A simplified introduction to quantum mechanics

Quantum mechanics is a conceptual framework for understanding the microscopic properties of the universe. There is a quote by Niels Bohr, one of the founding figures of quantum mechanics:

"Anyone who thinks they can talk about quantum mechanics without getting dizzy hasn't yet understood the first word of it.
-Niels Bohr

Now, why would that be the case? Why thinking about a fundamental concept make one dizzy? He intends that we are born with a remarkable instinct for classical physics but not quantum mechanics.

Classical physics and Quantum Mechanics:

Take a ball in your hand, toss it up in the air and try catching it. Most of us can do it; it doesn't require any particular skill set. Humans have evolved to survive; we need specific skills to know where to throw a spear or throw a rock to get the next meal. And consequently, we learned the fundamental physics of the everyday world without thinking much about it. We acquired that intuitively.

And that's why when you throw an object, you don't have to through some elaborate calculation to figure out where it is going to land. The classical way of understanding physics belongs in our being, and we witness it every day all around us. But when we investigate the world of the very small, we seem to be clueless. We don't have experience or intuition in that domain.

It puts us in a vulnerable position where we must use mathematics, experiment, and observation tools to gaze deeper into reality. And that's what quantum mechanics is all about. It's trying to describe what exactly happens in the micro-world. You might think that why should I learn about some weird subatomic particles that might not affect my life in any way? But think again, we are all nothing but a collection of these particles.

Any weirdness we find in the microworld, in some sense, has an impact on the macroworld. There's not even such a sharp divide between the small and the big. The microscopic weirdness we witness in the Quantum realm is inexplicably connected to us. And inadvertently, to understand the big, we need to start from small.

In this post, we will step into the Quantum world by deconstructing the classical view of reality. Classical mechanics, as it went deep down into the atoms' scale and the atoms' structure, our understanding just snaps and breaks. We couldn't even find out atoms existed till the 20th century. When we did find out, none of the macroscopic rules applied in the atomic world.

It took almost 30 years for Quantum Mechanics to merge into a coherent theory. But by 1928, formulas and rules were already put in place by the most genius of minds. We do make successful and accurate predictions using this conceptual framework, but no one understands what exactly is going on.

quantum mechanics explains the aspects of nature at small (atomic and subatomic) scales

Light and quanta:

The Quantum mechanical puzzle started when physicists tried to understand the nature of light. Before the puzzling properties of light send us down a spiral, we need to understand we need to know what quanta are.

The energy that exists in the universe transmits itself through electromagnetic radiation, and light is also a form of electromagnetic radiation. James Clerk Maxwell studied the nature of electromagnetic radiation and light; he ended up putting both of them together. He discovered that self-propagating electromagnetic waves would travel through space at a constant speed, that is, the speed of light. Through this observation, Maxwell concluded that light must also be a form of electromagnetic radiation.

In 1873, he published A Treatise on Electricity and Magnetism- a full mathematical description of electric and magnetic fields' behaviour, we call Maxwell's equations. Everyone agreed that light propagates in the form of waves like every other electromagnetic radiation out there. While no one seems to contradict the wave nature of light came Max Plank.

He suggested that light appears to propagate as waves, but the energy carried comes in tiny packets or lumps called quanta. It was a remarkable observation, but it was thought to be just an idea.

In 1905, Albert Einstein took the idea of light quanta, ran with it, and earned himself a Nobel prize in 1921. Einstein proved the existence of Plank's quanta through his photoelectric effect. The photoelectric effect is when light shines on certain metals; they knock off electrons from the metal, creating electricity. According to Einstein, a beam of light is a stream of tiny photons travelling at a constant speed that kicks out electrons from metals.

All these discoveries pose a difficult problem in front of us. Now we have in our hands' substantial experimental evidence that light is a wave but also composed of particles. What is the true nature of light anyway? Is it a particle or a wave? How can a wave be composed of particles?

The double-slit experiment and the wave-particle duality:

The Double Slit Experiment allows us to get to the heart of the wave-particle duality. This experiment emerged from an accident in the laboratory at Bell Labs. The basic idea is to take a light source and shine that light as a narrow beam on a screen with two gaps in it, and you look at the pattern of light behind the two slots (two slits) on the screen. So the slits are literally gaps in a black sheet of paper. The light's merely passing through them. So simple, right?

If the light is a particle, you'd expect a pattern where it has passed through one of the slits, and there is a large gap in between the slits. If the light is a wave, you might expect something different as the light coming through one part of the slit interferes with the light going through the other part of the slit. It would result in what we call an interference pattern.

And the weird thing about the quantum two-slit experiment is that it seems, light, in various ways, to be doing both of those things simultaneously.

Let's say we carry out the experiment the way we described, but we don't start with photons or electrons; we begin with bullets or something. So what would we expect to happen in this experiment?

You have the source of the pellets spitting out the bullets, and some of them go through the holes, and the ones that go through the holes travel straight ahead. And we get precisely two bands at the back, indicating the pellets that went through the right slit, on the right, and the left bar is the pellets that went through the left slit as a result. The result is straightforward, simple, and even dull if we think about it.

But if we took the bullets and dialed them down to a tiny subatomic size, we get something absolutely different.

This behaviour of particles leaves us with furthermore questions than answers. It is tempting to ask, okay; light behaves in weird manners, so what?

But wait, the reality is rather strange than science fiction. Matter particles also behave the same way.

Further reading: Two slits and one hell of a quantum conundrum

Matter particles are also waves:

In 1923, french nobleman Prince Louis De Broglie suggested that wave-particle duality applied not only to light but also to all fundamental sub-atomic particles. De Broglie showed that an electron in orbit around a nucleus could have wave-like properties.

In the mid-1920s, physicists Davisson and Germer at the Bell Telephone company produced experimental proof for Louis's equations.

They concluded that all matter particles have wave-like characteristics, and the wavelength of these matter particles is equal to Plank's constant.

The wavelength is so minuscule we cannot feel it in everyday life. Thus De Broglie's observation laid the foundation for Erwin Schrodinger to lay down the fundamental equation of Quantum Mechanics.

 the double-slit experiment is a demonstration that light and matter can display characteristics of both classically defined waves and particles
The double slit experiment

Why do particles behave like waves?

Let's repeat the double-slit experiment but this time with an electron beam, and see what happens. Yes, you guessed it. We get the same interference pattern again! Why is this the case?

Maybe the electrons somehow interfere with each other, so they don't arrive in the same places. Strangely, even when you shoot the electrons one by one so that they have no chance of interfering, you still get an overall pattern that resembles the interference pattern of a wave.

Let's place a detector by the slits to see which slit an electron passes through. It gets even more bizarre when we do that.

Once we set the sensor, the screen pattern turns into two strips' particle pattern resembling the bullet experiment. The interference pattern disappears. It's almost like they don't want to get caught!

What does the experiment tell us? It suggests that what we call "particles," such as electrons, somehow merge characteristics of particles and elements of waves. It also indicates that observing or measuring a quantum system has severe effects on the system. The enigma of precisely how that occurs creates the measurement problem of quantum mechanics.

When modern physics found out all sub-atomic particles, including protons, electrons, etc., possess wave-like characteristics, it changed everything we knew so far. It raised questions like what happens to the wave property in the macroscopic realm? If all matter has wave-like properties, why don't we see it in everyday life? These questions about the wave property of matter led to the various interpretations of Quantum mechanics, including the Copenhagen interpretation and the many-worlds theory, which are popular even today.

In quantum mechanics, Schrödinger's cat is a thought experiment that illustrates an apparent paradox of quantum superposition.

Schrodinger's equation and the probabilistic universe:

Austrian Physicist Erwin Schrodinger is one of the forebears of Quantum mechanics. In January 1926, Schrödinger published the paper "Quantization as an Eigenvalue Problem," which presented the Schrödinger equation.

Erwin Rudolf Josef Alexander Schrödinger 12 August 1887 Vienna, Austria-Hungary
Erwin Schrodinger

The Schrödinger equation determines how these so-called matter waves behave over time. Erwin Schrodinger suggested that matter waves are "smeared out electrons." Imagining electrons smeared out around an atom was almost inconceivable even to physicists.

In the same year, Max Born independently concluded we must interpret these waves only through probability. In places where the wave's magnitude is large, the areas are likely you can find an electron. Places where there's less or no wave magnitude mean no electron there. It led to the conclusion that,

"we must describe matter itself in a probabilistic manner.

These probabilistic waves are what we call the wave function of a particle.

What does it mean to have a probabilistic universe?

Schrödinger put forward an equation that governs the shape and the evolution of these probability waves, and it changed everything. Many, including Einstein, didn't like the idea of introducing probability into fundamental physics. In one of physics' most quoted statements, Einstein rebuked the quantum stalwarts saying, "God does not play dice with the Universe."

In Einstein's view, the universe had no room for an element of chance. But experiment after experiment convincingly confirms that Einstein was wrong. As Stephen Hawking once said, "Einstein was confused, not the quantum theory."

But, the debate about what quantum mechanics means continues to this day.

Everyone agrees on how to use the equations of quantum theory to make accurate predictions. There is no consensus on what it means in reality to have probability waves, nor how a particle "chooses" its path, nor even whether it indeed chooses or instead breaks off into an ever-expanding field of parallel universes. But it is clear that the universe unfolds itself only through probability, where everything becomes blurry and indeterministic.

Further reading: Einstein, Bohr and the war over quantum theory

As far as Quantum mechanics is concerned, there is no shortage of weirdness. We have not yet dealt with so much more weird stuff, like the uncertainty principle, Feynman's sum of paths, Quantum tunnelling, Quantum entanglement, etc., which we would discuss in the upcoming posts.

Thank you for taking this journey with us as we dive deep into the strange but fascinating areas of physics. If you like to read more from us, you can check out our other posts and subscribe to our newsletter for regular weekly updates.

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