The determinism of thermodynamics is in the structure of the theory itself. We can predict a deterministic evolution of temperature, for example, in thermodynamics, and first students of thermodynamics are generally not taught that this is just a statistical average they are solving. But quantum predictions are not framed deterministically, instead we speak of testing probability distributions explicitly in QM, via repetition of the same experiment-- a device never used in thermodynamics. In QM, we don't generally test expectation values, whereas in thermo, we are not even taught that the observables
are expectation values (even though they are). So thermodynamics is a deterministic theory, and quantum mechanics isn't.
In this context stochastic laws are not fundamental to the system, they are only fundamental to our level of knowledge about the system. Thus saying "fundamentally stochastic laws" is a misnomer of what the physics actually entail, at least in this context.
I'm not sure what context you mean. I would place the "fundamental" aspects of a law in the nature of the derivations used for that law, not in the nature of the systems the law is used to predict. That's mixing two different things.
In a classical regime stochastic is merely a consistently 'apparent' property resulting from a limitation in the completeness of our knowledge.
We don't actually know that, because our knowledge is always limited. We have no way to test your assertion. Indeed, in classical chaos, we generally find the stochasticity penetrates to all levels-- no matter what the ignorance is initially, it rapidly expands toward ergodicity. This has a flavor of being more than an apparent aspect of the behavior, instead the behavior is a kind of ode to ignorance. The idea that we could ever complete our information of a classical system is untenable-- ironically, classical systems are far more unknowable than quantum systems, because classical systems have vastly many degrees of freedom. It is that vastness that allows us to mistake expectation values for deterministic behavior, we see determinism in the context where the behavior is least knowable. Determinism is thus a kind of "mental defense mechanism," I would say.
Now the big question. If we as observers have fundamental limits on our knowledge that physical law dictates we cannot 'empirically' get around by any means, would that constitute "fundamental" stochastic laws even if the theory entailed a complete lack of stochastic behavior at the foundational level?
The laws
are the theory, so the foundation of the laws is only the structure of the theory, regardless of how successfully they test out. I think you take the perspective that there really are "laws", and our theories are kinds of provisional versions of those laws. My view is that the existence of actual laws is a category error-- the purpose of a law is not to be what nature is actually doing, it is to be a replacement for what nature is actually doing, a replacement that can fit in our heads and meet some limited experimental goals. I ask, what difference does it make the "foundational" structure of our laws? We never test their foundational structure, we only test how well they work on the limited empirical data we have at our disposal. The connection at the foundational level will always be a complete mystery, or a subject of personal philosophy, but what we know from the history of science is that the foundational level of any law is highly suspect.
That is what we have in classical stochastic behavior, but QM lack a similar underlying mechanism that defines stochastic behavior as purely a product of limited knowledge. That is THE key difference between classical and Quantum mechanics.
Yes, that is an important difference.
Saying "fundamentally stochastic laws" requires the presumption that a an ignorance of our ignorance is evidence of a lack of ignorance, i.e., "fundamental".
It is not the laws that are fundamental, because that makes a claim about their relationship to reality. It is only the fundamental of the law that we can talk about-- there's a big difference.
It is a whole range of these observations that leads me to assume it quiet likely that the conceptual problems in QM is not just ignorance, but an ignorance of our ignorance.
I think this is your key point here, the degree of ignorance is worse in QM applications. I concur, but then we are both Copenhagen sympathizers!
The concept of randomness will in fact ALWAYS be needed in science. We can never have perfect knowledge about any system period.
Yes, I agree that randomness in our models is inevitable-- chaos theory is another reason.
The key difference, that statistical mechanics illustrates, is that classically a perfect Maxwellian Demon could ONLY in principle do away with stochastic behavior altogether, but in QM we have no clue how to construct any model that would allow this Maxwellian Demon to do the same in that regime, even in principle.
Yes, I see what you mean, the absence of any concept of a quantum demon is very much a special attribute of quantum theory, although Bohmians might be able to embrace the concept.
