# Working Groups

You can choose to join one of the groups listed below. No registration is necessary.

Time: Tuesday – Friday, 14:00 – 15:30.

### Multi-Time Wave-Functions

Organizers: Matthias Lienert and Lukas Nickel.

Multi-time wave functions provide a straightforward extension of the Schrödinger picture to the relativistic domain. Instead of a wave function $\varphi(\mathbf{x}_1,...,\mathbf{x}_N,t)$, $\mathbf{x}_i \in \mathbb{R}^3$, as usual for $N$ non-relativistic particles, one considers a wave function $\psi(x_1,...,x_N)$ with $x_i = (t_i,\mathbf{x}_i) \in \mathbb{R}^4$, i.e. with space-time coordinates for each particle. In this way, one can achieve a manifestly covariant account of quantum physics on the wave function level. Multi-time wave functions furthermore seem necessary to embed wave function collapse into a space-time setting.

In this working group, we will carefully introduce the concept of a multi-time wave function, provide the necessary physical and mathematical background, as well as focus on the following aspects:

• use of multi-time wave functions in realistic relativistic quantum theories,
• multi-time formulation of quantum field theory,
• meaning of interaction for multi-time wave functions, new possibilities for wave equations.

Literature

General Overview

M. Lienert. Interacting relativistic quantum dynamics in the multi-time formalism, PhD thesis (2015). (Chaps. 1 and 2).

Historical References

P. A. M. Dirac. Relativistic Quantum Mechanics. Proc. R. Soc. Lond. A, 136:453–464 (1932).

S. Tomonaga. On a Relativistically Invariant Formulation of the Quantum Theory of Wave Fields. Prog. Theor. Phys. 1:27–42 (1946).

Research Articles

S. Petrat and R. Tumulka. Multi-Time Schrödinger Equations Cannot Contain Interaction Potentials. J. Math. Phys., 55(032302) (2014).

S. Petrat and R. Tumulka. Multi-Time Wave Functions for Quantum Field Theory. Ann. Phys., 345:17–54 (2014).

### Shape Space Physics: Classical and Quantum

Organizers: Niels Linnemann, Sahand Tokasi, and Antonio Vassallo.

The group will focus on the relational framework for mechanics originally proposed by Julian Barbour and Bruno Bertotti.

We will start by reviewing the motivations for adopting a Leibnizian/Machian stance on space-time metaphysics, and we will show how these ideas can be implemented in a fully relational classical theory of particles. More precisely, we will analyze the transition from Newtonian dynamics, defined over standard configuration space, to the “best-matched” dynamics defined over shape space, and discuss the sense in which this new dynamics dispenses with Newtonian backgrounds. A special emphasis will be placed on the notion of shape space and its mathematical characterization in terms of a Riemannian manifold equipped with a special metric.

We will then continue by tackling the problem of shape space quantization. We will point out that a Schröndiger-like dynamics can be quite easily defined in this context, and we will thoroughly discuss the meaning of the wave function defined over shape space.

Finally, we will discuss shape dynamics, that is, the theory that applies Barbour and Bertotti’s framework to gravitational physics. In particular, we will consider the question whether shape dynamics is a theory “dual” to general relativity, and the possible philosophical implications of this duality for long-standing conceptual issues such as the problem of time.

J. Barbour, B. Bertotti – « Mach’s principle and the structure of dynamical theories », Proceedings of the Royal Society A 382, pp. 295-306 (1982).

O. Pooley, H. Brown – « Relationalism rehabilitated? I: Classical mechanics », British Journal for the Philosophy of Science 53, pp. 183-204 (2002).

F. Mercati – « A shape dynamics tutorial », (2014).

J. Barbour – « Relational concepts of space and time », British Journal for the Philosophy of Science 33, pp. 251-274 (1982).

S. Gryb, K. Thébault – “Time remains”, British Journal for the Philosophy of Science doi: 10.1093/bjps/axv009, (2015).

### Quantum Non-Locality and Relativity

Organizers: Mario Hubert and Paula Reichert.

Quantum theory and relativity theory are the two most fundamental physical theories we have today. However, they seem to be incompatible. There is a famous quote by John Bell from 1984 (from his paper « Speakable and unspeakable in quantum theory ») capturing this issue and addressing the conflict which essentially still persists in physical theory today:

For me then this is the real problem with quantum theory: the apparently essential conflict between any sharp formulation [of quantum theory] and fundamental relativity. That is to say, we have an apparent incompatibility, at the deepest level, between the two fundamental pillars of contemporary theory.

In this working group, we want to derive a sharp formulation of this problem, or conflict, before presenting possibles ways out of it. This means we will discuss the EPR-argument and Bell’ inequalities, which together show that quantum mechanics is a non-local theory. We will then analyze the tension between non-locality and special relativity, both on an operational and on a fundamental level. That is, we will enlighten the difference between relativity as a fundamental concept and relativity obtained at an observational level and discuss faster-than-light signaling as well as superluminal matter transport. In the end, we will turn to different attempts to reconcile non-locality and relativity, both in Bohmian mechanics and spontaneous collapse theories.

J. S. Bell: Bertlmann’s socks and the nature of reality. Journal de Physique, Colloque C2, supple. au numero 3, Tome 42 (1981), pp C2 41-61.

T. Maudlin. Non-local correlations in quantum theory: how the trick might be done. In W. L. Craig and Q. Smith, editors, Einstein, Relativity and Absolute Simultaneity, pages 156–179. Abingdon: Routledge, 2008.

T. Maudlin. Quantum Non-Locality and Relativity: Metaphysical Intimations of Modern Physics. Chichester, UK: Wiley-Blackwell, 3rd edition, 2011.
(Chaps. 3, 4, and 7)

S. Goldstein et al. (2011) Bell’s theorem. Scholarpedia, 6(10):8378.

T. Maudlin. Quantum Non-Locality and Relativity: Metaphysical Intimations of Modern Physics. Chichester, UK: Wiley-Blackwell, 3rd edition, 2011.