Quantum Darwinism (Script) (Patreon)

This episode of space time is brought to you by the information flowing through an impossibly complex network of quantum entanglement, that just happens to mutually agree that you and I exist inside it. Oh, and Schrodinger’s cat is in here too.

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In quantum world things are routinely in multiple states at once - what we call a “superposition” of states. But in the classical world of large scales, things are either this or that. The famous thought experiment is Schrodinger’s cat - in which a cat is in an opaque box with a vial of deadly poison that’s released on the radioactive decay of an atom. Quantum mechanics tells us that the atom’s wavefunction can be in a superposition of states - simultaneously decayed or not decayed. So is the cat’s wavefunction also in a superposition of both dead and alive.

That seems absurd - but quantum mechanics appears to allow this. In fact the idea of superposition is fundamental to quantum mechanics. Pick any two valid quantum states - the sum of those states is also a valid state. In fact, at the quantum level, there isn’t a clear way to define what states are the most basic. Even very distinct-seeming properties can be expressed as superpositions -  for example a particle’s position can be expressed as a superposition of momentum states. I’ll come back to another example of this in a sec. But it raises the question: for Schrodinger’s cat, if alive AND dead is just as valid as alive OR dead, why do we only see the later in the real world?

The idea of decoherence seems to provide a partial answer - we talked about it last time - to observe a superposition there needs to be a knowable phase relation between two superposed states. But that doesn’t tell us why certain states that exist in the quantum world can survive this decoherence and become manifest in the classical world. To get the entire answer, we need to think about quantum entanglement. In fact we’ll see that the properties we think of as fundamental - for example the arrangement of atoms that define a living or dead cat - aren’t properties of the atoms. Rather, the information that defines these classical properties exists in the fantastically complex network of entanglement between those individual quantum system and its environment.

The ideas I’m about to lay out are mostly due to Wojciech Zurek, who calls this framework quantum darwinism - and you’ll see why. To get there we need to start by talking about quantum superposition.

Some quantum particles have a property called quantum spin. That spin has an axis that points in some direction, analogous to the axis of a rotating ball. To measure that spin axis you have to choose what angle you want to measure it at - say, vertically or horizontally. Measure vertically and you might see that the spin axis is pointing up or down, measure horizontally and it’ll be pointing left or right. Weirdly, if you measure vertically and see an up spin, then measure horizontally you will NOT find that there’s zero spin in that direction, as you’d expect for a classical spinning object. Instead the electron will randomly shift ot having left or right spin.

So the value quantum spin depends on how you choose to measure it - it depends on your “measurement basis”. And a well defined spin direction in one basis can be expressed as a superposition of two spin directions in another basis. For example, spin-up is equivalently a particular combination of spin-left and spin-right. Same with spin-down. 

Spin becomes defined in each new basis when you try to measure it that way, and in the process becomes undefined in any previous basis. This is an example of how seemingly-fundamental quantum states can be expressed as superpositions of other states. So again - why are only certain quantum states observable on large scales? The answer lies in entanglement.

The most famous entanglement experiment is the one that Einstein came up with to demonstrate an apparent absurdity predicted by pure quantum mechanics. This is the so-called Einstein-Podolsky-Rosen, or EPR paradox. A high energy photon decays into an electron and a positron. These particles both have spin values of 1/2, but the original photon had spin 0. So the axes of the new spins have to be opposite in order to cancel out and conserve angular momentum. But besides being opposite to each other they can be aligned in any direction. In fact each particle is in a superposition of states - measured in the vertical basis, each particle starts in a state of both up AND down, while in the horizontal each is left AND right, etc. The only thing we know is there’s this correlation - whatever spin direction gets measured for one particle, the other particle has to be opposite in the same basis. We say that two particles with these sort of correlated properties are entangled.

The crazy thing here is if I measure the spin of one particle - say the electron - my choice of measurement basis defines the spin of the positron. If I measure the electron in the vertical basis and get, say, spin-up, the positron will become defined in that basis and only that basis - in this case as spin-down. There’s a sense that a causal influence is transferred faster than light. This is what Einstein called spooky action at a distance, and we now know that this is a very real effect, even though you can’t actually transfer useful information this way. But we’re not here to talk about this crazy result directly - in fact we already did it a long time ago. We’re here to talk about how entanglement is connected to measurement and the collapse of the wavefunction.

Let’s think about exactly what’s happening when I try to measure the spin of one of those entangled particles. I’ll try to do that in the most subtle way possible. Here’s our measuring device - it’s a series of magnets designed to deflect the electron based on its up or down spin. Spin-up electrons are deflected upwards, spin-down electrons are deflected down. Then both types are deflected back to their original straight path. By itself this device isn’t useful - electrons passing through will still be in a superposition of spin states - both up and down, as though they traveled both paths.

But we can try to measure the spin state by placing a detection apparatus on one path. This “apparatus” is as subtle as possible: just a single atom with a very special property. If the electron passes close to the atom, the atom flips between two states. The nature of these two states doesn’t matter as long as it doesn’t change the spin or sap energy from the electron. One possibility would be that the spin of one of the electrons inside the atom gets flipped. But for simplicity, we’ll call these two states off and on.

OK, so, we put this atom along the up path of our device, and we start it out in the off state. If our electron takes the up path it flips the atom to the on state. If it takes the down path the atom remains in the off state. 

We should be able to just look at the atom to learn the electron’s path, and so learn its spin. So what happens after the ele ctron passes through our device. Does its spin count as measured? Does the positron’s spin immediately become defined? 

Actually no! After the electron passes through our device, we still have a superposition of states - but now that superposition includes the atom. We have to think of the electron PLUS the atom as being in a joint superposed state of: electron up, atom on AND electron down, atom off. The atom’s state is now correlated with the electron’s state - the two are entangled. Which means the atom’s state is also entangled with the positron’s state.

We could prove that by measuring the spin of the positron, which would instantaneously influence the combined state of the atom and electron. Or we could measure the atom’s state, which would influence the electron and positron. Here’s more evidence that the measurement hasn’t “happened” yet. Even with the vertically-aligned magnetic fields, which only affect the vertical component of the electron’s spin, we haven’t even defined the basis of the electron’s spin as up or down. It’s still undefined. See, the entangled atom now holds information about the electron’s left-right spin.

Whereas that information used to be expressible as a superposition of the electron’s up-down status, now it’s hidden in a superposition of the atom’s on-off status. Essentially, phase information got transferred from the electron to the atom.  I won’t go into the details here - suffice to say it’s possible to recover the horizontal spin information, even if it’s more straightforward to recover the vertical spin because of how we set up the device.

OK, so our atomic measurement device doesn’t “collapse the wavefunction”  and settle a measurement basis. So where does that happen? In order for us to be aware of a measurement we look at a macroscopic indicator - say, the pointer on a dial of our instrument. 

There’s a chain of quantum systems between that original atom and the pointer. Information spreads along this chain as these systems become entangled with each other. In fact that growing web of entanglement always contains all of the information about the quantum system being tested. The problem is, we never SEE all of that information. We only see the crude, macroscopic characteristics of the device - like the position of a pointer on a dial.

Zurek figured out why this might be the case. It turns out that as more and more particles join our entanglement web, information about quantum-level states get spread amongst them. It would be possible to extract this information if you could perfectly measure all particles in your measurement device. But eventually this entanglement cascade reaches the surrounding environment - it’s no longer bounded, and so the information about most quantum states can’t be recovered.

But there are certain very special quantum states whose information does NOT get hopelessly mixed through this entanglement web. These are properties of the quantum system - measurement bases - whose information is relatively simply reflected throughout the surrounding environment. We call these pointer states,   Pointer states are robustly copied and spread until the states of the surrounding macroscopic environment - for example our dial’s pointer - are strongly correlated with these states of our quantum system.

So what determines whether a quantum state can be a pointer state? Well to some extent the way you set up the experiment - whether you align your magnetic field vertically or horizontally. But ultimately they are states that can survive contact with the environment. We say that the environment selects certain sets of states to propagate - Zurek uses the term einselection, for environmentally induced superselection. And he coined the term quantum darwinism too, because we have these more “fit” states surviving and being replicated. There’s no meaningful mutation and natural selection, so the link to evolution is dubious. Still, makes for a great youtube video title.

OK, so how does any of this explain Schrodinger’s Cat? Well an important example of a pointer state is the position of a particle. Most quantum interactions depend heavily on the relative location of interacting particles. Therefore information about relative particle locations is robustly shared and propagated through the entanglement network. The individual particles do NOT have well-defined locations - they stay quantum-weird. But the entanglement network has this sort of collective consensus about those locations. The structure of macroscopic objects - including cats and dials - are strongly defined by the relative positions of their particles. Therefore the states of cats and dials will always appear well defined.

By the way - in case you missed it, I just told you how reality works. At least according to the framework of decoherence and propogating entanglement. The observable qualities of reality - object positions, feline mortality statuses, even the results of quantum measurements - do NOT exist in the underlying quantum objects. Quantum objects remain in undefined and superposed states with no prefered basis for observation. No, the macroscopic observables only exist as a sort of mutual agreement across the network of entanglements that connect those quantum systems. In a sense, WE exist in such a network. In this web of mutually consistent entanglement, even spooky-action-at-a-distance entangled particles maintain their correlations, no matter how far apart in boring old space time.

SHOOTING SCRIPT

This episode of space time is brought to you from the information flowing through an impossibly complex network of quantum entanglement, that just happens to mutually agree that you and I exist inside it. Oh, and Schrodinger’s cat is in here too.

—-

In quantum world things are routinely in multiple states at once - what we call a “superposition” of states. But in the classical world of large scales, things are either this or that. The famous thought experiment is Schrodinger’s cat - in which a cat is in an opaque box with a vial of deadly poison that’s released on the radioactive decay of an atom. Quantum mechanics tells us that the atom’s wavefunction can be in a superposition of states - simultaneously decayed or not decayed. So is the cat’s wavefunction also in a superposition of both dead and alive.

That seems absurd - but quantum mechanics appears to allow this. In fact the idea of superposition is fundamental to quantum mechanics. Pick any two valid quantum states - the sum of those states is also a valid state. In fact, at the quantum level, there isn’t a clear way to define what states are the most basic. Even very distinct-seeming properties can be expressed as superpositions -  for example a particle’s position can be expressed as a superposition of momentum states. I’ll come back to another example of this in a sec. But it raises the question: for Schrodinger’s cat, if alive AND dead is just as valid as alive OR dead, why do we only see the later in the real world?

The idea of decoherence seems to provide a partial answer - we talked about it last time - to observe a superposition there needs to be a knowable phase relation between two superposed states. But that doesn’t tell us why certain states that exist in the quantum world can survive this decoherence and become manifest in the classical world. To get the entire answer, we need to think about quantum entanglement. In fact we’ll see that the properties we think of as fundamental - for example the arrangement of atoms that define a living or dead cat - aren’t properties of the atoms. Rather, the information that defines these classical properties exists in the fantastically complex network of entanglement between those individual quantum system and its environment.

The ideas I’m about to lay out are mostly due to Wojciech Zurek, who calls this framework quantum darwinism - and you’ll see why. To get there we need to start by talking about quantum superposition.

Some quantum particles have a property called quantum spin. That spin has an axis that points in some direction, analogous to the axis of a rotating ball. To measure that spin axis you have to choose what angle you want to measure it at - say, vertically or horizontally. Measure vertically and you might see that the spin axis is pointing up or down, measure horizontally and it’ll be pointing left or right. Weirdly, if you measure vertically and see an up spin, then measure horizontally you will NOT find that there’s zero spin in that direction, as you’d expect for a classical spinning object. Instead the electron will randomly shift ot having left or right spin.

So the value quantum spin depends on how you choose to measure it - it depends on your “measurement basis”. And a well defined spin direction in one basis can be expressed as a superposition of two spin directions in another basis. For example, spin-up is equivalently a particular combination of spin-left and spin-right. Same with spin-down. Spin becomes defined in each new basis when you try to measure it that way, and in the process becomes undefined in any previous basis. This is an example of how seemingly-fundamental quantum states can be expressed as superpositions of other states. So again - why are only certain quantum states observable on large scales? The answer lies in entanglement.

The most famous entanglement experiment is the one that Einstein came up with to demonstrate an apparent absurdity predicted by pure quantum mechanics. This is the so-called Einstein-Podolsky-Rosen, or EPR paradox. A high energy photon decays into an electron and a positron. These particles both have spin values of 1/2, but the original photon had spin 0. So the axes of the new spins have to be opposite in order to cancel out and conserve angular momentum. But besides being opposite to each other they can be aligned in any direction. In fact each particle is in a superposition of states - measured in the vertical basis, each particle starts in a state of both up AND down, while in the horizontal each is left AND right, etc. The only thing we know is there’s this correlation - whatever spin direction gets measured for one particle, the other particle has to be opposite in the same basis. We say that two particles with these sort of correlated properties are entangled.

The crazy thing here is if I measure the spin of one particle - say the electron - my choice of measurement basis defines the spin of the positron. If I measure the electron in the vertical basis and get, say, spin-up, the positron will become defined in that basis and only that basis - in this case as spin-down. There’s a sense that a causal influence is transferred faster than light. This is what Einstein called spooky action at a distance, and we now know that this is a very real effect, even though you can’t actually transfer useful information this way. But we’re not here to talk about this crazy result directly - in fact we already did it a long time ago. We’re here to talk about how entanglement is connected to measurement and the collapse of the wavefunction.

Let’s think about exactly what’s happening when I try to measure the spin of one of those entangled particles. I’ll try to do that in the most subtle way possible. Here’s our measuring device - it’s a series of magnets designed to deflect the electron based on its up or down spin. Spin-up electrons are deflected upwards, spin-down electrons are deflected down. Then both types are deflected back to their original straight path. By itself this device isn’t useful - electrons passing through will still be in a superposition of spin states - both up and down, as though they traveled both paths.

But we can try to measure the spin state by placing a detection apparatus on one path. This “apparatus” is as subtle as possible: just a single atom with a very special property. If the electron passes close to the atom, the atom flips between two states. The nature of these two states doesn’t matter as long as it doesn’t change the spin or sap energy from the electron. One possibility would be that the spin of one of the electrons inside the atom gets flipped. But for simplicity, we’ll call these two states off and on.

OK, so, we put this atom along the up path of our device, and we start it out in the off state. If our electron takes the up path it flips the atom to the on state. If it takes the down path the atom remains in the off state. We should be able to just look at the atom to learn the electron’s path, and so learn its spin. So what happens after the electron passes through our device. Does its spin count as measured? Does the positron’s spin immediately become defined? Actually no! After the electron passes through our device, we still have a superposition of states - but now that superposition includes the atom. We have to think of the electron PLUS the atom as being in a joint superposed state of: electron up, atom on AND electron down, atom off. The atom’s state is now correlated with the electron’s state - the two are entangled. Which means the atom’s state is also entangled with the positron’s state.

We could prove that by measuring the spin of the positrion, which would instantaneously influence the combined state of the atom and electron. Or we could measure the atom’s state, which would influence the electron and positron. The measurement hasn't actually happened yet. The wave function hasn't collapsed. Here’s more evidence, even with the vertically-aligned magnetic fields, which only affect the vertical component of the electron’s spin, we haven’t even defined the basis of the electron’s spin as up or down. It’s still undefined. See, the entangled atom now holds information about the electron’s left-right spin.

Whereas that information used to be expressible as a superposition of the electron’s up-down status, now it’s hidden in a superposition of the atom’s on-off status. Essentially, phase information got transfered from the electron to the atom.  I won’t go into the details here - suffice to say it’s possible to recover the horizontal spin information, even if it’s more straightforward to recover the vertical spin because of how we set up the device.

OK, so our atomic measurement device doesn’t “collapse the wavefunction”  and settle a measurement basis. So where does that happen? In order for us to be aware of a measurement we look at a macroscopic indicator - say, the pointer on a dial of our instrument. There’s a chain of quantum systems between that original atom and the pointer. Information spreads along this chain as these systems become entangled with each other. In fact that growing web of entanglement always contains all of the information about the quantum system being tested. The problem is, we never SEE all of that information. We only see the crude, macroscopic characteristics of the device - like the position of a pointer on a dial.

Zurek figured out why this might be the case. It turns out that as more and more particles join our entanglement web, information about quantum-level states get spread amongst them. It would be possible to extract this information if you could perfectly measure all particles in your measurement device. But eventually this entanglement cascade reaches the surrounding environment - it’s no longer bounded, and so the information about most quantum states can’t be recovered.

But there are certain very special quantum states whose information does NOT get hopelessly mixed through this entanglement web. These are properties of the quantum system - measurement bases - whose information is relatively simply reflected throughout the surrounding environment. We call these pointer states,   Pointer states are robustly copied and spread until the states of the surrounding macroscopic environment - for example our dial’s pointer - are strongly correlated with these states of our quantum system.

So what determines whether a quantum state can be a pointer state? Well to some extent the way you set up the experiment - whether you align your magnetic field vertically or horizontally. But ultimately they are states that can survive contact with the environment. We say that the environment selects certain sets of states to propogate - Zurek uses the term einselection, for environmentally induced superselection. And he coined the term quantum darwinism too, because we have these more “fit” states surviving and being replicated. There’s no meaningful mutation and natural selection, so the link to evolution is dubious. Still, makes for a great youtube video title.

OK, so how does any of this explain Schrodinger’s Cat? Well an important example of a pointer state is the position of a particle. Most quantum interactions depend heavily on the relative location of interacting particles. Therefore information about relative particle locations is robustly shared and propagated through the entanglement network. The individual particles do NOT have well-defined locations - they stay quantum-weird. But the entanglement network has this sort of collective consensus about those locations. The structure of macroscopic objects - including cats and dials - are strongly defined by the relative positions of their particles. Therefore the states of cats and dials will always appear well defined. I should say none of this fully solves the measurement problem it only tells us why certain quantum states are observable on macroscopic scale while Schroedinger Cat states - weird superpositions are not. It still doesn't tell us why we observe one pointer state over the other unless of course there are multiple of these entanglement networks aka worlds. 

By the way - in case you missed it, I just told you how reality works. At least according to the framework of decoherence and propogating entanglement. The observable qualities of reality - object positions, feline mortality statuses, even the results of quantum measurements - do NOT exist in the underlying quantum objects. Quantum objects remain in undefined and superposed states with no prefered basis for observation. No, the macroscopic observables only exist as a sort of mutual agreement across the network of entanglements that connect those quantum systems. In a sense, WE exist in such a network. In this web of mutually consistent entanglement, even spooky-action-at-a-distance entangled particles maintain their correlations, no matter how far apart in boring old space time.

Hey Everyone! Before we get to comments, I wanted to let you know about “Antarctic Extremes,” a new mini-series from NOVA and PBS Digital Studios. Antarctic Extremes is about exploring how science is done in some of the harshest conditions on Earth. Caitlin Saks and Arlo Pérez take you through the biology, the geology, and the astronomy being done at the South Pole. Find Antarctic Extremes on PBS Terra, PBS Digital Studios’ new science channel.  Check out the episode in the description below, and tell them, politely, that SPACE TIME sent you.