Absent Relations: A Critical Look at Rovelli’s Relational Quantum Mechanics

by Tom Pashby

“[T]he fact that the problem of the reduction of the wave-packet has remained baffling for so long, and that we lack any clue at present to its solution, seems to me no reason at all either for despair, or for embracing … glib and inadequate pseudo-solutions. Real problems are not always ripe for solution.” Howard Stein, ‘On the Present State of the Philosophy of Quantum Mathematics’ (1982)

“Information? Whose information? Information about what?” John S. Bell, ‘Against Measurement’ (1990)

This paper concerns Carlo Rovelli’s proposed solution to the measurement problem he calls Relational Quantum Mechanics (1996, 2005, 2007, 2008). Following Brown (2009) I distinguish between the interpretative and reconstructive projects Rovelli commences in (1996), and argue that his pursuit of the interpretative project alone since then indicates that he regards it as standing independently. This project amounts to an attempt to answer the question ‘What is quantum mechanics trying to tell us?’, rather than ‘Why the quantum?’.

I begin with an analysis of Rovelli’s argument for the radically relativist position he adopts which concerns what he calls `the third person problem’ i.e. the ‘Wigner’s friend’ paradox of Wigner (1961). I argue that even if we accept the very high value he places on definiteness, the radical conclusion (that there is no observer independent description of reality) does not follow due to the availability of a similarly perspectival, but modal interpretation of Dieks (2005, 2009). The similarity of the incompatible value ascriptions allowed by these accounts is compared with the incompatibility of attributions of tense to events in Special Relativity, and a better analogy is found with Dieks’ interpretation.

The consideration that Rovelli might offer in preferring his scheme to Dieks’ – its ability to accommodate non-ideal measurements involving partial correlations – is shown to conflict with the defense offered on his behalf by Brown, where it is claimed that certain relations are invariant between observers. It is argued that this picture is inconsistent with Rovelli (1996, 1998) and that if Rovelli’s (2005, 2007) view of the quantum state as containing probabilities for certain ‘quantum events’ is taken into account, then the claimed consistency between accounts is almost entirely vacuous.

A key concept Rovelli employs is that of ‘information’. He takes care to distinguish two uses, one of which he claims corresponds to the technical concept of Shannon information. Following Timpson (2008), I point out that the technical concept is inalienably tied to the practical problem of communication and so argue that his use of the term ‘information’ cannot avoid being associated with the everyday, epistemic, concept closely linked to knowledge. As such, he faces Timpson’s potentially fatal dilemma for information-based accounts of measurement, implicit in Bell’s third rhetorical question: ‘Information about what?’ Timpson claims that the information in any such interpretation must either be about the values that a quantity takes prior to measurement (hidden variables), or the measurement outcomes themselves (i.e. instrumentalist).

Rovelli’s ontology of quantum events, and his assertion that his account is non-anthropocentric, indicates an attempt to avoid the second horn of this dilemma and the associated charge of instrumentalism. However, I argue that this attempt fails on three counts: a failure to take into account the epistemic character of ‘everyday’ information and the nature of communication, an inability to meaningfully distinguish the quantum events of Rovelli’s ontology from measurement results, and the failure of RQM to meet a key requirement for the naturalization of an observer within a theory: that it allow a representation of observers within the description of reality provided by the theory.  These complaints entail that in Rovelli’s interpretation the probabilities contained within the quantum state refer only to the relative frequencies of measurement outcomes, hence the charge of instrumentalism is unavoidable.  Furthermore, I argue on this basis that his position is unavoidably solipsistic.

Finally, it is suggested that the information-based approaches of Fuchs’ Quantum Bayesianism, where the probabilities are associated with subjective degrees of belief, and Bub’s reconstructive project (with Clifton and Halvorson), whose interpretation by Bub (2005) is essentially communication driven, are to be preferred. Markopoulou’s causal quantum histories approach is discussed as an alternative, or perhaps complimentary, event-based account that would provide some objective relations between events.

Thanks to all who managed to attend the talk on Friday.  Apologies for the ridiculous quantity of slides I had managed to churn out (62 in case you’re wondering) which meant I ended the talk with a whimper half way through the argument.  This actually helped concentrate my attention somewhat on what I was really trying to say.  The above is the product of that reflection. I would be happy to add more detail if anyone is interested, hopefully at a level in between quick-and-dirty abstract and tedious-and-endless presentation.