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ABSTRACT The main theme of the conference will be the unique collaboration between mathematics, physics and philosophy during the beginning of the 20th century. During this period modern physics and new basic mathematical structures were formed. Significant mathematicians such as Poincaré, Weyl, Minkowski, Hilbert, and von Neumann contributed to this development and created the mathematical disciplines that plays such a dominant role in modern mathematical physics and in other areas of mathematics. These mathematicians also played an important role in the philosophical discussions about nature and science during this period. This applies to such influential philosophical tendencies as logical empiricism, critical rationalism, and various neo-Kantian trends. We also want to touch upon the 19th century interactions between mathematics, physics, and metaphysics. -
DOWNLOAD ENTIRE PROGRAM IN PDF - LIST OF SPEAKERS Robert DiSalle (University of Western Ontario) Jeremy Gray (Open University) David Hyder (University of Konstanz) Michel Janssen (University of Minnesota) Jesper Lützen (University of Copenhagen) Ulrich Majer (University of Göttingen) Helmut Pulte (Ruhr-University Bochum) David Rowe (Mainz University, Germany) Erhard Scholz (University of Wuppertahl) Lawrence Sklar (University of Michigan)
TIME AND LOCATION All presentations will take place at the Carlsberg
Academia in Copenhagen, which is a beautiful house maintained by the Carlsberg Foundation. The address is
REGISTRATION Registration is free. Please write Pelle Hansen
TITLES OF TALKS Robert DiSalle
(University of Western Ontario) ABSTRACT:
Logical empiricism was intended, at least, to embody the philosophical
perspective that seemed to be implicit in, and an indispensable motivation
for, the revolutionary physical theories of the early 20th century. Beyond
offering a philosophical reflection on the state of contemporary physics,
however, the logical empiricists sought to connect the revolution in physics with late 19th-century transformations in the philosophy of logic
and mathematics above all, a transformed view of the nature of axiomatic
structures and their physical interpretation. Ironically enough, its account of the nature and interpretation of scientific theories came to be
seen, in the later 20th century, as a central reason for the failure of logical empiricism as a whole. My aim is not to excuse logical empiricists
of such failings, as to understand better the insight that they sought unsuccessfully to capture, and its relevance to the philosophy of physics
in the early 20th century. They were justified in thinking that insights concerning structure and interpretation had had sweeping consequences for
the foundations of mathematical physics, as well as for traditional
ABSTRACT: Federigo Enriques' book Problemi della Scienza of 1906 (English translation Problems of Science, 1910) is a prolonged attempt to define and distinguish between facts and theories in order to analyse what constitutes reality. It is a positivist, somewhat anti-Kantian work, and it can be read as a long conversation between Enriques and Poincaré. In this talk I shall draw out the views, sometimes in agreement, sometimes in conflict, of these two men, and illuminate contemporary issues in the philosophy of geometry.
In the reprinted version of his “On the Conservation of Energy” that appeared in his Wissenschaftliche Abhandlungen, Helmholtz expresses his unease with his aprioristic assumptions concerning the concepts of matter and force in his earlier work, which he now characterises as too Kantian. The cause for this unease is also the theory of electromagnetism, which calls into doubt his previous claims concerning the reducibility of forces to central ones. Helmholtz worries that these difficulties will lead to the result that we will need to introduce into physics “a relation between a mass and something that can never be the object of a possible experience,” namely absolute space. Since, as I will be arguing, Helmholtz's work on non-Euclidean geometry championed the claim that space was in itself bereft of metrical properties, and that these could only be defined with recourse to a notion of possible experience, it follows that he was aware in 1881 that his neo-Kantian philosophy of science was threatened with inconsistency. I will conclude with a few remarks on the ensuing shift in Helmholtz's philosophy, and its possible connection to Hertz's Principles.
ABSTRACT:
Einstein's 1905 paper on special relativity suggests that relativistic
mechanics is simply a matter of adjusting Newton's F = ma to make it
Lorentz invariant. Einstein, for instance, appears to have been quite happy with a theory combining Maxwell's equations to describe
electromagnetic fields and a Lorentz-invariant generalization of Newtonian
particle mechanics to describe the atomic matter interacting with those fields. To understand the
interaction of matter and field in the kind of spatially extended physical
systems studied at the time, however, a new mechanics was needed, providing the categories for dealing
with both matter and fields. Max Laue presented such a new mechanics in 1911 and it is essentially still with us today. The new mechanics is a
mechanics of fields rather than particles. The fundamental equation,
accordingly, is not some Lorentz-invariant generalization of F = ma
but $\partial_\nu T^{\mu\nu} = 0$, the vanishing of the four-divergence of the
energy-momentum tensor for closed systems. In 1912 Einstein singled out the rise to prominence of the latter
equation as "the most important new advance in the theory of relativity." I will illustrate the advantages of the new mechanics with a
few concrete examples of systems that had baffled physicists such as
ABSTRACT:
In his Prinzipien der Mechanik (1894) Heinrich Hertz presented a
mechanistic image of nature. In the introduction to the book he insisted
that when we theorize about nature we construct images in our mind of the
external world. These images must be logically permissible and correct in
the sense that their consequences are in accordance with the observable
facts. This does not uniquely determine the image. In particular, Hertz
insisted that any image of nature will contain inessential elements or
unobservables. We have no way of knowing if the image including the
inessential elements corresponds to nature in any other way than being a
correct image. We do not know if nature is simple, but Hertz insisted that
we must require our image to be as simple as possible, i.e. it must
contain as few inessential elements as possible.
Many philosophers have written on the influence of Hertz's image
theory on philosophers and physicists. In my talk I shall compare the
mature image theory as it was presented in Hertz's Principles of Mechanics
with Hertz's earlier ideas about physical theories as he expressed them in
his newly published lectures from 1884 in Kiel on the Constitution of
Matter, and in his papers on electromagnetism. I shall show that the
mature theory was constructed with the purpose of serving as a basis for a
theory of mechanics, and in particular for Hertz's particular image of
mechanics. ABSTRACT: Among modern physicists one can find a widespread prejudice, which roughly sounds like this: Because physics is an empirical science, and as such revisable in principle, it makes no sense to cast physical theories into an axiomatic form. Such an axiomatic form raises the impression as if the physical theory in question is complete and settled, and this view is, of course, incompatible with the empirical character of physical theories. Like many prejudices, this contains a grain of truth. It is, however, important for the future development of physics to distinguish, what is right and what is wrong with this particular kind of prejudice. It is well known that Hilbert was the champion of modern axiomatics. For this reason the prejudice should apply particularly well to his approach to physics. Therefore I'll take his axiomatic approach as a test case for the prejudice. This means I'll investigate, in which sense was his axiomatic approach to the foundations of physics a failure and in which respect, if there is any, was it a success. The answer, I will come up with, runs roughly like this. If one distinguishes carefully (what Hilbert not always does!) between the axiomatic presentation of a theory and the axiomatic method as a means to analyse the logical dependencies and, still more important, independencies between different sentences of a theory, then it will become clear that Hilbert is far away from any dogmatism regarding the axiomatic foundations of a theory. On the contrary, the axiomatic method turns out to be an important tool to clarify the logical structure of a theory and in this way the recognition becomes improved which sentences are empirically revisable and which are not, given that certain other sentences have to be maintained. In the talk I will present some examples.
ABSTRACT: Moritz Schlick was (next to P. Frank) most influential for the reception of A. Einstein's theories of special and general relativity by the Vienna Circle, and Einstein's `coincidence of events' became important for Schlick's attitude towards spatiality and geometry. But Schlick was also influenced by H. von Helmholtz's philosophy of geometry and by his epistemology in general. The talk will present and analyse these two different strands in Schlick's philosophy of geometry, whereby special emphasis is put on his attempt to sharpely separate intuitive experience of space and conceptual knowledge of space. This separation is decisive for his claim that Kant's synthetical principles are a `logical impossibility'. Schlick's foundation of this aim, however, seems to be in need of critical examination.
"On the Early Reception of GRT: Some Mathematical, Philosophical, and Physical Perspectives" ABSTRACT:
In practically all accounts of the early history of general relativity, two dates stand out as decisive for all that followed:
Einstein's discovery of generally covariant field equations in November 1915 and his subsequent presentation of this
work in his definitive paper from May 1916. This work gave his theory of gravitation a new and presumably firm foundation. But was there really a
consensus of opinion regarding the need for a generally covariant approach
to gravitation? Did Einstein's famous papers really provide a basis for answering all the central questions posed by such a
theory, thereby setting the stage for the famous British eclipse expeditions and the "final" confirmation of GRT in November
1919? Perhaps not surprisingly, a closer look at the reception of Einstein's theory in the intervening period reveals a far more complex
dynamic. By comparing the diverse perspectives of representative
mathematicians, philosophers, and physicists in the period 1916-1922 we can begin to understand some
important, but largely overlooked features in Einstein's
Erhard Scholz (University of Wuppertal): ABSTRACT: For his (first) unified field theory of matter in 1918 H. Weyl introduced a beautiful new geometrical structure, and a (slightly) extended frame for fields by emphasizing affine and “length” connections in addition to vector and tensor fields on the space-time manifold. Building upon (and extending) the Hilbert-Mie program for a derivation of the basic matter structures known at the time, Weyl hoped to achieve what Hilbert had attempted without (at least immediate) success. It was clear to him, though, that even in his extended framework he worked with field structures obeying essentially classical laws (“Gesetzesphysik”) and that this might turn out to be imcompatible with the rising new quantum physics. Before two years had passed, he had explored the relationship between classical “Gesetzesphysik” to statistical physics with highly speculative outlooks on how quantum physics, irreducible stochasticity of processes, and a somehow “reformed” concept of continuum might go together (in an article which has been attacked by P. Forman as a document of early Weimar culture “irrationalism”). In late summer 1920 Weyl finally gave up his (metaphysical) conviction in the correctness of the Mie-Hilbert (-Weyl) approach to matter by diverse reasons. From now on the “problem of matter” appeared again completely open to him. The text changes of the different editions (between 1918 and 1923) of Weyl's classic “Raum - Zeit – Materie” document the shifts in Weyl's perception of the problem of matter during that time period. These changes will be discussed and put into context in this talk.
(2) "From Weyl's "analysis of the problem of space" to gauge structures in relativistic quantum physics (1923-1929)" This talk starts with the situation where the other one ended, i.e. with a productive turn of Weyl's doubts as to the immediate possibility to solve the ”problem of matter” on the basis of his new (1918) gauge geometry. This turn consisted in a conceptual and mathematical analysis of the basic structures of the new type of ”purely infinitesimal” geometry (as Weyl called his perspective). Weyl took up motives from the 19th century ”analysis of the problem of space”, but changed the basic conceptual formulation and its mathematical content radically to adapt it to the new situation for physical geometry that had come about through the rise of the general theory of relativity. In this analysis, during the years 1920 to 1923, Weyl worked out a kind of two-level structure for groups characterizing infinitesimal congruence geometry in manifolds (which in today's mathematical language could be rephrased in terms of a fibre bundle with a (”large”) structure group H and a smaller group G < H as typical fibre, both acting on the `ìnfinitesimal neighbourhoods” of each point in the manifold, G the infinitesimal ”congruences”, in the relativity context the Lorentz group). When in the late 1920s Weyl investigated the question of how the Dirac equation of the relativistic electron (1928) might be put into the framework of general relativity, he encountered a similar two-level structure of infinitesimally acting groups (the ”small” group G now being SL(2,C), the universal covering of the Lorentz group, the larger one, H, a U(1)-extension of G). He could now build upon his knowledge of such geometrical constellations and introduce the appropriate connections to formulate a common frame for gravitation and electromagnetism of the ”spinning electron”. Parallel to and ”independently” from him V. Fock arrived at a similar construction, although formulated in slightly different terms and in a differing programmatic perspective. The theory of Fock and Weyl turned out to be an enduring contribution to the adaptation of the earlier gauge ideas of ”classical” geometry to the rising new quantum physics, although it was still of a semiclassical type (if compared with ”quantum fields” which started to be tentatively formed and explored about that time). The further history of this development had a lot of twists and turns and was far from a direct continuation of this episode at the end of the 1920s (and will not be part of this talk).
Lawrence Sklar (University of Michigan) ABSTRACT: The mathematics of probability was first introduced into physics by the great pioneers of statistical mechanics - Maxwell, Boltzmann and Gibbs. Two great puzzles arose from the theory. One was the origin of time asymmetry in physics. The other was the origin and rationale for the needed basic probability posits. I will explore some older and newer proposed answers to the letter question.
PROGRAM
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