6.3 The measurement problem
6.3.4 Can quantum field theory help?
By the fact that QFT, as it is found in textbooks, only involves unitary dynamics, it seems that QFT does nothing to clarify the measurement problem in addition to QM. This opinion is for example endorsed by Barrett (2000, p. 4 f.) and Wallace (2008, p. 83). The present section is a critical assessment of this view. To begin
with, it will be instructive to take a look on how measurements function in particle physics from the viewpoint of QFT.
The first argument for the relevance of QFT in measurements comes from experi- mental practice. Fundamental particles can only be measured in specially constructed detectors. I have already described the experimental basics of measurements in section 5.2.3 and only want to summarise the main points again. The condition sine qua non for measurement is that energy goes from the measured particle onto the detector. This is usually reached via two processes: ionisation or emission of radiation. Properties that are measured are usually time, momentum, velocity or total energy. Furthermore, every measurement of these properties can automatically be used to measure position; simply given by the fact that the detector covers a certain area in space and that the particle is in that area when it is detected. The accuracy of the position measurement depends on how small the parts can be made that a detector is composed from. In practice, these processes are described through approximations derived from an exact treatment in QFT. In the end, however, every interaction of a particle with a detector is a scattering event that can be described only in QFT, and not QM.
In comparing QM with QFT there is yet another interesting fact that is sometimes noted as a curiosity. While in QM the wave function evolves deterministically, measurement results can only be predicted with a certain probability, following from the Born rule. In QFT on the other hand, interactions or decays are the place where probabilities occur. Eugene Wigner expresses his surprise about probabilities in QM when he writes: “The place where one expects probability laws to prevail is the change of the system with time.” (Wigner, 1983, p. 326) The application of the Born rule, however, cannot be regarded as describing the ‘change of the system with time’. According to Cartwright (1978, p. 54), the received interpretation of | (x)|2 is that
it is the probability density that a particle is in a small region around x. Cartwright points out that this cannot be true literally, since experiments like the double slit experiment show that quantum mechanical particles are not located in that way. On the other hand, the usual alternative, to interpret | (x)|2 as the probability for
a particle to be at x when measured, is not feasible either since it leaves unclear what a measurement is and runs into the measurement problem (cf. Cartwright 1978, p. 55). Hence, the meaning of the probabilities remains unclear in QM. In the light of the foregoing discussion, however, it is hard to overlook the parallelism between QM and QFT. Measurements are nothing but interactions between different systems for which QFT assigns probabilities for an initial state to evolve into a final state. It is therefore tempting to identify the Born rule probabilities of QM with transition probabilities of QFT. This is exactly the programme that has been pursued by Cartwright (1978, 1980).22
Cartwright (1978, p. 55) proposes that
| (x)|2 does not represent a probability at all. Hence there is no problem of finding an event for it to be the probability of. [...] The only probabilities there
are in quantum mechanics are probabilities for energy interchanges (transition probabilities to energy eigenstates).
This is precisely a consequence of the fact that “[a] real detector cannot respond to the mere presence of a particle.” (Cartwright 1980, p. 110) Real measurements only happen when a particle transfers energy to a detector, and this process is a quantum field theoretical scattering process that cannot be described in QM.
However, given that the Born rule is actually applicable and gives probabilities for a range of real processes, the above proposal faces what Cartwright calls the ‘consistency problem’; it needs to be shown that the Born probabilities agree with the probabilities derived from QFT. More precisely, if we are not interested in the actual number of particles, then all what needs to be shown to answer the consistency problem is that relative probabilities in QM and scattering theory are equal, that is, the probability that a particle is (scattered) at x divided by the probability that it is (scattered) at x0. Indeed, Cartwright (1980) claims to have proven that this is
the case. I cannot sufficiently discuss Cartwright’s proof, and only wish to draw two conclusions. First, further work has to be done to solve the consistency problem and to show why the Born rule can give probabilities for real processes, a full description of which goes beyond the recourses of QM. Second, and more positively, it seems safe to say that in the discussions around the measurement problem the fact that “[t]he exchange of energy is the basic event that happens in quantum mechanics; and the basic event whose effects are theoretically described and predicted” (Cartwright 1978, p. 55) has been strongly under appreciated. I would therefore hope that more research in that direction will be done in the future.
Once it is agreed that measurement processes have to be described in QFT, the latter also seems to give hints for a possible solution of the measurement problem in quite another way than Cartwright’s programme. If decoherence is effective in ordinary QM, it is much more so in QFT. There are two ways for decoherence to work in QFT, either the matter is decohered by a field or a field is decohered by the matter (Here ‘matter’ and ‘field’ are merely common physicist’s jargon. One could also say ‘matter field’ and ‘force field’). Which description is right depends on the actual situation that is described.23 It is possible to find the reduced density
matrix either for the matter or the fields and describe their dynamics. Therefore, in realistic situations it might be the case that superpositions, which cause the most trouble according to the received measurement problem, do not take part in scattering events, but that only mixed states do. On top of that, Hartle (1994) has shown that on the basis of decoherence it is possible to define non-unitary dynamics for interactions that respect the most basic features of QFT like energy conservation and no signalling faster than light. Though it remains to be seen, if these suggestions actually are a step in direction to a solution of the measurement problem.
Additionally, it is interesting that proposals for non-unitary dynamics are relatively widespread in relativistic quantum physics. Starting from Hawking (1982) they
23See Kiefer (1992) and the chapter by Kiefer in Giulini et al. (1996). See also chapter 12 in Breuer
are discussed in relation to black hole physics and quantum gravitation (cf. Banks et al. 1984; Srednicki 1993; Unruh & Wald 1995). As Hartle (1994, p. 34) remarks, “[w]hen spacetime geometry is not fixed, as in quantum gravity, or when it is fixed but not foliable by spacelike surfaces, some modification of familiar quantum theory seems inevitable.” Furthermore, non-unitary dynamics are supposed to be the right description for the phenomenon of neutrino oscillation (cf. Goswami & Ota 2008), and important in the research on quantum dissipation, which is closely related to decoherence (cf. Garbaczewski & Olkiewicz 2002). I conclude from these ongoing research projects that philosophers should be more open towards non-unitary dynamics and investigate further the implications on the measurement problem.
In conclusion, QFT at the present stage does not solve the measurement problem, but at the same time there is no definite answer to the question whether QFT could solve it; more research in theoretical physics has to be done. Nonetheless, QFT certainly has implications for our understanding of the measurement process by making the latter much more lucid. Simply extending the insolubility proof of the measurement problem onto QFT, as it is found in textbooks, leads to an obstruction of one’s ability to appreciate ongoing developments in physics that could be relevant for the measurement problem. However, given that all what has been said does not solve the measurement problem, in the next section I will investigate what this means for the present project.