Symmetry is the language of perfection: Carlo Rovelli

Before we can discuss symmetry in the context of Physics, let’s talk about symmetries in general. So first of all, what is symmetry? Imagine a friend standing in front of you, holding a perfectly round red ball in his hand. Then you close your eyes, and your friend performs a transformation of the ball. Afterwards, you open your eyes again. If he rotates the ball while your eyes are closed, it is impossible for you to find out that he did anything at all. Hence, rotations are symmetries of the ball. In contrast, if he holds a cube, only very special rotations can be done without you noticing it. The profound and common objects that exhibit symmetries of one form or another that we encounter in our lives include the human face (approximate mirror symmetry), snowflakes (intricate radial symmetry), flowers like roses, sunflowers, and daisies (radial symmetry), and insects like butterflies, which exhibit bilateral symmetry in their wing patterns, etc. These are just a few examples, but symmetry is pervasive in the design and objects of nature.
Now let’s come to the symmetries in physics. In physics, all transformations which, in principle, change something but lead to an indistinguishable result are symmetries. Formulated differently, symmetry takes us from one state to a different one, which, however, happens to have the same properties. It’s important to note that, with this definition, symmetries are observable properties of objects or systems.
Symmetries play an important role in elementary particle physics, in particular, and physics in general, partly because of their relation with conservation laws and partly because they permit one to make some progress when a complete dynamical theory is not yet available. Arguably the most important example of symmetry in physics is that of the speed of light, which has the same value in all frames of reference. Similarly, crystals form a striking and most profound example of symmetry at an elementary level. The orbits of the stars, as believed by the Greeks, were assumed to be circular because such orbits exhibit symmetrical trajectories. Symmetry principles, such as rotational symmetry, translational symmetry, time symmetry, and gauge symmetry, lead to the laws of conservation of angular momentum, linear momentum, energy, and charge. These conservation laws have a very profound, deep, and fundamental understanding of physical systems. So let’s talk about some fundamental laws and theories that have played a gigantic role in our understanding of the universe and their relationship with symmetry.
Law of Gravitation: Formulated by Isaac Newton in the 17th century, this law explains the interaction between two point masses and states that the interaction is directly proportional to the product of point masses and inversely proportional to the square of the distance between them. The law exhibits spatial translation and rotational symmetry.
Laws of Electromagnetism: They are the set of four equations formulated by James Clarke Maxwell in the 19th century that describe the behaviour of electric and magnetic fields. These laws have made possible the invention of computers, modern gadgets, etc. The symmetries that they exhibit under various transformations include time-reversal symmetry, charge conjugation symmetry, space inversion, and gauge symmetry.
General Theory of Relativity: Formulated by Albert Einstein in 1915, it is an extension of his earlier theory on space-time and explains gravity as a curvature of spacetime caused by the distribution of matter and energy within it. It exhibits Lorentz local invariance, spacetime translation, and other symmetries.
Standard Model of Particle Physics: Formulated over a span of decades, it is the physicist’s best bet on the nature and description of fundamental particles and the three basic interactions of nature. This model exhibits gauge symmetries, chiral symmetry, CP symmetry, and CPT invariance.
String Theory: It is a comprehensive theoretical framework in modern theoretical physics that tries to reconcile gravity and quantum mechanics. It incorporates supersymmetry, duality, gauge, and conformal symmetry.
In short, as our understanding of symmetries continues to evolve, they remain essential tools for uncovering the underlying structure of the universe and our knowledge of physics.
Postscript: Whether this corollary to Occam’s Razor principle will continue to shape our understanding of Physical theories and laws will have to be seen.
Nasir Rather is a student of Theoretical Physics. He can be reached at [email protected]

Nasir Rather