Energy

                   1. Introduction 

Energy is a scalar quantity. But all conserved quantities are not necessarily scalars. The total linear momentum and the total angular momentum (both vectors) of an isolated system are also conserved quantities. These laws can be derived from Newton’s laws of motion in mechanics. But their validity goes beyond mechanics. They are the basic conservation laws of nature in all domains, even in those where Newton’s laws may not be valid. Besides their great simplicity and generality, the conservation laws of nature are very useful in practice too. According to Einstein’s theory,  mass m is equivalent to energy E given by the relation E = m c², where c is speed of light in vacuum. In a nuclear process mass gets converted to energy (or vice-versa). It also tells that mass and energy are inter convertible. This is the energy which is released in a nuclear power generation and nuclear explosions. It often happens that we cannot solve the full dynamics of a complex problem involving different particles and forces. The conservation laws can still provide useful results. For example, we may not know the complicated forces that act during a collision of two automobiles; yet momentum conservation law enables us to bypass the complications and predict or rule out possible outcomes of the collision. In nuclear and elementary particle phenomena also, the conservation laws are important tools of analysis. Indeed, using the conservation laws of energy and momentum for β-decay, Wolfgang Pauli (1900-1958) correctly predicted in 1931 the existence of a new particle (now called neutrino) emitted in β-decay along with the electron.  

           Conservation of energy 

According to the conservation law Energy can neither be created nor be destroyed, it can be only converted from one form to another. Conservation laws have a deep connection

with symmetries of nature that you will explore

in more advanced courses in physics. For

example, an important observation is that the

laws of nature do not change with time! If you

perform an experiment in your laboratory today

and repeat the same experiment (on the same

objects under identical conditions) after a year,

the results are bound to be the same. It turns

out that this symmetry of nature with respect to

translation (i.e. displacement) in time is

equivalent to the law of conservation of energy.

Likewise, space is homogeneous and there is no

(intrinsically) preferred location in the universe.

To put it more clearly, the laws of nature are the

same everywhere in the universe. (Caution : the

phenomena may differ from place to place

because of differing conditions at different

locations. For example, the acceleration due to

gravity at the moon is one-sixth that at the earth,

but the law of gravitation is the same both on

the moon and the earth.) This symmetry of the

laws of nature with respect to translation in

space gives rise to conservation of linear

momentum. In the same way isotropy of space

(no intrinsically preferred direction in space)

underlies the law of conservation of angular

momentum. The conservation laws of charge and

other attributes of elementary particles can also

be related to certain abstract symmetries.

Symmetries of space and time and other abstract

symmetries play a central role in modern theories of fundamental forces in nature.