Next week, FYP! in collaboration with FYFD is bringing you an exclusive Tumblr series on Pilot wave hydrodynamics. There will be a new post on FYP! and FYFD all through next week (Jan 8 – 12) exploring pilot wave hydrodynamics.

This has been the topic of spectacular experimental investigations and revelations (and controversies too) in Fluid Dynamics & Quantum Mechanics in recent times.

On Monday, we begin this journey in the labs of Michael Faraday and Chladni; And then embark on an exciting adventure through decades of research to arrive at where we are today.

When one stumbles upon the words ‘Discretized solution’, one is inclined to think of Quantum Mechanics. In quantum mechanics, the following are fundamentally discrete:

Electric charge

Weak hypercharge

Colour charge

Baryon number

Lepton number

Spin

BUT not energy. One only finds discrete spectra in bound states or where there are boundary conditions.

Discrete spectra and Boundary conditions

Consider a string that is clamped at x = 0 and x= L undergoing traverse vibrations. And you would like to know the motion of the string.

Maybe you know a priori that the solutions are sinusoids but you have no information on its wave number.

So you start trying out every single possibility of the wave number.

The important thing to understand here is that If there weren’t any boundary conditions that was imposed on the string then all possible sinusoidal wave would be a solution to the problem.

But the existence of a boundary condition ruins it.

This is the case with energy as well.

If
you have an electron in a hydrogen atom, there are only specific energy
levels it can be observed to occupy when its energy is measured.

But
if the electron is unbound because its energy exceeds the ionization
energy of the atom, then it’s in a scattering state and its energy and
angular momentum have continuous spectra.

Amalie Emmy Noether was a German mathematician known for her landmark contributions to abstract algebra and theoretical physics. And noether’s theorem is one of the most beautiful equation in all of theoretical physics.

The theorem explains the connection between symmetry and conservation laws.

It is remarkably surprising that there are a lot of people who are not aware of Noether’s contribution to physics.

The zeroth law of thermodynamics states that if two thermodynamic
systems are each in thermal equilibrium with a third, then they are in
thermal equilibrium with each other. Accordingly, thermal equilibrium
between systems is a transitive relation.

You may know that a pyramid has 4 faces ( excluding the base ) and the pyramid of Giza has been the popular exemplar for a pyramid.

But, the great pyramid has 8 faces ( excluding the base ), not 4!!

PC: The History Channel

In his book The Egyptian Pyramids: A Comprehensive, Illustrated Reference, J.P. Lepre wrote:

One
very unusual feature of the Great Pyramid is a concavity of the core
that makes the monument an eight-sided figure, rather than four-sided
like every other Egyptian pyramid. That is to say, that its four sides
are hollowed in or indented along their central lines, from base to
peak.

This concavity divides each of the apparent four sides in half,
creating a very special and unusual eight-sided pyramid; and it is
executed to such an extraordinary degree of precision as to enter the
realm of the uncanny. For, viewed from any ground position or distance,
this concavity is quite invisible to the naked eye.

The hollowing-in can
be noticed only from the air, and only at certain times of the day.
This explains why virtually every available photograph of the Great
Pyramid does not show the hollowing-in phenomenon, and why the concavity
was never discovered until the age of aviation.

It was discovered quite
by accident in 1940, when a British Air Force pilot, P. Groves, was
flying over the pyramid. He happened to notice the concavity and
captured it in the now-famous photograph. [p. 65]

Satellite image of the Great Pyramid.

Were the pyramids built this way on purpose or did it turn out this way over time is something that still requires a much deeper investigation.

One of my friends shared with me this gif of a butterfly getting caught in the front wing vortex of the car. The purpose of the vortex is to deflect the air flow from the front wing preventing its interaction with the front tire thereby reducing drag.

But how a butterfly got caught in this flow is beyond me. RIP butterfly.

** Check out our mini-series ‘Up up and away’ where we explored the physics of stalls, boundary layers, and F1 cars if this post fascinated you. Happy Thanksgiving!

Meet SAW (or Single Actuator Wave-like robot). A bioinspired robot that can move or swim forward and backward by producing a continuously advancing wave.