Superposition

08 Oct, 2025

Back in 10th grade, physics was simple. Back then, the biggest problem was just memorizing formulas. But then I read about Einstein, Max Planck, and all those famous names. Suddenly, physics wasn’t just about objects falling here and there, it was about particles misbehaving. Physics started showing me a completely different perspective of the world.

Imagine this: a particle that can be here and there at the same time. A coin that is both heads and tails until you look. A student who is both “studying seriously” and “doomscrolling social media” until the parents check. That’s the vibe of quantum mechanics. And the part that hooked me most? Superposition.

Then in 11th grade, it has gotten serious. In the “Atomic Structure” chapter, I met Schrödinger’s equation and Heisenberg’s principle. I realised with time these weren’t just symbols, they were much more than that. Add to that the Oppenheimer movie, with glimpses of Bohr, Heisenberg, Oppenheimer, and I was convinced: the real magic is quantum physics.

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Timeline

Let’s quickly rewind, cause I love HISTORY!!
Now quantum mechanics didn’t pop out of nowhere. It was a century long group project, with each scientist contributing something.

Max Planck (1900):

At the time, physicists thought energy flowed smoothly, like water from a tap. But Planck was staring at a weird problem: blackbody radiation. Classical physics predicted an “ultraviolet catastrophe”, infinite energy at high frequencies. Clearly nonsense. So Planck made a bold move: he said energy comes in tiny, discrete packets called quanta. Like Lego blocks. That solved the problem. He didn’t realize it, but he had just cracked open Pandora’s box.

Einstein (1905):

Planck’s quanta were controversial, but Einstein doubled down. He said light itself isn’t just a wave, it’s made of particles, photons. His explanation of the photoelectric effect won him the Nobel Prize. Funny twist: Einstein later became one of the biggest critics of quantum mechanics.

Niels Bohr (1913):

Bohr looked at the atom and said electrons don’t just wander around instead they occupy specific orbits, like steps on a staircase. When they jump, they absorb or emit energy. It explained hydrogen’s spectral lines beautifully. Every student has drawn this in their copy: circles and dots, the Bohr model.

Louis de Broglie (1924):

He asked a crazy question: “If light can act like a particle and a wave, why not matter too?” He proposed that electrons (and even you and me) have wavelengths. The smaller the mass, the longer the wavelength. This was the birth of wave-particle duality.

Erwin Schrödinger (1926):

Not happy with Bohr’s fixed orbits, Schrödinger came up with his wave equation. He showed that electrons are not little dots, but clouds of probability. This was the official entry of mathematics.

Werner Heisenberg (1927):

Then came Heisenberg. He realized you can’t measure both the position and momentum of a particle with infinite accuracy. The more you know one, the less you know the other. His uncertainty principle is literally amazing.

Together, they created a picture where particles aren’t just things, they’re possibilities stacked on top of each other.

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The Cat vs. The Tabs

So, what does superposition mean?

Classic analogy: Schrödinger’s Cat — the cat is locked in a box, alive and dead at the same time until observed. Legendary.

My analogy: Chrome tabs. You’ve got 37 tabs open (don’t deny it). YouTube, Twitter, your half-written assignment, memes, shopping. Technically they’re all running. But you only see the one you click. Before clicking, every tab exists in parallel. I hope this has given you an idea about what superposition exactly is.

Particles are like that. They’re in multiple states until measurement clicks one.

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Experiments

1. The Double-Slit Experiment

Shoot electrons at a wall with two slits.

If nobody’s watching, electrons interfere like waves, forming stripes. Each electron literally goes through both slits at once.
If you try to watch which slit it goes through, interference disappears. They behave like normal particles.

Observation changes reality.
You can watch this experiment by clicking below.
Click Here

2. Stern-Gerlach Experiment

Silver atoms were fired through a magnetic field. Instead of spreading smoothly, they split into two spots. Why? Because the atoms’ spins were in a superposition of “up” and “down,” collapsing only when measured.

You can watch this experiment by clicking below.
Click Here

3. Quantum Entanglement

Two particles can be linked so strongly that measuring one instantly sets the state of the other, no matter how far apart they are. Einstein called it “spooky action at a distance.” Today, we use it in quantum communication.

You can watch this experiment by clicking below.
Click Here

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Mathematics

Okay, time to flex a bit. Don’t worry, it won’t hurt.
Jokes apart, Mathematics is very important in order to under quantum mechanics and the world around it. These are some of the equations I have came across while studying. I’m still learning and figuring out their derivations. You can deep dive in any of them as per your interest, here I’m just elaborating them a bit. They are literally mind bending, have a look yourself!

Linear Algebra of Superposition

• A quantum state is represented as a vector in a mathematical space called a Hilbert space.
• The possible outcomes of a measurement correspond to the components of this vector.
• Transformations of states - such as rotations, time evolution, or interactions are expressed using matrices (operators).
• When a matrix acts on a state vector, it produces a new state that still obeys the rules of quantum mechanics.

In essence, linear algebra provides the precise language to describe, transform, and predict quantum states. Without it, the structure of quantum theory would collapse.

Superposition of states (qubit style):

$|\psi ⟩=\alpha |0⟩+\beta |1⟩$.

This is a quantum state. $|0⟩$ and $|1⟩$ are the “basis states” (like heads and tails).
α and β are complex numbers, telling us the probability.

• |α|² = probability of finding 0
• |β|² = probability of finding 1

And |α|² + |β|² = 1 (because total probability must be 100%).

This is the math backbone of qubits in quantum computers.

Schrödinger’s Wave Equation:

$i\hslash \frac{\partial }{\partial t}\Psi (x,t)=\hat{H}\Psi (x,t)$

This describes how the wavefunction evolves with time.

• Ψ(x,t) = wavefunction (the probability cloud).
• H = Hamiltonian operator (total energy of the system).

Now this is a complex one, you can study it in detail as per your interest. I’m using a simple analogy here to explain it.
Think of Ψ like Spotify’s playlist of all possible songs. Schrödinger’s equation tells you how the playlist changes with time.

Heisenberg’s Uncertainty:

$\Delta x·\Delta p\ge \frac{\hslash }{2}$

Δx = uncertainty in position.
Δp = uncertainty in momentum.
No matter how good your tools are, there’s always a limit. The particle is actually not hiding, it genuinely doesn’t have a precise position and momentum at the same time.

De Broglie’s Relation:

$\lambda =\frac{h}{p}$

λ = Wavelength
h = Planck’s constant
p = Linear Momentum
Every moving particle has a wavelength. Yes, even you. If you walk slowly enough, your wavelength increases (but still way too small to surf on).

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Application

Now you might ask: “Cool, but is this just nerdy theory?” Nope. Superposition is everywhere.

1. Quantum Computers – They use qubits in superposition. Imagine trying all passwords at once. That’s the speed.
2. Quantum Cryptography – Eavesdrop on a quantum key, and boom, it changes. Perfect for privacy.
3. Photosynthesis – Plants are basically tiny quantum computers, moving energy with ridiculous efficiency.
4. MRI Machines – Medical scans rely on quantum spin and superposition.

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Misconceptions

• “Superposition means cats are really alive and dead.”
  No, the cat example is just a metaphor.
  
  
• “Superposition is just probability.”
  Nope, it’s deeper. It’s not that the particle is in one state and we just don’t know. It’s literally in multiple states.
  
  
• “Observation means human eyes.”
  Wrong. Any interaction with the environment (a detector, a photon) counts as observation.

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Debates

Copenhagen Interpretation

The Copenhagen interpretation argues that superposition collapses when measured. Reality “waits” for us to observe it, and the act of measurement forces the system into a definite state. This interpretation emphasizes the central role of the observer, suggesting that quantum reality depends on interaction with the classical world.

Many-Worlds Interpretation

Contrasting sharply, the Many-Worlds interpretation claims that superposition never collapses. Instead, every possible outcome occurs in its own branching universe. In this view, all possibilities are real, and the observer plays no special role. The universe continually splits into parallel realities.

Einstein vs. Bohr – The Measurement Debate

Einstein was skeptical of the Copenhagen interpretation, famously saying, “God does not play dice.” He believed that quantum mechanics was incomplete and that reality must exist independently of observation. Bohr defended Copenhagen, arguing that quantum mechanics is complete and observation is fundamental. Their debates, often at the Solvay Conferences, highlighted the tension between determinism and the probabilistic nature of quantum theory.


Don’t worry if you are not able to understand each and every interpretation, I’m literally trying to explain centuries of data in a short form, so try to grasp as much as possible.
There are many more debates revolving around it. Nobody knows which is true. Physicists still argue over it in conferences. I guess Superposition is less about answers and more about asking better questions. Maybe someday I can get an opportunity to study about it deeply and then I can figure out the truth.

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Conclusion:

Superposition blew my mind in 10th grade, and it still does. It’s not just about electrons being fancy, it’s about reality itself being undecided until someone observes.

So next time you’re juggling between studying and procrastinating, remember: you’re basically in superposition. Both productive and lazy.

Oh man there’s a lot to learn and I can rant endlessly about physics, these are just some bunch of things which I wanted to share with you.

See you in the next one❤️.