Events, quantum field theory and the quantum substrate

The concepts of "event" and "measurement" in quantum physics have been discussed previously. In working physics, for practical purposes, the Born rule is used and is adequate for laboratory predictions. It is nonetheless mysterious what the measuring apparatus is doing physically. How does it sample a probability distribution? Outside the laboratory what triggers spontaneous events?  RTI [1] claims to answer these questions through an extension of transactional quantum mechanics to quantum field theory.

Quantum field theory (QFT) is usually considered a more fundamental development of non-relativistic quantum physics. And it is the case that it treats subjects such as relativistic invariance and particle creation and annihilation that standard quantum theory cannot cover. This has led some to tackle the formal ontological problems of quantum physics via field theory [2]. In addition, Kuhlmann argues for taking a formal representation of quantum field theory (Algebraic QFT) as fundamental for an ontological understanding. Whether or not this is the best approach is open to debate, but it is a worthwhile exploration with Kuhlmann taking analytical ontology seriously. One of the problems with Algebraic QFT, however, is that space-time regions are primary. That is, the physical information in quantum field theories is not contained in individual algebras but in the mapping \(\mathcal{O} \rightarrow \mathcal{A(O)}\) from spacetime regions \(\mathcal{O}\) to algebras \(\mathcal{A(O)}\) of local observables where the \(\mathcal{O}\)s are open and bounded regions in Minkowski spacetime [2]. Considering the previous posts covering relativistic transactional quantum theory (RTQT - which has been referred to as RTI, but we are dealing with more than just a reinterpretation) the role of the quantum substrate and the emergence of space-time was discussed but in what way is QFT ontologically more fundamental if it needs spacetime to get started. 

A field theory works with a function from a domain over which the field lies to whatever form the field values take. Classical electromagnetic theory provides a clear example. The domain is four-dimensional spacetime and the field values are three dimensional vectors.  This view of fields is usually carried over to the quantum domain. If space-time is needed to define the quantum fields, then the quantum substrate would be ontologically more fundamental than QFT.

I think Ruth Kastner avoids this. Particle position is also an important concept for the quantum substrate but here in the mathematical representation the position operators and the state of the system together constrain the set of possible spatial positions. This status of position as potentiality can be carried over to QFT. I think this agrees with Ruth Kastner's stance [1]. Interestingly, although he takes a very different approach, Kuhlmann also ends up proposing a dispositional ontology with observable take potential values that have a probabilistic propensity to occur [2].

So, how does RTQT use QFT to clarify the concept of quantum event? To understand this, I have found it useful to supplement the book length presentation of RTQT [1] with some of Ruth Kastner's papers. For the topics in this post, I found "On Real and Virtual Photons in the Davies Theory of Time-Symmetric Quantum Electrodynamics" [3] particularly enlightening. The discussion in the paper deals with photons but I believe the physics can be generalised to other particles.

Here are the main points extracted from [3] and wider reading on physical transaction in the relativistic quantum domain.

• A real photon is one that transfers empirically detectable energy 
• An absorber is a subsystem that can receive a transfer of energy while respecting conservation laws
• There may be many potential absorbers with the above characteristics and the probability of transaction will, in general, vary across them.
• The response of the absorber is what gives rise to the ‘free field’ that in the quantum domain is considered a ‘real photon’ 
• The virtual photon is just the potential for possible transaction between two currents—but one that was not realised
• A transaction is only attainable for virtual photons that satisfy the energy and momentum conservation constraints for the initial and final states of the system.
• The realisation of a photon happens due to an absorber response and random selection governed by the transaction probabilities
• In a realised transaction a virtual photon is elevated to a real photon
  
• In a situation that is not a prepared experiment it will not be possible to identify the subsystems that qualify as absorbers for a potential transaction.

In the sense understood here a transaction is an event. I believe this model can be generalised and the discussion of matter fields is important for this [4]. The creation and annihilation of photons is implicit in the points made above, but the role of creation and annihilation events needs to be made explicit in the generalisation to all particle types.

References

1. Ruth E. Kastner, The Transactional Interpretation of Quantum Mechanics - A Relativistic Treatment, Cambridge University Press, second edition 2022
2.  Meinard Kuhlmann, The Ultimate Constituents of the Material World: In Search of an Ontology for Fundamental Physics, Ontos Verlag, 2010
3. Ruth E. Kastner, On Real and Virtual Photons in the Davies Theory of Time-Symmetric Quantum Electrodynamics, [v2] 2016 
4. Ruth E. Kastner, Antimatter in the Direct-Action Theory of Fields, 2015