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## Symmetry in Physical Laws: PART II : Conservation and inner conversion of mass-energy

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# What is it?

In practical, we see that if we burn a coal, it emits heat & gives ash. Scientifically, the coal (matter) is converted into heat (energy) and precipitate (matter). This is a balance conversion that matter converts into energy. Similarly, we can generate a lot of energy after nuclear fission, in which also matter is converted into energy.

In inverse, similarly, energy can also be converted into matter. Physics’ most famous equation E= mc² given by Einstein also says the same. E (energy) is directly related to m (mass).

## Statement of Conservation of Mass(Matter)

Matter can never be created or destroyed, but it can convert itself into several other forms of either matter or energy or both.

## Statement of Conservation of Energy

Energy can never be created or destroyed, but it can convert itself to other forms of matter & energy.

## Statement of Conservation of Mass-Energy

One can easily regard this as a Symmetry operation, in which Energy ↔ Matter. Usually you can say, Matter (mass) and Energy both are conserved with their inner-conversions and the total value of mass+energy is a constant, since origin of universe.

The mass and energy can never be produced or destroyed — but they can be converted into one form to other.

# What is it?

The word symmetry commonly used in physics has a special meaning. A picture is symmetrical if one side is somehow the same as the other side. Precisely, a thing is symmetrical if one can subject it to a certain operation and it appears exactly the same after the operation.

For Example If we look at a base that is left and right symmetrical, then turn it 180° around the vertical axis it looks the same.

Newton’s laws of motion donot change when the coordinates are moved from one place to other i.e., translated. This is equally true for all other laws. Therefore, we can say that the laws of physics are symmetrical for translational displacements.

The same is true for rotational displacement. Not only Newton’s law, but all the other laws of physics known so far have the two properties which we call invariance (or Symmetry) under translation and rotation of axes.

On the basis of these properties a new mathematical technique has been developed for writing and using physical laws. A very powerful mathematical machinery has been devised called Vector analysis and in fact this is the symmetry of physical laws.

## What I shall discuss now?

### I shall discuss SYMMETRY OPERATIONS & THEIR CONSERVATION !

There are following main symmetry operations in physical laws:
Conservation of Mass-Energy
• Conservation of Momentum
Conservation of Angular Momentum
• Conservation of Electric Charge
• Conservation of Baryon Number
• Conservation of Lepton Number
• Conservation of Strangeness
• Conservation of Hypercharge
• Conservation of Iso-spin
• Conservation of Charge Conjugation
Conservation of Parity.

In this very first post on Symmetry, I shall discuss the last twos:

#### A. Charge Conjugation (C) & its Conservation:–

Charge conjugation C is the operation of changing
• a particle to its anti-particle & vice-versa,
• Positive into negative etc..

For Example:-
• C (π+)= π-
• C (+x²+5x-3) = 3-x²-5x
and so on…

In modern physics, the strong & electromagnetic interactions are symmetrical wrt Charge Conjugation but weak interactions are not symmetrical.

#### B. Parity(P) & its conservation:

The parity operation P is reflection of all coordinates through the origin. Thus
P(r)=-r
where r is the position vector of coordinates.

The wave function (ψ) of elementery particle generally have well defined symmetry under parity operation. Thus it is found that,
P|ψ(p)|= ψ(p)
Here ψ(p) indicates the wave function of particle p.