June 02, 2018 Saturday
Bedtime Story
Conservation Laws and Symmetry
As I had mentioned earlier, there are
several conservation laws in physics that serve as the fundamental laws of
nature and explain why the Universe is the way it is and why certain things are
simply not possible in nature.
Let me go in slightly more detail (I really
cannot go into complete detail for two reasons – one that I am not qualified
enough either in physics or in mathematics to do so {which is a pity} and
secondly perhaps it is beyond the scope of bedtime stories though this second
reason is not very convincing even to the storytelling chimpanzee himself for
nothing ought to be sacred or beyond the scope of any bedtime story) into the
story of conservation laws.
Conservation laws have a direct bearing on
the subject of three-body problem (which is a sub set of n-body problem) which
according to Ada Lovelace would be solvable by the Analytical Engine.
Conservation laws are fascinating not just
because they are fundamental to our understanding of the nature, but they bring
into play the notion of symmetry and a very interesting mathematician by the
name of Emmy Noether.
Perhaps I should elaborate little more on
Conservation laws before we proceed to look at Emmy Noether and her work
related to symmetry and conservation laws.
First let us see how the concept of
symmetry is related to Conservation laws and what the word symmetry means in
physics.
Conservation Law requires that for any
amount of conserved quantity at a point to change (may it be electric charge,
energy or angular momentum), there has to be a flow or a flux of that quantity
either into or out of that point.
This, at the very first look, looks so
obvious that one may even wonder why it should be even enunciated as a formal
law.
Well in science and in mathematics, great
effort is made to formalize the basic truths of nature into laws, as it is that
from such basic laws of nature that great complexity arises.
Let us consider a simple example of a
certain amount of electric charge at a specific volume A.
The amount of electric charge will never
change unless there is a flow of electric current either into or away from this
volume.
Since such a change would involve a
continuous and local change, such a type of conservation law is known as
Lorentz invariant.
Hendrik Lorentz, the Dutch physicist and
the first person to head the Department of Theoretical Physics of the
University of Leiden in 1877, is fundamental to relativistic physics.
The concept of symmetry that has been named
after him, that is the Lorentz symmetry which is also often known as Lorentz
covariance, implies that the laws of physics stay the same for all observers
that are moving with respect to one another within an inertial frame.
The other way of interpreting Lorentz
symmetry is this – the experimental results (such as those performed in the
particle accelerators of CERN and other places) are independent of the
orientation or the boost velocity of the laboratory through space.
We shall carry on this interesting story in
the nights to come.
Stay tuned to the voice of an average story storytelling
chimpanzee or login at http://panarrans.blogspot.com
Good night Mon Ami and my fellow cousin ape.
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Another great educator and a teacher that I am aware of is
Professor Subhashish Chattopadhyay in Bangalore, India.
While I narrate stories, Professor Subhashish an electronic
engineer and a former professor at BARC, does and teaches real mathematics and
physics.
He started the participation of Indian students at the
International Physics Olympiad.
Do visit him here:
All his books can be downloaded for free through this link:
For edutainment and English education of your children, I
recommend this large collection of Halloween Songs for Kids:
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