Tag Archives: Carlo Rovelli

Rovellifest 2

I thought it was about time I got around to finishing my comments on Rovelli’s “Relational QM” programme.

Relational QM (RQM) has a lot in common with the Everett/many-worlds interpretation, so it should be no surprise that it shares some of the same difficulties. In my opinion, the “basis problem” also applies to RQM, and one cannot appeal to decoherence in order to solve it as one does in many-worlds. Before discussing this, let me summarize the main differences between RQM and many-worlds:

  • In Everett, the state-vector of the universe is the full description of reality. It always evolves unitarily, but different observers can have different subjective impressions of reality depending on how they are described within this state.
  • In RQM there is no state-vector of the universe. State-vectors always describe the point of view that one subsystem has about another system. State vectors are therefore always subjective descriptions of reality.
  • In Everett, the concept of measurement is an emergent phenomenon that applies when a macroscopic system interacts with a microscopic one. The theory of decoherence is used to explain why measurement results appear to be stable.
  • In RQM, Rovelli states explicitly that he doesn’t want to treat microscopic systems any differently from microscopic ones. For example, if two electrons interact, then it is valid to think that one of the electrons acts as a measuring device on the other and vice versa. One description is valid from the point of view of one of the electrons and the other is valid from the point of view of the other electron.

The appeal to decoherence in Everett is designed to address the “basis problem”, which arises due to the ambiguity over which baisis the states are decomposed in. For example, suppose two qubits start in the (unnormalized) state

(|0> + |1>)|0>

and interact so that they end up in the state

|00> + |11> .

This is a typical example of a “measurement” interaction and we might want to say that the second qubit has measured whether the first qubit is in the state |0> or |1>. In Rovelli’s formulation, the state of the first qubit is definitely either |0> or |1>, relative to the second qubit, with 50/50 probabilities of each being the case.

However, we could equally well write the final state as

(|0> + |1>)(|0> + |1>) + (|0> – |1>)(|0> – |1>).

If the qubits are actually spin-1/2 particles and |0> and |1> are spin up and spin down in the Z-direction, then this is a decomposition of the state in the spin-X basis. Therefore, we might equally well say that the second qubit has measured whether the first qubit is in the state (|0> + |1>) or (|0> – |1>). In Rovelli’s formulation, we ought to be able to say that the first qubit is either in the state (|0> + |1>) or the state (|0> – |1>) with 50/50 probabilities.

Note that, this is not only an issue with the particular state |00> + |11>. Any bipartite state can be decomposed according to any basis for one subsystem, although the relative states of the other system will not generally be orthogonal.

I have seen no discussion of this issue from Rovelli. He seems to assume that there just is some natural basis in which to do the decomposition. I think the possible solutions are:

  • Accept multiple descriptions: The state of one subsystem is not only relative to another subsystem, but it is also relative to an arbitrary basis choice. The problem with this is that it does not explain why our subjective experience is always according to one particular basis. I always feel like I am in one particular location, observing one particular thing, and I am incapable of regarding myself as being in a superposition of two locations, despite the fact that such a decomposition of the wavefunction almost certainly exists.
  • Stipulate a basis: For example, the position basis might be a natural choice, since it generically corresponds to our everyday subjective experience. The question then arises as to why this basis is chosen rather than some other. What is there within the formalism of QM that compells us to make this choice?
  • Appeal to decoherence: Decoherence theory usually supplies a “pointer basis” in which the results of measurement outcomes are almost exactly stable. This is the usual solution of the Everettians. However, if Rovelli takes this option then he has to back away from the position that microscopic systems are to be treated in exactly the same way as macroscopic one. It would no longer make sense to talk of a single electron acting as a measuring device.
  • Use the biorthogonal decomposition: Most bipartite states have a unique decomposition of the form \sum_j a_j | phi_j> |psi_j>, where <phi_j | phi_k> = \delta_{jk} and <psi_j | psi_k > = \delta_{jk}. We could simply stipulate that this basis is the correct one to do the decomposition in. This is the solution advocated in some variants of the modal interpretation. Problems include the fact that there are special states like the one above (admittedly they form a set of measure zero) for which the decomposition is not unique. Also, the biorthogonal basis does not always correspond exactly to our subjective experience, e.g. it may be close to, but not exactly equal to, the position basis.

    My impression is that none of these solutions would completely appeal to Rovelli, so it would be interesting to see what he says about the matter. However, if we combine this issue with the previous comments I made, then I have a hard time seeing how the Everettian/many-worlds ontology can really be avoided in this sort of approach.

    Rovellifest 1

    Carlo Rovelli has recently put 3 papers on the arXiv, which have attracted some attention within the blogsphere (see here, here, here and here). The one that concerns us here at QQ is the paper about EPR in the relational approach to QM. I don't want to comment on the particular argument in that paper, which seems fine as far as it goes, but I do want to say a couple of things about Rovelli's approach in general, since it seems to be a popular topic at the moment. The main ideas of the approach can be found in Rovelli's original paper.

    Here is an (admittedly cartoonish) summary:

    1. We should shift attention from things like the measurement problem and instead try to derive QM from the idea that it is a theory of the information about one system that is available relative to other systems.

    2. Quantum states are not absolute concepts and the state of a system is only defined relative to some other reference systems. Different reference systems do not have to agree on this state. If they do come to agreement it is only after the reference systems themselves interact with each other according to some Hamiltonian.

    3. The question of whether a system has some particular property has no absolute meaning. However, some property of a system can be well-defined relative to some other system, provided the systems happen to have interacted in such a way that the second system records the appropriate information about the first system.

    4. All the relational states just represent the subjective point of view that one system has about another. There is no absolute meaning to such states and no meaningful "wave-vector of the universe" can be constructed because there is no external system for it to enter into relations with.

    5. This is all just a twist on the usual kind of relationalism that we have in other physical theories, e.g. special and general relativity.

    In my opinion, there is a good deal wrong with relational QM as formulated by Rovelli, although I am not particularly opposed to relationalism in general. In this post, I'll make some comments about 4 and 5. A forthcoming "Rovellifest 2" post will point out a problem with 3, which I believe is more serious.

    To address 5, it is worth noting a striking disanalogy between relational QM and other sorts of relational theories in physics. For example, in Newtonian mechanics we are very used to the idea that that there is no absolute meaning of the position of a particle A, but you can define its distance to a reference system B. This is generally different from the distance of A relative to another reference system C. Similarly, there is no absolute notion of when two events are simultaneous in special relativity, but this is well defined relative to any inertial reference frame.

    However, in these cases it is always possible to find some transformation that relates the descriptions relative to different reference frames, provided you know the relations between the frames themselves, e.g. the Lorentz transformations in special relativity.

    Now consider a quantum system composed of a subsystem A and two observers B and C. Suppose both B and C separately interact with A, possibly measuring different observables on A. Relative to B, A is supposed to have some definite property after this interaction and similarly for C. However, you generally can't convert between B and C's description of the situation if you only know the state of B relative to C. You can if they happened to measure the same observable, but that's a very special case.

    In fact, the only way to relaibly convert between different observers relative states of the same system is to know the entire "wave-vector of the universe", something that is meaningless for Rovelli due to 4.

    So, it seems we are left with two options:

    1. Add in a "state of the universe" so that one can reliably transform between different descriptions of the same subsystem.

    2. Abandon the classical notion that one can reliably transform between different descriptions of the same system.

    Adopting 1 would essentially entail accepting an Everettian/many-worlds type scenario, something that Rovelli is keen to distance himself from. Therefore, I conclude that he must accept 2.

    Abandoning reliable transformations is not a completely absurd thing to do, but it is important to note that this is a departure from what we usually mean by the term "relational". I am still not entirely convinced that it is consistent, although I haven't managed to think up a scenario where it would cause a problem yet. My suspicion is that it might be attacked by a "Wigner's Enemy" type of argument of the sort that was levelled against Chris Fuchs' Bayesian approach by Amit Hagar, which seems much more relevant to the relational approach than to its original target.

    N.B. "Wigner's Enemy" is a new name I just thought up for the argument.  I figure he must be an enemy rather than a friend because friends don't usually try to erase your memory.