Is The Wave Function The Building Block of Reality? (Script) (Patreon)

In the world of quantum mechanics, it’s no big deal for particles to be in multiple different states at the same time, or to teleport between locations, or to influence each other faster than light. But somehow, none of this strangeness makes its way to the familiar scale of human beings - even though our world is made entirely of quantum-weird building blocks. The explanations of this transition range from the mystical influence of the conscious mind to the grandiose proposition of multiple realities. But there’s one explanation that feels as down to earth as the classical world that we’re trying to explain. Let’s see if it makes any sense.

_____________

In the quantum world, particles don’t have definite properties. Rather they are described by something called the wavefunction. In fact, a particle IS its wavefunction: a fuzzy distribution of possible properties that only become sharply defined in particuxlar circumstances. For example when we make a measurement of a particle, the property that we’re measuring seems to be plucked from the wide range of possible values defined by the wavefunction. We say that the wavefunction collapses - it appears to shrink to a window whose narrow width is defined by the precision of our measurement

A famous example of this is Schrodinger’s cat. A scientist puts a cute kitty in a closed box with a radioactive atom attached to a vial of poison gas. The atom has a 50-50 chance of decaying, triggering the release of gas and so killing the cat. Prior to opening the box, from the scientist’s perspective the atom’s wavefunction exists in what we call a superposition of states. It is simultaneously in a state of decayed and not-decayed. So then, is the cat also in a superposition of dead and alive? Honestly, probably not. At some point between atom and cat the fuzziness of the atom’s wavefunction collapses into one of the two states. And becomes or. Decayed and not decayed becomes decayed OR not, and the cat is alive or dead, not alive and dead. The quantum becomes classical at some point between the subatomic and the macroscopic.

The idea of wavefunction collapse was first proposed by Werner Heisenberg, one of the principle founders of quantum theory. Heisenberg and his friend Neils Bohr were convinced that this wavefunction collapse was real. It’s a central part of their Copenhagen interpretation of quantum mechanics. But neither physicist claimed to know where or how wavefunction collapse actually happened. And fair enough, because it’s confusing. Quantum superpositions can involve many quantum particles. So how far can the superposition extend? The atom, the radioactive detector, the vial of poison, the cat, the scientist?

Opinions on the matter span all extremes. John von Neumann and Eugene Wigner thought that wavefunction collapse happens at the instant of subjective awareness - in other words, they thought that consciousness collapses the wavefunction. At the opposite end of the spectrum, many physicists believe that the collapse of the wavefunction is a fiction. For example in Hugh Everett’s Many Worlds interpretation, the wavefunction never collapses, rather  lasts forever, splitting into parallel realities. And we have the idea of quantum decoherence, where different parts of the wavefunction simply become unable to interact with each other. We’ve discussed all of these ideas in the past. We also have de Broglie-Bohm pilot wave theory, where particles already have defined properties that are hidden within the wavefunction. The wavefunction may collapse, but particles maintain a rigid physical nature.

Today we’re going to look at a different approach to collapsing the wavefunction. One that accepts the wavefunction as the fundamental building block of reality, unlike pilot wave theory. One  which avoids multiple universes by insisting that collapse does really happen. But it also avoids mystical-seeming explanations like consciousness-induced collapse.

Our story starts in 1986 when three italian physicists, Giancarlo Ghirardi, Alberto Rimini, and Tullio Weber published a paper that outlined what was to become known ad GRW theory -   the first in a new class of alternate quantum theories called “objective collapse theories.

In objective collapse theories, wavefunctions are real, physical entities that literally collapse when they’re measured. But the collapse has nothing to do with a conscious observer or any other subjective explanation. The wavefunction and the collapse are  completely real, completely objective — hence the name.

To understand how objective collapse theories work, we need just a little more quantum mechanics. The behavior of the wavefunction is described by the Schrodinger equation, which tracks its evolution through space and over time.

As we’ve discussed previously, the Schrodinger equation is a linear equation - which just means that if you add together the solutions to this equation, the result is also a solution to the equation. This is part of what makes superpositions possible - it allows different parts of the wavefunction corresponding to different possible measurement results to evolve independently to each other. Another thing about the Schrodinger equation is that it’s time-reversal-symmetric. Running it forwards generates future states, but running it backwards lets you perfectly recover the past states.

When wavefunction collapse happens, different parts of the wavefunction interact with each other instantaneously and non-locally and non-reversibly. This means that wavefunction collapse is a non-linear process and it’s non-reversible. It’s not part of the math of the Schrodinger equation.

So to model the effect of wavefunction collapse, Ghirardi, Rimini, and Weber added a non-linear term to the Schrodinger that could cause this wavefunction collapse in just the right way to explain why subatomic systems could be quantum but large systems were always classical. Think of this non-linear action as a rare and random hit that the ,wavefunction takes at a particular location. That hit causes it to collapse to a particular value. And when it collapses, it immediately collapses all parts of the wavefunction that it’s connected to.

The key to making this work is that these hits are very rare. It’s incredibly unlikely that a single isolated quantum particle will undergo collapse during the course of an experiment. But the more particles you add, the more likely that one of them experiences collapse, and that single single event collapses the wavefunction of the entire system. Any attempt to measure an isolated quantum system necessarily means bringing lots of particles into the picture - in the measurement device and in your own brain. With enough particles collapse becomes inevitable.

This “hitting” mechanism gives a potential explain for the quantum-classical divide - it simply depends on the number of particles involved. Small things can stay quantum, but the chance of collapse to classicality increases with size, and big things are essentially never quantum.

GRW suggested that the collapse rate should be about 10^-16 hits per second per particle. With this value, a single particle wavefunction remains uncollapsed for around 100 million years. But if you have Avogadro’s number of particles - the 6x10^23-ish of a macroscopic object, you expect a collapse every 10 nanoseconds or so.

GRW was a revolutionary theory that inspired many subsequent models, like Continuous Spontaneous Localization. In CSL, physicists imagined the localizing mechanism as a randomly jiggling field, like the frenetic Brownian motion of pollen grains floating on water. Matter’s interaction with this fluctuating field would continuously collapse the wavefunction, in contrast to the discrete and violent hits of GRW theory.

But neither of these models really tried to explain what the mechanism actually was. They just thought it was some mysterious field that interacted with all matter — almost like it was a fifth fundamental force. But Lajos Diósi and later, Roger Penrose, saw no need for some new fundamental force. They thought nature already gave us a perfectly good source of wavefunction collapse: gravity.

Gravitational decoherence would simultaneously explain two mysteries of physics. 1. What causes the transition from quantum to classical? And 2. Why can’t gravity be quantized like the other forces. All of the collapse models attempted to answer point 1, but only Diósi and Penrose’s model could answer 2: gravity can’t be quantized because gravity isn’t quantum. They proposed that gravity and the three quantum forces are diametrically opposed. Quantum mechanics rules when things are small, but add enough mass, and the gravity of the system will cause it to rapidly decohere into a classical object. Instead of gravity being quantized, Penrose’s theory predicts quantum mechanics will be “gravitized.”

For example, consider a massive object. General relativity says that the mass from that object will warp the space-time around it. But quantum mechanics says that this object can be in a superposition of two locations, where it is both “here” and “there” at the same time. Put these two facts together, and you will get a supersition of two different geometries of space-time. According to Penrose, this isn’t possible. The instability introduces a nonlinear term in the Schrödinger equation, causing the wavefunction to rapidly and randomly choose to make the object appear either “here” or “t here,” but not both.

Because each of these objective collapse models involve modifications to the Schrödinger equation, they are not mere interpretations of quantum mechanics — they are distinct theories with unique predictions. This means that, unlike other interpretations we’ve discussed — for example, Bohmian mechanics or Many Worlds — objective collapse models can actually be tested! Some tests have already ruled out some of the models and placed restrictions on the nonlinear parameters of others.

Direct tests of collapse models would involve putting a macroscopic object in a superposition of being “here” and “there,” then measuring how long it takes for the superposition to collapse. This time should be proportional to the size of the object. Experiments are approaching the masses necessary to make such direct measurements, but they’re not quite there.

Instead, physicists have come up with clever ways to look for other, indirect signs of the collapse models. For example, the models imply that a quantum wave function will be randomly tossed about and jostled by gravity (o r some other collapsing field). If the quantum object happens to be electrically charged, then the constant jiggling and acceleration caused by this Brownian motion means it will emit radiation. Last year, scientists working in Trieste, Italy tried to measure this radiation effect. They put an 8-by-8 cm germanium crystal in a cryostat and carefully measured the amount of radiation it emitted.

The predicted effect was so tiny, researchers had to go underground to try to minimize as many background sources as possible. In the Gran Sasso laboratory, a main source of noise, cosmic muons, was reduced by a factor of nearly 1 million. Then, they further shielded the crystal with layers of copper and lead. With such pristine conditions for a high-precision measurement, the scientists in Trieste were able to measure single photons emitted from the germanium crystal.

After watching the crystal for two months, they had detected a grand total of 576 photons. This incredibly low radiation emission rate allowed the scientists to place tight restrictions on the value of the free parameters in the Diósi-Penrose model. It even ruled out Penrose’s original version of the model.

There are still many candidates for objective collapse models that have not been ruled out by experiments, so stand by for a jubilant confirmation or a sheepish “never mind”. Whatever the case, it’s exciting that there are real and accessible experimental paths to investigating one of the biggest unanswered questions in physics. And one that we’ll be coming back to. What, in fact, is the quantum wavefunction? And how does this abstract system of shifting realities give rise to our solid, familiar, and singular space time.