto'-mechanics

15.2.7 'Quauterwelsch' and beyond

15.3 Meta-theory of material continua

15.3.1 Densities

15.3.2 Velocity field

15.3.3 Equation of continuity

15.3.4 Mass specific quantities

15.3.5 Uniform mass density

15.3.6 Meta-theory of stress laws

15.4 Meta-theory of turbulence

15.4.1 Turbulent fluctuations

15.4.2 Local balances revisited

15.4.3 Expected specific quantities

15.4.4 Turbulent diffusive flux

15.4.5 Isotropic turbulence

16 Local mechanics: fields

16.1 Dynamics of continua

16.1.1 Cauchy's 'universal' equation

16.1.2 Turbulent momentum diffusion

16.1.3 Boltzmann's equation

16.1.4 'Axiomatic' continuum mechanics

16.1.5 Spin: classical materials

16.1.6 Local balance of energy

16.2 Kinematics of continua

16.2.1 Velocity field: basic concepts

16.2.2 Convective rate of change

16.2.3 Balance of rotation

16.2.4 Substantial rates of change

16.2.5 Historical remarks

17 Local physics: internal states

17.1 Local balances of pressure etc

17.1.1 Pressure laws

17.1.2 Balance of pressure

17.1.3 Balance of deviatoric stress

17.2 Diffusive momentum flux

17.2.1 Various flux laws

17.2.2 Rational theory of continua

17.2.3 Stokesian fluids

17.2.4 Visco-elastic materials

17.2.5 Turbulent momentum diffusion

17.2.6 Recent developments

17.2.7 Lanczos' remarks

17.3 Newtonian fluids

17.3.1 Newtonian fluids: properties

17.3.2 Navier-Stokes equation

17.3.3 Kinetic energy

17.3.4 Rate of dissipation

17.3.5 Incompressible fluids

17.4 Local momentum production

17.4.1 Motions under gravity

17.4.2 Uniform potential fields

17.4.3 Example: ideal gas

17.4.4 Relative motions

17.4.5 General relativity

Part 3

Global and propulsion mechanics

18 Elementary global balances

18.1 Global balances: meta-theory

18.1.1 Elementary 'integrals'

18.1.2 Weighted integrals

18.1.3 Steady conditions

18.1.4 Boundary fixed in space

18.1.5 Moving boundaries

18.1.6 Balance of mass

18.2 Global balance of momentum

18.2.1 Momentum balance

18.2.2 Steady conditions

18.2.3 Boundary fixed in space

18.2.4 Moving boundaries

18.2.5 'Differing' views

18.3 Global balances of spin

18.3.1 Balance of spin

18.3.2 Staked global balances

18.3.3 'Line of action'

18.3.4 Moving reference frames

18.4 Global balances of energy

18.4.1 Balance of kinetic energy

18.4.2 Fixed boundaries

18.4.3 Moving boundaries

18.4.4 Minimum kinetic energy

18.5 Global stability criteria

18.5.1 Virtual energy

18.5.2 Principle of least constraints

18.5.3 Principle of least curvature

19 Partial energy balances

19.1 Generalised kinematics

19.1.1 Elementary 'principles'

19.1.2 Generalised kinematics

19.1.3 Generalised position

19.1.4 Forcibly driven systems

19.1.5 Generalised kinematics: applications

19.1.6 Transformations

19.2 Aggregate dynamics

19.2.1 Modes of aggregation

19.2.2 Partial energy balances: en detail

19.2.3 Partial energy balances: en gross

19.2.4 Partial energy balances: appraised

19.2.5 Special case: force free motions

19.2.6 Special case: potential 'forces'

19.2.7 'Energetik'

19.3 Aggregate 'forces'

19.3.1 Aggregate momentum diffusion

19.3.2 Aggregate momentum productions

19.3.3 Example: Stokesian fluids

19.3.4 Example: hyper-elastic material

19.3.5 Euler-Lagrangean equation: explicit

19.4 'Degenerate' case: holonomic speed

19.4.1 Lagrangean equation

19.4.2 Hamilton's 'canonical' equations

19.4.3 Further ramifications?

19.4.4 Absent, cyclic speeds

19.4.5 Elasto-mechanics: continued

19.4.6 'Statistical' mechanics

19.4.7 Discussion

19.5 Stability criteria

19.5.1 Principle of least curvature

19.5.2 Example: Kármán vortex street

19.5.3 General criteria?

20 Rigid body mechanics

20.1 Rigid body dynamics

20.1.1 Basic theory

20.1.2 Changes of frames

20.1.3 Rotation, precession

20.1.4 Relative motion

20.2 Rigid body kinematics

20.2.1 Basic concepts

20.2.2 Translational motions

20.2.3 Rotational motions

20.2.4 Global motions

20.2.5 Relative motions

20.2.6 Moving platform systems

20.3 'Central' motions

20.3.1 Celestial bodies

20.3.2 Central motions

20.3.3 Two and more bodies

20.3.4 Deflection of light

20.3.5 Perihelion precession

20.3.6 Energy dissipation

20.3.7 Einstein's theory validated

20.3.8 'Anomalies'?

21 Rigid bodies in fluids

21.1 Incompressible fluids

21.1.1 Diffusive flows

21.1.2 Bodies at rest

21.1.3 Bodies in motion

21.1.4 Potential flows

21.1.5 Momentum, inertia

21.1.6 Resistance, damping

21.1.7 Equation of motion

21.1.8 Stability of motion

21.2 Bodies in fluids: momentum convection

21.2.1 Moving force fields

21.2.2 Momentum convection

21.3 Identification

21.3.1 Constitutive equations

21.3.2 'Gravity'

21.3.3 Steady motions

21.3.4 Steady motions: unconstrained

21.3.5 Quasi-steady motions

21.4 Dynamometers

21.4.1 Calibration

21.4.2 Stiffness

21.4.3 Identification

22 Propulsion mechanics

22.1 Introduction

22.1.1 Problems of propulsion

22.1.2 Models of propulsion

22.1.3 Pragmatism pure

22.1.4 Inspectional analysis

22.1.5 Propulsion: Goals/Plans

22.2 Steady speed trials

22.2.1 Steady trials: traditional approach

22.2.2 Steady trials: rational approach

22.2.3 Steady trials: power supplied, current

22.2.4 Monitoring of trials

22.2.5 Steady trials: power required

22.2.6 Steady trials: contracted conditions

22.2.7 Steady trials: verification, 'validation'

22.2.8 ISO/DIS 15016 example

22.2.9 Steady trials: further developments

22.3 Meta-theory of propulsion

22.3.1 Ideal propulsors

22.3.2 Propulsion: axiomatic system

22.3.3 Propulsion: efficiencies

22.4 Ideal propulsors: open

22.4.1 Momentum theory

22.4.2 Ideal propulsor

22.4.3 Jet power, efficiency

22.4.4 Vortex theory

22.4.5 Pump theory

22.4.6 Merits of propulsors

22.5 Ideal propulsors: behind

22.5.1 Equivalent propulsors

22.5.2 Displacement wakes

22.5.3 Thrust deduction

22.5.4 Configuration efficiencies

22.5.5 Thrust deduction: transformed

22.5.6 Thrust deduction: limit

22.5.7 Energy and mixed wakes

22.5.8 Real propulsors in real wakes

22.6 Quasi-steady trials

22.6.1 Propellers behind

22.6.2 Energy balance

22.6.3 Local wake axioms

22.6.4 Alternative approaches

22.6.5 Momentum balance

22.6.6 Thrust deduction

22.6.7 Powering performance

22.6.8 'History'

22.7 Hull-integrated propulsors

22.7.1 Propulsor models

22.7.2 Ducted propellers

22.7.3 Internal losses

22.7.4 Propulsor theory interpreted

22.7.5 Basic procedure

22.8 Ducted propeller design

22.8.1 Propulsors are pumps

22.8.2 Equivalent propulsors

22.8.3 Feasibility study

22.8.4 Thrust distribution

22.8.5 Thrust deduction

22.8.6 Basic design

22.8.7 Review

22.8.8 Outlook

23 Motions in wave media

23.1 Subsonic motions of bodies

23.1.1 Wave equation

23.1.2 Body fixed space

23.1.3 Slender bodies

23.1.4 Longitudinal inertia 'in general'

23.2 Meta-theory

23.2.1 Abstract theory

23.2.2 Slender bodies

23.2.3 Consequences

23.3 Instance, 'analogy'

23.3.1 Shallow water

23.3.2 'Relativistic phenomena'

23.4 Waves in moving wave media

23.4.1 'Acoustic metric'

23.4.2 Other analogues

23.4.3 Classical approaches

24 Closing operations

24.1 Evaluation

24.1.1 General aspects

24.1.2 Preliminaries

24.1.3 Meta- and proto-mechanics

24.1.4 Elementary mechanics

24.1.5 Elementary physics

24.1.6 Continuum mechanics

24.1.7 'Global mechanics'

24.1.8 Rigid body motions et cetera

24.2 Assessment

24.2.1 Criteria

24.2.2 Satisfaction

24.3 Conclusions

24.3.1 Decisions

24.3.2 Future tasks

25 Epilogue

25.1 Sound knowledge

25.2 Live ideas

26 Post scriptum

27 Acknowledgements

End of Part 3

28 Conventions

28.1 Terminology

28.1.1 Rational names

28.1.2 Traditional names

28.2 Symbology

28.2.1 Operational notations

28.2.2 'Principles', 'laws'

28.3 References

28.3.1 Formats

28.3.2 Quotations

28.3.3 Translations

28.4 Copyright

28.4.1 Acknowledgements

28.4.2 Doctrine of fair use

28.4.3 Rules of conduct

29 References

29.1 Author's basic work

29.2 Sources referred to

30 Indices

30.1 Name index

30.2 Subject index

Tables, figures

" 'When I use a word' Humpty Dumpty said, in rather a scornful tone, 'it means just what I choose it to mean – neither more nor less.'

'The question is', said Alice, 'whether you can make words mean so many different things.'

'The question is,' said Humpty Dumpty, 'which is to be the master – that's all.'"

Lewis Carroll: Through the Looking-Glass (1988/196).

Most of the tables are rudimentary constitutive calculi, 'matrices' defining the meaning of terms and expressions as used in the present treatise by their positions in the 'matrices'.

Newton's axiomatic system

'Rational' elementary dynamics

Momentum production: terminology

Mechanics: 'dual model'

World model: levels

World model: aspects

Theories: dual model

Theories: purposes

Axiomatic theories: structure

Mechanics: levels of theory

Axiomatic theories: purposes

Methods of thinking

Sets: concept

Relations: concept

Functions: concept

Structures: concept

Structures: fundamental

Extensities: concept

Meta-probability: axiomatics

OOP: Variables

'Spaces'

Systems: concept

Systems: black box model

Systems: state space model

Systems: notation

Processes: notation

Systems: structure

Systems: macro-operations

Quantities: axiomatic system

Invariance: types

Abstract theory: instantiated

Quantitas motus: axiomatic system

Momentum production: concepts

Momentum production: terminology

'Gleich-zeitige' events

Einstein's experiment

Einstein's experiment analysed

'Gleich-zeitige' events

Pseudo-twins in absolute frame

Pseudo-twins in relativistic frame

Translation: axiomatic system

Names: traditional, rational

'Principles' qualified

'Laws' qualified

Activities: German, English

1 Preface

Unglücklicher, Sie scheinen auch an Idealen zu laborieren*.

Georg Büchner: Leonce und Lena. Ein Lustspiel (1952/35).

* "labour v.i.&t. Use labour, exert oneself; work hard; strive for…or to …; advance with difficulty …; be troubled … or impeded; suffer under …[the pains of childbirth]; (of ship) roll or pitch heavily; (arch. or poet.) till (ground); elaborate work out in detail, treat at length …; …"

The Concise Oxford Dictionary of Current English (FowlerHW, 1958).

Dear Colleagues, dear Friends!

This second edition of my lasting effort to 'reconstruct' the fundamentals of classical dynamics is a snapshot of work in progress. Even after twelve years of dedicated thinking and writing, extreme 'produktionsethischer Bravheit' (Thomas Mann), trying to render the structure and the underlying arguments as intuitive as possible and their expositions as clear as possible, it cannot possibly be more than a 'final' draft.

PROBLEM

In the preface to 'Sylvie and Bruno' Lewis Carroll has described the problems encountered (1982/256):

And thus it came to pass that I found myself at last in possession of a huge unwieldy mass of literature, - … - which only needed stringing together, up on the thread of a consecutive story; to constitute the book I hoped to write. Only! The task, at first, seemed absolutely hopeless, and gave me a far clearer idea, than I ever had before, of the meaning of the word 'chaos': and I think it must have been. ten years, or. more; before I had. succeeded in classifying these odds-and-ends sufficiently to see what sort of a story they indicated: for the story had to grow out of the incidents, not the incidents out of the story.

In trying to answer the questions concerning the foundations of science, classical mechanics in particular, bothering not only me but certainly many of you, I have been re-thinking, re-arranging and re-writing whole chapters, sections, sub-sections, every single sentence, based on the insights gained up to that particular stage and aware of Mallarmé's remark (Roe, 2007/402):

Er [Edgar Degas] könne sich nicht erklären, sagte er zu Stéphane Mallarmé, warum ihm Gedichte so schlecht von der Hand gingen, wo es ihm doch an Ideen nicht mangele. 'Aber lieber Degas, …, man schreibt Gedichte ja auch nicht mit Ideen, sondern mit Worten.'

The last complete re-arrangements of abstract elementary and of abstract global mechanics became possible and necessary while the manuscript was being revised following the suggestions of my lector, spell and grammar checked, finalised for printing. And I am still on my way to the ideal I see before me since early students' days, 'ideal' not to be misunderstood in the sense of 'The Platonic Self-Image of Scientists' as will be seen (Renn, 2004/25 f).

Following the suggestion of Lewis Carroll blank pages should have been inserted here and there, at least some spaces for meta-texts have been left for later completion (1988/529):

"' … the shyest and most intermittent talker must seem fluent in letter-[and book-]writing. He may have taken half-an-hour to compose his second sentence; but there it is, close after the first!'

'Then letters [and books] don't express all that they might express?'

'That's merely because our system of letter-[and book-] writing is incomplete. A shy writer ought to be able to show that he is so. Why shouldn't he make pauses in writing, just as he would do in speaking? He might leave blank spaces - say half a page at a time. …" [Italics]: MS.

BACKGROUND

In view of the vast literature the undertaking to reconstruct the foundations of classical mechanics looks extremely, maybe too ambitious and a warning is in place at this stage: This is not a textbook in the ordinary sense, but rather the draft of a research report and a reader, 'ein Lesebuch'. Closely related are the 'Foundations of Science' by Campbell, a work never completed, the 'Preface' starting with the paragraph (1957/V):

The object and nature of this book is sufficiently explained in the introduction; here I will only warn the reader who gets no further that, in spite of its title, it is not an elementary treatise on physics. On the other hand, although there is a just prejudice against an author who seeks to disarm criticism, I would explain here how the book came to be written – not in order to explain its faults away, but in order, by giving notice of them, to render them less harmful.

Another warning in connection with another work of Campbell is due to Suppes (1983.f/35):

Wenn Archimedes oder Ptolemäus Campbell's 'Physics: The Elements' gekannt hätten, [dann] hätten sie sicher den Rückgang im Anspruch auf Analyse und begriffliche Klarheit, der über eine Zeit von zweitausend Jahren stattgefunden hat, fast unglaublich gefunden.

Goethe in a conversation with Eckermann mentioned another problem (06.12.1829, 1911/274):"

'Da die Konzeption so alt ist,' sagte Goethe, 'und ich seit funfzig Jahren darüber nachdenke, so hat sich das innere Material so sehr gehäuft, daß jetzt das Ausscheiden und Ablehnen die schwere Operation ist.'"

Most of the basic themes of the present work have already been stated explicitly in notes jotted down in a card index during the years 1969 to 1973. Dominating topics have been metaphysics, the interrelations of formal and factual constituents of our knowledge and our 'principles' down to standards to be developed. At that stage even the project of a book has already been defined, from the language to be adopted down to its format, its production and its distribution.

Notes dated August 1982 stressed the importance of systematic axiomatisation. At the same time the whole pragmatic approach, supposed hopefully to avoid pitfalls and superstition, was allocated to the Preface. Further the importance of rules of procedure and their intelligibility has already been stressed, as it is now.

EXPERIENCE

But it took further thirty years of experience in mechanics, mostly in hydromechanical systems research and development at the Versuchsanstalt für Wasserbau und Schiffbau, VWS, the Berlin Model Basin, and continuous reflection of that experience to explore the early ideas and demonstrate their fertility.

Concerning experience the 'Operating instructions for a human brain' state (Hüther, 2005/11 f):

"Es hat lange gedauert, bis mir das endlich klar wurde und bis ich verstanden hatte, daß das, was uns bei all unseren Entscheidungen leitet, nicht unser Geist oder unser Bewußtsein ist, auch nicht all unser auswendig gelerntes oder von fragwürdigen Quellen übernommenes Wissen, sondern die Erfahrungen, die wir während unserer bisherigen Entwicklung gesammelt haben. Die Erfahrungen, die ein Mensch im Lauf seines Lebens gemacht hat, sind fest in seinem Gehirn verankert, sie bestimmen seine Erwartungen, sie lenken seine Aufmerksamkeit in eine ganz bestimmte Richtung, sie legen fest, wie er das, was er erlebt, bewertet, und wie er auf das reagiert, was ihn umgibt und auf ihn einstürmt. In gewisser Weise sind diese individuell gemachten Erfahrungen also der wichtigste und wertvollste Schatz, den ein Mensch besitzt. Er kann ihn nicht nur für sich selbst nutzen, sondern – wenn er einmal die Erfahrung gemacht hat, daß Verschenken sehr viel Freude macht – auch versuchen, ihn an andere weiterzugeben. Das Besondere an diesem Erfahrungsschatz ist, daß er dadurch, daß man ihn benutzt und verteilt, nicht immer kleiner, sondern immer größer wird." Italics: MS.

'My' present situation has been roughly described by Sepper (1988/96):

"… in the course of human life what turns possibility into actuality is the aperçu, the moment of insight in which we glimpse what the future may bring and which spurs us to invest the necessary labour. Through the aperçu we recognise a totality, the context in which the particular takes its place, and thus the aperçu is by its nature the anticipation of the whole, if not the whole. But the aperçu is problematic. 'A decisive aperçu is to be regarded as an inoculated disease: One does not get rid of it till one has fought the disease through' (Goethe; GA 16/713.)."

Thus Goethe's translation of Büchner's 'laborieren' is 'kranken' and not just 'arbeiten'.

At this stage I need to offer not only 'eine dunkle Totalidee' (Friedrich SchillerF), but already detailed elaborations permitting rigorous discussions and criticism. Despite their sheer 'volume' they are not a mere collection of material as Wohlwill's two volumes on 'Galilei und sein Kampf für die copernicanische Lehre' (Szabó, 1987/551):

Sicher hat Wohlwill mit bewundernswertem Fleiß, ja mit Verbissenheit, eine riesige, geradezu erdrückende Masse an Material über Galilei zusammengetragen, die durch viele Belanglosigkeiten amorph geworden war: Wohlwill wollte alles bringen, aber hinterließ einen wenig befriedigenden Torso.

And rigorous discussions and criticism, 'peer reviews' is what I am asking for as Leibniz did in his 'Specimen Dynamicum' (2000/241):

Seitdem wir eine neue, noch zu begründende Wissenschaft der Dynamik erwähnt haben, haben viele ausgezeichnete Männer an verschiedenen Orten eine ausführlichere Erläuterung dieser Lehre verlangt. Da nun die Zeit, um ein Buch zu schreiben, noch nicht zur Verfügung steht, werden wir an diesem Ort darbieten, was einiges Licht anzünden könnte, welches vielleicht sogar zu uns mit Gewinn zurückkehren wird, wenn wir die Meinungen derjenigen hervorlocken, die Kraft des Denkens mit Menschlichkeit im Ausdruck verbunden haben; wir erklären, daß auch deren Urteile uns willkommen sein werden, und wir hoffen, daß sie dem Fortschritt des Werkes hilfreich sein werden.

Although theories of classical general and special relativity will be developed in detail the present exercise is not an attempt to understand Einstein's theories but a reconstruction of classical mechanics in Einstein's spirit.

DISCUSSIONS

The original intention to discuss, with friends and specialists, various 'separate' subjects and aspects prior to publication of the whole draft turned out to be impractical, even impossible. There are no 'separate' subjects and

aspects. Sub-subjects became visible only during the evolution of the whole manuscript and make sense and can be scrutinised only in the whole coherent fabric of the underlying instinctive beliefs and their axiomatic formulations, where this stage of maturity has been reached.

In that sense I kindly ask as Fichte did in a Prologue (1961/9):

Die künftigen Beurteiler dieser Schrift bitte ich auf das Ganze einzugehen und jeden einzelnen Gedanken aus dem Gesichtspunkte des Ganzen anzusehen.

Similar requests are to be found not only in other philosophical works, of Hegel and others, but even at the end of Fielding's very strong 'Bones for the critics' in his 'Tom Jones' (1964/IV, 56-61; 2007).

Cervantes in his 'Don Quijote' addresses the problem as follows (2008/II, 41):

"' Jedenfalls ist es ein großes Wagnis, ein Buch in Druck zu geben, denn unter allen unmöglichen Dingen ist nichts unmöglicher, als eines zu verfassen, das alle, die es lesen, überzeugt und zufriedenstellt.'

'Besagtes über mich' sagte Don Quijote, 'wird wohl wenige zufriedengestellt haben.'

'Aber nein, im Gegenteil, stultorum infinitus est numerus, die Zahl derer, denen die Geschichte gefallen hat, ist unendlich groß.'"

And Popper in his 'Unended Quest' adds (1978/30).

… always remember that it is impossible to speak in such a way that you cannot be misunderstood: … If greater precision is needed, it is needed because the problem to be solved demands it.

As will be discussed in detail a completely formalised exposition is far beyond the horizon of my capability and beyond the goal of my treatise: to develop and to communicate a 'total idea' indebted to, but intended to transcend the traditions of many schools of mechanics. In view of the 'incredible' literature of any of these schools there was of course no chance to think about all problems and ponder all the ideas proposed, put them into context or dismantle pseudo-problems and sheer speculations based on incoherent models and professional superstition.

RULE DRIVEN

Though not fully formalised, such undertaking cannot be but rule driven and the rules are made explicit as far as possible. The procedure is similar to composition in literature and music. In the context given most things are 'self-evident'. A famous example is Beethoven's manuscript of the piano concerto in c-minor opus 37, in which the composer fill in the central piano part; he used to improvise this as being 'self-evident' – to him.

This does not imply that I was always successful in my ongoing endeavour to adhere to my own rules and meet the standards set forth, essentially

rules of self-organisation, 'natural unfolding', as close as possible to an ars inveniendi (Leibniz) and to some 'Kalkül des Verstehens' (Abel, 1995/405 f), both being unavailable.

Smart readers will immediately detect, not only when it comes to open ends and missing meta-texts, where I am still many hours, even weeks of hard work away from my goal and where I failed to reach my goal or am even utterly mistaken. Or where I stepped myself into the good old traps and pitfalls I carefully pointed out before, a very painful experience I often made.

They may correct and continue in the spirit and based on the results of my exercise so far, knowing that I could not possibly answer all the questions arising during the work, forget about all the questions that occur to readers in the context developed. But there is no way back!

The situation is very similar to any industrial research and development project, experienced over and over again. When the client receives the report on the work he ordered and hopefully paid for, he is wondering why the new questions arising from that work have not been studied. The simple answer is that the scope is creeping up with hindsight and that the client has not (yet) contracted, forget about paid for any further studies.

WORK IN PROGRESS

Readers will note that even at this advanced stage I am still experimenting, trying to find the most adequate orders, expositions and corresponding notations on every level of discussion. And they will note that I have not succeeded to update every sentence in every respect according to my latest findings. The maintenance of the large document, very similar to weeding, took continuously at least half the effort over the years.

The confusion of languages in mechanics gives the impression that a tower of Babel has been under construction over the centuries. In the process of clarification the work developed a dynamics of its own as described by Popper (1987/196):

"… everything depends upon a give-and-take between ourselves and our task, our work, our problems, our world 3; upon the repercussion upon us of this world; upon feedback, which can be amplified by our criticism of what we have done. It is through the attempt to see objectively the work we have done - that is to see it critically - and to do it better, through the interaction between our actions and their objective results, that we can transcend our talents, and ourselves.

As with our children, so with our theories, and ultimately with all the work we do: our products become largely independent of their makers. We may gain more knowledge from our children or from our theories than we ever imparted to them. This is how we can lift ourselves out of the morass of our ignorance; and how we can all contribute to world 3." Italics: MS.

And to 'lift ourselves out of the morass of our ignorance' is precisely the purpose of the present work.

Concerning 'world 3' Popper notes (1987/188-190):

"I suggest that the emergence of descriptive language is at the root of the human power of imagination, of human inventiveness and therefore of the emergence of world 3. For we may assume that the first (and almost human) function of descriptive language as a tool was to serve exclusively for true descriptions, true reports. But then came the point when language could be used for lies, for 'story-telling'. This seems to me the decisive step, the step that made language truly descriptive and truly human. It led, I suggest, to storytelling of an explanatory kind, to myth making, to the critical scrutiny of reports and descriptions and thus to science; to imaginative fiction and … to art …"

'Stories' will in fact play an essential role in the present treatise (Paulos, 2004), while 'lies', talking about 'the thing that is not' (Swift, 2003) will hopefully be avoided.

CRITICISM

My criticism may sound very harsh at times, but please keep in mind Goethe's remark about Zelter struggling for survival among the Berliners (04.12.1823; Eckermann, 1911/62):

Er kann … bei der ersten Bekanntschaft etwas sehr derbe, ja mitunter sogar etwas roh erscheinen. Allein das ist nur äußerlich. Ich kenne kaum jemanden, der zugleich so zart wäre wie Zelter. Und dabei muß man nicht vergessen, daß er über ein halbes Jahrhundert in Berlin zugebracht hat. Es lebt aber, wie ich an allem merke, dort ein so verwegener Menschenschlag beisammen, daß man mit der Delikatesse nicht weit reicht, sondern daß man Haare auf den Zähnen haben und mitunter etwas grob sein muß, um sich über Wasser zu halten.

At another place Goethe warns a friend (Walther, 2006.b/246):

Geben Sie acht, Freund, es sind Preußen, die wollen immer alles besser wissen als andere Leute.

Now I myself am asking my friends and colleagues for rigorous discussions and criticism, although parts are still collections of ideas and related material. In the Preface to the first edition of the Principia Newton notes (PM/XVIII):

Some things found out after the rest, I chose to insert in places less suitable, rather than change the number[s] of the propositions and the citations.

While 'changing numbers' is no problem with today's word processors the identification of 'suitable' places, the intellectual digestion of 'things found out after the rest' turned out to be not always that simple. Often a whole chain of arguments needed to be changed as mentioned at the beginning.

In asking my friends and colleagues for rigorous discussions and criticism at this stage, I am following Goethe's advice (1960/13-14; GA 16/848):

Man hat daher in wissenschaftlichen Dingen gerade umgekehrt zu verfahren, wie man es bei Kunstwerken zu tun hat. Denn ein Künstler tut wohl, sein Kunstwerk nicht öffentlich sehen zu lassen, bis er es vollendet hat, …. In wissenschaftlichen Dingen hingegen ist es schon nützlich, jede einzelne Erfahrung, ja Vermutung öffentlich mitzuteilen, ja es ist höchst ratlich, ein wissenschaftliches Gebäude nicht eher aufzuführen, bis der Plan dazu und die Materialien allgemein bekannt, beurteilt und ausgewählt sind.

The preliminary publications of Copernicus, the 'Commentariolus' in particular, may be considered as prominent examples of the practice Goethe is referring to (Zekl, 2006/LX-LXX).

But maybe this does only apply if the problems are of common interest. And common interest in the old-fashioned search for an intellectually satisfactory exposition of classical dynamics may not be taken for granted at a time when even the National Geographic tries to catch the interest of readers by featuring the evolution of galaxies, some hundred billions in the Universe, each with some hundred billions of stars (Cowen, 2003).

DRIVING 'FORCES'

Although the Universe or Cosmos is driven by gravitation this is the 'only' mechanism we still do not understand. The fact that this unsolved problem can be reconsidered in the context of a reconstruction of classical dynamics may lead to some interest in the present work.

The goals of this treatise, deeply rooted in the tradition of rationalism, 'enlightenment' (Aufklärung, not Erleuchtung) and classical mechanics, are to establish 'wissenschaftstheoriedienliche Verhältnisse' (Stegmüller) found lacking and, at the same time, quite pragmatically to provide the fundamentals for an adequate ISO standard, maybe following the structure of the present treatise.

The strategy is that of non-linear or dynamic programming (Bellman, 1968/1-49): 'No matter how we have arrived at the present state, in the morass of our ignorance, from here on we will proceed in an optimum fashion', in plain words, 'trying to do our best', as all our ancestors have always done and as we always do.

And we try to adhere to common sense. Lichtenberg has stated the simple rules (1984/533 f):

Ein gutes Mittel, gesunden Menschenverstand zu erlangen, ist ein beständiges Bestreben nach deutlichen Begriffen, und zwar nicht bloß aus Beschreibungen anderer, sondern soviel wie möglich durch eigenes Anschauen. Man muß die Sachen oft in der Absicht ansehen, etwas daran zu finden, was andere noch nicht gesehen haben; von jedem Wort muß man sich wenigstens ein Mal eine Erklärung gemacht haben, und keines brauchen, das man nicht versteht.

Instead of the metaphor of the morass Kant in the Preface to his 'Neues Organon' uses the popular metaphor of the labyrinth and Ariadne's thread leading us out (Martens, 2000/71 f):

Der Bau des Weltalls aber erscheint seiner Struktur nach dem Menschengeist, der es betrachtet, wie ein Labyrinth, wo überall unsichere Wege, täuschende Ähnlichkeiten zwischen Dingen und Merkmalen, krumme und verwickelte Windungen und Verschlingungen der Eigenschaften sich zeigen. … Die Spuren müssen an einem Faden festgehalten werden: Jeder Schritt muß von der ersten sinnlichen Wahrnehmung an in fester Weise gesichert sein.

From the beginning classical dynamics is understood as physics, not as mathematics, not as geometry or l'art pour l'art. The fact that the basic theory can be dressed in many guises is the reason for the hopeless confusion of the essentially simple issues.

For the solution of specific mechanical problems, often including singularities as in non-smooth and fracture mechanics, fancy mathematical artifacts are necessary, but not these artifacts, and not the possible foundations of single branches, but the intellectually satisfactory foundation of classical dynamics in general is subject and purpose of the present treatise.

NEED FOR STANDARDS

The availability of such a standard reference, which coherently reduces the state of the art to the essentials in the sense of Leibniz and which should not offend anybody's instinctive beliefs, is felt urgently required in science and engineering. The urgent need for and importance of such a reference in classical dynamics can hardly be overestimated. Already in 1919 Einstein noted (Gleick, 2004/198):

Let no one suppose that the mighty work of Newton can be superseded by this or any other theory. His great and lucid ideas will retain their unique significance for all time as the foundation of our whole modern conceptual structure in the sphere of natural philosophy.

The reference envisaged will drastically reduce the waste of brain power in producing inadequate lecture notes, textbooks and historical and philosophical studies and in learning the fundamentals of mechanics 'aus nachgeschriebenen Heften' (Goethe), today more than twenty thousand lecture notes and inadequate 'encyclopaedia' articles in the internet, classical mechanics often still just Newtonian mechanics of freely moving point masses, alias mass points.

This goal is in line with 'Objectivity and the Escape from Perspective' (Daston, 2001/127-155), the advantages and the obstacles having been stated by Goethe (1960/12-13; GA 16/846):

Es gilt also auch hier was bei so vielen andern menschlichen Unternehmungen gilt, daß das Interesse Mehrerer auf Einen Punkt gerichtet etwas Vorzügliches hervorzubringen imstande ist. Hier wird es offenbar, daß der Neid, welcher andere so gern von der Ehre einer Entdeckung ausschließen möchte, daß die unmäßige Begierde, etwas Entdecktes nur nach seiner Art zu behandeln und auszuarbeiten, dem Forscher selbst die größten Hindernisse sind.

In publishing this manuscript I hope to avoid the obstacle and rather convince colleagues to join me in my effort classical mechanics 'nicht nur nach meiner Art zu behandeln'. With Herman Melville I feel (Hochhuth, 2000/306):

Daß mein System auf den ersten Anhieb nicht vollkommen ausgeführt sein werde, habe ich eingangs erklärt … Dies ganze Buch ist nur ein Entwurf – ach, nur der Entwurf eines Entwurfs.

Maybe you yourself find the time to study and to think about my draft, to share your thoughts with me and to join a future work group drafting the ISO standard proposed. Or, maybe, you know colleagues interested in my effort as a whole or in one or the other of its aspects. Any comment will be welcome, will be discussed and will be acknowledged, find its way into future editions, if any, as work progresses – at the author's discretion.

Looking forward to your mails, maybe consent, I am of course aware of the fact (Abel, 1995/406):

"…, daß die Zustimmung anderer oder die Übereinstimmung mit anderen Personen nicht auch schon für die Wahrheit dessen hinreichend ist, wofür man da Zustimmung erhält." Italics: MS.

Whatever truth may be, one of the questions to be discussed.

Yours sincerely,

Michael Schmiechen.

Berlin, Summer 2009

2 Bootstraps

Hier hätte ich unfehlbar umkommen müssen, wenn nicht die Stärke meines Armes mich an meinem eigenen Haarzopfe, samt dem Pferde, welches ich fest zwischen meine Knie schloß, wieder herausgezogen hätte.

Karl Friedrich Hieronymus Freiherr von Münchhausen (BürgerGA, 2000/36).

PROBLEMS

We are lost in a swamp, the morass of our ignorance!

And Bismarck is not around to end our suffering and save our souls by shooting us according to the 'strange habits of the western barbarians' described in a Shanghai Illustrated (BriessenF, 1977/70-73).

MODELS

Actually Bismarck did not shoot his friend but frightened him to death. In his desperation the friend happened to step on a root hidden in the swamp and finally he saved himself. Afterwards Bismarck explained his strategy: if he would have had stepped into the swamp as well they both would have been lost.

We have to find the roots and get ourselves out!

GOALS

The goal of this initial chapter is to provide the roots, the tools for our first steps out of the swamp. In a treatise on mechanics Münchhausen's braid used in Germany or the bootstraps used in other countries will be less acceptable than some roots hidden in the swamp.

PLANS

Braids or bootstraps are necessary for two purposes: to pull ourselves out of the swamp and, afterwards, to keep our bits and pieces together in an orderly fashion.

The plan is to provide structural and procedural models of sufficient intricacy for the solution of the problems at hand.

The third 'purpose' of old braids, namely to be cut off, will be the central subject of the present treatise.

2.1 Levels of problems

… always remember that it is impossible to speak in such a way that you cannot be misunderstood: … If greater precision is needed, it is needed because the problem to be solved demands it.

Karl Popper: Unended Quest (1978/30).

In any treatise elaborations take place on many different levels, each requiring its own principles and model, its own distinct language. But in most expositions the various levels are not separated explicitly and the underlying principles and models are not explicitly stated and dealt with as necessary for unambiguous communication, nowadays maybe with computers and computer based.

According to the following generic model of problem solving even the opening and concluding operations on any given level of problem solving take place on a meta-level with respect to the elaborations proper.

The trained reader is expected to guess from the context the underlying philosophy, the level at which the discussion takes place, the model and the sub-problem being solved at any given stage of an exposition. But this ideal is hardly ever met due to the usual confusion of levels and languages in most treatises and due to the lack of readers trained to do the jobs the authors themselves should have done.

The problem is aggravated by the fact that any treatise itself is embedded into a cultural environment with 'threads' or 'links' to many more levels. In the present treatise the author tries to spin all these threads into one coherent thread, a 'Leitfaden', out of the labyrinth (Martens, 2000).

In classical mechanics these links are particularly strong, the concepts in question are related to the most fundamental experiences and instinctive beliefs of mankind and thus deeply rooted in our language. It has been maintained that the model of solid bodies is even at the root of our grammar, of distinguishing object and subject, body and mind (Bortoft, 1995/44):

"Wir haben inzwischen eine wachsende Zahl von Beweisen, die die Sichtweise stützen, daß es zwei hauptsächliche, komplementäre Formen des menschlichen Bewußtseins gibt. In unserer technischwissenschaftlichen Kultur haben wir uns auf die Entwicklung nur einer dieser Formen spezialisiert, auf den unser Erziehungssystem fast ausschließlich ausgerichtet ist. Dies ist die analytische Form des Bewußtseins, die sich in Verbindung mit unserer Sinneswahrnehmung und dem Umgang mit festen Körpern entwickelt. Indem wir die Erfahrung verinnerlichen, daß solche Körper bestimmte Grenzen haben, werden wir zu einer Denkweise geführt, die das Gewicht ganz natürlich auf Unterscheidung und Trennung legt. Da das grundlegende Kennzeichen der Welt der festen Körper Äußerlichkeit ist – das heißt, jedes Ding ist zu jedem anderen äußerlich –, ist diese Denkweise notwendig analytisch. Aus demselben Grunde ist sie notwendig sequentiell und linear, indem sie von einem Element zum anderen stückweise fortschreitet. …Das analytische Bewußtsein ist außerdem mit der Sprache verknüpft. Die Grundstruktur moderner Sprachen ist ihre Subjekt-Prädikat-Grammatik, was zur Folge hat, daß die Erfahrung in getrennte

Elemente zerlegt wird, die dann so behandelt werden, als bestünden sie unabhängig voneinander. Zum Beispiel scheint der Satz 'Ich sehe den Baum' aus einer äußeren Zusammenfügung verschiedener getrennter Elemente gebildet zu sein, nämlich aus Subjekt, Objekt und dem Sehakt, der sie verbindet. Aber die Erfahrung, die durch diesen Satz angedeutet wird, kann nur künstlich so betrachtet werden, als ob …"

And classical mechanics continues to be our standard reference. It is the proto-physics of mankind, the basic 'frame' of reference, even for relativistic and quantum mechanics, even in the most advanced measurements of the constant of gravitation and in the most advanced string theories 'explaining' the 'particle zoo' contained in nucleons in terms of eigen-functions and eigen-values of strings in 'The Cosmic Symphony' (Greene, 2001/133 ff), very similar to earlier explanations of atoms in terms of eigen-functions of Schrödinger's equation. Only Connes' approach in terms of non-commutative geometry 'looks' different (Hellemans, 2006).

An example of classical mechanics serving as model in completely different contexts may be taken from Clausewitz' 'Vom Kriege' (1991/209-210, quotation following Oetinger, 2005/196 f):

Der Krieg in der wirklichen Welt ist, wie wir gesehen haben, kein solch Äußerstes, was seine Spannung in einer einzigen Entladung löst, sondern er ist das Wirken von Kräften, die nicht vollkommen gleichartig und gleichmäßig sich entwickeln, sondern die jetzt hinreichend aufschwellen, um den Widerstand zu überwinden, den die Trägheit und Friktion ihr entgegenstellen, ein anderes Mal aber zu schwach sind, um eine Wirkung zu äußern; so ist es gewissermaßen ein Pulsieren der Gewaltsamkeit, mehr oder weniger heftig, folglich mehr oder weniger schnell die Spannungen lösend und die Kräfte erschöpfend; …

What Clausewitz called 'Friktion' is closely related to 'The Law of Leaky Abstraction' by Spolsky quoted by RosenbergS in a paper on Simonyi's Intentional Programming (2007/47).

And 'Friktion' is also related to 'Murphy's law'. In its simplest and most general version stating: 'Whatever can go wrong goes wrong'. In the internet murphys-laws.com provides 'all the laws of Murphy on one site' together with their history et cetera.

Another beautiful example of classical mechanics serving as model in completely different contexts is to be found in Engel's 'Anti-Dühring' (Marx, 1975/105).

2.2 Solving problems

It is foolish to answer a question that you do not understand. It is sad to work for an end that you do not desire. Such foolish and sad things often happen, …

Gustav Polya: How to solve it (1971/6).

Wer nicht weiß, wo er hin will, darf sich nicht wundern, wenn er woanders ankommt.

Mark Twain.

Gewißheit ist einer der billigsten Gebrauchsartikel, und sie kann augenblicklich erlangt werden, sobald das Problem in der richtigen Weise angepackt worden ist.

Paul Feyerabend: Methodologische Erwägungen (1999/103).

The second model underlying the present exposition concerns the process of solving problems. Kant in his 'Kritik der praktischen Vernunft' has elaborated on the motto (Hermlin, 1981/176):

Nachdem aber, wiewohl spät, die Maxime in Schwang gekommen war, alle Schritte vorher wohl zu überlegen, die die Vernunft zu tun vorhat, und sie nicht anders als im Gleise einer vorher überdachten Methode ihren Gang machen zu lassen, so bekam die Beurteilung des Weltgebäudes eine ganz andere Richtung und mit dieser zugleich einen ohne Vergleich glücklicheren Ausgang.

The second