#classical physics

Classical physics, pioneered by legendary figures like Newton and Maxwell, reveals an orderly clockwork universe with precise mathematical laws governing motion, gravity, and energy. However, in the early 20th century, the emergence of quantum physics uncovered a microscopic realm where uncertainty, probabilities, and spooky connections reign supreme. For decades, these two frameworks seemed…

"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.

[Image description: a second tumblr ask from archaeopter-ace reading, “(though I definitely agree that the nuance of 'centrifugal force is a fictitous force' is absolutely lost in most physics classes, who are either 100% for or against its existence, and treating it like it's real means kids won't understand how force works properly. Force has to come from somewhere, it doesn't just spring forth from the ether because you need an opposing force to explain what you're seeing)”]

Okay, so bear in mind that I’m an upper division undergrad, and it’s entirely possible that I am missing some aspect that is taught in graduate level courses. Also, whenever I use the word “you” in here, I am using the general you.

So, first off, I’d like to clarify the reason why the imaginary number i* is used in many physics cases is the simple fact that it’s easier to take the  integral/derivative of e^(iθt) than it is to take the integral or derivative of sin(θt) or cos(θt). However, no matter if you choose complex exponentials or regular trigonometry, you will get a real answer. This is used for things that are periodic and repeating. Examples of this being used are masses on springs and pendulums, circuitry, and likely many more cases because so many physical systems can be measured as simple harmonic motion.

* Not to be confused with the unit vector î. This is associated with the very real x-direction.

However, in quantum mechanics, the imaginary number i is used for multiple reasons. It’s sometimes used as an exponent of the natural number e in order to avoid using trigonometry for the wave, but it is also multiplied across the entire equation Ψ(t) so that the solution is a real number.

Treating the centrifugal force as a force never makes the math easier, in my experience. However, depending on the frame of reference (aka point of view) you choose, you may or may not need to treat the centrifugal force as a force in order to make the math work.

For example, have you ever been spinning around a mass on a string above your head and then suddenly you let go while still trying to maintain that rotating circle? The mass you’re spinning flies off in a straight line in the exact opposite direction. This is due to inertia (aka the thing that keeps objects in motion staying in that same motion and objects at rest staying at rest unless an outside force acts upon them), although some may call this the centrifugal force. As long as you are in an inertial frame of reference (aka you aren’t accelerating), then the centrifugal force is not a force, but rather the effects of inertia. Newton’s laws of motion work perfectly to describe the motion of you and the object. It is much easier to deal with an inertial frame of reference than a non-inertial one. However, there are situations where the observer is in a non-inertial frame of reference.

Have you ever been driving and you made a hard right turn, only to feel your body shift towards the left of the car? That is not something that Newton’s three laws of motion can explain, not from your accelerating non-inertial frame of reference. They can’t mathematically model how you’re moving... not unless you invent a force that is pulling you towards the left side of the car! In that case, the centrifugal force is something to be treated as very real, and is equal to the mass of the object (aka you) times the squared angular velocity times the distance from the axis of rotation. Of course, someone sitting on the sidewalk (and not accelerating with respect to the Earth) watching you can conclude that you’re experiencing the effects of inertia and that there is no centrifugal force acting upon you.

Now, technically, one can make the claim that gravity is just as real as fictitious forces found in non-inertial reference frames. After all, if you’re in a windowless room and you feel like you’re feeling gravity like you would on Earth, how can you be sure you’re actually on Earth and not just accelerating through deep space at 9.807 m/s²? Einstein made that exact claim and it’s now known as the equivalence principle. However, I would ignore this unless one has to deal with general relativity.

(Other case of a fictitious, non-centrifugal forces in cars include how when the driver suddenly slams the gas pedal, you feel yourself thrown back against the chair. From an inertial frame this is the back of the chair accelerating forward into you, but from your non-inertial frame of reference there seems to be a force shoving you backwards. Likewise, when the car suddenly stops (whether intentionally or unintentionally), you’re thrown forward. From an inertial frame of reference, this is your inertia causing you to move forward even as the car stops. From your non-inertial frame of reference, it seems that there’s a force throwing you forwards. This is why you need to wear a seat belt, because even if you don’t get in trouble with the law for not wearing one, the laws of physics will get you if you’re in a bad enough crash.)