Splitting the Quantum Multiverse (Script) (Patreon)

Why is it that we can see these multiple histories play out on the quantum scale, and why do lose sight of them on our macroscopic scale? Many physicists believe that the answer lies in a process known as quantum decoherence.

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The Heisenberg cut - is it the share of proceeds you send to Walter White to avoid, well, getting cut? Sure - but it’s also the elusive dividing line between the quantum and classical worlds. In last week’s episode we started down this rabbit hole exploring the measurement problem - the question of why and where the blurry quantum wavefunction collapses into well-defined measurement results. We focused on a simple question: does conscious observation of a quantum system cause the wavefunction to collapse? If you want the full story, this would be a good time to pause and catch that episode. Or whatever, do it later. The upshot is that more and more physicists think that consciousness - and even measurement - doesn’t directly cause wavefunction collapse. In fact probably there IS no clear Heisenberg cut. The collapse itself may be an illusion, and the alternate histories that the wavefunction represents may continue forever. The question then becomes: why is it that we can see these multiple histories play out on the quantum scale, and why do lose sight of them on our macroscopic scale? Many physicists believe that the answer lies in a process known as quantum decoherence.

Quantum decoherence is a deep and developing subject, and today we’re going to dip our toes and cover one aspect of it, by thinking in terms of the wavefunction. So quantum systems are described by this wavefunction thing - it’s the mathematical object that defines the distribution of possible outcomes if you were to try to make a measurement of that system. Wavefunctions evolve over time according to the Schrodinger equation, and that evolution tracks how the system’s properties might change. Another way to think about it is that the time-dependent wavefunction maps all possible histories for the object. Over time the histories of a quantum system separate to represent every possible future the laws of physics allow. 

But those separate histories don’t just split - they can also merge. The probability for a system going from one state to another can be calculated by summing all possible histories that would lead to exactly that final state. This fact is also reflected in Richard Feynman’s path integral formulation of quantum mechanics. But this only works if those histories - those branches of the wavefunction - remain “coherent”. If decoherence occurs then those separate branches are lost from each other forever - and we lose the ability to see branches beyond our own.

Let’s talk about what coherence and decoherence actually mean. In general wave mechanics, we say a set of waves are coherent if they match in frequency and if the shape of the waves is the same, and if there’s a constant phase difference between them - the peaks and troughs either line up exactly or have a constant offset. Laser light is an example of a coherent wave.

The best way to illustrate quantum coherence is the good ol’ double-slit experiment. Hopefully you remember it from last week - a quantum particle seems to pass through two slits simultaneously as a probability wave that ultimately “collapses” to leave it at a single position on a screen, and multiple independent particles then land in these bands - an interference pattern, which ultimately traces out the shape of the same wavefunction - the wavefunction of each independent photon.

Let’s think about a single photon traveling to a single spot in the center of the screen. We can imagine two equally likely ways for it to have got there - via either the left slit or the right slit. We can think of those paths as slices of the wavefunction that represent possible trajectories. 

The probability of the photon having reached this particular spot is determined by the sum of all possible trajectories to that spot. In this case that mostly means these two paths - these wavefunction slices, which we can represent with simple sine waves. Because the path lengths are the same, the peaks  of one wave line up with the peaks of the other - the two waves are perfectly in phase with each other. We call this constructive interference.

Because the wavefunction is amplified at that spot, there’s a high probability of the particle landing there. We just saw two alternate but coherent histories merging to the same final outcome.

Now just a little to the left, these two possible paths to that spot have different lengths. Here the peaks of one wave line up with the troughs of the other and the wavefunction completely cancels out. That’s destructive interference and the probability of the particle ending up there goes to zero. And as we continue to the left and right we find a new location where the peaks line up again. Here the path lengths differ by exactly one full wavecycle. And so on - so we ultimately see this series of bands - lots of particles where the wavefunction is amplified, few where it’s canceled.

In general we can see an interference pattern if there is coherence between different parts of the photon wavefunction. The key in this experiment is that all photons exit the slits with the same phase relationship. In this case, the phases match perfectly when the wavefunction leaves the slits - peaks and troughs come out at the same time. But it still works if they don’t match exactly, as long as we get the same relative phase offset between the two slits for every subsequent photon. A constant phase offset will just shift the interference pattern to left or right on the screen.

So we have two parts of the wavefunction - two branches or alternate histories if you like - that have a consistent phase relation between them. In principle we can bring those parts of the wavefunction back together to cause interference. That’s the case for two separate paths that reach the same point on the screen in the double slit experiment. If we see that spot, we can’t distinguish which of those histories led to it. In fact both did. We have to say that the photon passed equally through both slits, in what we call a superposition of states. And this is one of the weird, multiple history aspects of quantum mechanics that we can directly observe.

Let’s also think about two paths that reach different points on the screen. These also have a known phase relation, so they have quantum coherence relative to each other. That means we could potentially bring those branches back together again to produce the same quantum state - for example by cutting slits in the second screen and producing an interference pattern further down the track, and what seemed like completely alternate histories could still merge. - but only as long as the wave function defining those histories remains coherent. The photon remains in a superposition of states - it passed through both slits AND it reaches both points on the screen - as long the wavefunctions defining those outcomes remain coherent.

Got it? Sort of? Good. Now we’re going to talk about decoherence - the point where we lose our ability to distinguish the multiple histories. To destroy coherence, all we need to do is to mess up that phase relation. For example, add a collection of particles to one of the slits. The part of the wavefunction - corresponding to a possible path of the photon - is now disturbed by those particles. We can think of that wavefunction slice as the “possible photon” betting absorbed and reemitted by those particles, and so the wavefunction leaving that slit picks up a random phase offset compared to the other slit. 

Now, technically that emerging wavefunction can still interfere with itself - the random phase offset would just shift the pattern left or right for that photon. But that shift would then change for each subsequent photon - new photons land in unpredictable places - so in the end we would just see a blur corresponding to overlapping patterns, instead of a clean set of light and dark bands that we saw in coherence. The key here is that we lost information about the relative phase, and so we lost the ability to see interference patterns. We lost the ability to distinguish the effect of multiple histories. From our perspective the wavefunction has lost coherence - decoherence has occurred.

By the way, this is why any attempt to observe which slit the photon passes through destroys the interference pattern. Any measurement device must introduce some degree of decoherence to the wavefunction before it reaches the screen. According to the decoherence hypothesis, it’s not really some magical effect whereby the wavefunction “knows” that it has been observed and so collapses. It’s something else entirely. We’ll come back to that point.

So now we have a basic understanding of coherence and decoherence. So let’s leave the slits be and let the coherent photon wavefunction reach the screen again. There the photon energizes electrons in a pixel on the screen, which results in an electrical signal passing along wires to a computer and eventually into our brain. We can think about the photon wavefunction becoming mixed with the wavefunctions of the quantum particles along this chain. We can imagine separate possible histories continue, now with electrons simultaneously excited and not excited across the screen, and superpositions of signals traveling from those pixels ultimately to the brain of the observer.

But by now that wavefunction is getting pretty messy. The electrons in the detector and in the circuits will be at different locations and will have different energies. Phase differences get introduced between the different branches of the increasingly complex wavefunction. Imagine just two potential locations where the original double-slit photon might have landed. Two branches of the wavefunction will represent histories where the photon landed in different locations. As those branches propagate along the wires there’s still a particular phase offset between them. If we knew what it was then we could cause these alternate histories to merge again - just like when we cut new slits into the detector screen. Perhaps instead we could use that electrical current to generate a new pair of photons, which could then interfere. But that phase offset becomes less and less knowable the further the wavefunction advances, and the chaotic nature of the system also ensures that the phase offset changes between one incoming signal and the next. Without a consistent phase offset it’s not possible to map an interference pattern. The once coherent particles with their superposition of both separate histories that could merge, become decoherent. 

Ultimately, that expanding wavefunction includes the circuitry of the computer, and then the circuitry of your brain. There may still be multiple paths to the original double-slit wavefunction, but by now each of those paths corresponds to a specific configuration of matter and information - in the computer and in the brain. And that particular brain configuration will result in a conscious awareness consistent with that one branch of the wavefunction - corresponding to a single location for the double-slit experiment.

At this point, as far as you’re concerned, the wavefunction has collapsed - decoherence has occurred. But actually, the original double-slit wavefunction may well continue to expand and complexify as it mixes with the wavefunction of the rest of the universe. But there’s no way for you to see its other branches - those have decohered from your branch. So you shouldn’t think of yourself as this gods-eye observer, capable of seeing the whole wavefunction and causing it to collapse. Rather you are embedded within the wavefunction and see only a slice of it - a slice corresponding to a single history. It’s only on the smallest scales or in the most idealized circumstances that different different histories can still interact with each other due to the coherence of that part of the wavefunction.

In order to do quantum experiments we need to isolate a slice of the global wavefunction and maintain its coherence - we need to have information about the relative phase relationships across the parts of the wavefunction that we’re interested in. And that’s not just difficult - it’s fundamentally impossible. Any contact with the external environment causes that phase information to leak into the environment. And by environment I mean anything that isn’t as perfectly controlled as your tiny, isolated wavefunction slice. That includes yourself and your measuring device,  unless you know the exact quantum state of all particles in both.

So I just described decoherence in a very loose way. In fact the details have been worked out with mathematical rigor - starting with H. Dieter Zeh’s foundational paper in 1970. There’s a lot more to discuss - including the connection to quantum entanglement and to entropy. We’ll go deeper in upcoming episodes. I should also say that this decoherence framework isn’t universally accepted - but it is increasingly accepted. Nor is it accepted that decoherence fully explains the Measurement Problem and wavefunction collapse. I would argue that it does - but only in the context of the Many Worlds interpretation of quantum mechanics, in which there is no wavefunction collapses at all. Decoherence then explains how we lose the ability to see these alternate histories - the multiple branches of the wavefunction as it interacts on macroscopic scales. We see what remains visible to us, stranded as we are on a single branch of the universal wavefunction that contains so much more than our little, decohered slice of space time.