Symmetries and Asymmetries

El setiembre del año pasado, escribí por diversos motivos, en mi msn space, una entrada titulada: "Symmetries and Asymmetries", la escribí en ingles, porque creo que en español a veces no se me entiende, así que acompañado de varios artículos sobre el tema, me puse a hacer pequeños resúmenes. Ahora reescribo esas líneas, solo para recordar, lo inteligente que puedo ser al escribir....nah, me salió bonito, creo.

SYMMETRIES AND ASYMMETRIES

What is a symmetry? We can say that an object is symmetric (has a symmetry) if there is something you can do to it, so that, after you finish doing it, it looks exactly the same way it did before.

It’s possible to fit the definition of symmetry given for objects to our real space: a symmetry of a law of nature means that there is something we can do to a physical law which makes no difference and leaves everything unchanged in its effects. If we talk about symmetries, we need to mention the Theorem of E. Noether: invariances under a group of transformations implies the existence of conserved quantities.

The importance of these conserved quantities probably can be better summarized by the following observations of H. Weyl “As far as i see, all a priori statements in physics have their origin in symmetry”

Present day physics not only uses the existence of these symmetries to unravel the misteries of the universe, but also engaged itself in tackling more subtle questions, namely: what are the origins of these symmetries? Are they “fundamentals” or are they “derived”?.

Pierre Curie formulated the concept of broken symmetry in the following words: “C’est la dissymétrie qui crée le phénoméne” which when we translated means: “It is the broken symmetry which creates a lot of non-trivial physics”. It is an established fact that physics sistems which are initially uniform and time-independent possess a kind of self-organizing phenomena, that leads to ordered behaviour. The emergence of order (referred to as “symmetry breaking”) is often accompained by the appearence of spatially asymmetric patterns. Now we have two new words: Symmetry breaking and asymmetry.

Lorentz invariance (the one that is fundamental in special relativity) is broken in finite temperature field theory since the heat bath defines a privileged reference frame. Some discretes symetries (P, C and T, that are studied in relativistic quantum dynamics) or combinations thereof are violated in the microscopic world. It’s important to mention an asymmetry that is being studied lately, the barion asymmetry in the universe.

The word symmetry brings to our mind objects that are aesthetically appealing or the idea of a well-proportioned or armonious world, for that reason some people could find disappointing find asymmetries in the way to achieve symmetries. However, symmetries and asymmetries often coexist in nature....just as bad and good moments are parts of our daily life: They all have their right of being and without the hard times you would probably not appreciate the better ones to the right extend.