I don't know if this is going to speak to many here, I hope it does, but it's good anyway in the process of trying to understand what dialectical science would look like, as opposed to our current outlook on science which is metaphysical.
By which I don't mean the scientific method, or scientists themselves, but science as a whole and as itself. If we hold that it doesn't exist outside society (and of course it doesn't), then science has a philosophical character. Metaphysics being the contradiction to dialectics, it's also not the philosophy of the bourgeoisie but rather the philosophy that was the most advanced, the most usable for people's needs, before we discovered dialectics. Much like we first learned to make stone tools before we learned to make them with metal, we first had to know metaphysics and idealism before we could know dialectics and materialism.
Today, science is taught metaphysically; it is seen metaphysically, it's practiced metaphysically, and we take that as fact. We have trouble seeing science any other way because this way makes sense to us, it's all we know.
If you were already aware of this character (studying in isolation, with observations and facts plucked out of their dialectical process and studied by themselves), this question should make sense to you. How do we rethink science in a way that is dialectical. Basically, in a way that we are still doing and studying science, but dialectically?
And of course I don't mean generalities like "it would be placing dialectics back in science", I want to see how far we can struggle with it.
I think physics is currently affected by metaphysics because physicists tend to not see the dialectical relationship between the mathematical formalism of a theory and it's physical interpretation and as such often mistake the former for the latter which cause a lot of problems in the way physics is researched and taught.
For example, the most famous attempt at a "theory of everything" (i.e. uniting relativity and quantum mechanic), string theory, as been hipped up solely on the basis that it works well mathematically while the fact that it completely contradict many of our current physical observations such as its need for more than 3 spatial dimensions is simply hand-waved away with very ad-hoc conjectures such as when string theorists suppose that we don't see their additional dimentions because they are either compactified or because our observable universe in a 3d hyperplane of a higher dimensional space. Don't get me wrong, I'm all for continuing to give it a try, why not, but string theory certainly doesn't deserves its #1 spot as a potential theory of quantum gravity in my opinion, and it's also very sad that other candidates theories are completely overshadowed by it.
It also affect well established theories which end up lacking satisfying physical interpretations despite their success, for example, special relativity despite it's age is still stuck with this very counterintuitive almost mystical sounding interpretation of movement somehow affecting time itself in a way that's not ever really explained even though it is possible to give it a satisfying and even quite intuitive mechanistic interpretation.
I found a YouTube link in your comment. Here are links to the same video on alternative frontends that protect your privacy: