The quantum wavefunction could be less mysterious than we think
Quantum mechanics is at its best a theory of particles. Tiny constituents of matter with names like quarks, photons, electrons, and so on. It also describes many phenomena that we experience day to day like light polarization and permanent magnets. Some exotic phenomena like ultracold superfluids and superconductors also require a quantum description.
You can’t get away from quantum mechanics in the physical world, even if you ignore tiny particles. And the one common factor between all quantum descriptions of reality is the wavefunction.
The wavefunction is a description, not of something necessarily that is, but of potentiality. It describes where particles could be and with what probability.
(In reality, a wavefunction is a state vector that you have to combine with another copy of the wavefunction to get a probability. So, mathematically, it is the square of the wavefunction that is the probability. The wavefunction itself is more useful, however, because it is a complete description of the particle including anything about it you might want to measure.)
Wavefunctions generally “look like” waves, but they describe particles. This is part of the wave/particle duality.
Many physicists consider the wavefunction to be a mathematical convenience, sort of like any probability distribution. Its only job is to model the likelihood of finding a particle in a certain place or with a certain state. As for the particle itself, who knows what the reality is?
For the adherents of Bohmian mechanics, the wavefunction is a real thing but it guides another thing, the particle, which is also real. So the wavefunction is like a ghostly force telling the particle where to go.
Those who believe in the Many Worlds Interpretation of quantum mechanics see the wavefunction as a description of an infinite number of worlds, each containing its own copy of the particle.
Still others see the wavefunction as representing either potential realities, with only one actual reality, or actual realities most of which are hidden from us.
These last two might take some explaining. In the first case, the wavefunction describes all the possible realities that could exist. By some mysterious process, one of those realities is selected to be the “real” one that we measure. The wavefunction doesn’t let go of any of those other potentialities until we measure it but they were never real in the first place.
In the second case, the wavefunction carries with it all possible realities and they are all real but for some reason only one is mysteriously selected to be visible to us.
Others say this is all nonsense and the wavefunction is just a probability description that never has any reality at all. Consistent histories is an example of this. Consistent histories means that you choose a framework for selecting what is real randomly out of all the possibilities as it travels along through time. Your framework keeps everything consistent.
Another are Lindblad equations which say Schroedinger’s equation, the one we’ve been using for 100 years, is incomplete. Lindblad equations pretty much solve the problem at the expense of making the universe fundamentally random. They are one possible generalization of Schroedinger’s but there are others.
I’ve only scratched the surface of different interpretations and the dizzying variations on them. It is literally where physics meets meta-physics and tries to answer the question: what is real?
If all of this is confusing, it is because it is. We don’t know what the wavefunction really is. The best validated science of today says that the wavefunction is a mathematical description of the state of a particle. It gives us all the information we need to carry out experiments and make predictions. Moreover, we can never do better than the wavefunction in terms of those predictions. The limit isn’t in our ability to detect. It is fundamental to how particles work.
Much like any probability distribution, it tells us what to expect, but, unlike classical probability distributions, we don’t have an understanding of the underlying physics. For example, with a classical phenomenon like Brownian motion, the random movement of particles suspended in a gas or fluid, we understand that the randomness comes from particles we can’t see (molecules) bumping into a larger particle that we can see (e.g., a grain of pollen). Our probability distribution is designed to describe that randomness without knowing the precise dynamics of all those little particles. Nevertheless, we know how each one of those particles individually behaves even if we can’t predict it.
In quantum physics, it seems like the randomness is somehow built into the structure of the universe. A particle follows a random path despite being in a vacuum and exposed to no other particles. It acts like it is interacting with other particles when there are none. Indeed, it acts like it is interacting with copies of itself as evidenced by the wavelike probability distribution.
Likewise that randomness seems to reach back in time or across lightyears with mysterious phenomenon of entanglement where two separately measureable particles share a single wavefunction.
My intuition about this is that particles really are like grains of pollen suspended in liquid. It is just that, instead of bumping into random, invisible particles all around it, they are bumping into random, invisible particles and fields in another dimension.
My theory is that the wavefunction describes many histories of the same particle at different points in a 5th dimension. Thus, particles really are exposed to a “bath” of random influences that we can’t see. They really do change their histories in response to one another, reaching across lightyears. This suggests, in fact, that quantum mechanics works exactly like classical Brownian mechanics, but, instead of moving in time, they move in the 5th dimension. Instead of being round little particles, they are strands strung through time.
As the universe expands into the 5th dimension, history evolves across the possibilities contained within the wavefunction. So, for me, the wavefunction describes a set of histories (as it did for Richard Feynman’s sum over histories mathematics) but, while Feynman’s was less an interpretation and more a mathematical tool, my theory provides a description of the wavefunction in terms of an additional spatial dimension. We only measure one reality because only one reality exists at a time, but many realities can exist at many times.
Hence, my approach to the wavefunction is that it is a description of a statistical reality much like a probability distribution for Brownian motion is, but it is not a “real thing”. The individual particle histories are real and they all exist at different points in the 5th dimension.
A lot of this depends on descriptions of the universe that models the Big Bang as a shockwave expanding into the 5th dimension. This shockwave allows for a unique description of quantum theory as classical 5D mechanics. Instead of being points, particles are long strands that wiggle and vibrate, bumping into all the invisible influences in the 5th dimension just as particles of pollen bump into gas or water molecules.
I think I know what the wavefunction is but work still must be done proving it out. Until then, nobody really knows.
Overduin, James Martin, and Paul S. Wesson. “Kaluza-klein gravity.” Physics Reports 283.5–6 (1997): 303–378.