#classical mechanics

But idk how to resttt

So here's what I will do instead:

✨ Sem 3 prep

☞ Classical Mechanics II

☞ Solid State Physics

☞ Mathematics III

☞ Chemistry (idfk what is the syllabus it isn't mentioned on the website and idk who is the prof someone help me 😭😭)

☞ Optics

✨ Learn Python (and hopefully create some projects using it and inculcating physics into it)

✨ Start MCU

✨ Start doing the basics of my ISL internship (idk anything about it I am so scared wtff)

✨ Read more research papers and interact with professors more!

Physics Art Notebooks

... from original geometrical drawings on black paper.

Original - A4, colored pencils on black paper - printed to an A5 notebook (70 sheets, dotted)

Two different drawings on front and back side, in this case:

1) Theory of the gyroscope, Poinsot's cones annotated wih their German names 2) Special relativity, hyperboloid-shaped energy-momentum relation.

Three different combinations of two images available:

It's been a while since I shared anything to do with math or physics, but here we are!

My very rough and sketchy derivation of the Larmor angular frequency of a precessing magnetic dipole moment.

Fun fact: this solution came to me while I was solving my solid state physics final exam, I did not study this prior. The prof was kind enough to provide a diagram and a couple of assumptions as well the equation of motion:

μ = μ_x i + μ_y j + μ_z k

B = 0 i + 0 j + B k

dμ/dt = -(e/2m)μ×B

It's one of those days I'm ever grateful for my classical mechanics courses for teaching me much of the maths I use time and time again.

"Stop telling God what to do!"

The years 1900 to 1930 were called The thirty years that shook Physics. Because, with the dawn of the new century (1900), a new stream of physics emerged that threatened to shake the very foundations of science. It was called Quantum Physics.

Till the early 1900s, the most accepted theories of mechanics were called Classical Physics or Classical Mechanics. These theories, very clearly, explained the laws governing everyday objects - objects that we see and deal with in our daily lives, like cars, trains, balls etc, as well as large objects, like the Sun, Moon, planets, galaxies etc.

Sir Issac Newton, the father of Classical Physics, explained gravity, inertia, motion, momentum, speed etc. Einstein proposed the General and the Special Theories of Relativity that explained concepts like space-time for very distant objects. That won him a Nobel Prize and made him the first ever science-rockstar.

So far so good. Classical Mechanics was doing a great job. It was precise and deterministic - means, we could predict the position of Jupiter on its orbit around the Sun, 20 years from today, using the mathematics of Classical Mechanics.

Of course, there were still many unanswered questions. And a whole host of physicists were working on them. But it was Business As Usual (BAU).

Towards the start of the 20th century, a few Europeans - Max Plank, Niels Bohr, Shrodinger, Heisenberg and many others - observed that the laws governing everyday or large objects do not explain the behaviour of sub-atomic particles (particles within an atom). The discovery of the electrons, protons and neutrons led to a spate of experiments, debates and theories, which together were called Quantum Physics or Quantum Mechanics.

Truth be told, Scientists found Quantum Mechanics bizzare! Even till date, scientists still find the theories of Quantum Mechanics hard to grasp. But none of them could or can, dispute the results of Quantum Mechanics. In fact, Quantum Mechanics is universally considered to be the most successful theory propounded by science. It ushered in the Information Age. Lasers, Semiconductors, Computers, Telecommunications, Televisions, Electronics etc, all owe their existence to the application of the concepts of Quantum Mechanics.

Quantum Mechanics works. Its math works. No problem. The only problem is - no one knows how it works or why it works that way! That's why many scientists believe Quantum Mechanics is more a branch of philosophy than of science.

Quantum Mechanics spooked the greatest mind ever believed to have walked this earth - Albert Einstein. He famously said - God doesn't play dice! You will see what he meant as you read on.

Niels Bohr, the Great Dane (he was Danish), worked to defend the theories of Quantum Mechanics. Exasperated by Einstein’s repeated attacks on the Quantum model, he is supposed to have retorted - Einstein, Don't tell God what to do!

This tension between Classical Mechanics and Quantum Mechanics went on for a long time and was also called The thirty years war.

I have been reading up on Quantum Mechanics for some time now. Like layers of an onion, I keep getting clarity on one aspect after another, all in due course. I am still a long way from getting it all, but I find it all so fascinating that I want to share it with you. And I think a good way to understand all of this is by understanding what was called The Double Slit Experiment. Here goes!

Consider a bunch of marble balls, shot through a double-slit barrier (a barrier with two holes on it) onto a board placed behind it. They will create a distinct pattern on the board, hitting it straight where they were allowed to pass through. The remaining part of background board will be untouched. Why? Because particles travel in a straight line. That's their fundamental nature. That's Classical Mechanics. Simple so far?

What if a bunch of electrons were to be shot through the same double-slit arrangement onto the same background board? How would they behave? What pattern would they create on the background board? Since all matter consists of atoms, and electrons are a part of atoms, so electrons should behave like particles, right? But they behaved very strangely. They created the below pattern on the background board.

There were stripes of alternately bright and dark patterns on the background board. Some electrons even hit the board straight behind the opaque parts of the double-slit barrier. How's that possible? The background board looked something like this.

The scientists conducting the experiments knew what this pattern meant. This pattern could only be made by a wave, not by a particle. The below 4-second video explains how a wave creates this pattern. By the way, this pattern is called an Interference pattern.

How's this possible? Was it possible that electrons were waves? But that is absurd. They were particles - sub-atomic particles.

So, scientists reluctantly came to a bizzare conclusion - Electrons were both particles and waves!

Further experiments were even more bizzare. Scientists now decided, not to observe only the pattern on the background board, but to observe the electrons also. What they found made them think they had gone crazy!

The moment their observation apparatus was switched on, electrons reverted to their particle behavior. But when the observation apparatus was switched off, the electrons took on their wave character. Look at the interference pattern on the background board.

Spooky, right? Someone articulated these observations as below.

Observation changed the nature of electrons! An unobserved electron has a wave function. An observed electron has a particle function.

From here on, it gets even more bizzare, if that is possible.

One quantum physicist suggested that the wave function of an electron suggests the probability of finding it at any particular point. If that point is a crest (a wave's highest point), the probability of finding it there is maximum. If the point is a trough (a wave's lowest point), the probability of finding it there is the lowest. But to find it, you have to observe it. And the moment you observe it, the electron takes a particle nature. With particles, life is simple. The electron is either there or not there. No probability. Absolute certainty.

When Einstein heard this, he blew his top. Probability, my foot! This is not Science, he must have thought. "God doesn't play dice!", he asserted out loud. He said this once too often, without offering an alternative explanation.

Niels Bohr, who was also struggling to reconcile with the bizzare conclusions of Quantum theories, but convinced that the consistency of the results of the experiments was proof enough that the theory was right, retorted, "Einstein, Stop telling God what to do and what not to do."

Niels Bohr was awarded the Nobel Prize in 1922 for his work in understanding the theories of Quantum Mechanics.

Almost a century has passed between then and now. In the intervening times, Quantum Mechanics has proposed many more bizzare theories like Heisenberg's uncertainty principle, Quantum Entanglement, Quantum Teleportation etc. Unanswered questions about a Unified theory of everything led modern science to propose strange and stranger theories like String theory, Multiverses (multiple universes) and Cosmic holograms.