Introduction

I am having a look at different philosophical interpretations of quantum physics. This is the ninth post in the series. The first post gave a general introduction to quantum wave mechanics, and presented the Copenhagen interpretations. I have subsequently discussed spontaneous collapse, Everett, Pilot Wave, consistent histories, quantum Bayesian and Aristotelian interpretations.

Here I am going to look at Rovelli's relational interpretation. This is not actually an interpretation I know much about. Before preparing for this post I knew next to nothing about it. So it is quite likely that I have misunderstood details, or am out of date with the latest research. As usual, I would welcome any corrections in the comments. I will base this post on the original paper by Rovelli, this paper on the EPR paradox and the Stanford Encylopedia article. Aside from this introduction and the conclusion, this post will describe the two papers, mostly in my paraphrase although I directly quote Rovelli when I wish to cite his main conclusions in his words. The final section will give my own comments.

Relational Quantum Mechanics (RQM) is based on a number of postulates, including:

• Quantum physics provides a complete description of the system, i.e. even macroscopic objects are described by quantum physics.
• Quantum states are relational and frame dependent, in a similar way that velocity is frame dependent in special relativity.
• The wavefunction is not ontic, but merely a tool used to predict probabilities.

Consider, for example, the case of a spin half particle interacting with a measuring device. The Copenhagen account of this is well known. The particle (reducible to the ontic wavefunction) is in a superposition

It is then measured by an apparatus O and collapses into a given state:

In RQM this understanding is flawed, because it fails to take into account the wavefunction of O. What actually happens is that O moves into a state which is either O_↑ or O_↓, while O represents the initial state of the apperatus. Thus what actually happens in the measurement is

O need not be a conscious observer; it is merely any other system which interacts with the particle. If it is a conscious observer, then that observer might mistakenly think that equation (1) is true because they don't consider their own state.

This has a strong similarity to the many world's interpretation, but differs from it in that it does not believe this wavefunction is ontic, but merely a tool used to predict probabilities. It is also related to QBism, but rejects the strong subjectivity of QBism. Equation (2) is objective, and all observers can agree on it.

The ontology of the system is a flash event ontology, where the formalism only captures reality when we compare probabilities against the frequency distribution generated from the numerous events. While the formalism is epistemic, it does not deny that there is a real world, but it does deny a real world where all the parameters of the system have determined states. It is thus inconsistent with pilot wave models, but can be used to refine most other interpretations.

Clearly in this interpretation there is no wavefunction collapse. I will discuss the EPR experiment below.

Strategy

Relational quantum mechanics rejects the notion of an absolute or observer independent state of the system. There is an analogy with special relativity. In the orthodox interpretation of special relativity, there is no absolute or preferred reference frame. So, for example, one observer might see an object as blue and another as red depending on their relative speed to it. Similarly in quantum mechanics, it is argued that different observers give different descriptions of the same sequence of events.

Rovelli started by noting that each interpretation of quantum physics has areas which leave people uneasy. I have discussed this in previous posts. He argues that the key assumption that makes one uneasy about other interpretations is the idea that there is an observer independent state of the system. Instead he proposes to derive the formalism from a set of physical postulates about the world. While he might not have fully succeeded in this, he believes that he has made progress.

Consider an observer O -- whether a measuring device or human -- that makes a measurement on a system S. The quantity being measured can take two values, A and B, corresponding to states |A> and |B>. If the system starts in some generic superposition, then the observer can measure either of the two outcomes. Suppose that in a specific measurement E the measurement is A. The system is affected by the measurement, and after the measurement will be in a state |A>.

So, from O's perspective, the system moves from a state

to a state |A>. I will call this description 1.

Now consider a second observer, W. W measures a system formed by both S and O. S and O are subsystems of the larger system, so the states are described by both the states of S, |A> and |B>, and the states of O, which I will denote as |O₁>, |O_A> and |O_B>. |O₁> is the initial state of ignorance before O performs the measurement, which can perhaps be written as |O₁> = α|O_A> + β|O_B>. When O performs a measurement, its own state changes. Thus, from W's perspective, the system moves from a state

I will call this description 2. This describes the same event, but from a different perspective. Both expressions are perfectly valid and consistent with each other. They are both correct. Perhaps at a later time W will interrogate O, and W's superposition will collapse into one of the two states.

Different observers might give different accounts of the same sequence of events.

W knows that a measurement has been performed, and can create an observable to check whether the system has moved into the last of those states above. But he does not know the value of the observable without measuring it. We must distinguish between the statements W knows that O knows about Q and W knows what O knows about Q. The fact that O has measured Q is expressed by the existence of a correlation between the state of S and the state of O.

One can deny that the description of a system is observer dependent by denying the possibility that an observer can be described as a quantum system. This is the route that the Copenhagen interpretation takes, with its well known problems concerning how to divide between the classical and quantum realms.

One can also deny that the description of a system is observer dependent by supposing that either description 1 or description 2 describes the absolute state of the system, and the other is merely a description of knowledge.

If description 2 is correct, there is no collapse of the wavefunction, and the system never takes on definite states. However, this contradicts that we observe things in terms of properties rather than quantum states. The system never have definite properties, and we do not see how to match the description with observation. (I will depart from Rovelli's account here, and note that I think this proposal is similar to Wallace's approach to the Everett formulation).

If we suppose description 1 is correct, then that removes the potential interference effects that might affect subsequent observations made by W. One might also argue that after O's observation of S removes the interference effects due to decoherence. Rovelli states (without proof) that this would make a property of S either absolute or not depending on the subsequent observations of W.

We can also suppose that what is absolute and observer independent is the probability of a sequence of property ascriptions, independent from the existence of an observer measuring these properties. This observation is the basis of the consistent/coherent histories approaches. But it confirms the conclusion that different observers give different accounts of the same sequence of events. The probability of a sequence of outcomes is observer independent. But we also need to consider a sequence of real physical events that have happened in a single run of the experiment. The observer chooses the family of histories or framework to use to describe the system. Since the observer is also a physical system, we can consider how a second observer would evaluate the coupled observer-system system, and we return to where we were. The consistent histories interpretation confirms the conclusion that if an observer gives a description of a sequence of events, another observer might give a different description of the same sequence.

The alternative is to suppose that all systems are equivalent. Nothing distinguishes observer systems from quantum systems, and it is legitimate to describe the state of an observer using a quantum description.

If this is true, then each quantum mechanical description is relative to a particular observer. Thus the description should not be taken as an absolute description of reality, but as a formalisation of the knowledge an observer has about a system. Quantum mechanics is thus a theory about the relative information that systems have about each other.

Is there are deeper underlying theory that describes what happens in reality? This would possibly suggest a hidden variable physics. Or maybe there is some not-yet-understood physics which can produce a wave function collapse. But currently there is no physical indication that quantum mechanics is incomplete, and the practice suggests that it is the best we can say about the world at the present state of experimentation. Maybe we might have a metaphysical support to something that completes quantum mechanics, saying that there has to be observer independent reality underlying the observer dependent theory as it currently stands.

But Rovelli disregards the notion that quantum physics is incomplete. He supposes that quantum mechanics provides a complete and self-consistent scheme of description of the physical world, appropriate to our present level of experimental observations.

Thus Quantum mechanics is a theory about the relative information that sub-systems have about each other, and this is a complete description of the world. This implies that there is no observer independent description of the world or an absolute state of the system or an absolute property that the system has at a certain time. A system state is always described with respect to a certain observer.

Information is data collected about the world and organised into some theoretical structure. We can distinguish between a theory about the world and a theory about our knowledge of the world. This notion is too vague for a physical theory. It is more precisely expressed in information theory. Information is contained in the fact that a system is in a certain configuration correlated to some information source. The amount of information counts the size of the configuration space. So that O has information about S simply means that the states of O and S are correlated, or the S-O system is an eigenstate of an operator which measures that correlation. Information can be gained or lost (if the states become correlated or uncorrelated). We do not distinguish between correlations gained by chance and those from an actual measurement. Any physical system can contain information about another system, for example in the case of the spins of two entangled electrons.

Reconstruction of Quantum Physics

Every system can be considered as an observing system or an observed system (or both). An observing system stores information about the observed system, conveyed to it via physical interactions.

Information is a discrete quantity, with a minimum amount of information. Any acquisition of information can be reduced to its elementary bits. An elementary question, denoted as Q₁,Q₂,&hellips; receives an answer in the form of true, or false. There is a set of questions {Q₁,Q₂,…} which in turn lead to a set of answers {e₁,e₂,…}. Only some of this information might be relevant to the physically interesting questions we want to ask. These questions correspond to measurement. A true/false measurement is represented by a projection operator into a linear subset of a Hilbert space.

There is no distinction between quantum and classical systems.

The set of questions that can be asked corresponds to the set of observables.

Discussion of information which one system has about another system replaces the notion of a physical state.

The Interpretation rests on three postulates

1. There is a maximum amount of relevant information that can be extracted from a system. This means that any physical system is finite, and it is possible to give a complete description of the system. The maximal information capacity of a system N is given by the base 2 logarithm of the size of the Hilbert space. If one measures a complete set of commuting observables we can distinguish one possible outcome out of k alternatives.

   The number of questions included in S might be larger than N. These questions need not be independent, so a yes answer to Q₁ might always imply a yes answer to Q₂, denoted by Q₁=>Q₂. A question might fully determined by two questions, denoted as Q₃ = Q₁∪Q₂. Conversely, a question might determine the answers of two questions, Q₃ = Q₁∩Q₂. Q₀ is a question which always responds false and Q_∞ a question which always responds true. It is always possible to introduce not questions, !Q_i, and a notion of orthogonality if Q₁=> !Q_i.

   We can select at least one ensemble of N independent questions which give a complete description of the system. These might not be unique, so there can be many distinct families of N independent questions in S. The answers in the family α might be represented by {e₁ ^α,e₂ ^α, &hellips; } . This can take 2^N = k values, which can be denoted as s^α = {s₁^α,s₂^α&hellips;s_k^α}. From this we can construct a Boolean algebra.

   Alternatively, the observing system could use a different family of N questions, giving a family of answers β. This still gives the maximal amount of relevant information about S. We can have different kinds of descriptions of S by asking different questions. This means that the set of questions that can be asked of a system has the structure of a lattice with subsets which form Boolean algebras. This is the algebraic structure formed by the family of the linear subsets of a Hilbert space, which can be used to describe the information content of quantum physics.

2. It is always possible to acquire new information about a system. Suppose, having answered N questions, we ask a further question Q_N+1. This further question might or might not be independent of the existing N questions. If it is independent, it represents new information.

   This postulate is inspired by experiment. If we have a system where we know the quantum state exactly, we can perform a new measurement such that the quantum state is not an eigenstate of that measurement operator. Since the amount of information is limited, when new information is acquired, part of the old information becomes irrelevant. If a new question is asked, then we should lose some of the previous information. The total amount of information does not exceed N bits.

   To what extent is the answer to the new question determined by the original data? We can define a probability p(Q,Q_i^α) that we get a true answer to the question Q given the data s_i^α. This can be generalised to the probabilities linking two families of answers.

   p_ij = p(Q_i^β,Q_j^α).

   This must lie between 0 and 1 (given it is a probability), and its sum over either index might give 1. These conditions are strong constraints on the matrix, satisfied if

   p_ij = U^ij U^ij†,

   where U is a unitary matrix and † represents the complex conjugate. There are some complications when we expand this into the full Boolean algebra generated by a family, including the ∪ and ∩ operators. The usual rule of adding probabilities doesn't work; instead we need to add together the underlying unitary operators.

3. The superposition principle states that any question Q can be seen as part of the (Boolean) algebra generated by a complete family α of questions. The probability of two questions from different families being true is taken from the modulus square of the relevant component of the matrix mapping between the families.

   This means that we can consider any question in a complex Hilbert space, and from that obtain the standard state representations of quantum physics. This ultimately means that the formalism of quantum physics can be reconstructed from the three postulates.

Dynamics is included by adding a time variable to the questions. Any question can be labelled by the time variable, indicating the time when it was asked. If time translation is a symmetry in the theory, then the total set of questions would be unchanging over time. There must then be a unitary transformation linking the questions at different times

Where we can express the time evolution operator T as the exponential of a Hamiltonian.

Time evolution can be viewed as a transformation of the set of questions that can be asked on a system, linking sets of questions at different times.

This leads to the full formal machinery of quantum physics. But there are interpretational differences compared to (say) the Copenhagen interpretation. There is no state of the system, merely information possessed by various observers.

Information possessed by different observers cannot be directly compared. Discussing the information possessed by O is a statement concerning the physical state of O. Each observer is just another physical system. Having information about a system means that they are correlated with that system. In Rovelli's own words,

However, since there is no absolute meaning to the state of a system, any statement regarding the state of O is to be referred to some other system observing O. The notion of absolute state of a system, and thus an absolute state of an observer, is not defined. Therefore, the fact that an observer has information about a system is not an "absolute" fact: it is something that can be observed by a second observer O'. A second observer O' can have information about the fact that O has information about S. But recall that any acquisition of information implies a physical interaction. O' can get new information about the information that O has about S only by physically interacting with the O-S system.

Since an additional interaction is required for O' to know what is known by O, there is no way to compare the information possessed by each of them except in terms of their relationship with each other. The statement that an observer has information about a system is a physical notion that can be studied experimentally just like any physical property of a system. Asking whether two observers get the same answers from a system is meaningless, because it is a question about the absolute state of those observers. The question can only be rephrased in terms of a third observer.

In terms of dynamics, knowledge of the questions requires knowledge of the system's Hamiltonian. To know the dynamics of an O-S system is to know the Hamiltonians of O, of S, and the interaction Hamiltonian. The interaction Hamiltonian is required if O is to gain information/become correlated with S. However, O merely understands the system S, so can only use the Hamiltonian related to S. O cannot have information relating to itself or the O-S interaction because information is correlation, and saying you are correlated with yourself is meaningless. Since the evolution of S is affected by its interaction with O, O's knowledge of it breaks down. This (in other interpretations called wavefunction collapse) is simply because O does not have a full dynamical description of the interaction.

Two observers cannot gain information about a system independently. One would have to ask its questions first, and by doing so change the dynamics of that system.

So there are two basic principles to this interpretation.

1. There is no absolute meaning to the state of a system or the information held by an observer, only information of a further observer.
2. There is no way an observer can gain information about a system without interacting with it, and therefore breaking down any unitary evolution description in its Hilbert space description.

So the concept that quantum physics forces us to surrender is that systems can exist independently of observers. The concept of an absolute state of a system is invalid, or discussing a system as being in certain states.

Relation with other interpretations

1. QBism. Rovelli's interpretation is closest (in my view at least) to QBism. The main difference between them is that QBism consciously adopts di Finetti's subjective Bayesian interpretation of probability, while Rovelli is not so tied to any specific interpretation of probability. They also understand information in different ways. So while the overall approach is similar, there are differences in some of the details.

2. Copenhagen interpretation. The Copenhagen interpretation assumes a macroscopic classical world distinct from the microscopic systems of quantum physics. This interaction between classical and quantum gives rise to wavefunction collapse and so on. Suppose in relational quantum physics there were one privileged observer (perhaps God). This would define an absolute state. The Copenhagen interpretation states that there is a large consistent set of classical systems that play this God-like role. The weakness of the Copenhagen interpretation is in how it treats some physical systems as different from others.

   In the Copenhagen interpretation, there are two different kinds of evolution: under the unitary and deterministic Schroedinger equation, and then the instantaneous, probabilistic wavefunction collapse. In relational QM, the Schroedinger evolution breaks down when the system interacts with something not taken into account by the evolution equations. There is no wavefunction collapse, just a different Hamiltonian that includes the observer which makes it appear that the Schroedinger equation for the system breaks down.

3. Consistent history and coherent histories reduce the description of a system to the predictions of the system's responses to questions one can formulate about the system. One distinguishes the probability of observer independent histories with the statement that a certain history has occurred, meaningful only once we make contact with real observations. The histories interpretations are (according to Rovelli) consistent with his own interpretation, but his interpretation gives a better account of the process by which we can connect observer-independent probabilities of families of histories with actual descriptions of events.
4. Aristotelian interpretations Rovelli here refers to a work by Gordon Fleming which I wasn't familiar with, but which I now need to review (although it seems to be less detailed than I would like). Rovelli feels that this requires a preferred moment of time when a potentiality becomes actual. But the Aristotelian approach does not indicate when this time is; Rovelli's answer is that it is determined by when an observer system interacts with the studied system.
5. Spontaneous collapse interpretations violate Rovelli's hypothesis 2, and are inconsistent with this interpretation.
6. Many worlds interpretations raise questions about the branching process similar to wave-function collapse. When does it happen? Which systems are measuring systems which make the world branch? On the other hand, if we just consider a wavefunction evolving under unitary evolution, we obtain a description provided by a fully external observer, and we need to interpret observation of the individual observers. This is the problem addressed in relational quantum mechanics.
7. Pilot wave interpretations are inconsistent with relational quantum mechanics because they propose an absolute state of the system, and that the Schroedinger evolution is incomplete (i.e. an additional guidance equation is needed to describe the motion of the particles).

So most interpretations are, or can be, formed in a way which is consistent with relational quantum mechanics, but Rovelli views them as incomplete because they do not fully take into account the way information flows between observers and is subjective.

EPR

EPR style experiments are usually interpreted as implying that there must be some non-local aspect to reality. Rovelli questions whether there is not another assumption behind these explanations, namely that

There exists a physical reality independent of substantiation and perception.

Relational Quantum Mechanics rejects this strict realism. Physical reality is taken to be formed by individual quantum events through which interacting systems affect each other. "The character of each quantum event is only relative to the system involved in the interaction," as quantum events only exist in interactions. Physics is not concerned about what nature is, but with what we can say about nature.

The wavefunction represents the correlation between an observing system and an observed system. It has an irreducible epistemic character, and cannot be regarded as an objective property of the observed system independent of the observer. The wavefunction can also be used to predict future interactions between the observer and the observed system.

Rovelli defines Locality as "the principle that two spatially separated events cannot have instantaneous mutual influence." Formulated in explicitly RQM terms, this becomes "relative to a given observer, two spatially separated events cannot have instantaneous mutual influence." Locality is important in RQM, as it lies behind the principle that different observes can have different descriptions of the system. Locality also makes it possible to distinguish between two separate systems. He argues that this is not contradicted by EPR correlations in the RQM interpretation.

A property of the observed system only influences the observer after communication between them. That communication is slower than the speed of light. Different observers are bound to have different information about the observed system.

Rovelli also questions notions of separability in standard interpretations of quantum physics. For example, two entangled photons are regarded as a single, inseparable, system described by a global quantum state. However, measurements are performed on individual particles. This notion that the two entities can have their properties measured individually but are also inseparable seems incoherent.

Instead, Rovelli defines that two physical systems are separable if there exists a complete set of observables of the compound system whose values can be actualised by measurements on only one of the elements of the system.

Consider the simple example of an entangled system. A spin 0 particle decays into to spin-1/2 particles, which would have to have opposite spin along any particular axis. Two observers, A and B measure the spins of the two particles.

The state describing a pair of entangled quantum particles has to be defined in one particular basis. It can only encode at most one piece of evidence concerning the particle's state. For example, it might record the spin state orientated along the x axis or the z-axis. But it cannot record both of them. According to the the principle of locality, the choice made concerning the spin measurement of one particle cannot have an influence on the second, space-like separated, particle. To describe measurement results in both spin directions would require both spin-x and spin-z results to be encoded in the wavefunction simultaneously. This is impossible. Hence there are, and everyone admits this, real properties not described by the quantum state. So it seems like we have to choose between realism, locality, or the completeness of the quantum state (a one-to-one correspondence between the mathematical object and its real state).

This analysis depends on the principle that the actual properties of the particles revealed by the detectors are observer independent. So when we measure the spin of one particle, the measured value instantaneously acquires an objective existence also relative to the observer measuring the second particle. RQM rejects this principle. A cannot know the result of B's measurement except by measuring B's own state. This cannot be done instantaneously. What is measured is the distinction between elements of physical reality relative to A and elements of physical reality relative to B. The objection depends on the existence of a hypothetical super-observer which can sense both A and B's states instantaneously.

The non-locality argument only works if there is an objective reality about the measurement results, but there is not. Only subjective states correlated with each individual observer. Indeed, it is customary to think of the observers as classical systems, which is even worse.

When A performs his measurement, the objective state of the other particle does not change, but only its subjective relative state coding the information A has about that particle. This change is unproblematic, and does not violate locality. The state only encodes A's prediction of future measurements either of that second particle or the observer B.

The sequence of events described by B is different from that described by A, and B's quantum state will be different. But this is no problem for RQM. Both A and B's states are adequate physical descriptions relative to those observers. And every quantum state is relative to an observer.

Does this prescription mean that both observers can measure their particles as spin up, since their own correlations with the quantum state are independent until they communicate with each other? Rovelli answers No.

We are not dealing with properties of systems abstractly, but the properties of systems relative to one system. We can never juxtapose properties relative to different systems. RQM does not claim that reality is described by the collection of all properties. It admits one internally consistent description per observing system. So this example cannot happen because it cannot happen with respect to either observer. The two sequences of events are distinct accounts of the same reality. The notion of realism is weakened, but not to the point where it denies self-consistency.

Concluding thoughts

I'll start by evaluating the three premises listed in the introduction. The first premise was that all systems are quantum systems. I don't see a problem with this. Obviously decoherence means that superpositions in larger systems are suppressed, removing one of the distinctive marks of a quantum system. However, decoherence is still a quantum effect, explainable within the framework of quantum physics. Although classical mechanics might be a good description of macroscopic systems, so is quantum physics. I see no reason to introduce an artificial and arbitrary boundary between the quantum world and the classical world. I don't really see this premise as controversial.

The third premise, that wavefunctions should be interpreted in terms of our knowledge of the physical state rather than a physical state itself is more controversial. But it is a premise I personally accept. It completely removes any problems surrounding wavefunction collapse (which becomes an update of our knowledge rather than anything physical), and also resolve problems mapping between a supposedly ontic, single run of the experiment, amplitude derived from the wavefunction and the epistemic probability used to predict the frequency distribution after the experiment is repeated many times. That jump from ontic to epistemic is troubling, but resolved if the wavefunction is interpreted as epistemic. The only psi-ontic interpretation which escapes this problem is the pilot wave interpretation. Thus while many people would reject this premise, I personally think it reasonable and correct.

It is the second premise, that quantum states are purely relational in analogy to special relativity that I find troubling. For one thing, the analogy has its problems. In physics, we start with the real world, and map from that a mathematical representation. Part of constructing this representation is to impose on it an arbitrarily chosen coordinate system. We then perform calculations in the representation, and map back to reality to compare against experiment. Lorentz invariance states that the mathematical form of the laws of physics, specifically the action, is identical regardless of which (inertial) frame is used to parametrise the coordinates. The coordinate systems are not part of reality, but only the representation. A quantum state, on the other hand, does have its analogue in reality. It is mapped from reality to the representation, we perform the calculations, and then map it back to reality. The precise numbers used to parametrise it are frame-independent, but nonetheless equivalent after we map from one frame to another. In whatever frame, there is agreement that the quantum state exists. The quantum state represents something observed and is thus part of reality. The coordinate system is not part of reality, but imposed as we construct the representation.

This leads me to my main criticism of relational quantum mechanics. It claims that quantum states are purely observer independent. That it doesn't make sense to say there is an objective state of the system. Quantum states are also epistemic, so represent knowledge (using Rovelli's specific definition of that term). But knowledge of what? Another quantum state held in another observer. But that quantum state would also just be knowledge (in the sense of correlation with another system). Knowledge of what? Another epistemic quantum state. I cannot see how to avoid an infinite and viscous regress.

In other words, relational quantum mechanics fails to distinguish between representation and reality. It treats the cosmos as though there were just the representation. Information is a purely abstract concept, and abstractions belong in the representation.

Does relational quantum mechanics fails in one of the key tasks of an interpretation of quantum physics: to specify what the beables are? I guess that Rovelli would say that the beables are the relative information described by each observer's (or other system's) quantum state. But information regarding what? If it is information regarding a concrete object, then as that concrete object would exist independently and objectively, relational quantum mechanics would have to be incomplete as it doesn't say anything that object. If it is information regarding information, then you have a viscous infinite regress.

Then there is the postulate that the "set of questions that can be asked corresponds to the set of observables." How is the set of observables determined without an objective real world which we can interrogate? We are interested in the spin of the particles because we measure particle spin and it has physical consequences. But we can formulate quantum theories without spin and with only spin-zero particles. Why would we then need a question asking about the spin of a Fermion? The answer to this in most interpretations is that Fermions objectively exist and have this particular property. But if quantum states just concern subjective information, then why would we need a description of Fermions in that information? No problem if there is an objective reality underlying the quantum state. This is a problem if there is just information in some sort of abstract sense.

One of Rovelli's premises is that you cannot have information concerning yourself. Information means correlation between quantum states, and correlation with oneself is meaningless. This strikes me as problematic. For example, I know that I know that I have observed a particular Fermion in a spin-up state. This is knowledge about myself. A complex system can be split into various interconnected sub-systems, with correlations between those sub-systems. Can we know everything about ourselves? That might lead to an infinite regress, and is problematic. But we can certainly know some things about ourselves without creating any such regress. But Rovelli's construction seems to rely on the assumption that we can know nothing regarding ourselves, or our interactions with other systems.

Rovelli is correct to state that there is no way an observer can gain information about a system without interacting with it. But why does he think this breaks the unitary evolution of the system? The interaction with the system is still a part of physics; it is still ultimately described by the Hamiltonian of the larger system containing both the observed system and the observer. For this larger system, there is no break down of the unitary evolution. This is why Rovelli needs the assumption that an observer cannot have knowledge of himself. That would preclude knowledge of any system the observer is part of, including the larger system I have just described. However, distinguishing between full knowledge of yourself, partial knowledge of yourself, and no knowledge of yourself, I think Rovelli's argument here requires that there is no knowledge. For example, suppose the observer interacts with the observed by sending out a few photons, and then making note of the photons which are emitted in response. To incorporate this interaction into the Hamiltonian, and unitary evolution, of the observed system, he merely needs knowledge of the photons absorbed and emitted by the system. A partial knowledge of yourself could include this information. I don't see why an interaction would necessarily cause a breakdown of unitary evolution and apparent wavefunction collapse.

Is the assumption that systems cannot exist independently of observers a reasonable one to reject? The universe existed long before there was any life to observe it. (Obviously I exclude a possible divine observer here.) To say that some distant galaxy only started to exist when it emitted light which would reach our planet, but only if someone happened to be looking in the right direction, and only if life happened to emerge on this planet after the galaxy omitted this light, seems absurd. (Obviously inanimate objects might also count as observers in Rovelli's system, but only if their state is in some way correlated with the state of the distant galaxy, which wouldn't be the case in practice.) I think abandoning this assumption is far too high a price to pay for a philosophy which doesn't answer the fundamental questions of beables.

I am also far from convinced that Rovelli successfully deals with the non-local event correlations seen in entanglement experiments. Even if the information only reaches the observer later, the observer will still be able to take the data he has and say that at a certain time the state of this system was such and such and the state of that system a long distance from it was so and so, and there is a clear correlation between those two results. The difficulty is to explain why there is that correlation when it cannot be caused by a physical exchange of particles subject to the constraints of Lorentz symmetry, and there is no other way to explain a correlation in terms of local physical effects. The issue isn't that the subjective quantum states in the mind of observers are correlated, but that those subjective states correspond to knowledge of two objective systems (in the sense that all observers who gain knowledge of those systems will come to the same conclusions), and those two systems are correlated. "Physics is not concerned about what nature is, but with what we can say about nature."

His theory of knowledge as correlation between different quantum states might also be questioned. I'm not really an expert on the philosophy of mind, so I can't go into too many details. Aristotelians think of knowledge as grasping the form of the object in the intellect. There is some similarities between this and Rovelli's prescription, but the form extends beyond just the present state of the system. For example, it also includes information about other possible states of the observed system. Rovelli doesn't describe how we might gain knowledge of these other possible states. I think then that his theory of knowledge is too limited. It describes one type of knowledge, but I don't think its a complete description. not treated

In his favour, I think Rovelli makes good points, reminding us that what we have in our minds when we think about quantum physics is only a representation of our knowledge of reality, and different observers can have different representations corresponding to their different levels of knowledge. But his approach doesn't adequately answer some key questions concerning the beables or non-local correlations in entangled systems that you would hope that any viable philosophy of physics would answer. His extreme subjectivism is uncomfortable for me, as is that he concentrates on interpreting physical knowledge rather than the physical world itself. There is a hint of Hume's empiricism in his philosophy, and, to my mind, that's not a point in its favour.