Particles Versus Fields

CHAPTER 12. EVALUATION AND COMPARISON 150 change its significance when different ontological approaches are considered.

Arguments concerning non-localizability and unsharp properties are among the most important examples.

12.2 Comparison of Ontological Approaches

CHAPTER 12. EVALUATION AND COMPARISON 151 interpretation it can probably be at least weakened by a proponent of this view. He can argue that the possibility of counter-intuitive superpositions (see Schr¨odinger’s cat) is rather an odd trait of quantum physics than a peculiarity of the particle interpretation. In the light of my arguments in section 10.3 I would back this general line of reaction by pointing out that quantum physics is inherently dispositional.

Nevertheless, it is again not clear whether it would actually be a wise move by the particle ontologist to defend himself by reference to the dis-positional character of the quantum world. As I have argued in chapter 10 I think that not all ontological approaches can handle the dispositional nature of quantum theory equally well. I will come back to this point when discussing my own proposal of a dispositional trope ontology.

I wish to add a general remark. The evaluation of arguments against the tenability of a particle interpretation of QFT displays a characteris-tical feature which we will encounter again in other discussions. There are some traits and problems of quantum theory which tend to pop up in disguise and notoriously cause trouble. Such issues are for instance the quantum measurement problem, the dispositional character of properties and the emergence of classical properties which are all closely related to one another. My point now is that reference to these problems must not in itself make up a good argument against a particular ontology. Since these problems are either yet unsolved in general or something we have simply not quite get accustomed to, no single ontology should get all the blame.

However, the extent to which a general quantum feature is a problem can depend on the context, in particular on the ontology one has adopted.

One and the same feature can be completely against the spirit of one on-tology whereas it can be incorporated rather naturally into another onto-logical scheme. I think that the possibility of a superposition of particle states with different numbers of particles is such a feature which is against the spririt of a particle interpretation.

I discussed some further results in section 6.4 which can all be seen as demonstrations for the non-objectivity of the particle number of a physical system. The best known of these results is the existence of vacuum

fluc-CHAPTER 12. EVALUATION AND COMPARISON 152

tuations, i. e. local deviations from the global particle number zero. The second result was the Unruh effect which shows that the particle number is not independent of the state of the observer. The third of these results comes from the study of QFT in curved space-time and indicates that the existence of a particle number operator is a contingent property of the flat Minkowski spacetime. At least the first two apparent problems for a par-ticle interpretation can be challenged (and were challenged, e. g. by P.

Teller) in the same way as the above argument regarding the superposi-tion of particle states with different numbers of particles. Naturally, the corresponding counterargumentation can again be used as well.

Instead of elaborating on this discussion I will now leave the problems of the particle interpretation of QFT which are connected with the particle number in favour of a different problem which might be particularly dev-astating for the idea of a particle as basic entities, namely the problem of non-localizability.

Over a little more than the last two decades a number of results have been produced which purport to demonstrate an unavoidableclash of causal-ity and localizabilcausal-ity when quantum theory is considered in a relativistic setting. Most notable of these are theorems by Hegerfeldt, Malament and Redhead. It is immediately clear why so much notice has been given to these results in ensuing discussions. Provided that the general line of inter-pretation given by the above-mentioned authors is correct, then particles could not be localized in any finite region of space-time, no matter how large it is. While it is obvious that the notion of a point particle is just a mathematical idealization, the smearedness of particles over all of space-time seems to stretch the idea of a particle beyond its limits.

In section 6.3.2 I compared the theorems by Malament and Redhead in detail. It turned out that both theorems are equivalent although their appearances, their starting points, the formalism and mathematics used as well as the final conclusion drawn by the respective authors are quite different. Besides the in itself interesting fact of the equivalence of these results my comparative study effected a closer look at the respective as-sumptions and conclusions. Intuitive notions became explicit and could be

CHAPTER 12. EVALUATION AND COMPARISON 153 given a second, more sceptical look.

As with the evaluation of arguments concerning the objectivity of the particle number, the evaluation of arguments concerning the non-localiza-bility of particles does not have as straightforward an impact on the ten-ability of a particle interpretation as it first appears. Locating the origin of non-localizability is more delicate than one might expect. I think that the conclusion that non-localizability speaks against the tenability of a particle interpretation is a legitimate way of interpretation. However, it is not the one and only legitimate way. There are some other alternatives left.

I have considered other reactions to the problem of non-localizability which see its core not as a problem for a particle interpretation but rather as evidence the concept of sharp localization itself is flawed. When discusssing my own proposal for an ontology of QFT in subsection 12.2.3 I will argue for still another line of reaction to the problem of non-localizability. In short I will show that it depends on your ontological assumptions whether or not non-localizability is fatal for a particle interpretation.

On the other side it was pointed out that the particle interpretation of QFT is an option which one is not easily willing to surrender. After all, QFT rests on experiments with colliding particles. How can it be that the theory corresponding to these particle experiments tells us that there are no particles? Although this looks like a strange conclusion it is not absurd. It is perfectly possible that the impression that we have observed collisions of particles was deceiving. Like many other scientific observations the ‘observation’ of elementary particles is a highly interpretive business.

Whereas a particle interpretation of QFT is confronted with various direct arguments against its tenability a field interpretation has a very different kind of trouble. It is not even clear what to argue against. As I pointed out the first immediate reason why QFT is often considered as a field theory is the occurence of quantum fields in the formalism of QFT.

However, this does not lead to a viable conception of fields as the basic entities of QFT. ‘Quantum fields’ cannot be taken as these basic entities because they yield something physically real only together with the state vector. This problem cannot be cured by taking the state vector as a field

CHAPTER 12. EVALUATION AND COMPARISON 154 as well because it is a fundamentally different kind of quantity.

The other line of argumentation in favour of fields takes all arguments against a particle interpretation as evidence for a field interpretation which is tacitly taken to be the only alternative. However, this line of argument is even less apt to specify what these fields are. As I will explain later, I think there is a more promising way to handle arguments against a particle interpretation.