User:Marc Goossens/Günther Ludwig

THIS ARTICLE IS STILL IN SCAFFOLDING – PERSONAL DRAFT (intended for publication in 2008)

Günther Ludwig (January 12, 1918 - June 8, 2007), was a German theoretical physicist and philosopher of science. He studied physics in Berlin in Göttingen during and shortly after the war, and became theoretical physics professor at the Freie Universität Berlin in 1949. In 1963, he took on a professorship at Marburg's Philipps-Universität, where he stayed until his retirement in 1983.

Ludwig contributed to fields as diverse as relativity, stellar formation, fluid dynamics, statistical and quantum mechanics with additions to pure mathematics along the way. His main interest lay in the foundations and (precise and no-nonsense) interpretation of physics as a whole, and quantum mechanics in particular. This is where one also finds his two most important achievements: (i) a systematic theory of the foundations of physics (or metatheory), and (ii) an application of these concepts to an extensive investigation of the foundations of quantum mechanics, including a derivation of its Hilbert space structure.

In his function as professor and teacher, Ludwig was admired by many of his students, and respected by his colleagues in academia for his dynamism. Ludwig was married, but little is known in the public domain about his private life.

Günther Ludwig
Born	(1918-01-12)January 12, 1918 Zäckerick
Died	June 8, 2007(2007-06-08) (aged 89)
Nationality	German
Citizenship	Germany
Alma mater	Friedrich-Wilhelm University (now Humboldt University), Berlin
Known for	seminal contributions to the foundations of quantum mechanics
Scientific career
Fields	Statistical Mechanics Quantum Mechanics Theoretical Physics Foundations of Physics Philosophy of Science
Institutions	Göttingen Freie Universität Berlin Philipps Universität Marburg

Overview of 65 years of work in and on theoretical physics

• Unique scientific contributions – Günther Ludwig's initial academic work was on projective theory of relativity. In the 1950's, the focus of his research shifted towards quantum mechanics and its foundations. The fundamental questions on the formulation and epistemology of theoretical physics, which he encountered there, led Ludwig to investigate more generally the structure of physical theories, in their relation to physical reality on the one hand and abstract mathematics on the other.
Ludwig became best known for his structuralist meta-theory of physics, its application to a systematic understanding of quantum mechanics, and for his axiomatic derivation of the Hilbert space structure of quantum mechanics, using only basic postulates carrying an explicit physical interpretation. In Ludwig's explanation, the key to the interpretation of (the mathematical model of) any physical theory, is a list of specific correspondence principles (or 'mapping principles') linking the mathematical theory to physical observation. In the case of quantum mechanics, this is always achieved by sampling relative frequencies of a series of events, which are 'mapped' to mathematical probabilities. This leads to a strictly minimal and operational ensemble interpretation of quantum mechanics; Ludwig renders this operationally very concrete (and hence possibly controversial), as statistically interacting preparation and registration processes, necessarily implemented by macroscopic systems. As part of his work on theoretical physics, Ludwig also contributed to pure mathematics, formulating and proving several theorems in the domains of functional analysis, convex and mixture spaces and their representation theory and theory of uniform spaces.
• Stance on religion – As a protagonist of scientific rigor, precision and realism, Günther Ludwig comes out on the side of Christian religion, which he holds to be in full unison with the methods and findings of the exact sciences. As academic textbooks on theoretical physics go, Ludwig's series Introduction into the Fundamentals of Theoretical Physics' (in German) (refs) stands out in that it tackles the issues of physics as a human endeavor and its relation to religion head-on. As Ludwig sees it, single events (e.g. of religious content) can never contradict physics.
• Influence – Ludwig's meta-theory of physics is Hilbertian in inspiration, and characterized by a high degree of formal language content, making access comparatively demanding. This, together with the fact that many of his publications are available in German only, appears to have held back his influence outside German speaking countries. The significance Ludwig attached to an encompassing but systematic and down-to-earth view of nature and physics may be glanced from his final book, A New Foundation of Physical Theories (ref). He published it in English in 2006, one year before his death. Günther Ludwig's active academic work spanned 65 years.

Life, education and academic career

(ref Ziegler; uni berlin, Marburg obit)

Günther Ludwig was born on January 12, 1918, in the tiny village of Zäckerick, then in the German region of Brandenburg, on the east bank of the Oder river and some 50 kilometers to the north-east of Berlin. (His birth is also mentioned in the 1918 Berlin Chronicle).

• Berlin studies and the war years – Having studied chemistry and physics, he obtained a PhD in physics from the then Friedrich-Wilhelm University (now Humboldt University; see also Humboldt University website), on June 29, 1943 (ref. Ziegler), having submitted his doctoral dissertation, entitled Optimal Choice of Coefficients of a Characteristic Polynomial that describes the Stability of a Physical System capable of undergoing Vibration^[1] to the Mathematics and Natural Sciences Faculty on June 5, 1942^[1].
These were the war years, and Ludwig had been assigned in compulsory service (German: 'dienstverpflichtet') to the notorious research and test facility for military rocket science and missile development at Peenemünde (ref Marburg obituary).
• Via Göttingen back to Berlin – Soon after the war, Ludwig became a research assistant of Richard Becker at Göttingen University (see also Göttingen University website) during the period 1946-1948, where he obtained his habilitation on February 2, 1948 (ref. Ziegler). It was also while at Göttingen, that he got in touch with renowned theoretical physicists of that time, including Werner Heisenberg and Pascual Jordan ^[1]. During these early years, Ludwig himself published mainly on the projective theory of relativity.
On September 1, 1949, he accepted a chair as extraordinary professor at the newly founded Free University of Berlin (short: FUB; see also FU Berlin website), moving on to a full professorship on October 1, 1952 (ref Ziegler), to found the Institut für Theoretische Physik (Institute for Theoretical Physics (ref. FUB 97/MG version?). With great energy, he dedicated himself to setting up a well-structured academic teaching, whilst organizing and supporting a wide field of research, spanning such topics as applied hydrodynamics, problems of quantum measurement, statistical mechanics and quantum field theory (ref Marburg obituary). By this time, Ludwig had in fact directed his personal attention towards quantum mechanics, and a deeper understanding of its foundations—a theme which was to remain central to his entire academic oeuvre, and indeed a lifetime interest. This can be seen readily from the chronological list of his scientific publications, given below. In his short history of the Institute for Theoretical Physics, written in 1997 and published on the FUB website (ref.), G. Simonsohn (a physics student at FUB in the late forties) describes Ludwig, upon his arrival in Berlin aged 31, as "an unconventional and dynamic theoretician, fully dedicated to modern physics and its foundations". The same reference hints (without further detail or explanation) at the fact that "one could hardly imagine a sharper contrast between Ludwig on the one hand, and the (experimental) Physikalisches Institut, its director (Hans Lassen) and its research fields on the other." At that time, the experimental physics, theoretical physics and mathematics departments all shared the same building, Boltzmannstraße 20. The chronicle proceeds to say that life "in this cramped space" was harmonious nonetheless. An FUB picture taken in 1950, indeed shows Ludwig and his colleagues on the lawn, cheerfully experimenting with gravity, apparently during a garden party (Ludwig & colleagues at play).
• Marburg period – In 1963, Günther Ludwig took on a theoretical physics chair at the Philipps-Universität in the town of Marburg (then in Western Germany), where he stayed on until his retirement as professor emeritus in 1983.
Even at advanced age, he continued to work and publish, paying regular visits occasional visits to his former department throughout the nineties^[1]. Günther Ludwig died on June 8, 2007. His last publication was the book A new Foundation of Physical Theories, written together with Gérald Thurler and published one year before Ludwig's death, presenting a refreshed and simplified account of his 'theory of theories', and its implications for our understanding of theoretical physics (Ludwig & Thurler 2006).

Ludwig was married and dedicated his 1983 2-volume book Foundations of Quantum Mechanics Vol. I (Ludwig 1983) and Vol II (Ludwig 1985) to his wife. At the time of this writing, little is known in the public domain about his life as a private person.

influenced by? (berliner kreis? = footnote)

http://books.google.be/books?id=e0mC9StvaOIC&pg=PA139&lpg=PA139&dq=%22g%C3%BCnther+ludwig%22+professorship&source=web&ots=feDyox4ZVS&sig=96DfchbjNDviwVECU7PRBMU1F1Q&hl=nl

Publications

An informative angle on Ludwig's progress and thinking is obtained by this survey of his publications. It shows that already by the early 1960's, the cornerstones of his foundational edifice are in place, even though it will take him another 20 years to work things out in full depth and detail. (For an extensive Ludwig bibliography, see the article on works by Günther Ludwig.)

• Early work and the start of Ludwig's foundational enquiries – In 1951, Ludwig publishes Fortschritte der projektiven Relativitätstheorie, summing up his work in this domain.
His next publication, On the Position of the Subject in Quantum Mechanics, appearing in a bundle by Freie Universität Berlin (where he is then professor) celebrating the 200 years Columbia University jubilee, gives a first clear indication of Ludwig's perspective on the interpretation of quantum mechanics and his keen interest in its philosophical implications. This will be worked out further soon afterwards in several publications such as The measurement Process, The Foundations of Quantum Mechanics, or On the Conception of Observation in Quantum Mechanics. This work will culminate in a series of monographs on the foundations of quantum mechanics around the time of Ludwig's retirement from active academic life. Early on in this research, Ludwig establishes the link between a statistical description of macroscopic systems, as dealt with in Axiomatic Quantum Statistics of Macroscopic Systems, and the quantum mechanics of what he terms microsystems. For Ludwig, this link is twofold: he develops the common model of statistical selection procedures, universal to all statistical descriptions of physical systems and operationally more transparent than the traditional Kolmogorov model (note), and goes on to explain quantum effects as a certain class of statistical interaction between macroscopic systems.
• Deeper insights and a broadening perspective – As he delves deeper into the rational, methodological and epistemological fundamentals of physical theories and theoretical physics and assigning to these a realistic operational meaning in the world surrounding us humans, Ludwig encounters in his research no obstacle to or contradiction with religious belief—quite on the contrary. This view is laid down in his 1962 paperback booklet Das naturwissenschaftliche Weltbild des Christen, which approximately translates as 'The Christian's Conception of the World in line with Physical Sciences'.
By 1964, Ludwig is ready to take on the actual systematic axiomatization of quantum mechanics, based on rigorous mathematical axioms, but in such a way that a transparent physical interpretation is ensured. Witness to this is his article Attempt at an Axiomatic Foundation of Quantum Mechanics and of General Physical Theories, the final part of its title already hinting at the broader foundational vantage point adopted by its author. Some three years later, Fundamental Laws on Measurement as a Basis of the Hilbert Space Structure of Quantum Mechanics proves that Ludwig's attempt to recapture the ubiquitous formalism of quantum mechanics by starting from axiomatically formulated physical assumptions, meets with success. With (ref), this work is essentially completed. Understanding the Concept "Physical Theory" and an Axiomatic Foundation of the Hilbert Space Structure of Quantum Mechanics through the Fundamental Laws of Measurement illustrates that meanwhile he also achieves progress regarding his thoroughgoing analysis of the of the structure and scope of physical theories in general. Ludwig often combines the general concept of theory and its application to, say, quantum mechanics in the title of his publications. This underscores his view that a full understanding of the latter cannot be obtained without a solid grasp of the former.
• Towards an encompassing vision and presentation – With further publications like The Measuring Process and an Axiomatic Foundation of Quantum Mechanics, , Macroscopic Systems and Quantum Mechanics or Measuring and Preparing Processes, Ludwig continues to refine and complete his efforts at clarifying quantum mechanics. But by now, the time has come for him to try and present a unified view of the bulk of theoretical physics in the form of a university textbook.
Ludwig faces up to this challenge with the 4-volume series Einführung in die Grundlagen der Theoretischen Physik (An Introduction into the Principles of Theoretical Physics).: Vol I – Space, Time, Mechanics; Vol II- Electrodynamics, Time, Space, Cosmos; Vol III – Quantum Theory; Vol IV – Macrosystems, Physics and Man. As a physics textbook it remains 'traditional' in its use of calculus and coordinate expressions, but true to its title, the book does pay considerable attention to the principles underlying theoretical physics, and the motivation of each concept introduced. This already starts with the way the classical notions of space and time are explicitly introduced and motivated, rather than simply taken for granted. As one may expect from this author, quantum mechanics gets a lot of attention, and selected parts of its full axiomatics are presented.

Research

Ludwig as a mathematician

Ludwig's 'Theory of Theories'

Main article: Ludwig metatheory

In order to help clarify the interpretation and the (apparent) paradoxes of quantum mechanics and theoretical physics as a whole, Günther Ludwig set out to construct a rigorous meta-theory of physics: a theoretical framework or super-structure (hence 'meta'), for describing and analyzing any physical theory. In contrast to foundations of mathematics, which is an established and well developed discipline in mathematics, no comparable counterpart existed in physics. As is the case in mathematics, one may expect that systematic foundational research may help to clarify philosophical as well as practical questions in the field. While not necessarily exclusive, Ludwig's theory of theories – Hilbertian in flavor and herculean in scope – goes a long way towards filling this gap; even so, it remains comparatively little known, possibly with the exception of Germany.

Hilbert VI

Ludwig's proposal follows the line sketched below:

1. Avoid ambiguity through using formal language – To allow rigorous and unambiguous analysis, one must exploit the setting of formal languages.
• This holds for a general investigation of the structure of physical theories, as well as for any individual such theory.
• For practical and philosophical reasons, Ludwig adopts a Bourbaki-style formalization.
2. Set up unified mathematical framework before doing any physics – Each physical theory requires proper mathematical infrastructure. This consists of three parts: we need to build a mathematical 'engine' in the form of a specific, chosen mathematical model at the core of each physical theory that has to comply to a generic specification to make sure it fits; but first, we need to set up a general meta-mathematical toolbox (unique and common to all physical theories) for building, servicing and operating this engine.
3. The Ludwig MTP common math toolbox – So first, for the intended general mathematical working environment, Ludwig…
• … starts with a formal Bourbaki language.
This choice will help ensure that the mathematical engine (theory) is a stand-alone formal construct in its own right. As such, the model and its constituents are (designed to be) devoid of any a priori interpretation or relationship to the real world. Indeed, in the context of a Bourbaki formulation, any mathematical entity or expression can be reduced to (a purely formal meta-statement about) a string (or typographical sequence) of symbols from a finite pool, called the alphabet.
• … assumes only classical binary logic as a cornerstone for any subsequent mathematical constructions and proofs.
Importantly, within this setting, the 'truth' of a mathematical statement is purely intrinsic and 'mechanical': the requirement being that the statement (sentence) can be formally proved according to classical logic and the traditional proof schemes. In this context, and relative to the mathematical theory, a theorem ('true' statement) holds no further ontological or philosophical significance or value whatsoever. (Only with respect to a physical theory with this particular mathematical model, may it be endowed with such a meaning.)
• … always uses an extensional mathematical theory, i.e. a theory that encompasses ('is stronger than') set theory. So the intuitively tangible concept of a set (including the empty set) is always at hand and thanks to the constructive definitions, its possible paradoxes are avoided.
Still proceeding by explicit construction, the sets of natural, integer, rational, real, … numbers are also available if needed. What was said above about the 'truth' of statements, also applies to the theory's mathematical entities ('objects'): constants, sets or other 'nouns' posses no interpretation or meaning other than the intrinsic and formal mathematical relations relative to other entities within the model, that one may be able to prove.
4. The generic math engine specification
• … requires that the defining axioms of the mathematical model will form species of structure axioms, defined over the relevant basis sets. This means that they are such that the structures (relations) induced on the sets, are transportable under faithful mappings. Well known examples of such structures are "group", "vector space", "measure space", "topology", "Hilbert space", "convex space", "Lorentz manifold" etc.
• … demands that, for the concrete mathematical theory to be of any use as an engine, it has to be consistent, i.e. it must not allow a statement and its negation to hold both.
5. Revving the engine – At the core of any physical theory lies the 'engine': a (formal) mathematical theory, its mathematical model. We have the toolbox and an outline spec. But what is it made of, and where does one get the detailed blueprint for building it?
• base sets, axioms, constants
• Relative to the physical theory she intends to mount it into, the physicist has to come up with a suitable mathematical model by a creative process of inspired guessing: this engine is not obtained from 'physical observation' in any fixed procedural or algorithmic fashion—neither by deduction, nor by induction.
Moreover, as is always the case in mathematics, any relevant and useful theorems <ithin the mathematical model have to be made up and conjectured too, and their proofs built through keen insight, great mathematical skill and hard work, possibly combined with trial and error. Any 'deduction' is established only once the proof has been found. (Of course, if an established mathematical theory is adopted as model for some physical theory, an adequate supply of proved theorems may already exist.)
6. observations; correspondence; hypothesis
7. For the purpose of serving as a model for the physical theory, one must allow the mathematical core to be extended with observational as well as hypothetical ("assume that…") statements.
Observations of empirical facts (from experiment, say) that are deemed relevant to the theory are appended ('one by one') to the mathematical model as additional statements or sentences. More precisely, these statements are formally added to its list of axioms. What this means is simply that the Ludwig scheme 'imports' (admissible) empirical facts into the model in the shape of 'mathematical truths'.

This was a Herculean task by any standards.

- ref. positivisme – wiener kreis http://plato.stanford.edu/entries/vienna-circle/#OveDoc hj schmidt verwijst in stanford enc phil (strucuralism http://plato.stanford.edu/entries/physics-structuralism/) naar "neo-positivism"

tenor

• approximate, partial model (comp. Truesdell)

“ The statement of facts which are self-existent in the sense that they do not exert any influence on other things is self-contradictory. Such facts are completely inaccessible. Nevertheless, in physics we endeavor to describe, as completely as possible, 'portions' of the real world as if these portions were self-existing. The attempt to describe the real world in complete detail would make physics impossible. Physics is possible only because we are able to make structural assertions about portions of the real world, without taking into account the structure of the world in all its particulars. Only a few "global structures" of the world as a whole are introduced into the description of the physics of its parts, as, for example, the space-time structure (and gravitation, which for sufficiently small regions of space can be neglected due to the existence of local inertial reference frames). We have made the assumption that the experiments composed of a preparation and a registration procedure can be described as such portions of the world using only space-time as a global structure of the world. ” — Günther Ludwig (Ludwig 1983, p. 27)

• yet overcomplete (idealizations, hypotesis-completeness, …)

• patchwork / network of theories

• intertheoretical relations

• math devoid of phys meaning

• phys as creative human endeavor

• extensional formulation; classical logic

• description / disclosure of reality (though formally ontology-invariant)

• normative program

formal structure

- further developments: Schröter; L&Thurler • appreciation / criticism: o Bourbaki (though as analytical means, not didactical) o "structuralism"" does not do full justice

The Ludwig interpretation of quantum mechanics

qm

• Quantum carriers mediate interaction between macroscopic preparation and registration systems – Quintessentially, the Ludwig picture of quantum mechanics reveals quantum systems (or like atoms, electrons, …) as carriers of a certain class of statistical interactions between macroscopic systems, one of which acts as a 'sender' or preparation arrangement (like a heated oven emitting XXX through a punctured hole, a remote stellar object, …), with the second one functioning as a 'receiver' or registration arrangement. (spatial = send-receive / temporal = write-read)
• 'Wave function' and other representations – Ludwig proves that the relevant 'signal characteristics' of the preparation arrangement relative to the interaction may be represented mathematically by a wave function (Hilbert space vector) or density operator. Depending on its makeup, a given registration arrangement 'probes' certain facets of the prepared signal it intercepts; it can be represented by a self-adjoint operator. In this way, one recovers the traditional formalism of quantum mechanics, though only as a 'secondary' representation albeit of great practical value.
• Operational 'ensemble' interpretation – The wave function (or density operator) expresses the statistical behaviour encoded by the preparation in the signal. This is usually termed the ensemble. In other words, the wave function is not ascribed to some individual quantum carrier; instead, it represents the statistical interaction pattern (onto some registration arrangement) that is generated by the preparation arrangement over a (large enough) series of 'identical runs'. So one can say that the Ludwig picture renders concrete the less specific ensemble interpretation of quantum mechanics in a very operational way, which is close to experiment. With Ludwig's proposal, the broad variety of mathematical representations (wave function "in position space", wave function "in momentum space",density operator, POVM, …) of a "quantum state" or its evolution (Schrödinger picture vs. Heisenberg or Dirac / interaction picture) is no longer confusing as to the actual interpretation: though not necessarily fully equivalent, all of these shapes are merely (mathematically) practical choices for representing the ensemble generated by the preparing macrosystem; the latter remains 'invariant' under whatever of these pragmatic choices we may adopt.
• Heisenberg inequalities express physical limitation on the possibility of preparing ensembles – (The preparation of) a quantum 'state' is characterized by a statistical ensemble. Irrespective of its expression in terms of wave functions, density operators, … , the 'Heisenberg inequality' relations are therefore a statement about ensembles, not about individual microsystems.
To the extent that the inequalities (and of course the Ludwig picture) are valid, they state in fact that there exists pairs of observables, such that it is physically impossible to construct a preparation producing an ensemble that is arbitrarily sharp in both. So if a given setup generates a state that disperses little (over many trials) for some observable A, there will always be an observable B for which that same ensemble unavoidably scatters significantly. One obtains the best known example for this by taking the position and momentum observables for A and B. The claims than simply reads that no preparation arrangement (device, …) occurs or can be constructed in the application domain of quantum mechanics, so that the results form a long enough sequence of trials (or possibly a continuously emitted beam) will both vary little in the position as well as in the momentum with which they enter a detector.
• Galilei Transformations – a
measurement transformations apparent collapse = artefact due to black-box model of interaction no new logic • appreciation / criticism: o mainstream, though original and contentious o Aerts 94 "convexe struct = enkel wisk"  L Ansatz begint bij natk vlg MTP (reg/prep)  >< Freter Anhang B (calculus of devices) o Busch, Lahti, … ("Ludwig claim on compatibility is wrong") / Mittelstaedt • as adopted by Werner, Davies, Holevo, … • ref http://www.newworldencyclopedia.org/entry/Axiomatic_systems

statistical

theory of measurement

The basic idea is that 'measurement operations distinguish between states'. Mathematically, this leads to functionals (= measurements) resolving

other theories in Ludwig formulation

STT

Ludwig on science and religion

mg: ludwig mild positivistisch; maar niet "dat er niks anders / geen ander inzicht" is (oa religie, maar ook rol van creativitieit / inspiratie ("erraten") in bv kiezen / maken van goede wisk theorie, stellingen,… (deductie is a posteriori: een bewijs VIND je immers ook niet deductief)

Ludwig as a teacher and colleague

(Schelb 1997, pp. 49–59).


^[1].

Papers in honor of Günther Ludwig

• On the theory of the transverse dynamic magneto-conductivity? Dedicated to Gunther Ludwig. on. the occasion of his 60th birthday ...... the limitations of our theory, we point out that dynamical screening effects have ... www.iop.org/EJ/article/0022-3719/11/19/011/jcv11i19p3993.pdf - http://www.iop.org/EJ/abstract/0022-3719/11/19/011 On the theory of the transverse dynamic magneto-conductivity W Gotze et al 1978 J. Phys. C: Solid State Phys. 11 3993-4008 doi: 10.1088/0022-3719/11/19/011 PDF (828 KB) | References | Articles citing this article W Gotze and J Hajdu Phys. Dept., Tech. Univ., Munchen, West Germany Abstract. The dynamic magneto-conductivity is expressed by a relaxation kernel which is evaluated in a lowest-order correlation approximation. The present theory yields in particular both the static magneto-resistance and the cyclotron resonance damping in terms of integrals over the single-electron spectral functions. In the quantum limit all results are given by simple closed formulae. Print publication: Issue 19 (14 October 1978)

PhD students

Notes

1. ^ ^a As reported in a private communication by Joachim Plumbaum, then assistant at the department.
2. ^ ^a Ludwig may already have known P. Jordan (who was an NSDAP member, yet considered politically unreliable by the nazi's) from the days in Peenemünde; see e.g. Wikipedia article on Jordan.
3. ^ ^a Original title of Ludwig's doctoral dissertation in German: Günstigste Wahl der Koeffizienten eines charakteristischen Polynoms, das die Stabilität eines schwingungsfähigen, physikalischen Systems beschreibt.
4. ^ ^a A copy of Ludwig's PhD dissertation was recovered by the US as part of the Peenemünde archives, ref. 86/105. It is now included in collection of Peenemünde Technical Reports (Fort Bliss / Putkammer Collection) of the US National Air and Space Museum, Archives Division as document nr 1 in box 3, see [1].

References

• Ludwig, Günther (1951), Fortschritte der projektiven Reltivitätstheorie, Vieweg (Progress in Projective Theory of Relativity)
• Ludwig, Günther (1953), "Die Stellung des Subjekts in der Quantentheorie", 'Veritas, Justita, Libertas' (Festschrift der Freien Universtität Berlin zur 200-Jahr-Feier der Columbia University), Berlin: Colloquium-Verlag, pp. 262–272 (The Position of the Subject in Quantum Theory)
• Ludwig, Günther (1953). "Der Meßprozeß". Zeitschrift für Physik. 135: 483–511. doi:10.1007/BF01338813. (The Measurement Process)
• Ludwig, Günther (1954), "Die Grundlangen der Quantenmechanik", Grundlehren der Mathematischen Wissenshaften, Band 70, Springer (The Foundations of Quantum Mechanics)
• Ludwig, Günther (1954). "Zur Deutung der Beobachtung in der Quantenmechanik". Physikalischen Blätter. Band 11: 489–494. (On the Conception of Observation in Quantum Mechanics)
• Ludwig, Günther (1960), "Axiomatic quantum statistics of macroscopic systems (Ergodic theory)", in Caldirola, P. (ed.), Proceedings of the International School of Physics 'Enrico Fermi', Course XIV, Academic Press, pp. 57–132
• Ludwig, Günther (1962), Das naturwissenschaftliche Weltbild des Christen, Osnabrück: Verlag A. Fromm (The Christian's Physical Sciences Conception of the World)
• Ludwig, Günther (1964). "Versuch einer axiomatischen Grundlegung der Quantenmechanik und allgemeiner physikalischer Theorien". Zeitschrift für Physik. 181 (3): 233–260. doi:10.1007/BF01418533. (Attempt at an Axiomatic Foundation of Quantum Mechanics and of General Physical Theories)
• Ludwig, Günther (1967). "Hauptsätze über das Messen als Grundlage der Hilbert-Raum-Struktur der Quantenmechanik". Zeitschrift für Naturforschung. 22a (9): 1303–1323. doi:10.1515/zna-1967-0904. (Fundamental Laws on Measurement as a Basis of the Hilbert Space Structure of Quantum Mechanics)
• Ludwig, Günther (1968). "Attempt of an Axiomatic Foundation of Quantum Mechanics and More General Theories III". Communications in Mathematical Physics. 9: 1–12. doi:10.1007/BF01654027.
• Ludwig, Günther (1970), "Deutung des Begriffs «physikalische Theorie» und axiomatische Grundlegung der Hilbertraumstruktur der Quantenmechanik durch Hauptsätze des Messens", in Ehlers; Hepp; Zurich (eds.), Lecture Notes in Physics 4, Springer (Understanding the Concept "Physical Theory" and an Axiomatic Foundation of the Hilbert Space Structure of Quantum Mechanics through the Fundamental Laws of Measurement)
• Ludwig, Günther (1971), "The measuring process and an axiomatic foundation of quantum mechanics", in D'Espagnat, B. (ed.), Foundations of Quantum Mechanics (Proceedings of the International School of Physics 'Enrico Fermi', Course IL), Academic Press
• Ludwig, Günther (1972), "Makroskopische Systeme und Quantenmechanik", Notes in Math.Phys. 5, Marburg{{citation}}: CS1 maint: location missing publisher (link) (Macroscopic Systems and Quantum Mechanics)
• Ludwig, Günther (1972), "Meß- und Präparierprozesse", Notes in Math.Phys. 6, Marburg{{citation}}: CS1 maint: location missing publisher (link) (Measuring and Preparing Processes)
• Ludwig, Günther (1974), Einführung in die Grundlagen der Theoretischen Physik; Band II: Elektrodynamik, Zeit, Raum, Kosmos, Vieweg, ISBN 3-571-09182-5 (An Introduction into the Principles of Theoretical Physics, Vol II: "Electrodynamics, Time, Space, Cosmos")
• Ludwig, Günther (1976, 1984), Einführung in die Grundlagen der Theoretischen Physik; Band III: Quantentheorie, Vieweg, ISBN 3-528-09183-5 {{citation}}: Check date values in: |year= (help)CS1 maint: year (link) (An Introduction into the Principles of Theoretical Physics, Vol III: "Quantum Theory")
• Ludwig, Günther (1978), Einführung in die Grundlagen der Theoretischen Physik; Band I: Raum, Zeit, Mechanik, Vieweg (An Introduction into the Principles of Theoretical Physics, Vol I: "Space, Time, Mechanics")
• Ludwig, Günther (1978, 1990), Die Grundstrukturen einer physikalischen Theorie, Springer {{citation}}: Check date values in: |year= (help)CS1 maint: year (link) (The Fundamental Structures of a Physical Theory)
• Ludwig, Günther (1979), Einführung in die Grundlagen der Theoretischen Physik; Band IV: Makrosysteme, Physik und Mensch, Vieweg, ISBN 3-528-09184-3 (An Introduction into the Principles of Theoretical Physics, Vol IV: "Macrosystems, Physics and Man")
• Ludwig, Günther (1981). "Quantum theory as a theory of interactions between macroscopic systems which can be described objectively". Erkentniss. 16: 359–387.
• Ludwig, Günther (1981), "Eigenschaften und Pseudoeigenschaften von Mikrosystemen", in Nitsch, J.; Pfarr, J.; Stachow, E.-W. (eds.), Grundlagenprobleme der modernen Physik, Festschrift für Peter Mittelstaedt zum 50. Geburtstag, B.I.-Wissenschaftsverlag, pp. 217–242 (Properties and Pseudoproperties of Microsystems)
• Ludwig, Günther. "The Objective Description of Preparation and Registration as a Basis of Quantum Theory". Nuovo Cimento.
• Ludwig, Günther (1983), Foundations of Quantum Mechanics I, Springer
• Ludwig, Günther (1985), Foundations of Quantum Mechanics II, Springer
• Ludwig, Günther (1985), An Axiomatic Basis for Quantum Mechanics, Vol I: "Derivation of Hilbert Space Structure", Springer
• Ludwig, Günther (1987), An Axiomatic Basis for Quantum Mechanics, Vol II: "Quantum Mechanics and Macrosystems", Springer
• Ludwig, Günther (1990), "Die Katze ist tot", in Audretsch, J.; Mainzer, K. (eds.), Wieviele Leben hat Schrödingers Katze?, B.I. Wissenschaftsverlag, pp. 183–208 (The Cat is Dead (in: How many Lives does Schrödinger's Cat have?)
• Ludwig, Günther (1993), "Die Stellung des Subjekts in einer physikalischen Theorie", in Geyer, B.; Herwig, H.; Rechenberg, H. (eds.), Werner Heisenberg, Physiker und Philosoph (Verhandlungen der Konferenz 'Werner Heisenberg als Physiker und Philosoph in Leipzig' vom 9.-12. Dez. 1991 an der Univ. Leipzig), Spektrum, pp. 244–250 (The Position of the Subject in a Physical Theory (in: "W. Heisenberg, Physicist and Philospher)
• Ludwig, Günther (1994). "Die Methode der Physik und ihre Grenzen". Ethik und Sozialwissenschaften. 5: 458–460. (The Method of Physics and its Limitations)
• Ludwig, Günther; Thurler, Gérald (2006), A New Foundation of Physical Theories, Berlin: Springer
Reichenbach ref http://www.iep.utm.edu/r/reichenb.htm#H2
• Ax, James (1978). "The Elementary Foundations of Spacetime". Foundations of Physics. 8 (7–8): 507–546. doi:10.1007/BF00717578.
• Basri, Saul A. (1966), A Deductive Theory of Space and Time, Amsterdam: North Holland
• Ehlers, J.; Pirani, F.A.E.; Schild, A. (1972), "Ch.4 - The Geometry of Free Fall and Light Propagation", in O'Raifertaigh, L. (ed.), General Relativity. Papers in honour of J.L. Synge., Oxford: Clarendon Press, pp. 63–82