Ontology: particles and fields
For any theory, the question of its not only mental and linguistic, but also ontological representation is topical. It is the answer to the question: "What objects exist according to the content of the theory?". Something that exists must be understood within the framework of the theory, this is the essence of the ontological approach. The reference to the theory with its far from obvious concepts immediately informs the question of reality of conceptual acuity. Can the theory testify to reality? If yes or no, why?
The author has long thought about these issues, comparing the data of various sciences, and came to the following conclusion. The reality is evidenced by all the concepts that are not distorted due to certain circumstances. If, while simplifying the theory, deliberately operate with abstractions and idealizations, then it is unnatural to think that they represent reality in an adequate form. On the other hand, no matter how complex the undistorted concepts of the theory, there is no reason to deny them ontological significance. Otherwise, their effectiveness is incomprehensible. Of course, the growth of scientific knowledge leads to a change in the perception of reality. And this means that we have to put up with the lack of our knowledge of reality.
Another general scientific observation is that in thinking about reality, as a rule, two approaches are combined - atomic and structural. At the atomic approach, the whole is reproduced as composed of "bricks", i.e. from individual things that do not have an internal structure. With a structural approach, the whole is given fundamental importance, which is often called a system or structure. Atomic is considered a manifestation of the structure. The struggle between the atomists and the structuralists was sometimes fierce, but the winner was never clarified. This suggests that both approaches are consistent, and not one of them.
Finally, I note one more actual fact that should also be taken into account when discussing ontological issues. In theory, any object is understood as a unity of attributes. The equations of physics indicate the masses, momenta, lengths and durations that characterize certain objects, for example, elementary particles, nuclei of atoms and molecules.
So, when discussing ontological issues, one should keep in mind the following provisions of general scientific content.
1. Things are judged on the basis of theory.
2. Ontological significance is possessed by all undistorted, in particular, abstraction and idealization operations, concepts.
3. The winner in the opposition between the atomic and structural approaches was not found.
After what has been said, it is reasonable to turn directly to the ontology of quantum field theory, in which, as a rule, the basic value is attached to the relationship of elementary particles and fields. At the atomic approach it is considered that the field consists of particles. In the structural approach, the particles are interpreted as components (excitations) of the field. We can say that the atomic approach consists in the corpuscular interpretation of the theory, and the structural approach in the field theory. I also note that researchers, when dealing with the dilemma of the particle - field, as a rule, compare its classical, quantum-mechanical and quantum-field interpretations.
Classical interpretation is usually associated with the status of Maxwell's electrodynamics. In it, the fields are interpreted as transmitters of interactions from one macrobody to another. The field components are not bodies, i.e. they do not have macroscopic forms. As long as the macrobodies are compared to the fields, their fundamental difference from each other is "catches the eye" and there is no doubt. But the situation changes dramatically in the transition to quantum mechanics.
In quantum mechanics, not macro-, but microbodies in the status of either elementary particles or microparticles are considered. By definition, elementary particles, unlike microparticles, do not have an internal device, i.e. do not consist of other corpuscles. In contrast to macrobodies, they do not have clearly defined lengths and durations. This alone makes it difficult to distinguish them from classically understood fields.
Quantum field theory has made it possible to describe the structure of fields by relating it to the existence of ... particles. The dilemma of the macrobody - the field seems to have been resolved by the transition to the ratio of one particle with their totality. But as soon as they start ontology, i.e. take into account the conceptual arrangement of quantum field theory, it immediately becomes clear that the above conclusion is superficial. The question of corpuscular and field interpretation of quantum field theory turns out to be saturated with numerous problematic aspects. Their discussion is determined by the need to clarify the conceptual content of quantum field theory. If, for example, we are talking about particles, then it is not enough to postulate their reality on the basis, for example, of fixing tracks in bubble chambers or clicks in Geiger counters. What the physicist fixes in the experiment must be explained through concepts. Physical reality is evidenced by physical theory, including its experimental part, and nothing more. It is not excluded that the very idea of particles and fields is outdated. Undoubtedly, however, that both corpuscular and field interpretation of quantum field theory is encountered with considerable difficulties. Let us first turn to the corpuscular interpretation of quantum field theory. She received a meaningful and rather detailed coverage in the review article of M. Kulman. Let's list its main arguments.
1. In 1939 E. Wigner showed that if relativistic quantum mechanics can be corpuscularly interpreted, then irreducible unitary representations of the Poincare group correspond to possible types of particles. Many believed that Wigner's theorem is a proof of the existence of particles. In fact, the question of the inevitability of corpuscular interpretation was not even discussed.
2. According to the Ray-Schlieder theorem, measurements do not allow us to distinguish between the quantum field states of the n-th particle and the vacuum. Consequently, it does not make sense to talk about a single particle.
3. In 1996, D. Malament proved the theorem on the impossibility of combining for systems with a fixed number of particles within the framework of relativistic quantum mechanics the position of the existence of a localized individual particle with causality conditions. He did not prove the inconsistency of the concept of a particle, but significantly undermined the belief in the need to understand the particle as a local formation.
4. According to the Unruh effect, in the absence of thermal radiation in the inertial frame of reference, it is nonetheless present in the accelerating frame of reference. It seems strange that the very existence of particles depends on the chosen frame of reference.
Kuhlman does not believe that it was possible to show the inconsistency of the corpuscular interpretation of quantum mechanics. He, however, notes its many problematic aspects. Now we turn to the field interpretation of quantum field theory.
Quite often it is believed that the lack of corpuscular interpretation testifies to the field interpretation. But such an argument is not very convincing, because it also needs an appropriate detailed conceptual analysis. As it turns out, like a corpuscular interpretation, the field interpretation of quantum field theory assumes an ontological analysis. It is preceded by a question about the status of the physical field. What field differs from a particle?
Unfortunately, classical physics can report little about the status of the field. Unlike a particle, it is considered a physical reality, which is defined at every point of space. Stressing this circumstance, they say that the field has an infinite number of degrees of freedom. In the transition to quantum field theory, each of these degrees of freedom is given by some operator, which is called a field operator, since it belongs to the field by definition. But the field concept itself is used in its indefinite, intuitive shell. Meanwhile, the introduction of operators leads to dramatic changes. The classical concept of the field is completely out of work. Operators specify possible, not actual, values of observables that correspond to different points of space. But this space itself needs to be defined, and the concept of the point is doubtful.
A certain tonality in the analysis of the state of affairs in question was posed by R. Teller in his sensational book. He introduced the concept of deterministic quantity ( determinable ), which appears as a set of attributes, its determinant, only one of which can belong to a quantum individual. He writes: "The field configuration of deterministic quantities (or their collections) is a specific distribution by which each point of space-time is assigned a value (or value to each deterministic value of a given collection)."
It is not possible to name a field configuration or a collection of deterministic quantities by the Teller field. As a result, he comes to the conclusion that the field interpretation is untenable. Taking into account the conceptual content of quantum field theory, one can speak of the aggregate of field operators, deterministic quantities observed, which are signs of some field quanta, but not of the field as such. Adjective field indicates not on the field, but on the theory, which for historical reasons was called the "quantum field theory".
Teller's argument found support among many authors opposing the field interpretation. D. Baker in this connection draws special attention to the Fock space, the algebraic construction used to describe in a quantum field theory a variable or an unknown number of particles. Often it is with Fock space that the reality of the quantum field is connected. According to Baker's argument, the concept of the "Fock space" developed on the basis of corpuscular interpretation. Its failure also entails the inadequacy of the field interpretation in the event that it is justified by references to Fock's space. In the same vein, the concept of secondary quantization, which is supposedly related to the field, is also criticized, but again understood by corpuscular interpretation.
Thus, both corpuscular and field interpretation are encountered with considerable difficulties. From a certain point of view, this situation does not seem strange. It is meant that initially the concepts of a particle and a field were worked out in classical physics. There is nothing surprising in that, perhaps, they should be abandoned in quantum field theory. Nevertheless, without the concept of particles and fields, the ontology of quantum field theory seems to be artificially devastated. But is there any alternative to corpuscular and field interpretation? According to the author, there is.
Let's recall those three positions of general scientific content, which were given at the beginning of the paragraph. It seems that they are quite relevant in the development of quantum ontology. Of decisive importance is the following: all undistorted concepts of quantum field theory correspond to certain types of reality. And this means that there is no need to contrast particles and fields as champions of reality with operator-significant functions and algebra of observables. There is no true quantum reality in a single form. It is multifaceted and conceptually informative.
The second conclusion concerns the belonging of the observed. They do not exist on their own. How to name those things to which they belong? You can call them quantum objects, or even quanta, as Teller suggested. At the same time, there is no need to make any commitments to the dilemma of the particle - field. Whenever these obligations are followed, a priori ideas initiated by scholastic reasoning, rather than conceptual content quantum field theory.
Finally, one should also mention the opposition of the atomic and structural approaches. It is unlikely that the first of them should be associated with the concept of a particle, and the second with the concept of a field. In the author's opinion, both approaches are used in quantum field theory. To put it somewhat risky, we can say that the part defines the whole, and the whole defines the part. Two of these approaches are complementary in the Bohr sense. The emphasis on one of the approaches somehow leads to the detriment of the merits of the other method.
It remains to note that the negation of the corpuscular interpretation does not veto the use of the term "particle". A particle is a kind of quantum objects. Ontology of quantum field theory does not deny that there are photons, electrons, quarks and other particles. However, when discussing particles, one should avoid the danger of uncritical attitude to the corpuscular interpretation of quantum field theory.
1. The reality studied by quantum field theory is determined directly in the theory itself.
2. It is reasonable to introduce the idea of a quantum field object, distinguishing it from objects of classical and quantum-mechanical physics.
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