Insincere nature of Symmetry- I
29th July 2017


"It is only slightly overstating the case to say that physics is the study of symmetry.”

- P. W. Anderson

"The universe is NOT a universe of points, with time flowing along irrespective of points, but rather, this is a A UNIVERSE OF EVENTS, - everything that happens, happens at a certain place AND at a certain time."

- Lillian R. Lieber, The Einstein Theory of Relativity: A trip to the fourth dimension.

"Symmetry dictates interaction."

- Chen Ning Yang

    The definition of the symmetry is given as: the correspondence in size, form, and arrangement of parts on opposite sides of a plane, line, or point; regularity of form or arrangement in terms of like, reciprocal, or corresponding parts.

    The symmetry plays a crucial role when we interpret our surroundings.
Our interpretation itself, is based on the measurements made by our senses which essentially are our measurement tools. The optics (eyes) and acoustics (ears) play an important part in measuring distant information which is not in our close proximity, either in time or in space. The conventional symmetries which contribute to our aesthetics, themselves are heavily dependent on the information coming from our optical sensory inputs. We can also create apparatus which can perform more sophisticated measurements and discover new symmetries. Nevertheless, the results from conventional measurements either from human senses or the measuring apparatus, are restricted to the information obtained by the mechanism of electron-photon interactions.

    If we consider the definition provided above, the structures which are important for discrete measurement space or j-space are "point" and "form or arrangement". The measurement of the "point" is the most important measurement. Once the "point" is determined the "form or arrangement" can be constructed using the definition of the "point".

    The observer Obsc (v ~ c) measures the point. Next the macroscopic observer ObsM (v<<c) uses the definition of the "point" provided by the
Obsc, to establish "form or arrangement", which eventually leads to the perception of various symmetries. We must realize that a symmetry can not be described unless the observer ObsM can measure the boundary or the surface around a structure with complete precision. We call these measurements as PE1 measurements.

    The process of measuring boundary or surface is called, forming the circuit. If the measurements are made with complete precision then the circuit is completed.  In the following figure,
Obsc and ObsM are able to complete the circuits as the information content being measured is much smaller than that of true j-space.
    Let us say that the measurements made by the observer ObsM are of low information content. These measurements will be affected by the environment conditions such as temperature. The observer Obscan complete the circuit under certain environmental conditions, but as the environmental conditions are changed the circuit is broken. Therefore the observer may have been measuring the symmetry earlier, but change in the environmental conditions break the circuit as more information needs to be measured than earlier. This process is called the spontaneous symmetry breaking.

An example is the magnetization of ferromagnetic materials below Curie Temperature. Here the environmental condition being changed is the temperature. As the temperature is lowered the spatial symmetry is broken and magnetization is realized. The thermal noise once reduced, allows the measurement of the underlying exchange interaction which is a quantum phenomenon. The classical circuit definition measuring spatial symmetry, is no longer valid as the quantum phenomenon prevents the circuit from completing.

    There is always a possibility that the change in environment may not be severe enough to break the circuit, but may modify its nature
. In such cases different "form or arrangements" (~ different particles or phenomenon), invariant within the same symmetry, will be observed.

    Generally speaking, the symmetries are respected by a system until it is returned to its ground state or the vacuum state. In ground state the circuit no longer can be completed as the information which needs to be measured is massive and beyond
ObsM's capacity. Since the circuit can not be completed, the symmetry is spontaneously broken. Another example of spontaneous symmetry breaking is the symmetry breaking of Chiral Symmetry.

    We can say that if the phenomena associated with Thermodynamics or Statistical Mechanics are eliminated, the observed symmetry is likely to be spontaneously broken as the underlying phenomena of quantum nature are exposed. It does not mean that the symmetry does not exist. It is just that the measurements under new environment conditions provide much larger information landscape, of which the existing symmetries are an important part.
    Alternatively we can also say that as the entropy of the measurement system or equivalently that of observers
Obsc and ObsM, is increased, the measurements are made less precise. As the consequence, more symmetries are likely to exist for a higher entropy observer whether they are measured or not, hiding the true nature of the information space being measured. This is the insincere nature of the symmetry. 

We continue this discussion with explicitly broken symmetry next.
To be continued....

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