What are symmetry and symmetry breaking?

[vincentryan]

hi

What is symmetry? hi explain symmetry and symmetry breaking in details with example


Regards
Ryan

 

[mjsd]

hi

What is symmetry? hi explain symmetry and symmetry breaking in details with example


Regards
Ryan

symmetry? you can think of it in many different ways. loosely speaking, it can be regarded as (an object) having a property when certain operation/action is done to the object, the object remain unchanged/invariant. A simple example is say a circle, you can rotate it by any angle in clockwise or anti-clockwise direction about its centre and it looks the same. So we say the circle has a rotational symmetry about certain axis. Precise definition of a symmetry can be defined by the language of group theory which is itself motivated by these simple observations.


symmetry breaking? well... it means taking away those properties so that when the object is acted upon, the original object is no long the same as before the operation. A simple example: rotation by 120 deg about the centroid of an equilateral triangle is a symmetry. But we can break this symmetry by identifying that each of the three vertices as distinct (eg. color them differently). If so, that rotational symmetry is broken because rotating by 120 deg no longer leaves the triangle looking the same. And now you need to rotate it by 360 deg or 0 deg etc. for it to be invariant.

 

[sir-pinski]

Hi Ryan,

Symmetry refers to a fundamental principle in physics and mathematics that describes the balance and regularity of an object or system. It is the property of an object or system that remains unchanged when it undergoes a transformation, such as rotation, reflection, or translation. In simpler terms, symmetry is the quality of being made up of exactly similar parts facing each other or arranged around an axis.

Symmetry breaking, on the other hand, refers to the process in which the symmetry of a system is disrupted or broken, resulting in a state that is no longer symmetrical. This can happen due to external influences or internal dynamics of the system itself. This phenomenon is often observed in nature, where seemingly symmetrical objects or systems exhibit broken symmetry.

An example of symmetry breaking can be seen in the formation of snowflakes. Snowflakes are formed when water vapor freezes around a tiny dust particle in the atmosphere. Due to the random movement of air molecules, each snowflake crystal grows in a unique way, resulting in a vast variety of shapes and patterns. While the basic structure of a snowflake is symmetrical, the random factors involved in its formation lead to broken symmetry, resulting in the intricate and diverse shapes of snowflakes we observe.

In physics, symmetry breaking is an essential concept in understanding the behavior of particles at the subatomic level. The Standard Model of particle physics, which describes the fundamental building blocks of matter and their interactions, is based on the principle of symmetry. However, scientists have observed that this symmetry is broken in certain situations, leading to the discovery of new particles and phenomena.

In summary, symmetry and symmetry breaking are two interconnected concepts that are crucial in understanding the natural world and the laws that govern it. While symmetry represents the fundamental balance and regularity in objects and systems, symmetry breaking serves as a tool for exploring the complexities and diversity of nature. I hope this explanation helps. Let me know if you have any further questions.