Psychology has a bad reputation for not being reproducible. Theories are conceived; they fit into some evidence but not another. Neuroscience is slightly better but still not as trustworthy as physics. Physics is where you have strong theories backed up by mathematics (formulas are always fancy). However, there is a lot of mismatch between physical theories as well; one would just need to dig a little bit deeper. This time I read a book, “The Meaning of the Wave Function: In Search of the Ontology of Quantum Mechanics,” by Shan Gao. I landed on this book after discovering that Shan wrote a book about consciousness and quantum mechanics. I didn’t have access to that one, but I thought I might find clues in this book. And I did. Sort of.

Quantum mechanics is a physical theory that describes matter (the substance that the universe is made of) on a subatomic scale. Quantum mechanics describes the behavior of quantum systems. A quantum system may consist of photons, electrons, or other elementary particles. Quantum state is a description of the full physical state of a quantum system at a given moment. A wave function describes the quantum state of a given isolated quantum system. If there are N particles, the wave function would be defined in 3N-dimensional space. The evolution of the wave function is linear and governed by the Schrödinger equation. The Schrödinger equation is similar to other wave equations, and a wave function mathematically is a “wave”. The problem (or peculiarity) is that the wave function defines the probabilities of a particle being at a certain place if measured. In the macroscopic world, when the speed and the initial position of an object are known, one may compute the exact position at a defined time. In a quantum system, all that is given are probabilities.

The measurement problem can be formally constructed as the following:

(Claim 1) The wave function of a quantum system entirely and in all respects describes this system.

(Claim 2) The wave function evolves according to Schrödinger’s equation.

(Claim 3) Every measurement has a specific and unequivocal result.

If (C1) and (C2) are both strictly correct, (C3) cannot be derived from (C1) and (C2) without additional assumptions, which leads to the measurement problem.

The author suggests denying (C2) and revising the equation for the evolution of the wave function. For that, he starts by introducing random discontinuous motion (RDM) of particles. The proposal describes the particle as not moving smoothly and classically but instead exhibiting a random, instantaneous "jumping" motion across different locations. From that it follows that physical entities are discrete particles, not continuous fields. We detect fields because of the jumping. Wave function, in turn, is not just a description of the motion, but it’s tied to the propensity of particles to exhibit random jumps. This propensity to jump is a fundamental property of particles.

Besides the tendency to jump, particles have another tendency—for random stays. The particle may stay at one location for some time. It’s not that it consciously chooses to stay. The particle is more likely to reappear or persist in regions where the wave function has higher amplitude—this creates the appearance of “staying”. These random stays consecutively change the evolution of the particle wave function. Therefore, the feedback loop appears: the wave function determines the position of the particle at a given instance, while the particle may remain at the position, thereby influencing its wave function. Over time, these jumps lead to concentration in one state, which is a collapse. Thus, collapse is the emergent effective dynamics of a system in which particles have a property to move randomly and discontinuously. Under this idea, collapse doesn’t require the system to be observed; it happens naturally due to the intrinsic property of particles.

The theory also explains why we (macroscopic observers) do not see stochasticity. According to the author, particle jumps are instantaneous, and our perception operates at a much slower time scale. Therefore, we see effects that are integrated over a period of time. The ostensible continuity of macroscopic motion is emergent from averaging over RDM. Similarly, a gas (seemingly) has pressure and temperature even though its molecules are bouncing around randomly. Our perceptual organs are such that we perceive averages, not microscopic chaos.

It was a difficult read. The author introduces many concepts in a small book, and I admit I have not understood all lines of argument. Additionally, it was not clear which of the introduced concepts have been experimentally tested (or could be experimentally tested). Although the author gives a hint of how his version of collapse could be tested. Lastly, other solutions to the measurement problem were covered and argued against, but it felt that they were not covered at a substantial depth. I think other theories should be my next dive into the quantum world.

The book is fairly short but packed with formulas, which I actually enjoyed. However, the formulas are not necessary to understand the proposed theory.

There are many things in physics that just don’t match. Wave function is one of them. But it’s both overwhelming and inspiring.

Favorite quote

“In each neuron, the main difference between two states lies in the motion of 106 Na+ ions passing through the membrane. Since the membrane potential is on the order of 10-2 V, the energy difference between the firing state and the resting state is 104 eV. … the collapse time of a superposition of these two states of a neuron is 105 s. When considering the number of neurons that can form a conscious perception is usually on the order of 107, the collapse time of the quantum superposition of two different conscious perceptions is 10-9 s. Since the normal conscious time of a human being is on the order of several hundred milliseconds, the collapse time is much shorter than the normal conscious time.”

July, 2025