Is there a mechanism for randomness?

Question

I couldn't think where to post this, so I decided physics is the closest to answering this. Apologies for my amateur understanding of QM (0 understanding of QFT), I learn on free time by internet, so prepare for silly misconceptions.

If I understand correctly, our descriptions of QM objects will always be probabilistic. Their wave-like nature manifests itself in a relationship between, for instance, location (how well a wave is localized at one point) and momentum (how well a wave is defined over a large scale). But the particle is still bounded by it's environment and certain rules - if we pick a point in space we will know what is the probability of finding the electron there (say roughly 90% at 0.053nm from the proton of a H atom).

Question 1: Is the probability for finding an electron conditional? What I mean is, if we know the electron is found a few times more often than usual at a certain location per unit of time, will the electron be statistically 'compelled' to be found elsewhere to compensate? In other words, over a very short timescale, does the probability fluctuate?

Question 2: Is there any known / theoretical mechanism that produces true randomness? The more I think / read about it the more it seems that what randomness means is a question of definition. For instance random.org considers atmospheric noise 'truly random', but the only reason we consider it so is because of our 'ignorance' - the calculation has far too many variables and is too complex for our current understanding and tech. To my understanding QM objects do not appear random because of our ignorance - they truly are random. But how can such a mechanism exist? Is it simply that the most precise measurement must have a degree of randomness and the world is deterministic? Is the truth simply that all quanta are random, and causality is just emergent? Could we 'design' a blueprint of a mechanism that is truly random?

Thanks!

Answer 1

Observing the electron changes its state. Thus (except in the case where the electron is already in an eigenstate of your measurement), it is impossible to repeat a given observation of a given electron in a given state, and therefore your question 1 makes no sense.

Answer 2

Question 1: Is the probability for finding an electron conditional?

All the analysis of high energy physics particle experiments is based on the hypothesis that the probability of finding a particle is not conditional. Each event is a throw from the probability distribution. At the LHC, one scatters a huge number of protons on protons, looks at the probability distributions, plots the background probability distributions and if new enhancements appear one starts talking of new physics. This is the way the Higgs was discovered a while ago.

What I mean is, if we know the electron is found a few times more often than usual at a certain location per unit of time, will the electron be statistically 'compelled' to be found elsewhere to compensate?In other words, over a very short timescale, does the probability fluctuate?

It is a basic QM postulate that the probabilities calculated are what nature orders. Now if an enhancement is seen at a specific energy one looks at the statistical significance in standard deviations, before deciding there is a deviation in the assumed probability distribution, i.e. how many throws of the dice were measured , usually the gaussian is assumed for the standard deviation, and also systematic errors are estimated. But the ideal probability distribution does not fluctuate.( draw from the urn for that interval is assumed random)

Question 2: Is there any known / theoretical mechanism that produces true randomness?

One has to define randomness to start with. I have found this discussion on mathematical randomness enlightening.

To be a random number sequence, the numbers in the sequence must be generated as if they were independent draws from a well mixed urn where each number is represented once in the urn.

The idea of randomness comes from drawing a number from the urn. You write down that number, replace the token in the urn, mix the urn well and draw another number. This idea of unpredictability and equal probability is embodied in the random process.

italics mine.

So for example if I count the time between atomic events, say the ticks on a Geiger counter, then I need to show some transformation that makes this equivalent to drawing balls from an urn. If I do this, I know that I'm also generating random numbers by my new method.

The above is adequate for me, an experimentalist, i.e the equal probability and unpredictability. Unpredictability ( which I equate to uncertainty, for example the Heisenberg uncertainty principle) for an individual event is built in in quantum mechanics. Probabilities are not equal but follow dynamical constraints.

Could we 'design' a blueprint of a mechanism that is truly random?

So I will say yes, with the definition of randomness as equal probability and unpredictability, there is a mathematical framework for randomness.

Answer 3

There are deterministic theories of non relativistic quantum mechanics and probabilistic theories of non relativistic quantum mechanics that make the same statistical predictions.

The deterministic ones have the uncertainty of particular final outcomes be a function of the uncertainty of the initial setup. The probabilistic ones have it be inherent. But since they make the same predictions there is no reason to favor one over the other.

They both admit that when you try to control the initial setup you have limits. And so you have uncertaintiy in the final outcomes. The probabilistic theories say that there is nothing beyond the thibgs you can control, which is 100% and totally reasonable.

The deterministic ones paint an easy to visualize picture, but have extraneous parts beyond what you can control, and hence test. So it's window dressing on the science. It could be helpful if it makes anything easier for you as an individual, but can be abandoned anytime of requires any effort on your part.

Is the truth simply that all quanta are random, and causality is just emergent?

There is no evidence of randomness since deterministic theories exist. There is no evidence of determinism either, since a probabilistic theory could have produced the results we've seen. This is always the case. Whatever data you see, can always be generated by both a deterministic theory and a probabilistic theory. So asking which is real isn't a scientific question that can be address by experimental test.

Could we 'design' a blueprint of a mechanism that is truly random?

Even if you could build one and did build one, you would never know you had one. Because a deterministic theory could predict exactly when and how you built whatever you built and predict how it operates when you actually operate it.