Symmetry arguments and the totalitarian principle in the physics of liquid crystals and other condensed matter systems

ABSTRACT

Symmetry arguments constitute one of the most powerful tools of physics. As shown by Emmy Noether, continuous symmetries correspond to physical conservation laws. In analogy with dimensional arguments, symmetry arguments can also be used to predict the behaviour of physical systems. Mistaking symmetries, on the other hand, can lead to grave errors. In this paper, we describe and give examples of certain types of symmetry arguments which can be useful in general and, in particular, in the field of liquid crystals. In using symmetry arguments to predict physical phenomena, the totalitarian principle, made popular by Murray Gell-Mann, is often used, either explicitly or implicitly. We discuss the totalitarian principle, its origins, history and philosophical implications. Our goal is to outline a simple symmetry-based procedure which may be useful in gaining insights into and describing the behaviour of complex physical systems such as liquid crystals.

GRAPHICAL ABSTRACT

KEYWORDS:

• Symmetry
• condensed matter
• liquid crystal
• totalitarian

Acknowledgments

We are grateful to the organizers of ILCC2022 for providing the opportunity to present this work.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1. meta – Greek origin: ‘after, behind’. In the modern sense, this is interpreted as ‘higher than, transcending’. We note that current usage of ‘meta’ as meaning ‘beyond’ stems from a misinterpretation, by Latin writers, of a reference to the customary ordering of texts.

2. We note here that ‘everything’ here should be understood in the general and not the specific sense. For example, there is a symmetry allowed radial vector field around a spherical star, which allows the orbiting of satellites. The orbiting of objects in general is thus not forbidden, hence, according to TP, such orbiting must happen. However, although the orbiting of specific objects, say of a specific blue teapot, is not forbidden, it is not mandated by TP.

3. The acceleration of a ball in a gravitational field is allowed by symmetry, but will not be observed if the ball is constrained by the floor to remain at rest.

4. They can, however, represent wind blowing towards the centre of the rotating plate from both directions along the axis, and also wind, blowing radially perpendicular to the axis.

Additional information

Funding

This work was supported by the Office of Naval Research through the MURI on Photomechanical Material Systems (ONR N00014-18-1-2624). One of us (P.P-M) acknowledges inspiring discussions with Shlomo Alexander and grateful for valuable comments from Michael Freeman.