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.
Before we get to comments, we wanted to let you know that if you’re looking for a fun
show for the young scientists in your lives, than you should check out MEGAWOW on the PBS
Kids Youtube Channel. This show is designed
to get kids excited about science through fun experiments. If you check it out, remember
to tell them, politely, that Space Time sent you!
Last episode we talked about this one very weird white dwarf star that scientists think
may be the first observation of the result of the merger of two white dwarfs - and how
this may have huge implications for all of cosmology. Let’s see what you had to say
Tom MS asks how can you rule out that this white dwarf got its weird properties like its rapid rotation from being
the result of a merger, rather than being a more usual white dwarf accreting from a partner star
before being ejected from that binary system. OK, so Tom has a couple of good insights here
- first is that a white dwarf could potentially gain a lot of angular momentum or spin by absorbing
material from another star, hence perhaps explaining that high spin. And the second is
that, in order for that explanation to be valid we’d need to know what happened to
the other star.
Let’s turn to another comment by awuma to help answer this. Awuma tells us that such
rapidly rotating white dwarfs are found in post-common envelope close binary systems
- V471 Tauri with its 7 minute rotation being a good example. For those non-white-dwarf-astrophysicists out
there, a common envelope binary system is one where the stars are so close together that they
share an envelope - you can also describe that as saying he white dwarf orbits inside
the other star. Now V471 is a post-common-envelope system, meaning the white dwarf presumably
ate up the surrounding envelope, leaving behind a red dwarf.
So this tells me that yes, you can greatly spin up a white dwarf by feeding it the envelope
of its binary partner. But is there a way to then get rid of the rest of that partner?
Well, one possibility is that the partner goes on to explode as a supernova. But the
mass transfer onto the white dwarf actually makes this less likely because losing mass
reduces the internal pressure, the fusion rate, etc. You can actually defuse a potential future
supernova by sucking away its outer layers. The question is the can you absorb just enough
gas to spin up the white dwarf while still allowing the partner star to explode? Well, I'm not
sure - but it seems these scientists think that, that's less likely that the white dwarf collision explanation,
which at any rate we know must happen at least sometimes.
Cyber Persona asks what happens to the star’s magnetic fields after it goes supernova. And
then guesses the correct answer - it dissipates into space with the matter, potentially leading
to electromagnetic radiation. And that is exactly it. The supernova shock front is a mixture
of high energy particles and magnetic fields. Those magnetic fields do lots of things - including
accelerating particles to even higher energies. This is believed to be one source of cosmic
rays that reach the earth. The magnetic fields then go on to add to the galaxy’s magnetic field.
We see that field in many ways, including by watching the radio light emitted by electrons
spiraling in that magnetic field - what we call synchrotron radiation. Galactic magnetic
fields have very clear bubble-like structures that come from past supernovae.
Now I started that episode with a mangled quote - scientific progress is accompanied not by
cries of “Eureka”, but instead by murmurs of “huh, that’s weird”. Vingador das
Estrelas pointed out that the more common version is “The most exciting phrase to
hear in science, the one that heralds new discoveries, is not 'Eureka!' but 'That's
funny…” attributed to Isaac Asimov. Turns out the true origin is probably even more obscure
- It appears in the 1976 textbook Introduction to the History of Mycology by G. C. Ainsworth,
recounting Alexander Fleming’s discovery of the bacteria-killing power of penicillin
- upon noticing the “lysis of the staphylococci” his cry of Eureka was “that’s funny”.
The Asimov attribution first appeared in fortune, a random quote generator program
in UNIX - so a totally reliable source. I got the real answer from this from the quote investigator
web site, but not before spending … way too long trying to find out. The real lesson
is don’t get stuck down quote verification rabbit holes. Which apparently I’m never
going to learn. Of course as Einstein said, "The definition of insanity is doing the same thing over
and over and expecting different results.” Which, by the way, is also a misattribution - that
was in the 1981 book produced by narcotics anonymous. Dammit. See what I mean?