Parity Symmetry, Broken Symmetries and their Physical Significance

^{Image credit: Shutterstock}

^{By Amal Pushp, Affiliate Physicist at the Resonance Science Foundation}  

The mathematical property named “symmetry” manifests itself essentially at all scales in nature. From the petals of flowers down to the domain of atoms and molecules, symmetry plays a crucial role in shaping the structure of matter and unveiling the nature of physical reality. The definition of symmetry can change depending on the situation for example, the geometry of an object and its invariance under certain rotations or reflections might give a general mathematical idea of its symmetry but in physics, symmetry specifically concerns a change in a particular physical process or interaction. A physical process is said to be symmetric with respect to a change if it remains invariant despite the induced change.    

There exist several types of symmetry in nature, and when it comes to particle physics, we are primarily interested in something called parity symmetry. Parity can be described as an inversion in the sign of a spatial coordinate, for example x changes to -x. In general, it specifies whether a property associated with a physical phenomenon change or doesn’t change when we look at its mirror image. Essentially, all fundamental physical forces associated with elementary particles remain invariant under parity transformation, or in other words they display parity symmetry. However, as an exception, weak nuclear force violates this symmetry. 

Now it is important to realize that in nature, asymmetry is manifested as equally as symmetry and there are several instances in the universe that exhibit this. For example, it is a known fact that our universe is dominated by matter over antimatter although symmetric considerations should have led to equal amounts of both, a scenario typically referred to as the baryon asymmetry. This is yet one of the major unsolved problems of physics. Look at a previous RSF article that I wrote for more details about the same.  

Furthermore, a crucial aspect related to symmetry that is worth discussing here is the concept of symmetry breaking or in other words broken symmetry. Essentially symmetry can be categorized into three types depending on specific situations, namely: exact, approximate, or broken. From inference, it can be understood that the symmetries that are exact are valid under all circumstances and those that are approximate are valid but under certain constraints. The last one i.e., broken symmetry is specifically of interest to particle physicists since it is fundamental for understanding the various aspects of the standard model. Explicitly, a broken symmetry can be understood from the following diagram. 

Explanatory diagram showing how symmetry breaking works. At a high enough energy level, a ball settled in the center (lowest point), and the result has symmetry. At lower energy levels, the center becomes unstable, and the ball rolls to a lower point - but in doing so, it settles on an (arbitrary) position, and the result is that symmetry is broken - the resulting position is not symmetrical. Image and Description: Wikimedia Commons 

For a more elaborate perspective on broken symmetry, consider a particular phenomenon that occurs under certain conditions in a particular medium. For the phenomenon to take place smoothly, the symmetry of the medium needs to be broken down to the symmetry of the phenomenon by an external agency. Thus, symmetry breaking essentially corresponds to a situation wherein the original symmetry has been lowered down to a condition that possesses less symmetry. For more details on symmetry breaking and its types, the reader is advised to refer to this link.  

Recently there has been a significant advance in discoveries related to symmetry breaking as well as parity symmetry violation in the universe. We’ll briefly discuss one case for each of the two. Starting with the former, a group of researchers from the Max Born Institute teamed up with researchers from the University of Duisberg-Essen to display for the first time a new way to probe coherent phonons, that are essentially quanta of acoustic vibrations, using symmetry breaking [1]. This work opens a new dimension of research in opto-acoustics such as determining novel excitation properties of a crystal among others.  

We already looked at what parity symmetry means and why it is important for physics. Now a violation of this symmetry corresponds to a situation in the early universe wherein the laws of physics were essentially different from today and which in turn has strong implications for the evolution of the universe. A recent publication in Physical Review Letters (PRL) aims to search for parity violation using a model of galaxies [2]. The motivation behind this research is to figure out whether the universe prefers left-handed or right-handed shapes which is essentially an analogy drawn for simplicity (our left hand and right hand are mirror images). Even a small hint of parity violation would suggest that the universe does indeed have a fondness for either of the two. The research team carried out their mathematical analysis using what is known as a correlation function, in this case, a 4-point correlation function (4PCF). In simple terms, a correlation function in astronomy describes the distribution of galaxies in the universe.  

Succinctly, although the current research didn’t clarify whether the preference is towards left-handed or right-handed shapes it was discovered that the universe indeed prefers one shape over the other, thus confirming a violation of parity symmetry. For more information about the work and its implications, look at this article.  

RSF in Perspective: 

A significant number of modern research probes have shown that the standard model of particle physics is not accurate enough to describe most of the physical phenomena accurately. Even in the new paper by Cahn et al, they have anticipated a model beyond the standard one that could specifically explain the matter-antimatter asymmetry. This is one of the explicit cases that bring forward the inconsistency within the standard model. Previously, we have also looked at other pieces of research that tend to navigate us in this direction, for instance, look at this RSF article that considers one such scenario.  

It is thus high time for us to now look at novel models that have a good foundational base with respect to the theoretical standards as well as has the potential to explain the empirical results from a first-principles analysis. Physicist Nassim Haramein’s generalized holographic model is one of them. The goal is to reformulate the fundamental principles and unify them into a coherent structure that would yield accurate and empirically testable results, for example, the values of various coupling constants.  

The new paper by Haramein et al entitled “Scale Invariant Unification of Forces, Fields & Particles in a Quantum Vacuum Plasma” which would be published shortly, aims to provide answers to some of the problems that the research described in this article poses and many more general issues that lie at the heart of fundamental physics.  

References 

[1] Azize Koç et al, Quantum pathways of carrier and coherent phonon excitation in bismuth, Physical Review B (2023). DOI: 10.1103/PhysRevB.107.L180303 

[2] Robert N. Cahn et al, Test for Cosmological Parity Violation Using the 3D Distribution of Galaxies, Physical Review Letters (2023). DOI: 10.1103/PhysRevLett.130.201002