On the quantum scale, we can see these multiple histories play out and even talk to each other. So why can't we see that happen on our familiar large scale world? Many physicists believe that the answer lies
in a process known as quantum decoherence. 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 - don’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 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 alternate 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 that a set of waves are coherent if they match in frequency and if the shape of the waves are 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 with 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 as 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 particle. This time we'll use particles of light - photons as our quantum particle. So imagine 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 - either via 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. Now, we just saw two alternate but coherent histories
merging into the same final outcome. Now just a little left of center, 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 we find a
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 - 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 being made. 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” being absorbed and reemitted by those particles, and so the
wavefunction leaving that slit picks up a random phase offset compared to the other
slit. 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
level 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. And we will come back to that point. So now we have a basic understanding of coherence
and decoherence. Let’s now leave the slits alone 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 for
the original double-slit photon. 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 that phase offset 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 wave 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 alternate histories propagating from the original double slit wavefunction, but by now each of those wavefunction branches corresponds to a specific configuration of matter and information - in the computer and in your brain. And that particular brain configuration will
result in the 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 phases across the parts of the wavefunction that
we’re interested in. And for macroscopic scales that’s not just difficult - it’s fundamentally impossible. Any contact with the external environment
causes the phase information to leak into that 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 of the particles of 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
is not universally accepted - but it is increasingly accepted. Nor is it accepted that decoherence fully
explains the measurement problem and wavefunction collapse. But I would argue that it does - 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 only see what remains visible to us, stranded as we are on a single branch of the universal wavefunction that itself contains so much more than our little, decohered slice of space time.
