Interpreting physics despite the measurement problem

What conclusions can be drawn from the previous two sections for the interpretation of QFT. Can this physical theory be interpreted despite the still unsolved measurement problem? The first result of the foregoing discussion is that the hope to solve the measurement problem within quantum physics, and not by a philosophical theory, is not completely illusory. The argument for the insolubility of the measurement problem in quantum physics rests on the premise that only unitary transformations occur. This argument, however, is only correct if a global solution is demanded and it is false for local solutions, because of decoherence. The latter is clearly relevant for all measurements, it is experimentally verified and it leads to a non-unitary evolution of quantum states. It is therefore not true that quantum states always evolve according to unitary dynamics and the possibility is open to solve the measurement problem by, e.g., finding special conditions within quantum physics, in analogy to decoherence, under which a superposed quantum state reduces to a definite state. Therefore, the conclusion of the strong measurement problem, as I named it above, does not follow. However, the weak measurement problem, that is, to find some description of how measurement results come about, remains. This leads is to QFT.

The credo of Maxwell and Bohm to ban the term ‘measurement’ from physics, or at least reduce it, cannot be given justice in QM, but quite possibly in QFT. It is clear that a measurement process is not fully captured within QM by taking the object state | ni, the apparatus state | ri, coupling both to the joint state | i = | ni | ri

undergo scattering processes in detectors that can only be described by QFT. Roughly, a measurement nowadays is just an ionisation or excitation interaction by which an electronic signal above a certain threshold can be created. Thus, QFT is a contender for what Maxwell (1976) calls a “micro realistic theory of measurements”.

From the viewpoint of QFT, the description of a measurement in QM is not even a simplification, but at least in some cases clearly false. Measurement processes that involve the creation or annihilation of particles, as for instance all measurements of photons or energy do, cannot be described just by coupling the object to the apparatus. From this perspective it is astonishing how it can be expected to reach a full description of measurements, including a solution to the measurement problem, by using only the limited tools of QM. Applying QFT makes measurements a more complicated process, but at the same time opens up possibilities for new discoveries. To gain better understanding of the implications of QFT on the measurement problem, it certainly has to be investigated what happens with superpositions under scattering processes in detector materials. The results of such investigations remain to be seen, but the door is open for solving the measurement problem within QFT.

At this point two possible objections to my general argument in favour of QFT and the philosophical interpretation thereof have to be discussed. First, one might argue that I ignored a phenomenon that is equally important and problematic as the measurement problem and connected to the latter, namely entanglement and EPR-correlations that show up in experiments. Since I have been expressing the hope that a satisfying description of the measurement of superpositions can be found in QFT, it is reasonable to ask of me to explain how spacelike separated measurements of an entangled state can be correlated. A description of measurements in QFT that leaves out Bell-experiments cannot be considered to be complete. I will discuss entanglement in more detail in the next chapter and for now only have one brief comment. It is possible that a full quantum field theoretical description of measurements of superpositions has implication for Bell-experiments. The reason is the connection between the so-called no-signalling condition and linearity. If | ABi

is an entangled state of A and B with density matrix ⇢AB then measurements at all

times made on system A can only depend on the reduced density matrix of A, if there is no interaction, i.e., signalling between A and B. The reduced density matrix is gained by the trace rule, ⇢A= T rB⇢AB ={pi, ˆPAi}, where the ˆPAi are the projection

operators for the states |Aii and the pi are the corresponding probabilities. Now, if

ˆ

H is the evolution operator, the no-signalling condition is equal to the linearity of ˆ H, i.e., ˆ H X i piPˆAi ! =X i piH ˆˆPAi.

In other words, the no-signalling condition is equal to the condition that the measure- ment statistics at A do not change over time, no matter what is done at B, and hence equal to the linearity of the time evolution for the density matrices. On the other hand, if non-linear dynamics should turn out to be important for measurements,

as the dynamics for open quantum systems imply (cf. Breuer & Petruccione 2002, ch. 3), this could lead to a relaxation of the no-signalling condition (cf. Simon et al. 2001; Holman 2008). A full description of measurements therefore could have important consequences for the problem of EPR-correlations. For these reasons, EPR-correlations do not threaten the ontological interpretation of QFT additionally to the measurement problem.

The second objection is that even though the foregoing argumentation might be correct and it is not necessary to follow Decoherence-Everett, GRW or De Broglie- Bohm, it is certainly still possible to follow them, under the assumption that they work. So it might be argued that even now it is somehow more rational to take one of these three solutions instead of leaving the measurement problem unsolved. Though it is trivially true that it is better to have the measurement problem solved, I do not share this rationale. For one thing, it is clear that leaving the measurement problem open cannot be the final word, but adopting GRW, Decoherence-Everett or De Broglie-Bohm might not be any better. Discussing these positions is beyond the scope of this chapter, but it is well-known that all of them come only with a price. Which one is cheaper, GRW, Decoherence-Everett, De Broglie-Bohm or an open measurement problem is hard to estimate and quite possibly only a matter of taste. Furthermore, considering the overwhelming success that QFT has had, if there is just the slightest chance that a satisfying description of measurements can be found in QFT, it is not absurd to be optimistic and hope that QFT can overcome this problem rather than to break down.

However, the most compelling argument in my eyes comes from naturalism. This position roughly inherits that physics and not a priori philosophy is the way to show what the world is like. It goes without saying that therefore philosophers should follow physics as far as possible. If now it were true that the measurement problem is insoluble within physics, this would be the end of the physical road and the naturalist had to (at present) choose between GRW, Decoherence-Everett or De Broglie-Bohm. A decision between them cannot yet be grounded in physics, because neither one has any empirically verified consequences. However, since the insolubility proof is invalid, it seems to be more in the spirit of naturalism, so to speak, to hope for a physical solution of the measurement problem, rather than to abandon physics.

To conclude, I hope to have shown that it can be a fruitful task to interpret QFT, even though the measurement problem is still unsolved and that the measurement problem does not necessarily need a philosophical solution. Having said that, I want to stress the following. In this chapter I have pointed towards some very speculative ideas in physics, e.g. non-unitary evolutions, that, so my conjecture, might have some impact on the measurement problem. I do not endorse any of these speculations that go beyond the standard model. The point I wanted to make was merely to show that physics is not defeated yet, and that it is reasonable and in the spirit of naturalism, to hope for a physical solution to the measurement problem, rather than a philosophical one. In other words, by holding on to the strong measurement problem we rob ourselves of interesting possible solutions. The investigation into QFT also has shown that the usual description of measurements in QM is not only

simplified, but also clearly false for most cases. However, for a clear account of how the measurement process functions and where exactly the problem is, the behaviour of superpositions in QFT has to be examined. More research in theoretical physics has to be done. Only if we have a precise and accurate question, an answer can be found.