# Arches and Scaffoldings

**Continuity and Discontinuity in the Genesis of Special Relativity, General Relativity, and Quantum Mechanics***3 ^{rd} International Interdisciplinary Summer School 2014with Michel Janssen, University of Minnesota*

**Tuebingen, August 4 - August 8, 2014**

### Call for Applications

Application deadline: June 20, 2014

**Introduction**

We kindly invite graduate students and junior scientists of philosophy, physics and mathematics, to apply for the 3^{rd} Forum Scientiarum's International Interdisciplinary Summer School

The Summer School takes place in Tuebingen (Germany), a classical university town with a charming old town center, from Monday, August 4 to Friday, August 8, 2014.

**Topic**

In five lectures Michel Janssen will present five case studies illustrating a metaphor for theory change in modern physics. In principle, new theoretical structures in physics, unlike arches and other architectural structures, could be erected without any scaffolding. After all, that is essentially how the four-dimensional formalism of special relativity, the curved space-times of general relativity, and the Hilbert space formalism of quantum mechanics are introduced in modern textbooks. Historically, however, such structures, like arches, were first erected on top of elaborate scaffolding provided by the structures they eventually either partially or completely replaced. After briefly discussing prospects and limitations of the metaphor, I will examine five examples of arches and scaffoldings in the history of relativity and quantum theory, drawing heavily on my earlier work (much of it co-authored with either Tony Duncan or Jürgen Renn).

The first two examples concern special relativity. Lorentz’s theorem of corresponding states for Maxwell’s equations formed the scaffolding for Minkowski’s new space-time geometry. Abraham’s electromagnetic mechanics formed the scaffolding for Laue’s relativistic continuum mechanics. These contributions of Minkowski and Laue transcended their electrodynamical roots and could serve as a new foundation for all of physics.

The second example concerns general relativity. Lorentz’s theory of the electromagnetic field provided Einstein with the scaffolding for developing theories of the gravitational field, both his own and the so-called Nordström theory. It was only after this strategy had led him to identify the field equations for these theories that he removed the scaffolding and presented these theories as naturally suggested by the geometry of curved space-times.

The last two examples are taken from the history of quantum theory. The Kramers dispersion formula, in which only quantities referring to transitions between orbits occur, provided Heisenberg with the scaffolding for a new theory for all of physics, not just dispersion, formulated entirely in terms of such transition quantities.

Finally, Jordan suggested in early 1927 that in quantum mechanics the usual rules for the composition of probabilities hold for complex probability amplitudes and not for the probabilities themselves, which are the absolute squares of these amplitudes. The formalism Jordan used to implement this insight was rooted in the theory of canonical transformations familiar from classical mechanics. Von Neumann showed that the peculiar behavior of probabilities in quantum mechanics is much more naturally captured in his new Hilbert space formalism and he discarded Jordan’s scaffolding.

**The Lecturer**

Michel Janssen is Professor in the Program in the History of Science, Technology, and Medicine at the University of Minnesota. He was a member of the editorial team of the Einstein Papers Project, then at Boston University. He has published extensively on the relativity and quantum revolutions of the early twentieth century. In 2012 was named a Fellow of the American Physical Society for his “path-breaking contributions to the history of early twentieth-century physics.”

To apply for the international summer school, participants need to submit an online **application form**. Deadline for the complete applications is June 20, 2014. A letter of admission will reach successful applicants via email by June 30, 2014.

There is no program fee. The Forum Scientiarum may provide participants with limited grants for covering part of their travel expenses and will assist participants finding inexpensive accommodation.

For further information please contact:

Marco Giovanelli

**marco.giovanelli[at]uni-tuebingen.de**