collapse of the wavefunction

A basic concept of quantum mechanics which states that by observing a quantum system which is in some superposition of many eigenstates you will measure only one of many possilbe eigenvalues and force the system to only be in this one state thereafter.

This concept plus the Heisenberg uncertainty principle allows some modicum of free will.

The only information one has about a particle (or a system for that matter) in quantum physics is its wavefunction.

The wavefunction is related directly to the probability distribution of the particle. In other words, the wavefunction allows one to find out the probability that the particle will be found in a given place if you were to measure its position. The shape of the wavefunction itself is harder to figure out; the Schrodinger Equation can be nasty to solve.

When one actually performs the measurement (in this case, position), one gets a specific location as a result. If you redo the measurement immediately afterwards, you should measure the same position again.

This means that the wavefunction of that particle has collapsed. In other words, instead of a complicated function with lots of peaks and valleys, the wavefunction is now a sharp spike at the location where you measured the particle. The probability of finding the particle there is now 100%, and all information about what the wavefunction was is now gone.

Let the system sit, though, after the first measurement, and due to the uncertainty principle, the wavefunction begins to creep outward again, slowly... until you again have a probability distribution, with no sure knowledge of where you'll find the particle. Back to square 1!

Collapsed wavefunctions don't stay that way

This concept is often confusing for initiates to quantum mechanics. The wavefunction should not be viewed as an inherent property of a particle or a system. Rather, it represents our knowledge of that particle or system.

The wavefunction is nothing more than a probability distribution. If we know nothing of the state of a system, it might be anything, and therefore the probability distribution would be very broad. However, if we know some of the properties or boundary conditions, the wavefunction can no longer be anything, it must adhere to those conditions. Therefore, the more we know about a system, the more sharply peaked the probability distribution, and hence the wavefunction, will be.

The collapse of a wavefunction does not necessarily change the system or particle in any special way. However, since real-life measurements tend to influence the system, and wavefunctions are closely related to phenomena like interference patterns (take for example the double slit experiment), one might think that it is an inherent property of the system.

The wavefunction is an inherent property of a particle (putting aside quantum field theory, which is even more fundamental). The wave function is not what we happen to know about a particle.

It's true that through measurement, we can narrow the range in space in which a particle must exist. But it is not correct to interpret that (and no physicist I know of does) to mean the particle was originally in that space and now we just know more about it. This is not just a philosophical/semantical issue. For example, in the double-slit experiment, if a particle really had a precise location before its location was measured, then it would not create the interference effects that show that the particle's truly probabilistic wavefunction goes through both slits. There are dozens of other experiments (e.g. Stern Gerlach) that clearly show the "now we just have more information" interpretation is wrong.

But I digress. What I wanted to write about was a question I've pondered. It is universally accepted among physicists that measurement changes the wavefunction of a particle. Measurement means something as simple as noticing there's a book on your desk (I am, in a real scientific sense, measuring the average position of the book's atoms), or as complicated as measuring the location of a photon exiting the slits of a double-slit experiment. Either one changes the world. But this measurement thing is mysterious, and it makes physics non-deterministic. We know how wavefunctions evolve over time, in the absence of "measurement." But if somebody "decides" to measure, that changes everything! There is no way to account for people "deciding" to measure.

Which brings up my question--is the "decision" to measure actually governed by physics as well? If you look at decision making as the result of physical interactions in the brain of an intelligent organism, then in a sense, the fact that measurements will be made in the future can be added into the quantum mechanical framework. This begs the fundamental question that physicists have wrestled with unsuccessfully for decades--what exactly is measurement? We know that human beings can collapse wavefunctions, disrupting their normal evolution and potentially drastically altering them. We just don't know how we do it, whether, say, a dog can do it, or whether we can "decide" to do it with some ability outside the realm of understood physics.

I know such talk can come across as gobbledy-gook, but I believe such questions are very real, very fundamental, and definitely fascinating.