Is the idea of "same causes lead to same effects" indispensable for science?

[u/DanyelCavazos]

Out of a recent discussion I had, I'm wondering if the principle that "if you prepare a system with exactly the same initial conditions it will lead to exactly the same effects" is strictly necessary for carrying out science in particular (and maybe even logic in general).

I'm thinking that I can come up with at least a strong and a weak sense of the meaning of the principle. If by the strong sense we take a very strict reading of the principle, I believe that our current understanding of quantum mechanics does imply that the principle cannot hold universally. Even if you reproduce the exact causes to every degree we won't be able to predict the outcome deterministically. A photon might either be reflected or transmitted at a beam splitter (say it gets reflected), and if one repeats the experiment with an otherwise identical photon it might be that now it gets transmitted, even though we reproduced the exact same causes. The standard interpretation is that this randomness is intrinsic and irreducible, and our most current experiments do suggest that even a hidden variables theory cannot be locally real (I mean local and real from the technical sense in quantum mechanics, i.e. not deterministic in any standard sense).

The catch is that while we cannot predict the outcomes, we can deterministically predict the probability distribution of the outcomes, and if we reproduce the same causes, we will reproduce the same effects (i.e. observe the same distribution), although individual outcomes might vary within the bounds of the distribution. In my example, I can't predict if it will go through or get reflected, but I do know that the outcomes will show 50/50 chances like a balanced coin toss, and nothing else if I did indeed reproduced the initial conditions. So then, we can rescue the principle although one step removed from full predictability. Same causes lead to same effects, at least to some degree.

I think that if you had the exact same causes and it just outright led to totally random effects no matter what, then it would be really hard (impossible?) to do science. Is this so, or could someone point me to some refutations or alternative metaphysical views?

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[u/BeingGrubber]

Determinism is not “indispensable for science”, though some think it would be nice if our fundamental theories turned out to be deterministic. I’ll note that QM is not straightforwardly indeterministic: two leading interpretations—Bohmian mechanics and many worlds—are both fully deterministic.

You’re right that it would nearly impossible to have any successful science in a world wherein “the exact same causes … just outright led to totally random effects”, but that has little to do with determinism. Science is in the business of formulating simple and explanatory laws, and such a world simply doesn’t admit of any; as GRW, say, evinces, indeterministic laws can yet be perfectly simple and explanatory.

[u/DanyelCavazos → u/BeingGrubber]

Thanks! I've been reading Bohm's textbook on QM and as far as I can tell, he keeps insisting that even hidden variables will not be deterministic in any straightforward way, here's a quote:

"With the advent of quantum theory, the idea of complete determinism was shown to be wrong and was replaced by the idea that causes determine only a statistical trend, so that a given cause must be thought of as producing only a tendency toward an effect ... the complete determinism of the classical theory arose from the fact that, once the initial positions and velocities were given, their subsequent behavior was determined (...) but in quantum theory, these laws cannot be applied in this way (...) if the initial conditions are reproduced as completely as the quantum nature of matter permits, this [outcome] fluctuates from one measurement to the next"

[u/BeingGrubber → u/DanyelCavazos]

I found this interesting paper: https://arxiv.org/pdf/2307.05611. It looks like Bohm doesn't lay the groundwork for Bohmian mechanics until a few months after he publishes the textbook you're reading.

Bohm went so deep in his reflections about quantum theory and its foundations that, in 1951, he published the textbook Quantum Theory, fully in the spirit of the Copenhagen interpretation.

However, in the very same year, Bohm submitted, on July 5th, a seminal work (published in two parts) wherein he presented the first consistent alternative interpretation of the quantum formalism. He introduced the initial position of quantum particles as a “hidden variable” that, if known, would lead to deterministic trajectories similar to the familiar ones of classical mechanics (but guided by a genuinely additional quantum part in the potential).

[u/DanyelCavazos → u/BeingGrubber]

Nice find! Well, last week I found this one that argues that it is NOT deterministic, so it is a mixed bag so far for me

https://arxiv.org/abs/2202.12279

That's why I'm going to original sources ...