To whom quantum theory may concern

In today’s blog we talk to Dr. Peter Evans, PhD from the University of Sydney, Australian Research Council Discovery Early Career Research Fellow in philosophy of physics at the University of Queensland, on the foundations of quantum theory.

David: Does the possibility of many very different ontologies for quantum physics suggest we are farther from understanding fundamental reality than we think?

Pete: There is a sense in which we are further from understanding fundamental reality than we think, but it is not in my opinion due to the many different proposed ontologies for quantum mechanics. I think that, despite appearances, the variety of proposed ontologies for quantum mechanics has some significant benefits for understanding quantum theory, if perhaps not exactly for understanding fundamental reality. Let me get to fundamental reality in a moment, but first let me mention three distinct but related potential benefits to having a range of proposed ontologies.

Firstly, part of what we are attempting to do in science when we systematise a series of related phenomena into an ontological framework or model is to provide an explanatory picture that yields insight in to why the phenomena arise in the way that they do. Different proposals will provide differing explanations of the same phenomena. Secondly, proposing an ontological framework, so long as it is empirically adequate, can provide an indication of which phenomena to explore further to gain deeper insight. So different proposals will illuminate differing paths for further exploration. And, thirdly, the proposal of an adequate ontological framework will provide tools with which quantum mechanics can be taught more effectively. So different proposals will provide differing educational resources.

Thus, despite the fact that we are unable to say, given the range of different ontologies for quantum mechanics, which one provides the 'true' picture of reality, each 'interpretation' can indeed provide a respective guide to understanding quantum phenomena, illuminate paths for further exploration, and provide tools for teaching quantum theory more effectively (I've borrowed the broad outline of this line of response from Reutlinger et al (2018) who are addressing models in science. We can think of different interpretations of quantum mechanics as different modelling frameworks).

Why I think we are further from understanding fundamental reality than we think is due to new results in the form of 'no-go theorems'. A no-go theorem is generally an argument beginning with a group of assumptions and ending with a claim that contradicts quantum theory. So long as the claims of quantum theory can be tested experimentally (which is usually the case, and has so far shown quantum theory to be correct every time), then this shows the conclusion of the no-go theorem to be incorrect, and so one or more of the assumption must also be incorrect. That is, one or more of the assumptions is barred from our logical terrain -- hence, 'no-go'. The most famous no-go theorem is Bell's theorem.

The no-go theorems have done a great job over the past few decades or more at strongly delimiting the logical space that adequate ontologies of quantum mechanics can occupy. Two more recent no-go theorems are significant in this context. One (Shrapnel and Costa (2018)) all but rules out the possibility of quantum mechanics being underpinned by a classical ontology (a claim that has a history stretching all the way back to the birth of quantum mechanics, but is, in my opinion, much closer to being settled against classicality as a result of this no-go theorem). The other (Bong et al. (2020), with earlier versions due to Frauchiger and Renner (2018), and Bruckner (2018)) rules out the possibility of an absolute observer-independent reality. Now this latter result, I think, is a major reason why we are further than we think from understanding fundamental reality.

David: How can I tell if my theory is indeterministic? How do I distinguish that from my theory being incomplete?

Pete: There is a track record in the history of physics of finding more fundamental accounts of reality at a finer 'level of grain' of description. The typical example is the revolution of statistical mechanics in the late nineteenth century. As a result of this, one could surely be forgiven for expecting that the puzzles of quantum mechanics that emerged over the first few decades of the twentieth century would ultimately be explained by an underlying theory, comprised of variables at a finer grain of description. This is the essential thought behind the notion that quantum theory is incomplete, famously expressed by Einstein variously over the first decades of the development of quantum theory. But it's probably a misrepresentation of Einstein's view that he was driven by the indeterminism of quantum mechanics, rather than, say, puzzles about locality.

However, quantum mechanics aside, it should be perfectly reasonable to establish whether a theory at some level of grain is deterministic or indeterministic -- one need only look at the dynamical structure of the formalism. If it is indeterministic, whether the theory is then also incomplete I would think is a different and independent question, and that question relates to whether there is a finer level of grain at which some further (perhaps supplementary) theory can be described. But I would think that those two questions, one concerning indeterminism, and one concerning completeness, would be independent. And then whether that further theory is deterministic or indeterministic would also be entirely independent of whether the coarser-grained theory is complete.

I guess that if a theory at some level of grain is indeterministic, one might take that as a 'clue' that it is also incomplete. (And I take it that this is what this question is getting at.) But whether there is a finer level of description or not is not *necessitated* by indeterminism, I would think.

David: Does quantum theory do more to upend our notion of cause-and-effect than relativity theory?

Pete: This is a good question. Each of relativity and quantum theory has influenced how we understand the notion of causation. But I wouldn't go so far to say that either of those theories has 'upended' our notion of causation, rather they have simply helped refine the notion. Relativity shows us that there are formal constraints on the connectedness of regions in spacetime by which causal relations need to abide. But the basic conception of spacelike surfaces providing the data with which subsequent surfaces are determined remains unchanged, albeit importantly refined, by the development of relativity.

It's hard to say whether developments later in the 20th century in the philosophy of causation were driven by problems understanding causation in quantum mechanics, but quantum mechanics has certainly played a role in refining these developments, to the point where there is now a subfield of quantum causal modelling in quantum foundations. One point of significance in the development of the philosophy of causation comes from Cartwright (1979) who claims that efforts to do away with our causal notions as a result of global theories underpinned by purely second-order partial differential equations (like general relativity) are misguided. She argues that we do indeed have a need and use for a causal vocabulary in science: "causal laws cannot be done away with, for they are needed to ground the distinction between effective strategies and ineffective ones".

This conception of causation arguably sparked the growth of what we can call manipulability accounts of causation, where what we label cause and effect is a function of how the world changes as a result of our own manipulations on the world (identifying effective strategies in the world). One of the better known and technical treatments in this tradition is Pearl's (2009) structural equation and interventionist account of causation. Thinking of causation in this way has arguably opened the door for developing a quantum account of causation. So while quantum theory hasn't exactly been the stimulus that upended any traditional notion of causation, it has certainly been instrumental in giving these sorts of manipulability accounts of causation the sort of physical credibility that generates impetus in the further development of the program.

David: Given your experience with questions about quantum theory, the new ideas, the sociology, etc., can we estimate a narrowing down of the versions of quantum theory in the coming decades? Are we today learning subtle features of the world that show promise in giving quantum theory a unique ontology?

Pete: It would be brave to predict any narrowing down of the versions of quantum theory in coming decades. The only possibility I see for a really definite change in the way we currently think of the range of interpretations (i.e. that they are all empirically adequate) is a truly novel recalcitrant experimental observation. And it would be very hard to put a realistic probability on that happening. But since that is the holy grail, there is currently plenty of research in foundational experiments that push the boundaries of quantum theory.

But I do think that progress on this 'narrowing down' front is possible. And, as I indicated above, I think that it is in the development of novel no-go theorems that this progress can be made. But while no-go theorems restrict possibilities, there's always scope for a variety of interpretations to be consistent with any such theorem. So while we may not necessarily see a dramatic narrowing of interpretations, we will slowly get a better idea of the sorts of classical assumptions concerning the ontology of quantum theory that we are more likely to need to give up.

My personal assessment is that quantum theory is emphasising for us more and more that the role of the observer, or more significantly the role of agency, is crucial to understanding what the theory is telling us about the world. That is, the theory is telling us that at the scales at which we now explore the world we can no longer formulate a description of the world that is independent of the agent doing the describing. And the no-go theorem I mentioned above ruling out an observer-independent reality is one of the more recent data points I take to be notable on this point.

This sort of idea will not give quantum theory a unique ontology in a more traditional sense. It will simply downplay the agent-independence or observer-independence of that ontology. I think that Bohr was on the right track in his philosophy of quantum theory.

David: What is quantum theory about?

Pete: This is a difficult question. And I won't be able to provide a very definite answer. Perhaps I can begin by saying what quantum theory is not about. Quantum theory is not about objectively real, counterfactually definite, uniquely spatiotemporally defined, local, dynamical entities with determinate valued properties, and where typically 'quantum' behaviour emerges as a function of our own in-principle ignorance of such entities. But this is a conjunction of attributes, so quantum theory could still be about entities that are characterised by a collection of these attributes, but cannot be characterised by all.

It's often said that quantum theory is about probabilities -- quantum mechanics is a probability calculus for predicting observed phenomena. Relatedly, it can be said that quantum mechanics is about operations -- preparations, measurements -- or processes. I don't disagree with these sentiments, but I don't find them entirely illuminating, either. But I think that a crucial element of probabilities and operations is that they are both concepts that are *for us*: probabilities are ordinarily understood to be subjective, and operations are always directed from an agent. And this feeds back into the answer to the previous question, that I think lessons around agency and our role in the world is the big lesson that quantum mechanics is teaching us.

So if I had to answer the question concerning what I think quantum theory is about, I'd probably have to say that I think quantum theory is about 'us'.

David: Thank you Professor!

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