The many worlds interpretation of quantum mechanics proposes that every time a quantum event gets decided, the universe splits so that every possible outcome really does occur.

But where exactly are those worlds, and can we ever see them?

In one branch of the splitting quantum multiverse a radioactive nucleus decay, in another it doesn’t; in one “world” a quantum event in your brain produces a neural cascade that leads you to choosing pizza, in another it's salad.

Or at least this is the popular conception of Many Worlds: that of a many-branching tree, a universe that divides into unthinkably many alternate realities.

We’ve talked before about this interpretation of quantum mechanics, and whether it’s plausibly true.

TLDW - it may be but there are problems, and it’s so far untestable.

Now, I’ll come back to possible ways to test this in an upcoming episode.

But today I want to cover something different - If Many Worlds is true - where exactly are those worlds?

Before we get to worlds, let’s think about ponds.C.S Lewis fans will know that ponds can lead to other worlds, but that’s not what I want to talk about - at least not today.

I want to talk about ripples.

If you drop a pebble into a pond, a series of circular ripples will expand outwards.

That pattern will complexify if the ripples are, say, broken by a barrier; it’ll be as though two sources of ripples overlap, leading to higher peaks and lower troughs in the processes of constructive and destructive interference.

Same if the ripples reflect off the edge of the pond.

Or if multiple pebbles are dropped.

Here, we’re seeing the principle of superposition in action.

In wave mechanics, this principle tells us that when two waves overlap, their amplitude - in this case the height of the ripple - is the sum of the component waves.

But the superposition principle also tells us something much cooler.

If we want to know how this complex pattern of overlapping ripples will evolve, we only need to track the individual ripples.

Each ripple moves as though it’s the only wave on the pond.

You can calculate the overlapping pattern at any point in time by calculating the motion of all ripples separately and then adding them together.

And the complexity of the sum has no effect on the motion of the individual.

The weirdness of this is clearer if we watch two waves cross each other in one dimension.

This complex fluctuation at their collision seems to hold no record of the shapes of the incoming waves, and yet its motion perfectly regenerates those waves, which travel on as though nothing happened.

The superposition principle only applies up to a point.

If the amplitude of the waves is is too high, the principle can break down.

But for small ripples on a pond, we could have many separate systems of ripples, each moving around as though the pond is otherwise flat.

At the risk of getting technical, the superposition principle holds for any linear system - and I’ll say more about that another time.

The main point is that this holds approximately for familiar waves, up to some amplitude.

But the superposition principle seems to always hold for the waves that drive quantum mechanics.

And the ability for the quantum wavefunction to co-exist and overlap without being affected by that overlap is how we’re going to create our many worlds.

Ok, we are ready to jump through the pond and to explore some worlds.

And by jump through a pond I mean learn some quantum mechanics.

Quantum mechanics is a theory about waves.

It tells us that everything in the universe can be described by a wavefunction.

Where a pond ripple is an oscillation in surface height, the wavefunction is an oscillation in probability, or more accurately probability density.

It represents the shifting distribution of possible results you might get if you were to try to measure a certain property of a quantum system.

Those measurements appear to be randomly selected based on the current state of the wavefunction - more likely where the wavefunction is stronger, less where it’s weaker.

The wavefunction is what underlies our perceived reality.

We never see the wavefunction - we only see measurements - we pluck our reality from this fantastically complex structure.

Every particle position and momentum and orientation is chosen from a vast array of possibilities, a sprinkling of the high points of the cosmic wavefunction.

The actual mechanics of quantum mechanics is all about determining the shape and evolution of the wavefunction.

To calculate this we use the Schrodinger equation, which tells us how the amplitude of the wavefunction changes over time and space.

Just as with our pond ripples, the wavefunction can overlap and either stack stack up or cancel out - constructive or destructive interference.

An example of this behavior is in the double-slit experiment, where the position wavefunction of an electron passes through two gaps in a screen and then interferes with itself to produce a complex wavefunction structure.

When we try to measure the final location of the electron on a detector screen, we find that we’re more likely to see it where the wavefunction is high - and so electron after electron we trace out these interference bands.

But what decides where the each electron lands?

The most mainstream interpretation of quantum mechanics - the Copenhagen Interpretation - tells us that the wavefunction “collapses” - it instantaneously shrinks from encompassing a huge range of possible measurement outcomes to encompassing only the outcome that was measured - and that value is selected randomly, but weighted by the pre-measurement wavefunction.

Whatever causes this random selection is not the Schrodinger equation - it’s something extra, and Copenhagen doesn’t explain why or when this really happens.

The Many Worlds interpretation is rather different.

It says that the wavefunction never collapses - it evolves forever by the Schrodinger equation.

The wavefunction of the electron joins the wavefunction of the detector screen at all points, rippling onwards.

So why does an electron end up looking like a single spot on a screen?

What happens to the rest of its wavefunction?

To understand that we have to remember that the electron’s wavefunction is only a tiny sliver of a great cosmic wavefunction that includes every electron and every other particle in the universe.

When we “see” that the electron hit one spot on the screen, what we’re really seeing is a cascade of ripples in the cosmic wavefunction, which encompasses the piece-wise wavefunctions of many particles as it makes its way to us.

So the wavefunction ripples through the detector, along wires, through computer circuitry, as photons from the screen, as action potentials down our optical nerves, and finally as signals in our neurons.

Only there does it manifest as a conscious awareness of a dot on a screen.

The Copenhagen interpretation says that at some point in this process, most of the wavefunction vanishes.

The paths to the electron's wavefuntion not corresponding to our observation of that spot cease to exist.

Many Worlds says the wavefunction persists.

It says that a cascade of ripples for every possible location on the screen travel down the same wires, through the same circuitry, into the same brain.

They still overlap - stack on top of each other - but they no longer interfere, either constructively or destructively.

That’s because the many, many interactions that these wavefunction branches experience on their way to your brain render them forever inaccessible to each other.

We can see what this means a bit better if we track the experiment backwards.

Even prior to hitting the detector screen, we still had many worlds - or at least the seeds of them.

For example, right after passing through the double slit, we had two broad classes of world - one for each slit that the particle may have passed through.

But the key is that the wavefunction slice corresponding to those two worlds was still coherent.

That means its peaks and troughs could still line up in a systematic way to produce high and low points in the wavefunction - meaningful blips in the probability distribution.

But imagine you placed detector devices in front of those slits to measure which slit the electron passed though.

There’s no way to make a perfectly reliable measurement without corrupting the phase of the wavefunction in a way that destroys coherence - destroys the relationship between phases of the wavefunctions emerging from both slits.

Past the detectors you still have two parts of the same electron’s wavefunction, but now the phase relationship, the correlation between peaks and troughs, is destroyed and so you don’t see an interference pattern.

At this point we may say that the “worlds have split” because there may be no way bring them back into coherence.

We’ve talked about this decoherence before - and it’s an increasingly favored explanation for both the splitting in many worlds or the apparent collapse in Copenhagen.

Once decohered, these “worlds” overlap and move through each other, but they can’t add together in interesting ways.

Once there’s no longer a recoverable phase relation between the branches of the wavefunction, the worlds have separated forever.

That means the wavefunction of your brain also has branches - different internal states that correspond to each of the branches of the wavefunction from the experiment.

But those parts of your brain wavefunction are out of phase with each other.

They match in many ways - including physical location, but there are subtle differences - on one branch a collection of neurons fired to register a spot here, on another branch a different set of neurons fired leading to the mental experience of a different spot.

So both mental experiences exist simultaneously, but you only experience one - because you ARE that particular mental experience.

OK, so you’ve observed the result of the experiment.

Different yous have observed all results.

Now let’s say you record the results of the experiments by tallying spots on two sheets of paper - one to your left for electrons that hit the left of the screen, and one to your right for right-landing electrons.

After your visual cortex gets an image of the computer screen, a small slice of your brain's wavefunction splits in response to the possible results.

And the split grows, triggering different, decohered responses in your motor cortex.

Ultimately your body’s position wavefunction splits - in one version you move left, in the other you move right.

To the left you may bump over your coffee and cleaning it up are late, only just catching your train.

You don’t find a seat and so end up standing next to where the you of the other branch sits.

And, I don’t know, maybe next to the love of your life, who convinces you to leave research and start a small bed and breakfast in Argentina.

Two lives diverge, and worlds are irreconcilably split.

But where are they really in relation to each other?

Is right-turning you sitting right there on the same train, but out of phase with left-turning you?

Well, sort of - in the sense that the position wavefunctions of the two yous can be mapped to these spatial locations.

In that sense, we can think of the different worlds as separate patterns of ripples on the surface of the pond.

They overlap in location, but are so hopelessly out of phase that they can never interfere with each other - they just pass straight through.

In our pond analogy, it’s as though the ripples that make up the other worlds fill all locations with all possible phases and so it's as though those ripples aren’t there at all.

A ripple pattern - a “world” - is only there if you share a phase relation with it.

You become entangled with the final state of the electron - correlated with it - one version of you maps only to the right-landing electron, one only to the left.

Now I’m not saying Many Worlds is right.

Certainly some ways in which its represented are definitely wrong.

For example, worlds don’t split constantly and irreversibly.

On a quantum scale, worlds - or wavefunction components - recombine all the time.

Splitting happens when phase relations are scrambled due to interactions - and that’s - the entire universe doesn’t split with every atomic wiggle.

Many Worlds should also not be taken on faith - we should keep trying to come up with tests.

And one idea does exist - which may allow us to actually send messages between worlds - assuming they exist.

But that’s for another time - and I’ll do my best to bring it to every future branch of our splitting quantum space time.