Philosophers and many scientists seem to distinguish between the macro and micro world a lot. Things in the micro world seem to be indeterministic, atleast through the standard interpretation of QM.

My question is two fold.

A) If quantum events are truly indeterministic and unpredictable, how is it that the probabilities defined in that sphere are of a certain number? Why isn’t there complete chaos?

B) Why or how does quantum indeterminism lead to the laws in which we know the macroscopic world operates in such as the net force on an object being equal to its mass multiplied by its acceleration? Why a particular equation rather than another one?

In other words, why is there not complete chaos if at the most fundamental of stages, there is a lack of deterministic behavior? Is it at all possible that we could be wrong about this indeterminism? (Although I suppose even if the universe was deterministic, it would beg the question of why those deterministic laws are there, but that seems to open up fewer questions)


3 Answers 3


Leaving aside quantum physics for the moment, there are at least two general ways in which indeterministic and deterministic rules can co-exist at different scales.

The first way is when deterministic laws emerge at some higher level, and can be explained from averaging fundamentally indeterministic events. You can see this happen in most views of classical statistical mechanics, where microscopic events can be treated as fundamental and random, but when the number of particles gets very large, macroscopic rule-following behavior can emerge, like the heat equation.

A totally different perspective is when deterministic fundamental rules end up looking indeterministic in practice. Imagine that everything is fully determined, given both some fundamental rules and also some "input" data (say, an initial state). As we analyze events in such a situation, our ability to make perfect predictions depends on perfect knowledge of the system and the inputs. If we don't know something precisely, we have to drop back to a probabilistic/indeterministic viewpoint, assigning probabilities to the unknown parameters. If new inputs keep coming into the system, of which we continue to have imperfect information, then the rules of the universe, in practice, look indeterministic. One example here is how indeterministic Brownian motion can be derived from fundamentally deterministic laws with unknown noise/inputs.

Okay, so which of these is most analogous to quantum theory? That's an open debate in quantum foundations, which no evident resolution in sight. The first perspective above would tend to be aligned with spontaneous collapse models, and the second perspective would be more aligned with Bohmian mechanics. And it's possible that both are happening at different scales, that deterministic fundamental rules look to us to be indeterministic, because of lack of knowledge, but then those indeterministic rules get averaged out to make deterministic classical rules at some large macroscopic scale. (The Everettians would fall in this two-stage category, and presumably the Bohmians as well.)

And just to add one more wrinkle to all this, our traditional viewpoint of what should be considered "fundamentally deterministic" might be too restricted in the first place. For example, Emily Adlam has argued that a universe which depends on both the past and the future could be considered "globally deterministic" in a well-defined sense. And since we don't know the future, that "global determinism" would inevitably look to us like local-indeterminism. This view would work well with future-input-dependent interpretations of quantum theory.

But back to your question, yes, it's possible that we're wrong about "all this indeterminism" existing in our fundamental laws. Certainly many quantum physicists will tell you that there is no indeterminism in the fundamental laws, at least if they had a solution to the Measurement Problem. But it seems extremely doubtful that we're wrong about needing indeterministic rules in practice, because of that second perspective, combined with all the microscopic details that we don't know.


Although the observable outcomes of quantum mechanics are probabilistic, the evolution of the state of a system is fully determinist and is governed by Schrodinger's equation.

The probabilities are determined according to how this equation evolves a state and hence, is a definitive procedure.

As the quantum system interacts with a larger environment, its quantum state experiences decoherence and the cumulative evolution of the system is reduced to that modeled by classical physics.


I am not sure what do you mean by deterministic. In standard Quantum Mechanics, there are 2 dynamics, and one is linear and deterministic - it's given by the Schrodinger equation. In fact, knowing the Hamiltonian and thewave function at one time is enought for you to know all the history of the wave function. The second dynamics is given by the wave function reduction postulate, which is non-linear and stochastic.

If however for deterministic you mean that the description of the system is given in terms of well-know values at every time $t$ for position and momentum as it is in classical mechanics, than it is an open problem and the answer by @KenWhartog is very precise on this. In this case, I suggest you to read "Dynamical Reduction Models" By G. Ghirardi and A. Bassi, it is a complete review on the foudantions of quantum mechanics, from decoherence to collapse models, bohmian mechanics and in particular the ontology and mathematical structure of the theories.

If you are interested in seeing how to go from quantum to classical statistical mechanics, I suggest you to read the book "Deterministic Chaos in Infinite Quantum Systems" by F. Benatti, where there is a very nice review for the current state of art on the topic, expressed in terms of algebraic quantum field theory.

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