Quantum physics is weird. How weird? “Too weird for words,” as we used to say, and there is a literal truth to words being inadequate in this case. There is no way to look at the quantum world that doesn’t break one’s mind a little. No one truly understands it (other than through the math). It’s like trying to see inside your own head.
Since we’re clueless we make up stories to fit the facts. Some stories advise that we just keep our heads down and do the math. (Which works very well but leaves us thirsty.) Other stories seek to quench that thirst, but every story seems to stumble somewhere.
One of quantum’s biggest and oldest stumbling blocks is wave-function collapse.
My relationship with quantum physics predates quarks. I was already an avid physics fan when The Tao of Physics and The Dancing Wu Li Masters came out. (For old time’s sake, both books still sit on my shelf along with the newer ones that obsolete them.)
I’ve watched the field evolve. String theory grew from an early gravity theory into a career-consuming institutional juggernaut. What started a sensible physical theory ended a monstrous mathematical swamp.
Through it all, the wave-function collapse remains an enduring mystery.
Understanding why requires looking into wave-functions and what we mean by “collapse.” (I’ll end with a story I think might explain these things.)
That equation is sometimes written like this:
It’s a complex-valued equation, meaning it uses complex number math. The star of the show is Ψ (psi, typically pronounced “sigh” although some say “sea”). It’s the complex vector representing the current state of the quantum system.
The co-star, Ĥ (“H-hat”), is the Hamiltonian operator that sums the kinetic and potential energies of the system in question.
What the whole thing describes is the quantum system defined by H-hat. The vector, Psi, is the system state at any given time, t.
Solving the equation gives the probability of finding the system in the specified state (value of Psi). Note that using the equation at all requires defining the Hamiltonian for the system in question.
It’s worth emphasizing that the Schrödinger equation describes a quantum system’s wave-function (the wave-like nature and evolution of that system). The actual ontological nature of a system’s wave-function is unknown.
A quantum system has a property called phase, which is the source of quantum interference.
The wave-function sees (quantum) reality as fundamentally wave-like, and phase is essentially a point on a wave. Think of it as a single hand on an analog clock marked, not by hours, but by degrees around the circle (noon is 0°, six o’clock is 180°).
Waves (mathematically speaking) go ’round and ’round like clocks. Phase is what o’clock it is (expressed in degrees).
When a quantum system has more than one path from point A to point B, the clock ticks separately along each path. If the paths are the same length, the clocks match when they meet. If the paths have different lengths, the clocks show different times.
Quantum interference involves the two clocks. If they show the same time, they combine. If they show the opposite time (say 3 o’clock and 9 o’clock) they cancel. Between same and opposite, they average out (between 0 and 2×).
(This is adding and cancelling is what generates the pattern in the two-slit experiment.)
What’s important here about quantum phase is that it’s very fragile. (A key difficulty in designing quantum computers involves protecting the phase of quantum computing bits.)
A quantum system with detectable phase is said to be coherent. (Related to, for instance, coherent laser light, a situation in which all the clocks show the same time.)
But the phase of a target system, S, is easily lost to surrounding quantum systems. It often requires a vacuum and near absolute zero temperatures to prevent decoherence of a system under study.
What happens, if not prevented, is that the wave-function of S entangles with the wave-functions of surrounding systems, each of which has its own wave-function and phase.
When two phases combine, the phase of the resulting wave is their average. That means the resulting phase is shifted from both (unless the two were exactly in phase). So the phase of S is smeared out among all the surrounding systems it interacts with.
In turn, those surrounding systems affect S. Their phase information combines with S, and the result is like trying to hear one voice in a room with hundreds of people talking.
The bottom line is that S decoheres and its phase information and quantum interference behavior is lost. The surrounding systems also change to reflect the interaction with S.
This interaction is called a measurement.
It’s directly implicated in the apparent “collapse” of the wave-function.
With that background, let’s consider what happens in a specific quantum system — a single photon in a two-slit experiment.
For definiteness, let’s say we have a laser capable of emitting single photons. It shines through two thin slits in a metal wall to our detector — a piece of film capable of responding to individual photons (more on that in a bit).
A photon is a simple enough system that we can define a Hamiltonian for it. If we use it and solve the Schrödinger equation for every point between the laser and the film, we get a wave pattern. It looks very much as if someone dropped a rock where the photon leaves the laser. The ripples spread out from the source.
Crucially, after they pass through the two slits, they meet and interfere.
The peaks are places the photon is most likely to be found if we look in that spot. In particular, the peaks and troughs along the piece of film are places where the two paths reinforce and cancel out. (Forming the famous interference pattern.)
Ultimately, the photon’s flight must end, either in the various walls of the experiment or in the film (it can’t just vanish; it has to end up somewhere).
If it ends up in the walls, it generates a tiny, tiny bit of heat as the wall atom absorbs it and jumps to a higher energy level. That atom immediately dissipates the energy to nearby atoms. Eventually the disturbance is lost as the system reaches equilibrium. The energy distributes and dilutes to nothing.
If the photon hits the film, it again increases the energy of an absorbing atom, but here the material is primed to record the photon. (There may even be a cascade effect that alters the state of multiple atoms.) The energy of the photon causes a chemical change in the film that later chemical processing amplifies and fixes.
At this point, I want to mention something very important: Note that in all cases, the photon, which came into existence in the laser, ends that existence when absorbed by an atom. This will be important later.
This brings us back to the great mystery, the idea of wave-function collapse.
The problem is that the Schrödinger equation describes the linear evolution of a quantum system. Further, it’s fundamentally a wave description. The abrupt change from this smooth wave behavior to localized point behavior represents a discontinuity physicists haven’t truly explained.
Worse, there are implications of non-locality. (Experiments testing Bell’s Inequality seem to establish quantum physics is non-local under almost any reasonable interpretation. It seems something we’re stuck with.)
But the show-stopper is trying to explain, exactly, mathematically, what happens when a coherent wave-function appears to collapse.
The story solutions range from ignoring it to specifying infinite worlds. I find both too extreme. Next time I’ll tell you the story that I think might account for it.
Stay coherent, my friends!