Widely misconceptualized in popular science…

The Beautiful Ingenuity of Parallel Worlds

Quantum Physics Explained Intuitively from the Ground Up

Once upon a time, you were a playful, curious, physicist. Your physicist alter-ego is given a screen and a canvas.

The screen has two slits in it.

You throw paint covered tennis balls at the screen in random directions.

Most of the tennis balls will bounce off the screen, but a few lucky ones will make it through one of the two slits.

What do you see on the canvas? That’s easy to find out — just put down your tennis balls, walk around the screen, and take a look. You see 2 splatters of paint.

2 splatters of paint on the canvas

Thats boring. Two concentrated locations on the canvas with paint doesn’t make for some very interesting art. You want to make something cooler. You submerge both your screen and a new canvas in a tub of paint.

Don’t try this at home, kids.

You drop a tennis ball in the paint and watch the paint wave propagate outwards.

The wave expands until it hits the screen, then splits into 2 smaller waves, each passing through a slit.

Left: The wave through slit 1. Right: The wave through slit 2.
Combined wave through slits 1 and 2

At some places, the peak of one wave meets the peak of another wave, the 2 waves combine and make a SUPERWAVE!

Waves adding up makes BIGGER WAVES 🌊 (AKA constructive interference, for the physics nerds)

At other places, the trough of one wave meets a peak of the other one. The opposite amplitudes cancel each other out, making a total amplitude a grand zero.

The peak of one wave cancels out with the trough of the other wave (AKA destructive interference)

When the two paint waves hit the canvas, the wave interference creates a regular pattern of highs and lows — places with more paint and places with less.

What do you see on the canvas? The areas where the two waves combine for higher amplitudes will have more paint, & vice versa. You can expect to see something like this:

We call this a “wave interference pattern.” Hope you are still following along.

Now, that’s some interesting art!

Side view to help you put things into perspective

This is similar to what happens when passing a wave in water through a double slit:

Source

What’s the Significance?

You’d expect the tennis balls (a particle-like entity) to leave one type of paint-distribution on the canvas. You’d expect the paint waves (a wave-like entity) to leave a different paint-distribution.

It is the 1880s, and physicists are confused about whether photons, the units of light, are particles or waves. On one hand, Maxwell theorized that light exists as vibrations in the electromagnetic field (“waves”), which explains the behaviour of light perfectly most of the time. On the other hand, “light is a wave” creates some weird calculations where an infinite amount of ultraviolet light is expected to be emitted from black body radiation, and Planck’s theory of light being emitted in packets (“particles”) fixes those calculations.

Photons sometimes acted like a particle and sometimes acted like a wave. To solve this problem once and for all, physicists got the brilliant idea to shoot light through a double slit, similar to you throwing paint through a double-slitted screen. If the distribution of photons on the other side of the wall is 2 clusters of photons (like tennis balls), then we can conclude that light exists as particles. If it looks like the wave interference pattern (like you got when splashing paint-waves through the double-slitted screen), then light exists as waves.

That’s exactly what they did. Your physicist alter ego set up the screen with 2 slits and a wall, then fired individual photons through the slits at the walls. He went to check what pattern they created on the wall.

What did you see?

The wave interference pattern you see on the wall

Photons are waves! Nothing particle-y about it. Mystery solved!

Remember that the photons are being fired individually at the double slits. It’s as if each photon is passing through both slits at once, then interferes with itself to make the pattern. This makes perfect sense if you think of each photon as a wave.

Let’s put a photon detector on each of the two slits. If each photon-wave is passing through both slits, then we should be able to detect that.

Once again, set up the 2 slits and started firing individual photons.

What do you see on the detectors? It turns out, you never actually detected a photon going through both slits at once. Your sensors show that every single photon either passed through the left slit or the right one, never passing through both.

Now, if you look at the pattern on the wall:

It’s like the tennis balls!

These photons acted completely differently depending on whether we look at them or not. We’re able to influence how they act by placing detectors. It’s as if they know when we’re looking 👁👄👁

Maybe this is a fluke? Remove the sensors and repeat the process:

Put the sensors back and conduct another run:

The double slit experiment set out to answer one simple question of whether light is a particle or a wave, and instead created more: why do photons act one way when observed and one way when not? Do they know that we’re looking at them? Is it something to do with human consciousness influencing the behaviour of light?

What is a Wave?

What does it mean for a photon to be a wave?

When we drop tennis balls in paint to create a wave, that wave has meaning: peaks of the paint-wave are where the height of the pain is the largest, its troughs are where the height of the paint is the smallest.

Cross section of a paint wave

What does a photon wave mean?

Sure, photon waves can move around, have a mass and velocity, and we can predict the state of the wave using the Shrodinger’s equation (just like predicting the future state of a particle using Newton’s law knowing its position and velocity.) Sure, we know all about the applications of waves and use our equations to make accurate predictions about their future positions and velocities. But none of that provides an answer to our question, “What is the wave?”

Simply put, waves represent probability.

Wave = probability

When you look at the wave, it spontaneously changes into a particle at one position. The intensity (amplitude) of the wave at each position is the probability of the particle being there when you measure.

Particles are at one distinct location. Waves are spread out over many positions — the ripple of a pond is not at one point in space but multiple positions (i.e. a “superposition”). When you measure the position of the wave, the wave suddenly changes into a particle with one distinct position. How do you know what position the particle will be at?

Wave = superposition

The answer: it is random. Measuring the same wave 5 times will get you 5 different positions. However, not all positions were created equally. The probability of each position is not equal. The intensity (amplitude) of the wave at each position is proportional to the probability of finding the particle there.

Electron orbitals are wave functions, or “probability clouds”: They have higher amplitudes near the nucleus, and lower amplitudes far from the nucleus. This equates to a higher chance of electrons being near the nucleus, and a lower chance of being far from the nucleus. Source

For the math nerds, the probability is equal to the amplitude squared.

The Measurement Problem

Each photon is a wave until you measure it, then it instantaneously, dramatically, randomly becomes a particle. Does this make you uncomfortable?

This change from wave to particle is known as the “collapse of the wave function.” (Or, the collapse of a superposition.) It’s as if photons are playing hide and seek: we can never actually see any photon as a wave because it turns into a particle as soon as we look at it. We can only indirectly measure the wave-like properties through the double slit experiment.

This is one of the most intuition bending parts of quantum physics. In classical mechanics, observing objects never would change their properties, you simply measure what’s there.

But… why? Why do photons suddenly change from wave to particle? What causes that change? How do they know we’re looking?

What even… is a measurement? What if I use a camera? Will the photon still become a wave? What if a cat looks at it? What if a dead cat looks at it? What if Shrodinger’s cat in a superposition of dead and alive looks at it?

These questions are collectively known as the measurement problem.

This description of spontaneous wave-to-particle change is known as the Copenhagen interpretation of quantum physics. It is the general quantum physics taught to students, and is also known as the “textbook interpretation.”

Yet, the Copenhagen interpretation does not have an answer to these questions, other than “That’s how quantum physics works bruh, just accept it.”

Even Einstein didn’t think the Copenhagen interpretation is good enough. He thought that quantum physics wasn’t complete. Yet, 100 years later, physicists still have no consensus answer to the measurement problem.

This is what Richard Feynman meant when he said

I can safely say that no one understands quantum physics. — Richard Feynman, Quantum physics professor, Nobel Prize winner

There are many proposed theories, or “interpretations” of quantum mechanics, that seek to answer the measurement problem. One of them is the many worlds interpretation, or what is referred to as parallel universes in pop culture.

Before that, take a philosophy break:

The Inherent Randomness of Quantum Physics

If we set the universe back to the exact condition it was 200 million years ago, then let the events naturally unfold from then onward, will the world 200 million years later look the same as it does now?

Up until the 1900s, physics showed that yes, it will be completely the same. The Newtonian mechanical view was that the universe is 100% deterministic. Everything you think is random is not. Take dice rolls, for example: the outcome from 1–6 seems random to us, but is only random because we have incomplete information. If we knew all the forces acting on the die with absolute precision — spin, force applied upwards, mass, air resistance, gravity, etc. — we can predict with 100% certainty which number the die will land on. The randomness exists because of a limit in knowledge and not because nature is inherently random.

In Newtonian physics, if you know the position and velocity of every object, particle, and wave in the whole universe, you are able to deduce everything that will ever happen and everything that has ever happened. Everything that you are unable to predict is due to your human inability. (Gives me the vibe of math before Godel’s Incompleteness Theorem)

Many 20th century physicists thought the same about our inability to predict the collapse of quantum superpositions. After all, the wave function represented a cloud of probabilities. It would seem logical that those probabilities represent the probability that humans place on finding the electron in any one location because of our incomplete information, just like placing a 1/6 probability on rolling a 4 because we have incomplete info.

However, the quantum worldview is that some elements of nature are inherently random: when an electron in a 50/50 superposition of being here and 1 metre away is observed, it collapses into one of the two locations at absolute random. Quantum mechanics says that nobody has any way of saying with certainty what spin you’d observe, even with all the information in the world.

God does not play dice with the universe. — Einstein, expressing discomfort with absolute randomness

If we set the universe back to its exact condition 200 million years ago, then let the events play out, the world will not look the same as it looks now. Because wave function collapses are random, quantum systems will not play out the same way. Since the universe is built on quantum systems, quantum systems playing out differently impact macro situations. How much the two worlds would differ we do not know, but they will certainly differ.

Proving that the universe is inherently random does not prove free will, but it does prove the role that luck plays.

We arrived at our current world partly due to luck. If we reverse the universe 200 million years, and certain superposition collapses play out differently, maybe humanity would be extinct by now. Or maybe the cognitive revolution happened a hundred thousand years earlier and we would’ve been a Type III civilization by now. Whether it’s good or bad luck we do not know, but it’s luck nevertheless.

Think about quantum physics next time you debate hard work vs luck. (Or next time you debate free will.)

Entanglement Explained

Suppose two photons, Donald and Joe, heading towards each other from opposite directions.

Each are in a wave, a superposition of position. They bump into each other.

After, they’ll continue on their paths, moving farther and farther away from each other. Each photon’s position got altered by the interaction with the other photon. After Joe and Donald have moved far away, if I measure one of them, I’ll know the velocity of the second one, since the velocity of each depends on the other one since altered by each other.

Let’s say that Donald and Joe can either be going slow or fast. They’re each in a superposition of these two states.

Joe is measured 1 hour after colliding, now they are a light-hour apart.

If we measure Joe to be fast, we know Donald also had to be moving fast at the time of collision, therefore know that Donald is moving fast now. If we measure Joe to be slow, know that Donald is also slow.

This is entanglement: by measuring the velocity of one photon, you can accurately deduce the velocity of the other one. If you collapse one wave function, you simultaneously collapse both.

Even after Donald and Joe are light years apart, as long as they remain entangled, measure one know the potion of the other. No communication is happening between Joe and Donald (just like no constructive communication happen between them in real life), the nature of the superposition itself has been altered before measurement.

Entanglement = combined superposition

When 2 quantum systems interact, they(eir superpositions) entangle with each other.

Parallel Worlds

You are made up of atoms. Your atoms are made up of quarks and electrons, which are quantum objects, each in its own superposition. You are made up of quantum systems [entangled with each other], therefore you are a quantum system.

When you observe a photon that is in a superposition of here and a meter away, you interact with it. When two quantum systems interact, they entangle with each other, therefore you get entangled with the photon

When you observe your photon, you become in a superposition of seeing the photon here and seeing the photon there. You and the photon are in a combined superposition of you seeing the photon here and the photon being here, and you seeing the photon a meter away and the photon being a meter away.

It’s impossible that you see the photon here and the photon is a meter away. If I knew that the photon was a meter away, I can predict with 100% certainty that you saw the photon is a meter away. If I knew that you saw the photon is here, I will know with 100% certainty that the photon is here. You and the photon meets all traits of an entangled system.

The photon has not instantaneously changed from a wave into a particle, or from a superposition into a definite state. The photon is still in superposition after your measurement, just that you can only see one state.

The photon has not changed, you have changed.

You have changed from being separate from the photon to being in a superposition of seeing the photon here and seeing the photon a meter away.

But… the problem is that you never feel like you are in a superposition of seeing the photon here and a meter away. You feel that you have seen the photon in one distinct place. That’s because you are not the combination of both the person who saw the electron spin up and the one who saw it spin down. The wave function of the universe has split, and now there are two of you.

This solves the measurement problem: the measurement is precisely when a previously isolated quantum system becomes entangled with the observer.

Furthermore, the universe itself is a superposition of multiple states. (Known as the “wave function of the universe.”) When a photon in a superposition of here and there interacts with you, it is interacting with the rest of the universe, and thus becomes entangled with the rest of the universe.

The wave function of the universe itself splits into two superpositions: one superposition where the electron spins up and you see it spin up, the second one where the electron spins down and you see it spin down.

This is many worlds.

A misconception about many worlds (or “parallel universes” in popular science) is that additional universes are being created every time a decision is made. There are 2 problems with that statement:

  1. The one existing universe splits into branches; there are no additional universes being created. The branches are simply different parts of the universe’s wave function or different states of the universe’s superposition.
  2. No decisions are being made. The wave function branches every time a previously isolated quantum system becomes entangled with its environment, not when decisions are made.

No longer is the instantaneous change from wave to particle at the arbitrary timing of when a human looks at it. No more weirdness about particles knowing whether we’re looking at them — implications about the core nature of consciousness.

Many worlds is deduced logically by the sole premise that entanglement exists.

What an elegant way to solve the century old measurement problem.

Closing Thoughts

From your kid asking why the sky is blue to hunter gatherers staring at the stars wondering what’s really out there, it is an innate part of the human condition to seek to understand not just how the world works, but why it works that way. That’s the beauty of physics: why do apples fall, why are black holes un-escape-able, why do photons act one way when observed and another way when not? Quantum physics had already been widely successful in terms of application: you wouldn’t be reading this right now if it weren’t for our knowledge of quantum physics powering your computer’s transistors. Yet despite our immaculate understanding of how quantum physics works (i.e. being able to do math to make predictions with it), we are unable to understand why it works that way. We don’t know something as fundamental as why photons act one way when observed and one way when not, despite superpositions being what you’d find in chapter 1 of introductory quantum physics textbooks. It’s shocking how little we know about the why of quantum physics.

The many worlds interpretation is an elegant way to explain this why.

Looking for the nature of reality is an art. Pure theoretical physics isn’t fuelled by wanting its breakthroughs to be useful, but by a desire to understand how the universe truly operates. When Einstein was developing his theory of special relativity, he had no clue that it would one day enable precise global positioning systems with satellites. In math, Fourier never expected the Fourier transform to be fundamental to how computers store and view images, but he developed it because it’s just elegant.

Have you seen how breathtakingly elegant this is… Source

Newton saw the apple fall, and he wanted to get to the bottom of it because of innate human curiosity and a fundamental human desire to understand reality. It’s only when you have a thirst for knowledge that you’re able to dedicate your whole life to scientific research.

The many worlds interpretation isn’t elegant only for using the simplicity of entanglement to solve a century old problem; it represents the never-ending pursuit of truth. Many worlds represents seeking understanding: wanting to understand the why of quantum physics even after we’ve mastered its applications.

That’s the art of pure theoretical physics.

If you enjoyed this article on counterintuitive science, maybe you’ll enjoy some counterintuitive math too:

Hey! I’m Laura, an innovator at TKS, currently building quantum computing algorithms, and the host of the First Principles podcast.

What I’m currently working on: 2021 Bucket List

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Quantum software intern @ Zapata Computing. More work: lauragao.ca