The concept of symmetry has been central to physical and cosmological thought since the emergence of natural philosophy. The notion that the properties of particles such as ‘atoms’ remain unchanged after being subjected to a variety of symmetry transformations or “operations” has been present since the 6th century BC (e.g. Greek natural philosophy, Pythagorians).

The two outstanding theoretical achievements of the 20th century, relativity, which describes cosmic behavior on the biggest of scales, and quantum mechanics, which treats energy and other physical entities as discrete units (quanta) at the subatomic scale, both involve notions of symmetry in a fundamental way. Since the early 20th century, a central goal of physics has been to combine relativity and quantum theory into an overarching ‘theory of everything’, capable to describe all physical phenomena.

Quantum theory explains electromagnetism and the strong and weak forces, but a quantum description of the remaining fundamental force, gravity, has not been achieved. After developing relativity, Albert Einstein sought a so-called ‘unified field’ theory, with a space-time geometry that could encompass all the fundamental forces, but his endeavor was unsuccessful. Other theorists have since attempted to merge general relativity with quantum theory, but the two approaches treat physical forces in fundamentally different ways. In quantum theory, forces arise from the interchange of certain elementary particles, not from the shape of space-time. Furthermore, quantum effects are thought to cause a serious distortion of space-time at an extremely small scale, the Planck length, which is much smaller than the size of elementary particles. This suggests that quantum gravity cannot be understood without investigating the behaviour of space-time at very small scales.

Although the connection between general relativity and quantum mechanics remains elusive, some progress toward a fully unified theory has been made. In the 1960s, the electroweak theory provided partial unification by demonstrating a common basis for electromagnetism and the weak force within quantum theory. Recent research suggests that superstring theory, in which elementary particles are represented not as mathematical points but as extremely small strings vibrating in 10 or more dimensions, shows promise for providing a framework for complete unification (including gravitation). Until confirmed by experimental results, however, superstring theory remains an untested hypothesis.

We invite frontline researchers and authors to submit original research and review papers that explore these and relevant themes.