Does the existence of a probability distribution in quantum mechanics imply that each measurement has a reason?

Question

The evolution of the wave function which is determined by Schrödinger’s equation, is said to evolve deterministically.

The wave function represents the probability distribution of potential measurements of a system. Each individual measurement is proposed to be truly random. Thus, it is proposed that the result of the measurement is occurring for no reason.

Now, probability is just related to frequencies. If X has a 5% probability, with enough trials, X will occur 5% of the time.

Now if an electron’s position has a certain probability distribution, shouldn’t there be something, some force, some reason, that is causing that probability distribution to materialize?

If the position at each measurement is truly occurring for no reason, then an amalgamation of things occurring for no reason shouldn’t create a probability distribution. For otherwise, without a guiding physical reason at each measurement that occurs, how would the electron have a “propensity” to be in a position such that over time, the positions agree with the probability distribution defined by the wave function?

An analogy would be coins. In each specific coin toss, we have a reason to prefer no side over another. Given the symmetry of the coin and the constant environmental conditions, we thus have a physical reason that gives each coin toss a “propensity” to land on heads 50% of the time. If the coin was biased, the coin would now have a “propensity” to land on the biased side more often.

Without this propensity which is governed by a physical reason, how could any probability distribution realize?

Answer 1

Quantum mechanics did not find any reason for the result of measuring a given single event from microphysics. And the Copenhagen interpretation argues that there is no reason.

This result was disturbing already from the beginning in the 1920's.

Lessons learned: We cannot prescribe nature the rules that we prefer or are used to from mesocosmos. Instead we have to accommodate our expectations to the answer, nature gives to our questions, the experiments.

Keywords: Copenhagen interpretation, hidden parameters in this blog.

Aside: The Schroedinger equation is a differential equation not for the probability distribution but for a function psi which attains values in the complex numbers. But the modulus | psi | ^2, a real number, is the probability distribution.

Answer 2

Your question gets to the heart of the core philosophical challenge of quantum mechanics, which is how do we interpret the mathematics of quantum mechanics - what part of nature is it (specifically) describing when we make a "measurement" from a viewpoint of scientific realism. From this comes the myriad of interpretations of quantum mechanics, each with a different answer to your question. The first two paragraphs of the SEP: Quantum Mechanics speak to exactly this issue:

Quantum mechanics is, at least at first glance and at least in part, a mathematical machine for predicting the behaviors of microscopic particles — or, at least, of the measuring instruments we use to explore those behaviors — and in that capacity, it is spectacularly successful: in terms of power and precision, head and shoulders above any theory we have ever had. Mathematically, the theory is well understood; we know what its parts are, how they are put together, and why, in the mechanical sense (i.e., in a sense that can be answered by describing the internal grinding of gear against gear), the whole thing performs the way it does, how the information that gets fed in at one end is converted into what comes out the other. The question of what kind of a world it describes, however, is controversial; there is very little agreement, among physicists and among philosophers, about what the world is like according to quantum mechanics. Minimally interpreted, the theory describes a set of facts about the way the microscopic world impinges on the macroscopic one, how it affects our measuring instruments, described in everyday language or the language of classical mechanics. Disagreement centers on the question of what a microscopic world, which affects our apparatuses in the prescribed manner, is, or even could be, like intrinsically; or how those apparatuses could themselves be built out of microscopic parts of the sort the theory describes.1

That is what an interpretation of the theory would provide: a proper account of what the world is like according to quantum mechanics, intrinsically and from the bottom up. The problems with giving an interpretation (not just a comforting, homey sort of interpretation, i.e., not just an interpretation according to which the world isn’t too different from the familiar world of common sense, but any interpretation at all) are dealt with in other sections of this encyclopedia. Here, we are concerned only with the mathematical heart of the theory, the theory in its capacity as a mathematical machine, and — whatever is true of the rest of it — this part of the theory makes exquisitely good sense.

(Source: Quantum Mechanics, Stanford Encyclopedia of Philosophy, accessed 1:52 US Central Time, https://plato.stanford.edu/entries/qm/)

Even more challenging is that we can't necessarily take the wave function itself as indicative of anything, since there is not one but at least nine equivalent formulations!

Answer 3

I'm not sure if this observation will help, but you can easily imagine arrangements in which randomness leads to clear-cut probabilities. For example, suppose I have a large tray which I divide into three areas, A,B and C, whose relative sizes are 1,2,and 3. If I leave the tray on the ground outside in the rain, I can still say that the chance of a raindrop landing in area C is 50%, even though the rain is randomly distributed. The probabilities arise from a combination of a random set of events (ie the rain-drops), plus a structure (ie the relative sizes of the subdivisions in the tray. There is no reason why a particular rain-drop landed where it did.

Answer 4

You're basically rehashing some past debates, which makes this easy in my opinion. At the most general level...in the 1950's we got (a version of) Reichenbach's Principle: every statistical correlation entails specific causes. I see no barrier in your text to equating correlations and probability distributions. We can clearly see there are correlations in QM statistical data, and hence must seemingly conclude there are causal reasons behind the statistics. The correlations in QM include different probabilities at parts of the wavefunction (which depends on space and time), and when pairs of particles have predictable joint outcomes. Reichenbach's principle is larger than the debate about QM, it's about probabilities and causes in general, although some have directly applied it to QM (in favor of there being hidden, even local, causes/variables).

But QM also includes theories like GRWf, where there are theoretically posited random physical processes. Is that a reason or not, seems like not. Are there any non-tautological reasons in many worlds if it's all just self-locating? Again seems like not.

So it would seem the gamut varies from yes to no. GRWf is truly random, there is no causal model. Without a causal model existing, there are no reasons and R's principle is wrong. Measurement outcomes would not have non-probabilistic reasons, contra R's principle.