Through the looking-glass, and what relativists can find there

In 1965, Jean-Marc Lévy-Leblond discovers a new non-relativistic limit of the Poincaré group, obtained by sending the speed of light to zero, while the Galilean group is obtained in the limit of infinite speed of light. At the level of the causal structure of the spacetime, this limit contracts light cones on the time axis and any motion in the spacelike directions becomes non-causal. In his paper Missed opportunities [1], Freeman Dyson summarized this work in the following terms:

The "group C" describes a universe in which space is absolute, in contrast to the Galilei group G which has time absolute. It was discovered by Lévy-Leblond [2] and called by him the Carroll group. In the Carroll universe all objects have zero velocity although they may have nonzero momentum. Lewis Carroll was a pure mathematician who had already foreseen this possibility in 1871 (in Through the looking-glass, and what Alice found there) :

"Well, in our country," said Alice, still panting a little, "you’d generally get to somewhere else — if you run very fast for a long time, as we’ve been doing."
"A slow sort of country," said the Queen, "Now, here, you see, it takes all the running you can do, to keep in the same place."

But his mathematical colleagues once again missed an opportunity by failing to take him seriously.

Since this pionneering work, Carrollian physics has been playing a key role in several research directions, including fluid/gravity and holographic correspondences, asymptotically flat spacetimes at null infinity and the related BMS symmetries, cosmology and geometries of null hypersurfaces such as black hole horizons. The main purpose of the CARROLL WORKSHOPs is to gather people who are currently participating to this research endeavor around the world and share our interest in Carrollian physics!

The first CARROLL WORKSHOP was hold in Vienna in February 2022. The second edition will take place in Mons from the 12th to the 16th of September 2022. Anyone engaged in the fascinating research effort is most welcome to join us to have a look through the Carrollian looking-glass and see what we can find there!

We are also excited to announce that this second edition will also welcome, in addition to research talks on recent results in Carrollian physics, a special focus on Carrollian geometry understood as initial/asymptotic data for the evolution problem in GR with several invited talks by mathematical relativists.

Download the poster!

Original illustration of the first edition of Lewis Carroll's Through The Looking-Glass And What Alice Found There (1871).
"Alice In The Looking-Glass House" illustrated by Sir John Tenniel (1820–1914).

Organizing comittee

Local organizers: Nicolas BOULANGER, Andrea CAMPOLEONI, Yannick HERFRAY (UMONS);

Partner organizers: Laura DONNAY (TU Wien, SISSA), Adrien FIORUCCI, Romain RUZZICONI (TU Wien).

The workshop is organised with the support of the research unit Physics of the Universe, Fields and Gravitation of the University of Mons.

We also gratefully acknowledge the support of the following sponsors:
Fonds de la Recherche Scientifique (Belgium) | Université de Mons (Belgium) | Technische Universität Wien (Austria) | Fonds zur Förderung der wissenschaftlichen Forschung (Austria)

Header picture: Original illustration of the first edition of Lewis Carroll's Through The Looking-Glass And What Alice Found There (1871). "The Red Queen's Race" illustrated by Sir John Tenniel (1820–1914).

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