June 29, 2018 Friday
Bedtime Story
Pondering over Mach's Cryptic Verse
Strange enough, even if you look very
attentively at the words of Ernst Mach, they do not seem to be asking anything
wise or profound.
Please read those lines of Mach once again,
pause and give it some thought.
“Investigator must feel the need
of…knowledge of the immediate connections, say, of the masses of the universe.
There will hover before him as an ideal
insight into the principles of the whole matter.
From which accelerated and inertial motions
will result in the same way.”
There is some kind very vague reference of
‘masses of the universe’ (which itself sounds very ambiguous) with the Newton’s
concept of inertia related to inertia of accelerating bodies on planet Earth.
And yet, it is exactly such an ill-defined
statement of Ernst Mach, lacking both in mathematical rigor or logical depth,
that Einstein derived his explosive idea or at least, this is who the modest
man gives credit to.
Mach’s principle in modern physics can be
stated in several ways far better then he himself came up with.
I found the following two general
statements to be very decent generalizations of the Mach’s principle:
(a) Local physical laws are determined by
the large-scale structure of the universe
(b) Mass out there influences inertia here.
Yet in spite of Mach’s ideas, the origin of
inertia till date remains the most obscure subject in the theory of particles
and fields.
Mach’s principle though it gives a hint of
the origins of inertia, does not still fully explain its origins.
There are at least eleven ways in which
Mach’s Principle can be rephrased and restated.
It is an interesting exercise to go through
each of them to see how so disparately looking statements are in truth
reflections of the same idea.
Statement 1 – The universe, as represented
by the average motion of distant galaxies, does not appear to rotate relative
to local inertial frames.
Statement 2 – Newton’s gravitation constant
G is a dynamic field.
Statement 3- An isolated body in otherwise
empty space has no inertia.
Statement 4 – Local inertial frames are
affected by the cosmic motion and distribution of matter.
Statement 5 – The universe is spatially
closed.
Statement 6 – The total energy, angular and
linear momentum of the universe are zero.
Statement 7 – Inertial mass is affected by
global distribution of matter.
We shall consider the next four statements
of Mach’s principles 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.
Advertisements
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:
No comments:
Post a Comment