July 17, 2018 Tuesday
Bedtime Story
Abstract from “More is different – Broken symmetry and the nature of the hierarchical structure of science” - Part 1
Such is the hold of the study of symmetry
over the fundamental laws of nature that the American physicist P. W. Anderson
or Philip Warren Anderson in a paper titled “More is different – Broken
symmetry and the nature of the hierarchical structure of science” published in
the journal Science in August of 1972 had this to say:
“There are at least three inferences to be
drawn from this.
One is that symmetry is of great importance
in physics.
By symmetry we mean the existence of
different viewpoints from which the system appears the same.
It is only slightly overstating the case to
say that physics is the study of symmetry.
The first demonstration of the power of
this idea may have been by Newton, who may have asked himself the question:
What if the matter here in my hand obeys the same laws as that up in the sky –
that is, what if space and matter are homogenous and isotropic?
The second inference is that the internal
structure of a piece of matter need not be symmetrical even if the total state
of it is.
I would challenge you to start from the
fundamental laws of quantum mechanics and predict the ammonia inversion and its
easily observable properties without going through the stage of using the
unsymmetrical pyramidal structure, even though no ‘state’ ever has that
structure.
It is fascinating that it was not until a
couple of decades ago that nuclear physicists stopped thinking of the nucleus
as featureless, symmetrical little ball and realized that while it never really
has a dipole moment, it can become football-shaped or plate-shaped.
This has observable consequences in the
reactions and excitation spectra that are studied in nuclear physics, even
though it is much more difficult to demonstrate directly than the ammonia
inversion.
In
my opinion, whether or not one calls this intensive research, it is as
fundamental in nature as many things one might so label.
But it needed no new knowledge of
fundamental laws and would have been extremely difficult to derive
synthetically from those laws; it was simply an inspiration, based, to be sure,
on everyday intuition, which suddenly fitted everything together.
The basic reason why this result would have
been difficult to derive is an important one for our further thinking.
If the nucleus is sufficiently small there
is no real way to define its shape rigorously: Three of four or ten particles
whirling about each other do not define a rotating “plate” or “football.”
It is only as the nucleus is considered to
be a many-body system – in what is often called the N
∞ limit – that such behavior is rigorously
definable.
We say to ourselves: A macroscopic body of
that shape would have such-and-such a spectrum of rotational and vibrational
excitations, completely different in nature from those which would characterize
a featureless system.”
We shall continue with the seminal paper of
the physicist P. W. Anderson 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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