Just a little bit before my graduation from computer science, I attended a course about computational intelligence, and my professor then challenged us to debate on whether the world/universe follows a deterministic model or a stochastic model. I have never read a single book about those topics and only until recently I started reading philosophical books but since then I have been thinking over it on my own, like ancient greek philosophers would do with all the parameters and consequences involved in each aspect. I have also talked a lot with ordinary people about the subject. For example a murderer is not in fault for his crime in determinism model, in stochastic modeling there is such thing as a free will etc. Personally, as an engineer I incline towards the deterministic approach and I would also love to hear other people's opinion, debate on the subject and provoke people that support Stochasticism to take a step and present their arguments on why they believe there is randomness in the world, and not just the human's inability to comprehend all the available chaotic finite non-measurable parameters of the system called universe. Although, lately, with quantum mechanics and the new quantum computer from Google, my firm beliefs took a blow because although computers follow determinism in their functions and systems, Google's PC had a 0.1% error based on indeterminism. I am digging into the issue and may form another question in the stackexchange, but my intuition about this uncertainty leads me to the principal of uncertainty from Heisenberg where you cannot predict precisely both the position and momentum
This is an important question, and one that to answer, one must dig into some of the subtleties of physics.
The most common answer one will find is that we thought our universe was deterministic under Newtonian "classical" physics, such that LaPlace's Demon who could know the location and momentum of all particles, could predict the behavior of the universe forever. But that the development of quantum mechanics in the early 20th century requires that our universe be stochastic. This was the view of the founders of quantum mechanics theory, who all embraced stochasm. However, this view is not 100% valid -- there are subtleties about both classical and quantum physics.
Relative to classical physics, several physicists in the last several decades have been exploring "classical" cases which lead to stochastic solutions. Here is one such reference: https://www.journals.uchicago.edu/doi/full/10.1086/594526?casa_token=jcR7Qn5Ji-cAAAAA:rxtSGXk98L_jfEBttu1Lt2LD3DGjsRXmhk6C_4AcUByNqWdELIjk_3ehV_rhVWe0TM9DbprEJkLj Note the language is not particularly clear, but for every case where "uniqueness fails" or "there is more than one solution" -- that translates into classical physics having multiple possible outcomes to an event, and thus being stochastic rather than deterministic. These are recent discoveries, and thus have not been subjected to multiple decades of critique, but the linked paper is a decade and a half old, so there has been a fair amount of time for rebuttal, so far without success. These are also rare and exotic cases, so classical physics could be described as "mostly deterministic" based on them alone.
Another discovery, a little older but also recent, was that even deterministic models can be unpredictable. This was first discovered in weather models, where a complex weather simulation code, which was entirely deterministic in character, ended up giving radically different predictions when one of its inputs was rounded off at the 4th decimal place. These are now called chaotic systems, and weather is considered a prime example of classical physics "deterministic" chaos in nature.
A good example of chaotic behavior in a much simpler system than a weather model, is this illustration of chaotic behavior from triple pendulums: https://jakevdp.github.io/blog/2017/03/08/triple-pendulum-chaos/ Note, one of the beliefs I have heard is that while quantum might be stochastic, our macro universe is not. The triple pendulums provide an example where that is not the case, because it is SUCH a sensitive system, that variations on the order of the Heisenberg uncertainty principle in initial state, quickly lead to the sort of chaos this video illustrates. IE -- macro scale chaos phenomena lead to quantum stochasm bleeding into macro-scale stochasm.
If the importance of a triple pendulum example is not fully obvious to everyone -- basically all physical structures have vibratory modes -- basically analogous to a pendulum cycle. And these modes overlay on each other, potentially changing the location of a surface point at any given time, very similar to how the point of the three pendulums depends on the phase of all three. These vibrations are of much smaller amplitude than a pendulum swing, but the surface location of all solids is subject to this sort of vibration-dependent chaos. Any IMPACT between two macro sized objects, therefore, will not be at a predictable instant in time, but will be stochastic-- based on the instantaneous location of each surface. This leads to some intrinsic variability of impact time, and also resulting impact directions between the two objects.
One of the ways thinkers have tried to reconcile chaos to causation, is to accept that one form of causation can be a bounded envelope, such as the range of motion of a vibrating solid, or a triple pendulum -- plus a statistical probability within that envelope. This approach also works for QM.
While the founders of quantum theory embraced stochasm, not all their peers have done so. And while stochasm has been one of the main motivators behind attempts to reinterpret quantum theory, it has not been the only philosophical concern that has motivated their peers to try to recast Quantum Mechanics. The efforts to recast quantum theory have lead to a proliferation of "interpretations". The original purely stochastic understanding of quantum mechanics remains the dominant one (it is now called the Coopenhagen Interpretation), but the stochasm of QM has at least been debated among physicists.
The two key legs of stochasm have been Heisenberg's Uncertainty Principle, which notes that one cannot actually discover the product of pairs of terms to less than a certain uncertainty content. The clearest product to illustrate this is time and momentum. https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Quantum_Mechanics/02._Fundamental_Concepts_of_Quantum_Mechanics/Heisenberg%27s_Uncertainty_Principle If we cannot know either the initial or final states of a system precisely, that brings not just predictability into question, but Heisenberg thought the entire concept of causation was now suspect.
The other leg has been quantum mechanics -- that the behavior of elementary particles is like waves, that decompose into particles for interaction purposes at stochastic locations within the wave-field. One of the clearer aspects of quantum mechanics, is that the decay of a single radioactive atom -- will not occur at a predictable time but will occur randomly based on its "half-life". The developers of QM recognized that this is a violation of not just determinism, but also of normal understandings of causation.
One of the other features of QM is that it also appears to violate either relativity, or the mind-independent realism of our world. Bell's Inequality spelled out a test case between local realism and QM's predictions and the tests to date have demonstrated that QM's violations of local realism are confirmed as how our world works: https://www.quantiki.org/wiki/bells-theorem
Einstein was one of the major leaders in the effort to challenge the stochastic nature of QM, but not only that, the local and unreal aspects of it as well. He postulated a set of alternative interpretations of QM observations, which failed test after test. His final effort was the concept if intrinsically hidden variables, unable to ever be observed. He got grief over this, as he seemed to be violating one of the key aspects of science-- refutability of one's theories. But Einstein, as a good scientist, pushed for ways to test his "interpretations" vs Copenhagen. Note if tests can distinguish between them, alternative "interpretations" are actually alternative theories. The Bell's Inequality tests were inspired by an effort to make this final intrinsically hidden variable theory testable, and it too failed those tests.
Other "interpretations" try to preserve locality, by embracing "unreality", IE that the observer is inseparable from quantum events. A list of many of these interpretations is here; https://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics Most of the advocates of these alternative interpretations have not been as aggressive as Einstein was in trying to derive test cases between them and Copenhagen, hence most have not been as clearly recognized as actually competing theories.
The only two alternatives from this list with significant support from physicists today are Bohm-DeBroglie, and Everett's Many Worlds. Bohm's is a hidden variable model, with global rather than local hidden variables. What that means is that every event is influenced by every other object in the universe, regardless of distance, and regardless of speed of light limits. Bohm sacrificed compatibility with General Relativity, for the comfort of a deterministic model. It has now been fairly widely recognized that Bohm's theory is different from QM, and it is often now described as Bohmian Mechanics. The results of test cases to date, have been strongly trending against Bohm and in favor of Copenhagen; http://settheory.net/Bohm https://www.physicsforums.com/threads/back-pedaling-on-bohm.905194/. Bohm -- has not been widely considered refuted yet -- but these observations and test cases have drastically dampened enthusiasm for Bohm's theory.
Many Worlds postulates that for every quantum event, all possible outcomes occur, and the universe splits to create alternate non-interacting universes for each possible outcome. Many Worlds is claimed to be a "deterministic" theory per the Wiki page, and many advocates. But this does not appear to be the case. For any observer, there will only be one outcome to any event, and that outcome is not deterministic, but stochastic. Postulating that other observers exist, and that all possible outcomes are observed between the theoretical collection of all of them -- still leaves each of them as a single observer, experiencing a stochastic event. per the standard for determinism set for classical physics -- LaPlace's Demon could neither know the current state of the universe (it would still be limited by Heisenberg Uncertainty Principle), nor could it predict the outcome of any measurement (echoing Earman's language relative to classical physics, "there is not a singular solution"). "All of the Above" is not really determinism. Plus -- postulating excess universes that are undetectable in principle -- is a violation of science basics, for which Einstein received some justified grief.
Additionally, Many Worlds, from a pragmatic causal point of view-- explicitly abandons causation, and cannot even adopt the envelope/probability approach that plausibly can encompass chaos events. This is because probability between the worlds becomes a nonsense concept -- all of them exist, and there is no "bandwidth" feature to these different universes to the theory than can distinguish "frequency". Putting this in personal terms, I could in the next 20 minutes, complete this entry, and post it, abandon the project and play video games instead, or walk next door and murder the neighbor family. All are possible, none are any more "caused than the other, and each occur in SOME world per MW "interpretation". such a radical elimination of the concept of causation, is not what most determinists are looking for, and the popularity of the MW interpretation is likely due to its non-physics adherents not understanding how it destroys any coherence to causation.
At any rate, Bohm appears to be heading down the same path of refutation that Einstein's hidden variable theories followed, and MW is not really a deterministic model. Quantum mechanics is reasonably understood as refuting determinism in physics. This combined with both the indeterminism in classical physics, and the intrinsic unpredictability of chaos phenomenon (and actual indeterminism once one includes Heisenberg's uncertainty), leads to a definitive answer -- physics is not determined.
So, there are three models of quantum mechanics which maintain determinism: non-local hidden variables; superdeterminism; and determinism across many worlds. These are constrained by the Bell Inequality having being violated.
This is because, sensitivity to unitial conditions, the underlying characterustic of chaotic systems (such as whenever more than two oscillators interact), mean any quantum measurement could in principle be enough for a different outcome from otherwise the same initial conditions.
So. Non-local hidden variables are problematic because they violate Occam's forbidding of multiplying entities, a hidden invisible layer of order is required that seems to be unfalsifiable. Superdeterminism is problematic because from inside the system it would be unpredictable, and the implication has to be, for it to be verfiable, that you could step outside the system to view how it is deterministic, violating that determinism - so again it's unfalsifiable. Many world's (also called relative state interpretatiin) is probably the most popular interpretation of quantum mechanics among physicists, it allocates the randomness to which branch of the system we find ourselves in, and the system evolves down all posdible branches in a higher dimensional Hilbert space. It seems possible there is a fundamental limit to the information per unit of space-time, linked to the Planck length & time, which would help explain black hole behaviour. This would seem to place a constraint on the total number of paths a system could go in, but it's an extremely high number.
There is another option. The interpretations of quantum mechanics hinge on observer and observed, many worlds pictures states as relative, one quantum system observing another. The It From Bit doctrine suggests matter is not fundamental, information is. Emergent properties are self-stabilising systems, like life, and minds. I see these pieces as pointing towards a materialst-physicalist pan psychism, that the universe is on a deep level the result of it's own enquiry into itself, exploiting it's own lack of knowledge about itself to determine how to be, by amplifying those indeterminisms in a way that is self stabilising, like a mind. Like Indra's Net. Just a hunch though really.
I was talking about free will recently, and this may make the idea clearer: Free will from a self-conscious being's perspective; unfree will from the universe's perspective. Only, the universe has no perspective, there is in fact only intersubjectivity, no universal transcendental perspective, only relative local ones. Mind then wouod be the fundamental strata of being, and world and physicality arises from that, but is prevented from being arbitrary and purely subjective by arising with and in a shared intersubjective mental space. Arising at the 'door' (sense-gate) between mind and world. It's a logical continuation of the private language argument's intersubjectivity. To boil it down, we have freewill for the same reason we have identity, 'I' ness, or that fiat currency exists: we have a convention and act as if it's real, creating a world in which it is. You can say money isn't real, and I point to observables in the world which say it is - but the way in which it's real is not like atoms, it's like the category 'things you can sit on'. Relative, but social. See also peer-to-peer simulation hypothesis
In a deterministic universe nothing ever happens at random nor at will. A deterministic universe could not be intentionally created nor could it have evolved unintentionally through random fluctuations or probabilistic indeterminacy.
A deterministic universe is a logical impossibility. Determinism precludes both methods for determining the contents of a universe.
For a similar question on the physics site, the top-voted answer mentions indeterminism, but says the mechanism "is still not well understood". A significantly-upvoted comment says the alleged source of indeterminism is "sweep[ing] things under the rug" and alludes to non-locality. The second answer just says "no one knows". The third answer mentions indeterminism, but also points out that abandoning locality is an alternative. The fourth answer says it is deterministic. Interpret that how you will.
There are various interpretations of quantum mechanics which vary in terms of whether it is deterministic or stochastic, among other factors, and we don't know what the correct interpretation is.
I don't expect philosophy to produce better answers to this question about physics than ... well, physics, or for laypeople to be able to produce better answers than physicists. Anyone acting otherwise should be treated with significant skepticism.
Philosophical determinism vs measurement determinism
There's also an important distinction between philosophical or physical determinism and measurement determinism. We can perhaps say that the exact path of a falling feather released outside is indeterministic from a measurement perspective, as in we can't predict where it would go, because tiny, functionally-immeasurable differences in air pressure could change the result, and we may model this probabilistically. But it may nonetheless be philosophical or physical deterministic, as in if you could hypothetically release it under the exact same circumstances, it may travel along the exact same path every time.
Now we wouldn't typically describe a falling feather as indeterministic from a measurement perspective, because we understand the underlying mechanisms that would affect its behaviour (even if controlling for all of that may not be practically achievable, except maybe in a vacuum, and quantum effects could factor into it). For quantum mechanics, we don't understand the underlying mechanisms, and the most accurate model we have at this point to describe behaviour is probabilistic, and we may say it's indeterministic from a measurement perspective. This is the core of quantum mechanics.
Where interpretations of quantum mechanics differ is whether it's actually intrinsically deterministic. Some interpretations, including the popular Copenhagen interpretation, propose that quantum mechanics is fundamentally indeterministic, but not all of them do. Quantum informational interpretations, for example, state that "quantum mechanics is said to describe an observer's knowledge of the world, rather than the world itself".
Quantum mechanics is not magic
It's probably also worth pointing out that QM is not magic: it does not suddenly everything possible, even though some people seem to treat it as such. It's commonly referenced by free will proponents, but even being as generous as possible, the probabilistic behaviour of independent atomic particles wouldn't get you anywhere close to anything resembling meaningful human agency, under pretty much any interpretation of quantum mechanics.