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Table of contents
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Table of contents

0:00
Intro
0:18
What do you hear
1:23
Superposition Principle
2:33
Other Interpretations
2:56
The Schrdinger Equation
4:30
Sound Waves
6:39
Nonlinearities
9:36
The Everett Wheeler Telephone
13:42
Comments
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00:00:00
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.
00:00:17
Listen to the world around you for a moment… What do you hear? My voice, obviously.
00:00:23
No doubt a sublime subjective experience - but only subjective. Outside your skull, that
00:00:28
sound is nothing but an expanding series of density waves - air molecules mindlessly bumping
00:00:34
and shoving each other, oblivious to the complex wave structure that they propagate. And that
00:00:39
sound wave itself can be deconstructed into an overlapping set of simple sinusoidal waves
00:00:45
that move independently of each other, in exactly the combination of frequencies and
00:00:49
amplitudes to encode me talking about them.
00:00:53
And there are other sounds - the background music, maybe your computer’s fan, or the
00:00:58
dishwasher, or the wind, birds, traffic. Each sound is its own configuration of overlapping
00:01:03
sinusoidal waves. All these waves overlap to produce a fantastically complex bath of
00:01:09
density fluctuations. A snapshot of particle positions in the room would reveal a hopeless
00:01:15
scramble. And yet somehow your ear and your brain’s audio processing network can pick
00:01:21
out and focus on each individual sound.
00:01:23
Everything I just described is real, but it’s also an analogy for the quantum multiverse.
00:01:29
A tenuous analogy - but bare with me. In a recent episode I showed you how overlapping
00:01:34
systems of ripples on a pond evolve independently of each other due to something called the
00:01:40
superposition principle. This principle also applies to the wavefunction in quantum mechanics.
00:01:46
In the Many Worlds interpretation of quantum mechanics, the universal wavefunction is the
00:01:50
reality, encompassing all possible histories and futures and all exist. But we are only
00:01:56
sensitive to a slice of the wavefunction corresponding to our “world”, and due to the superposition
00:02:02
principle our world can happily do its thing unperturbed by other parts of the wavefunction
00:02:08
- other “ripples”, or worlds. It’s as though you were only sensitive to one source
00:02:13
of sound - say, my voice - and your brain filtered out all the others. The presence
00:02:17
of those other sound waves has no impact on how my voice propagates.
00:02:22
OK, cute analogy, but perhaps pointless because we don’t even know if Many Worlds is right.
00:02:29
There are other ways to interpret the math of quantum mechanics that don’t require
00:02:32
a multiverse. For example there’s the Copenhagen Interpretation, which says that the wavefunction
00:02:37
collapses at the point of measurement, leaving only one reality; or de Broglie-Bohm pilot
00:02:43
wave theory, which says that particles are particles and waves are waves - and the wavefunction’s
00:02:47
job is to shuttle actual real particles around - again, leading to one reality. And there
00:02:53
are quite a few others besides.
00:02:56
We’re now approaching 100 years since the discovery of quantum mechanics, and we still
00:03:01
don’t know which of these - if any - are right. So what’s the holdup? A clue to the
00:03:05
problem lies in the word “interpretation” - an interpretation of quantum mechanics is
00:03:11
exactly that - it’s a story about what's really happening behind the math - what “physical”
00:03:16
mechanisms give rise to the equations of quantum mechanics. And the fact is, every prominent
00:03:22
interpretation of quantum mechanics is perfectly consistent with the equation that lies at
00:03:27
the heart of the theory - that’s the Schrodinger equation.
00:03:30
The Schrodinger equation describes how the wavefunction of a quantum system changes over
00:03:35
space and time - and so it should completely determine the measurements we can make of
00:03:40
that quantum system. But if our observations are 100% determined by the Schrodinger equation,
00:03:46
and all interpretations give the same Schrodinger equation, then how can any measurement ever
00:03:51
tell between these interpretations?
00:03:55
It turns out there might be a way - but only if the Schrodinger equation is wrong. Well,
00:04:01
not wrong but incomplete. There are certain additional terms that we could add to the
00:04:05
Schrodinger equation that may have such a tiny influence that we haven’t noticed them
00:04:09
before. But if they’re real we could distinguish between these interpretations. And much more than
00:04:16
that - they’d give us some pretty crazy science fiction powers - I’m talking faster
00:04:21
than light communication, and even the ability to send messages between the worlds of the
00:04:26
quantum multiverse - if it turns out that actually exists.
00:04:30
To understand all of this, let’s first go back to sound waves. As we discussed in that
00:04:35
previous episode, this ability for waves to pass through each other without being scrambled
00:04:40
is due to the superposition principle. Let’s dig a little deeper. This principle says that
00:04:46
you can determine the evolution of multiple overlapping waves by calculating the evolution
00:04:50
for each wave separately and then adding together the result. For that to be true, the medium
00:04:56
carrying the wave has to behave in a particular way - whether that medium is water, air, the
00:05:02
fabric of spacetime itself. Waves can happen in any elastic medium - anything that tends
00:05:09
to return to an equilibrium state after being stretched or displaced, because that can produce
00:05:14
an oscillation, and in which adjacent points pull on each other, cause that can cause the
00:05:19
oscillation to travel.
00:05:21
In the simplest imaginable case, the force that tries to bring the medium back to equilibrium
00:05:27
is just proportional to the displacement at each point. That’s the case for the most
00:05:32
idealized oscillation - the simple harmonic oscillator. And that tends to be a good approximation
00:05:39
for any elastic medium as long as the displacement is small.
00:05:43
The restoring force of a simple harmonic oscillator is what we call linear - which just means
00:05:49
that the output - the restoring force - is proportional to the input - the displacement.
00:05:54
That’s what allows two overlapping displacements to be treated independently. A linear restoring
00:06:01
force leads to a linear wave equation - and a linear wave equation is what you need for
00:06:07
the superposition principle to be satisfied.
00:06:09
Now in the physical world the superposition principle only holds to a point. Real pond
00:06:14
surfaces or air density fields don’t behave like simple harmonic oscillators if you try to change
00:06:21
them by too much. Non-linearities creep in which can do things like damp the waves - cause
00:06:27
them to lose energy.
00:06:28
But the Schrodinger equation as we usually write it is a perfectly linear equation, and
00:06:34
in quantum mechanics it’s always assumed that linearity and the superposition principle
00:06:39
hold. Stack wavefunctions on top of each other and they behave as though the others aren’t
00:06:43
there. This gives us a sense of why it seems impossible to test the Many Worlds hypothesis
00:06:47
- those other worlds by definition have no effect on our own. That’s true as long as
00:06:54
the Schrodinger equation is perfectly linear. But here’s the rub: it turns out that if
00:07:00
the Schrodinger equation has extra terms, however tiny, that are non-linear, then everything
00:07:07
changes. Not only can we test quantum interpretations, but we can do some things that really should
00:07:12
be impossible.
00:07:14
It was the Nobel laureate Steven Weinberg who had the first insight. He realized that
00:07:19
even a tiny deviation from linearity in the Schrodinger equation would add extra non-linear
00:07:24
observables to the wavefunction. The normal linear observables are things like position,
00:07:30
momentum, spin - the physical stuff that makes up our world. Extra observables would be non-local
00:07:36
- they would exist across the entire wavefunction. And that, in principle, could give a way to
00:07:41
explore what happens to the wavefunction after measurement. Does it vanish as Copenhagen
00:07:46
demands, or persist as many worlds would have us believe?
00:07:50
Weinberg’s fun little paper may have been overlooked if it hadn’t caught the attention
00:07:54
of another brilliant physicist, Joseph Polchinski. In a single 1991 paper, Polchinski showed
00:08:00
how Weinberg’s “non-linear observables” would make it possible to achieve some pretty
00:08:05
crazy science fiction effects.
00:08:08
First Polchinski showed that almost any non-linear addition to the Schrodinger equation would
00:08:13
mean that information could be sent between entangled pairs of particles. Now we’ve
00:08:17
been over entanglement before, but to remind you: if two particles are entangled then their
00:08:22
properties are correlated. By choosing how to measure one of the pair, you influence
00:08:29
the state of its partner - essentially instantaneously and over any distance. However the nature
00:08:35
of this influence makes it impossible to send actual information this way. You can only
00:08:39
detect that the influence happened by comparing the measurement statistics of multiple entangled
00:08:45
pairs - and to do that you need to send regular, sub-light-speed information. It’s almost
00:08:51
like the universe conspires to prevent any superluminal effects.
00:08:55
But in exactly 11 lines of math, Polchinski shows that this conspiracy is delicate. Almost ANY
00:09:03
deviation from perfect linearity in the Schrodinger equation would make it possible to send real
00:09:09
information between entangled pairs of particles, enabling instant communication at any distance,
00:09:15
and even backwards in time. Now Polchinski doesn’t actually tell us how to do this
00:09:20
- he only proves that it should be possible in principle.
00:09:23
But he was only getting started. He follows up by finding a way to write one non-linear
00:09:29
Schrodinger equation that avoids the causality-breaking prospect of faster-than-light communication.
00:09:36
And it turns out that in doing so he stumbles upon a way to communicate between the worlds of the
00:09:42
quantum multiverse. And this time he actually tells us how to do it, inventing what he calls the
00:09:49
Everett-Wheeler telephone, after Hugh Everett - the guy who came up with the Many Worlds
00:09:53
interpretation, and John Archibald Wheeler, Everett’s graduate advisor.
00:09:57
Let me run you through it. We’re going to use a Stern-Gerlach device - something we’ve
00:10:01
talked about a bunch. Basically it’s a pair of magnets - a north and south pole - that
00:10:05
deflect particles with spin and charge. It measures the direction of spin by whether
00:10:10
the particles are deflected to the north or south pole. Quantum particles will always
00:10:15
be found to have a spin in the direction that you choose to align the magnets. So your choice
00:10:20
affects the quantum wavefunction. Polchinski lays out the steps very clearly: you send
00:10:27
a spin half particle like an electron through a Stern-Gerlach device and then you measure
00:10:32
the direction of the spin. It has to be pointing either to the north or south poles - we’ll
00:10:38
call them up or down. In the many-worlds interpretation, by making that measurement you just split
00:10:44
the world in two and you split yourself. In one world you measure spin down - we’ll
00:10:51
call that spin-down you … you. In the other world, other you will measure spin up - we’ll
00:10:58
call spin-up you “other you”. So now you will now try to send a message to other you.
00:11:05
First, you, but not other you, need to inject some information into the electron’s wavefunction.
00:11:11
You’ll do that by making a choice: either you leave the electron with spin-down, or
00:11:15
you rotate it to spin-up. After that, both you’s send their version of the electron
00:11:21
to some hypothetical and perhaps impossible device that subjects both branches of the
00:11:25
electron wavefunction to a non-linear field. That field sort of spreads the local information
00:11:32
from each branch - each world - through the entire electron wavefunction. Finally, the
00:11:37
electrons go back through the Stern-Gerlach device and other you measures the spin once
00:11:42
again. If you chose to rotate your electron from down to up, other you will find their
00:11:48
electron rotated from up to down. If you did nothing, other you will also find no change.
00:11:53
You’ve now successfully transmitted a single bit of information between quantum timelines.
00:12:00
The real math is quite a bit more complicated, but I've given you a sense of it. In order to
00:12:05
build an actual telephone you probably want to send more than a single bit. Unfortunately
00:12:10
you can’t just use more electrons, because each electron further splits the worlds - you’ll
00:12:15
just be sending a single bit to more you’s. Polchinski’s idea really just serves as
00:12:21
a proof of concept that in a non-linear quantum mechanics, actions can influence the entire
00:12:27
wavefunction - spanning different “worlds”. Perhaps real communication would be possible,
00:12:33
however there’s one hard limitation - you can only talk to worlds created by the action
00:12:38
of the telephone itself. I’m afraid that the world where you made all of those better
00:12:43
decisions about your life remains forever out of reach.
00:12:47
OK to summarize: either quantum mechanics is perfectly linear and you should forget I said anything,
00:12:53
OR it’s nonlinear and we can instantly communicate across any distance and back in time, OR we can communicate
00:13:01
across the branches of the quantum multiverse. According to Polchinski exactly one and only
00:13:07
one of those must be true. Perhaps there’s a me on a different timeline, or in the future,
00:13:14
who’s smart enough to figure all of this out and is now sending me a message. I
00:13:21
guess he chose a different me. There are, after all, many worlds in the greater Everettian
00:13:26
space time.
00:13:40
Before we get to comments, we wanted to let you know that if you’re looking for a fun
00:13:46
show for the young scientists in your lives, than you should check out MEGAWOW on the PBS
00:13:51
Kids Youtube Channel. This show is designed
00:13:54
to get kids excited about science through fun experiments. If you check it out, remember
00:13:59
to tell them, politely, that Space Time sent you!
00:14:02
Last episode we talked about this one very weird white dwarf star that scientists think
00:14:07
may be the first observation of the result of the merger of two white dwarfs - and how
00:14:12
this may have huge implications for all of cosmology. Let’s see what you had to say
00:14:17
Tom MS asks how can you rule out that this white dwarf got its weird properties like its rapid rotation from being
00:14:25
the result of a merger, rather than being a more usual white dwarf accreting from a partner star
00:14:31
before being ejected from that binary system. OK, so Tom has a couple of good insights here
00:14:36
- first is that a white dwarf could potentially gain a lot of angular momentum or spin by absorbing
00:14:42
material from another star, hence perhaps explaining that high spin. And the second is
00:14:46
that, in order for that explanation to be valid we’d need to know what happened to
00:14:51
the other star.
00:14:53
Let’s turn to another comment by awuma to help answer this. Awuma tells us that such
00:14:59
rapidly rotating white dwarfs are found in post-common envelope close binary systems
00:15:05
- V471 Tauri with its 7 minute rotation being a good example. For those non-white-dwarf-astrophysicists out
00:15:13
there, a common envelope binary system is one where the stars are so close together that they
00:15:20
share an envelope - you can also describe that as saying he white dwarf orbits inside
00:15:24
the other star. Now V471 is a post-common-envelope system, meaning the white dwarf presumably
00:15:30
ate up the surrounding envelope, leaving behind a red dwarf.
00:15:35
So this tells me that yes, you can greatly spin up a white dwarf by feeding it the envelope
00:15:41
of its binary partner. But is there a way to then get rid of the rest of that partner?
00:15:46
Well, one possibility is that the partner goes on to explode as a supernova. But the
00:15:51
mass transfer onto the white dwarf actually makes this less likely because losing mass
00:15:57
reduces the internal pressure, the fusion rate, etc. You can actually defuse a potential future
00:16:03
supernova by sucking away its outer layers. The question is the can you absorb just enough
00:16:09
gas to spin up the white dwarf while still allowing the partner star to explode? Well, I'm not
00:16:15
sure - but it seems these scientists think that, that's less likely that the white dwarf collision explanation,
00:16:21
which at any rate we know must happen at least sometimes.
00:16:27
Cyber Persona asks what happens to the star’s magnetic fields after it goes supernova. And
00:16:31
then guesses the correct answer - it dissipates into space with the matter, potentially leading
00:16:37
to electromagnetic radiation. And that is exactly it. The supernova shock front is a mixture
00:16:43
of high energy particles and magnetic fields. Those magnetic fields do lots of things - including
00:16:48
accelerating particles to even higher energies. This is believed to be one source of cosmic
00:16:52
rays that reach the earth. The magnetic fields then go on to add to the galaxy’s magnetic field.
00:16:58
We see that field in many ways, including by watching the radio light emitted by electrons
00:17:03
spiraling in that magnetic field - what we call synchrotron radiation. Galactic magnetic
00:17:08
fields have very clear bubble-like structures that come from past supernovae.
00:17:12
Now I started that episode with a mangled quote - scientific progress is accompanied not by
00:17:17
cries of “Eureka”, but instead by murmurs of “huh, that’s weird”. Vingador das
00:17:22
Estrelas pointed out that the more common version is “The most exciting phrase to
00:17:27
hear in science, the one that heralds new discoveries, is not 'Eureka!' but 'That's
00:17:31
funny…” attributed to Isaac Asimov. Turns out the true origin is probably even more obscure
00:17:37
- It appears in the 1976 textbook Introduction to the History of Mycology by G. C. Ainsworth,
00:17:44
recounting Alexander Fleming’s discovery of the bacteria-killing power of penicillin
00:17:50
- upon noticing the “lysis of the staphylococci” his cry of Eureka was “that’s funny”.
00:17:57
The Asimov attribution first appeared in fortune, a random quote generator program
00:18:05
in UNIX - so a totally reliable source. I got the real answer from this from the quote investigator
00:18:12
web site, but not before spending … way too long trying to find out. The real lesson
00:18:19
is don’t get stuck down quote verification rabbit holes. Which apparently I’m never
00:18:24
going to learn. Of course as Einstein said, "The definition of insanity is doing the same thing over
00:18:30
and over and expecting different results.” Which, by the way, is also a misattribution - that
00:18:38
was in the 1981 book produced by narcotics anonymous. Dammit. See what I mean?

Description:

Check Out Megawow on PBS Kids: https://www.youtube.com/watch?v=meU4f31gqYI 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. And while it may seem like it would be physically impossible to have any connection between worlds, it may turn out to be entirely possible to communicate between them. More About Steven Weinberg: https://www.scientificamerican.com/article/learning-to-live-in-steven-weinbergs-pointless-universe/ Sign Up on Patreon to get access to the Space Time Discord! https://www.patreon.com/pbsspacetime Check out the Space Time Merch Store https://crowdmade.com/collections/pbsspacetime Sign up for the mailing list to get episode notifications and hear special announcements! https://mailchi.mp/1a6eb8f2717d/spacetime Hosted by Matt O'Dowd Written by Matt O'Dowd Graphics by Leonardo Scholzer, Yago Ballarini, Pedro Osinski, Adriano Leal & Stephanie Faria Directed by Andrew Kornhaber Assistant Producer: Setare Gholipour Executive Producers: Eric Brown & Andrew Kornhaber End Credits Music by J.R.S. Schattenberg: https://www.youtube.com/user/MultiDroideka Special Thanks to Our Patreon Supporters BIg Bang Sponsors Kyle Bulloch Ananth Rao Charlie Mrs. Tiffany Poindexter Leo Koguan Sandy Wu Matthew Miller Scott Gray Ahmad Jodeh Alexander Tamas Morgan Hough Juan Benet Vinnie Falco Fabrice Eap Mark Rosenthal David Nicklas Quasar Supporters Ethan Cohen Stephen Wilcox Christina Oegren Mark Heising Hank S Hypernova Supporters william bryan Kaci Parker drollere Joe Moreira Marc Armstrong Elizabeth Smith Scott Gorlick Nick Berard Paul Stehr-Green MuON Marketing Russell Pope Ben Delo Nicholas Newlin DrJYou Антон Кочков John R. Slavik Mathew Danton Spivey Donal Botkin John Pollock Edmund Fokschaner Joseph Salomone Matthew O'Connor chuck zegar Jordan Young m0nk John Hofmann Daniel Muzquiz Timothy McCulloch Gamma Ray Burst Supporters Andre Stechert Ross Bohner Farhan Wali Paul Wood Kent Durham jim bartosh Nubble Chris Navrides Scott R Calkins Carl Scaggs G Mack The Mad Mechanic Ellis Hall John H. Austin, Jr. Diana S Ben Campbell Lawrence Tholl, DVM Faraz Khan Almog Cohen Alex Edwards Ádám Kettinger MD3 Endre Pech Daniel Jennings Cameron Sampson Pratik Mukherjee Geoffrey Clarion Nate Adrian Posor Darren Duncan Russ Creech Jeremy Reed Eric Webster Steven Sartore David Johnston J. King Michael Barton Christopher Barron James Ramsey Justin Jermyn Mr T Andrew Mann Jeremiah Johnson Peter Mertz Isaac Suttell Devon Rosenthal Oliver Flanagan Bleys Goodson Robert Walter Bruce B Ismael Montecel Simon Oliphant Mirik Gogri Mark Daniel Cohen Brandon Lattin Nickolas Andrew Freeman Protius Protius Shane Calimlim Tybie Fitzhugh Robert Ilardi Eric Kiebler Craig Stonaha Martin Skans Michael Conroy Graydon Goss Frederic Simon Tonyface John Robinson A G Kevin Lee Adrian Hatch Yurii Konovaliuk John Funai Cass Costello Tristan Deloche Bradley Jenkins Kyle Hofer Daniel Stříbrný Luaan AlecZero Vlad Shipulin Cody Malte Ubl King Zeckendorff Nick Virtue Scott Gossett Dan Warren Patrick Sutton John Griffith Daniel Lyons Julien Dubois DFaulk GrowingViolet Kevin Warne Andreas Nautsch Brandon labonte

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