Oh Hello There.

I’m Matt from a different quantum timeline.

I figured out the secret truth behind quantum mechanics and I’m sending it to Matt in your timeline so he can tell you.

Stand by.

Listen to the world around you for a moment… What do you hear?

My voice, obviously.

No doubt a sublime subjective experience - but only subjective.

Outside your skull, that sound is nothing but an expanding series of density waves - air molecules mindlessly bumping and shoving each other, oblivious to the complex wave structure that they propagate.

And that sound wave itself can be deconstructed into an overlapping set of simple sinusoidal waves that move independently of each other, in exactly the combination of frequencies and amplitudes to encode me talking about them.

And there are other sounds - the background music, maybe your computer’s fan, or the dishwasher, or the wind, birds, traffic.

Each sound is its own configuration of overlapping sinusoidal waves.

All these waves overlap to produce a fantastically complex bath of density fluctuations.

A snapshot of particle positions in the room would reveal a hopeless scramble.

And yet somehow your ear and your brain’s audio processing network can pick out and focus on each individual sound.

Everything I just described is real, but it’s also an analogy for the quantum multiverse.

A tenuous analogy - but bare with me.

In a recent episode I showed you how overlapping systems of ripples on a pond evolve independently of each other due to something called the superposition principle.

This principle also applies to the wavefunction in quantum mechanics.

In the Many Worlds interpretation of quantum mechanics, the universal wavefunction is the reality, encompassing all possible histories and futures and all exist.

But we are only sensitive to a slice of the wavefunction corresponding to our “world”, and due to the superposition principle our world can happily do its thing unperturbed by other parts of the wavefunction - other “ripples”, or worlds.

It’s as though you were only sensitive to one source of sound - say, my voice - and your brain filtered out all the others.

The presence of those other sound waves has no impact on how my voice propagates.

OK, cute analogy, but perhaps pointless because we don’t even know if Many Worlds is right.

There are other ways to interpret the math of quantum mechanics that don’t require a multiverse.

For example there’s the Copenhagen Interpretation, which says that the wavefunction collapses at the point of measurement, leaving only one reality; or de Broglie-Bohm pilot wave theory, which says that particles are particles and waves are waves - and the wavefunction’s job is to shuttle actual real particles around - again, leading to one reality.

And there are quite a few others besides.

We’re now approaching 100 years since the discovery of quantum mechanics, and we still don’t know which of these - if any - are right.

So what’s the holdup?

A clue to the problem lies in the word “interpretation” - an interpretation of quantum mechanics is exactly that - it’s a story about what's really happening behind the math - what “physical” mechanisms give rise to the equations of quantum mechanics.

And the fact is, every prominent interpretation of quantum mechanics is perfectly consistent with the equation that lies at the heart of the theory - that’s the Schrodinger equation.

The Schrodinger equation describes how the wavefunction of a quantum system changes over space and time - and so it should completely determine the measurements we can make of that quantum system.

But if our observations are 100% determined by the Schrodinger equation, and all interpretations give the same Schrodinger equation, then how can any measurement ever tell between these interpretations?

It turns out there might be a way - but only if the Schrodinger equation is wrong.

Well, not wrong but incomplete.

There are certain additional terms that we could add to the Schrodinger equation that may have such a tiny influence that we haven’t noticed them before.

But if they’re real we could distinguish between these interpretations.

And much more than that - they’d give us some pretty crazy science fiction powers - I’m talking faster than light communication, and even the ability to send messages between the worlds of the quantum multiverse - if it turns out that actually exists.

To understand all of this, let’s first go back to sound waves.

As we discussed in that previous episode, this ability for waves to pass through each other without being scrambled is due to the superposition principle.

Let’s dig a little deeper.

This principle says that you can determine the evolution of multiple overlapping waves by calculating the evolution for each wave separately and then adding together the result.

For that to be true, the medium carrying the wave has to behave in a particular way - whether that medium is water, air, the fabric of spacetime itself.

Waves can happen in any elastic medium - anything that tends to return to an equilibrium state after being stretched or displaced, because that can produce an oscillation, and in which adjacent points pull on each other, cause that can cause the oscillation to travel.

In the simplest imaginable case, the force that tries to bring the medium back to equilibrium is just proportional to the displacement at each point.

That’s the case for the most idealized oscillation - the simple harmonic oscillator.

And that tends to be a good approximation for any elastic medium as long as the displacement is small.

The restoring force of a simple harmonic oscillator is what we call linear - which just means that the output - the restoring force - is proportional to the input - the displacement.

That’s what allows two overlapping displacements to be treated independently.

A linear restoring force leads to a linear wave equation - and a linear wave equation is what you need for the superposition principle to be satisfied.

Now in the physical world the superposition principle only holds to a point.

Real pond surfaces or air density fields don’t behave like simple harmonic oscillators if you try to change them by too much.

Non-linearities creep in which can do things like damp the waves - cause them to lose energy.

But the Schrodinger equation as we usually write it is a perfectly linear equation, and in quantum mechanics it’s always assumed that linearity and the superposition principle hold.

Stack wavefunctions on top of each other and they behave as though the others aren’t there.

This gives us a sense of why it seems impossible to test the Many Worlds hypothesis - those other worlds by definition have no effect on our own.

That’s true as long as the Schrodinger equation is perfectly linear.

But here’s the rub: it turns out that if the Schrodinger equation has extra terms, however tiny, that are non-linear, then everything changes.

Not only can we test quantum interpretations, but we can do some things that really should be impossible.

It was the Nobel laureate Steven Weinberg who had the first insight.

He realized that even a tiny deviation from linearity in the Schrodinger equation would add extra non-linear observables to the wavefunction.

The normal linear observables are things like position, momentum, spin - the physical stuff that makes up our world.

Extra observables would be non-local - they would exist across the entire wavefunction.

And that, in principle, could give a way to explore what happens to the wavefunction after measurement.

Does it vanish as Copenhagen demands, or persist as many worlds would have us believe?

Weinberg’s fun little paper may have been overlooked if it hadn’t caught the attention of another brilliant physicist, Joseph Polchinski.

In a single 1991 paper, Polchinski showed how Weinberg’s “non-linear observables” would make it possible to achieve some pretty crazy science fiction effects.

First Polchinski showed that almost any non-linear addition to the Schrodinger equation would mean that information could be sent between entangled pairs of particles.

Now we’ve been over entanglement before, but to remind you: if two particles are entangled then their properties are correlated.

By choosing how to measure one of the pair, you influence the state of its partner - essentially instantaneously and over any distance.

However the nature of this influence makes it impossible to send actual information this way.

You can only detect that the influence happened by comparing the measurement statistics of multiple entangled pairs - and to do that you need to send regular, sub-light-speed information.

It’s almost like the universe conspires to prevent any superluminal effects.

But in exactly 11 lines of math, Polchinski shows that this conspiracy is delicate.

Almost ANY deviation from perfect linearity in the Schrodinger equation would make it possible to send real information between entangled pairs of particles, enabling instant communication at any distance, and even backwards in time.

Now Polchinski doesn’t actually tell us how to do this - he only proves that it should be possible in principle.

But he was only getting started.

He follows up by finding a way to write one non-linear Schrodinger equation that avoids the causality-breaking prospect of faster-than-light communication.

And it turns out that in doing so he stumbles upon a way to communicate between the worlds of the quantum multiverse.

And this time he actually tells us how to do it, inventing what he calls the Everett-Wheeler telephone, after Hugh Everett - the guy who came up with the Many Worlds interpretation, and John Archibald Wheeler, Everett’s graduate advisor.

Let me run you through it.

We’re going to use a Stern-Gerlach device - something we’ve talked about a bunch.

Basically it’s a pair of magnets - a north and south pole - that deflect particles with spin and charge.

It measures the direction of spin by whether the particles are deflected to the north or south pole.

Quantum particles will always be found to have a spin in the direction that you choose to align the magnets.

So your choice affects the quantum wavefunction.

Polchinski lays out the steps very clearly: you send a spin half particle like an electron through a Stern-Gerlach device and then you measure the direction of the spin.

It has to be pointing either to the north or south poles - we’ll call them up or down.

In the many-worlds interpretation, by making that measurement you just split the world in two and you split yourself.

In one world you measure spin down - we’ll call that spin-down you … you.

In the other world, other you will measure spin up - we’ll call spin-up you “other you”.

So now you will now try to send a message to other you.

First, you, but not other you, need to inject some information into the electron’s wavefunction.

You’ll do that by making a choice: either you leave the electron with spin-down, or you rotate it to spin-up.

After that, both you’s send their version of the electron to some hypothetical and perhaps impossible device that subjects both branches of the electron wavefunction to a non-linear field.

That field sort of spreads the local information from each branch - each world - through the entire electron wavefunction.

Finally, the electrons go back through the Stern-Gerlach device and other you measures the spin once again.

If you chose to rotate your electron from down to up, other you will find their electron rotated from up to down.

If you did nothing, other you will also find no change.

You’ve now successfully transmitted a single bit of information between quantum timelines.

The real math is quite a bit more complicated, but I've given you a sense of it.

In order to build an actual telephone you probably want to send more than a single bit.

Unfortunately you can’t just use more electrons, because each electron further splits the worlds - you’ll just be sending a single bit to more you’s.

Polchinski’s idea really just serves as a proof of concept that in a non-linear quantum mechanics, actions can influence the entire wavefunction - spanning different “worlds”.

Perhaps real communication would be possible, however there’s one hard limitation - you can only talk to worlds created by the action of the telephone itself.

I’m afraid that the world where you made all of those better decisions about your life remains forever out of reach.

OK to summarize: either quantum mechanics is perfectly linear and you should forget I said anything, OR it’s nonlinear and we can instantly communicate across any distance and back in time, OR we can communicate across the branches of the quantum multiverse.

According to Polchinski exactly one and only one of those must be true.

Perhaps there’s a me on a different timeline, or in the future, who’s smart enough to figure all of this out and is now sending me a message.

I guess he chose a different me.

There are, after all, many worlds in the greater Everettian space time.