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Can a physical theory be fundamentally probabilistic (such as the popular interpretations of quantum mechanics) without contradicting pratitya samutpada?
Clarification
Pratitya samutpada is about how all things arise in dependence on conditions. If there is such a thing as a probabilistic event, then I would say there is some part of that event which does not depend on conditions, only on chance, whatever that might mean.
Dependent origination is about how sorrow & grief arise. It is not related to physics.
Physical theories would be classified under "name and form" in dependent origination:
MN9:52-54.7: Feeling, perception, intention, contact, and attention—this is called name. The four primary elements, and form derived from the four primary elements—this is called form.
The notion of chance and probability is also discussed in DN1, which describes various views that do not yield an end to suffering:
DN1:2.32.2: It’s when some ascetic or brahmin relies on logic and inquiry. They speak of what they have worked out by logic, following a line of inquiry, expressing their own perspective: ‘The self and the cosmos arose by chance.’
DN1 enumerates this and other views and simply states that they are a trap for those interested in the end of suffering:
DN1:3.72.3: In the same way, all of these ascetics and brahmins who theorize about the past or the future are trapped in the net of these sixty-two grounds, so that wherever they emerge they are caught and trapped in this very net.
Physical theories enable grasping as well as continued existence. We can reliably place artillery shells or subatomic particles where we wish with high probability and evaluate the results using the six sense fields. Yet the search for the end of suffering leads us to understand and relinquish the craving that drives such grasping.
The Buddha therefore acknowledges physical theories. The Buddha also teaches us that the end of suffering cannot be found in those physical theories.
Rovelli's relational interpretation and Nagarjuna (really the Buddha's anatta doctorine) agree, in that both deny the usefulness of observer independent states of systems.
Huike said to Bodhidharma, "My mind is anxious. Please pacify it." Bodhidharma replied, "Bring me your mind, and I will pacify it." Huike said, "Although I've sought it, I cannot find it." "There," Bodhidharma replied, "I have pacified your mind."
.. Also QM is only probabilistic upon measurement. Measurement is some acceptance of self, an 'x' or a 'y'.
Edit - chance within QM is qualified by observing a collapse of a wave-function without interference by the observer (spontaneous collapse).. that is, just a thing, changing in and of itself. This has not been observed even once.
All other interactions within QM are relational - because only upon an observer affecting the observed, does any wave function collapse happen. There is no independent collapse observed yet. If there were, Dhamma would suffer unless there was an underlying layer to QM where collapse was made to become not-independent.. kinda like hidden variables. Both hidden variables and independent collapse seem to be unjustifiable through observed experiments atm though.
