Is randomness in quantum physics adequately formulated?

Question

According to most experts' interpretations of quantum physics, some quantum event outcomes are random; they are not part of any cause-and-effect chain.

I'm struggling to find a thorough definition of what this really is supposed to mean. Perhaps because this has long been settled and no one finds it interesting anymore.

Let me expand on why I think this concept is in need of a much more thorough discussion than merely stating it as the absence of causation and a mathematical definition of expected results.

It may intuitively seem that randomness is a simple and fundamental concept in little need of clarification, since we deal with random events all the time. However, the events that we are familiar with, such as dice throws or computer generated random numbers, are (at least typically) completely deterministic. In the layman's sense, 'random' therefore just means that something is too complicated to be predicted. Therefore, quantum randomness - although it seems familiar - is in reality a completely new concept, something that we have never encountered before. If it seems familiar because it reminds us of processes that are deterministic but not determinable, that should make us suspicious that this effect too is deterministic but not determinable. It should not make us feel that it is simple and unremarkable.

A fundamental property of non-quantum random events are that they are bounded. For instance, when we throw a six-sided die once we get exactly one result, and that result is between 1 and 6 inclusive. We never get sixteen results from one throw and we never get pi as a result. The reason for this is that the deterministic method used to achieve the random result is bounded so as to produce uncertainty along certain parameters, while other parameters are completely predictable.

However, this property seems to be exactly the same for quantum random events. While we do not know when a particle decays, we can quite precisely determine the probability that it will do so within a certain time frame. And that probability remains the same; it is bounded. But if it is not part of any chain of cause and effect, how can it be bounded? Is this proposed to be some fundamental property of the universe that controls random events in the general, while still not influencing any specific random events?

The feeling I get is that while the argument for quantum randomness is that it results in a simpler theory than non-locality or other complicated alternatives and therefore better satisfies Occam's razor, it seems to me that this results from hiding the complexity of the theory in the seemingly simple concept of randomness.

Quantum physics involves many strange and non-intuitive concepts, such as the 'spooky action at a distance' concept that has been examined by so many theorists. Where can I find any equivalent treatment of the fundamental nature of quantum randomness? I'm not here talking about logical or experimental consequences of what randomness leads to in the quantum context, but about the fundamental nature of the proposed quantum randomness itself.

Apparently my question is not sufficiently clear. I will try to clarify it as follows.

It would seem to me that in physics, we can divide everything into one of these classes:

1. Matter/energy duality
2. Forces
3. The spacetime

And possibly we may consider any one of these groups as the interaction between the other two, rather than a separate phenomenon.

But it would seem to me that randomness is an altogether separate phenomenon, which does not fit into any of these groups and which is therefore very substantially unlike anything else that we know. Of course this does not mean it cannot be real - but I would expect to somewhere find a discussion about it.

Instead, I find that randomness is always taken as the starting point. Some doubt it, based on intuition. Some intuitively embrace it, usually since they want to believe in some concept of 'free will' that they think would require something similar. Most seem to accept it because it is seen as a 'simple' explanation for experimental results. But I find it hard to accept this 'simplicity' as it seems to me it is nothing more than inventing a very complicated thing, assigning this an intuitively familiar term, and then forgetting about the whole thing. It is to me as though Bohm theory was never formulated in all its unappealing details, and instead just given a name and then accepted because it 'seems true - it explains the results'.

Answer 1

If your theoretical objective is to have a theory that makes clear predictions, then yes, randomness in quantum physics is adequately formulated. The theory assigns probabilities to possible outcomes, according to definite rules (e.g. Schrodinger equation combined with Born rule), and standard statistical notions (e.g. the idea of a random sample) allow us to relate individual observations to the theoretical probabilities.

However, the way in which randomness shows up in quantum theory is not what a newcomer or outsider would expect. One might suppose that the physical picture of e.g. a particle moving, is that it always has a definite position, but the position changes randomly, in a 'random walk'. In a theory like that, the particle's position might be described by a probability distribution, but in reality, the particle would always definitely be somewhere.

Quantum mechanics is a lot more peculiar than that. The fundamental descriptions are not probability distributions (in which each possibility is assigned a number between 0 and 1), but 'wavefunctions' which associate complex numbers to the various possibilities. Furthermore, certain properties (e.g. position and velocity) are mutually exclusive, in the sense that the theory literally cannot assign a probability to the scenario in which a particle has a definite position and a definite velocity, simultaneously.

Quantum theory, therefore, is based on not-quite-probability-distributions, which are not derived from any deeper dynamical picture (whether deterministic or nondeterministic), which are valued in complex numbers, and which structurally forbid certain conjunctions of properties from simultaneously having definite values.

Despite these differences from the usual notion of a probability distribution, a 'wavefunction' nonetheless provides the same service, of assigning probabilities to physical possibilities; and these probabilities are where randomness shows up in quantum theory.

Even having understood all this, one may still find quantum mechanics to be perplexing, or necessarily not the last word on the nature of reality. And a new perspective on the nature of this physical randomness is usually a part of these attempts to go beyond orthodox quantum theory. But within quantum theory itself, randomness is not a problem, it's just a fact.

Answer 2

When something appears random, but has a cause, we usually refer to that as stochastic. As far as is currently known, the quantum mechanical world is truly random and is NOT stochastic. There is not the slightest evidence (experimental or theoretical) for any combination of variables in the environment that might potentially explain quantum outcomes.

The exception for this broad statement is that IF there are faster than light (FTL) influences, then it is possible such causes might exist. The reason we know this particular exception is due to Bell's Theorem. If you are not familiar with that, it is going to be difficult to explain much further. But generally the problem is that if there are FTL influences that explain apparently random behavior, we have no tools with which to explore that physically. All (theoretical) interpretations of QM which feature FTL action also postulate that those "nonlocal hidden variables" are unknowable. The most prominent example is Bohmian Mechanics, which postulates that the positions of other quantum particles are the hidden variables which influence something called a pilot wave: https://plato.stanford.edu/entries/qm-bohm/ (Of course, the pilot wave cannot be directly accessed.)

As to study on the nature of quantum randomness: of course there is a lot of material out there. Here is a recent paper by one of the top teams exploring the subject, and I recommend you read it to get a feel for the subject even if it does not directly answer your question. https://arxiv.org/abs/1709.06779

And another paper on the subject of randomness in quantum physics by another top researcher (both experimental and theoretical): https://arxiv.org/abs/1012.2536v1

The direction of your question is one that any researcher in the field is well aware of. Ultimately, you either accept that there are a) no local hidden variables that explain random quantum outcomes; or b) there are nonlocal hidden variables, but they are unknowable; or c) you are waiting for a magic bullet that will reverse the results of existing experiments. There are definitely those in the c) group, but it is not a large group. :)

As to the comments trying to steer you to the idea that there is always cause-and-effect: Again, there is no known local causality in modern physics post-Bell. Anyone who says otherwise is twisting the meaning of words.