Helgoland or the case for the Relational Interpretation

Helgoland (Heligoland) is important in the history of quantum mechanics. The young Heisenberg went to this barren rock in the North Sea because of his severe hay fever and in this barren place developed matrix mechanics theory of quantum physics. At the time this was a radical departure from the practice of theoretical physics. Schrödinger returned to more familiar mathematics with his wave theory. A return to Heisenberg has been a theme of this blog and been a major influence on Carlo Rovelli and his relational interpretation of quantum theory [1].

A few years ago Carlo Rovelli published "Helgoland" and he goes back to the Heisenberg story to set the back ground for a historical and philosophical tour that finishes modestly with his reinterpretation of quantum physics. Having read Rovelli's and other papers on this interpretation several years ago, I felt little need to read his "popular" presentation. A few weeks ago it came to my attention again and I thought it might provide some insights into the interpretation that I have been drawn to but in the end have found unsatisfying. Reading it has confirmed my view that his interpretation does not solve the problems associated with quantum physics. In this and in following post I want to set out why I think this.

Searching back through these blog post I was surprised that I have not mentioned the Relational  Interpretation (RI) of quantum mechanics formulated and defended by Carlo Rovelli. The initial motivation for the discussion of quantum physics presented in this blog was the attempt by Popper to provide a statistical dispositional interpretation of quantum mechanics. It became clear that Popper's attempt failed. Then for a time I had hopes for the relational quantum mechanics developed by Rovelli [1] . However, in trying to develop an ontology for quantum theory in which particles exist and have objective properties it became clear that Rovelli's relational approach would not do. Rovelli's presentation is dependent on an informational analysis and in Rovelli [2], the central importance of information is confirmed. Information is an epistemological concept rather than ontological. Rovelli takes inspiration from Wheeler, 1991, and his concept of "It from bit" that attempts to bridge from the epistemic to the ontological domain. Without falling into idealism, it is difficult to see how a bit of information can exist without a physical substrate. Let us now concentrate on the physics. 

The relationships in the RI are between physical subsystems. These subsystems are entities that are described by Hamiltonian operators in standard quantum mechanics. If the type of physical interaction between such subsystems is known then a Hamiltonian operator for the combined system can be obtained. In standard quantum mechanics the Hamiltonian governs dynamics before measurement of the system (this is not the place to go into the technicalities of operator algebras and state spaces - that has been covered in earlier posts). There is a further process in standard quantum mechanics in which a measurement is made, and the result is generated by sampling a probability distribution obtained from the system state space. These are two distinct processes in standard quantum mechanics. The Relativistic Transactional Interpretation (RTI) of Quantum Mechanics (see previous posts) brings both processes together in one coherent theory but I do not think the RI manages this. In the RI not only are interactions relative to the participating subsystems but events are. This is made clear by Rovelli's discussion of Schrödinger's cat. In Helgoland [4] in a subsection called "Facts are Relative" he argues this point:

Suppose that you are the cat in Schrödinger’s thought experiment. You are shut in a box and a quantum mechanism has a one in two probability of releasing the sleeping drug. You perceive whether the drug has been released, or not released. In the first case you sleep; in the second you remain awake. For you, the drug was delivered, or it was not delivered. There are no doubts. As far as you are concerned, you are asleep, or you are awake. You are certainly not both at once.

I, on the other hand, am outside the box and do not interact either with the bottle of sleeping draught or with you. Later on I can observe interference phenomena between you-awake and you-asleep: phenomena that would not have been produced if I had seen you asleep, or if I had seen you awake. In this sense, for me you are neither asleep nor awake. This is what it means to say that you are ‘in a superposition of sleeping and waking’.

For you the soporific is released or not, and you are asleep or awake. For me you are neither awake nor asleep. For me, ‘there is a quantum superposition’. For you, there is the reality of being awake, or of not being so. The relational perspective allows both things to be true: each relates to interactions with respect to distinct observers: you and me.

Is it possible that a fact might be real with respect to you and not real with respect to me?

Quantum theory, I believe, is the discovery that the answer is yes. Facts that are real with respect to an object are not necessarily so with respect to another. A property may be real with respect to a stone, and not real with respect to another stone.

In this well-known thought experiment (sanitised for sensitive souls by having person (You) sleep rather than a cat be put to sleep) we have three macroscopic subsystems (Bottle (B), You (Y) and Rovelli (R) and one triggering subsystem (T), usually taken to be a radioactive source. Using the unitary process in standard QM we can in principle describe the evolution of the total system. If there is no interaction between R and any of the other subsystems then the system T+B+Y will evolve independently of R. It is even possible to include the Hamiltonian describing Rovelli but because there is no interaction between R and the others, R's evolution will take place in his orthogonal state space. The system T+B+Y will evolve unitarily with no reduction to Y being in a sleeping or a wake state. Contrary to what Rovelli claims there is no definite outcome for you under quantum evolution. To get a definite outcome the "measurement process" needs to be invoked as in standard QM as Rovelli knows. In a footnote Rovelli writes:

The problem of quantum mechanics is the apparent contradiction between two laws of the theory: one describes what happens in a ‘measurement’, and the other in the ‘unitary’ evolution, namely when there is no measurement. The relational interpretation is the idea that both are correct: the first regards the events relative to the systems in interaction, the second regards the events relative to other systems.

So the unitary evolution of  T+B+Y is its evolution relative to any subsystem that is not in "interaction" with it. I put interaction in quotation marks because it is now clear that Rovelli is using the term for a type of quantum measurement process and not for the type of interaction that is including in the Hamiltonian for the total interacting system unitary dynamics.

What is it that determines whether a combined system produces a state reduction event rather than an interacting unitary evolution? RTI provides a specific transactional quantum mechanism, but RI does not more than the state reduction of standard quantum mechanics but generalised. Rovelli's position is that any quantum subsystem that can register a change can act as a measurement system. The registered change in the subsystem is an event that happens for that subsystem and all subsystems in interaction with it. For the rest of the universe nothing has happened. 

In the example above let us assume R knows the initial prepared state of T+B+Y then has no further interaction but has the well tested quantum theory. R can model how T+B+Y changes in time. R will know from that model that after a certain time has passed that the bottle will have been broken and Y will be asleep. This knowledge is model based not measurement based. Rovelli claims that unless he physically interacts with T+B+Y the event will not happen for R. Not just that R will not know about it. So we have a situation where there is a model base prediction, that only requires reliable information on radioactive decay rate and the glass breaking mechanism, saying that it is highly probable that an event will have happened and a relativist ontological theory that says it has not happened for R but has probably happened for Y. If the discussion is restricted to what Y and R know then nothing would be puzzling here. It is the relativistic ontology that is strange. But strange does not mean wrong.

Rovelli's QM is relative rather than relational. RTI is relational and describes which relations give rise to events. The events in RTI are not relative in the sense of them having occurred for one system but not for that same system from the perspective of another system.

The “being” of things is indifferent to whatever things might be “for someone”.

 Above is this blog's moto. The ontology proposed by Rovelli contradicts this statement. Is Rovelli's ontology free from contradiction and if so true? This is a challenge, but it turns out that Rovelli has found it necessary to modify his interpretation of QM [5]. On this, more to follow.

References

1.   Rovelli, Carlo (1996). Relational quantum mechanics. In: International Journal of Theoretical Physics 35(8), pp. 1637-1678.

2.   Rovelli, Carlo (2022). The Relational Interpretation of Quantum Physics. In: Oxford Handbook of the History of Interpretation of Quantum Physics. Oxford University Press.

3.   Wheeler, John A (1991). It from bit. In: Sakharov memorial lectures in physics. Vol. 2, p. 751.

4.   Rovelli, Carlo (2021) Helgoland: The Strange and Beautiful Story of Quantum Physics. Penguin Books  

5.   Adlam, Emily and Rovelli, Carlo, 2023. Information is Physical: Cross-Perspective Links in Relational Quantum Mechanics. Philosophy of Physics,  1(1), p.4.DOI: https://doi.org/10.31389/pop.8