Copenhagen interpretation as an improvement

A similar objection can be raised in a somewhat different form against the statistical interpretations put forward by Bopp and (on a slightly different line) by Fenyes.

Bopp considers the creation or the annihilation of a particle as the fundamental process of quantum theory, the particle is `real’ in the classical sense of the word, in the sense of materialistic ontology, and the laws of quantum theory are considered as a special case of correlation statistics for such events of creation and annihilation.

This interpretation, which contains many interesting comments on the mathematical laws of quantum theory, can be carried out in such a manner that it leads, as regards the physical consequences, to exactly the same conclusions as the Copenhagen interpretation. So far it is, in the positivistic sense, isomorphic with it, as is Bohm’s.

But in its language it destroys the symmetry between particles and waves that otherwise is a characteristic feature of the mathematical scheme of quantum theory. As early as 1928 it was shown by Jordan, Klein and Wigner that the mathematical scheme can be interpreted not only as a quantization of particle motion but also as a quantization of three-dimensional matter waves;

Therefore, there is no reason to consider these matter waves as less real than the particles.

The symmetry between waves and particles could be ensured in Bopp’s interpretation only if the corresponding correlation statistics were developed for matter waves in space and time as well, and if the question was left open whether particles or waves are to be considered as the `actual’ reality.

The assumption that particles are real in the sense of the materialistic ontology will always lead to the temptation to consider deviations from the uncertainty principle as `basically’ possible.

Fenyes, for instance, says that `the existence of the uncertainty principle [which he connects with certain statistical relations] by no means renders impossible the simultaneous measurement, with arbitrary accuracy, of position and velocity.’ Fenyes does not, however, state how such measurements should be carried out in practice, and therefore his considerations seem to remain abstract mathematics.

Weizel, whose counterproposals to the Copenhagen interpretation are akin to those of Bohm and Fenyes, relates the `hidden parameters’ to a new kind of particle introduced ad hoc, the ‘zeron,’ which is not otherwise observable.

However, such a concept runs into the danger that the interaction between the real particles and the zerons dissipates the energy among the many degrees of freedom of the zeron field, so that the whole of thermodynamics becomes a chaos. Weizel has not explained how he hopes to avoid this danger.

The standpoint of the entire group of publications mentioned so far can perhaps best be defined by recalling a similar discussion of the theory of special relativity. Anyone who was dissatisfied with Einstein’s negation of the ether, of absolute space and of absolute time could then argue as follows: The non-existence of absolute space and absolute time is by no means proved by the theory of special relativity.

True space and true time do not occur directly in any ordinary experiment; but if this aspect of the laws of nature has been correctly taken into account, and thus the correct `apparent’ times have been introduced for moving co-ordinate systems, there would be no arguments against the assumption of an absolute space.

It would even be plausible to assume that the center of gravity of our galaxy is (at least approximately) at rest in absolute space.

The critic of the special theory of relativity might add that we may hope that future measurements will allow the unambiguous definition of absolute space (that is, of the `hidden parameter’ of the theory of relativity) and that the theory of relativity will thus be refuted.

It is seen at once that this argument cannot be refuted by experiment, since it as yet makes no assertions which differ from those of the theory of special relativity. But such an interpretation would destroy in the language used the decisive symmetry property of the theory, namely, the Lorentz invariance, and it must therefore be considered inappropriate.

The analogy to quantum theory is obvious. The laws of quantum theory are such that the `hidden parameters,’ invented ad hoc, can never be observed. The decisive symmetry properties are thus destroyed if we introduce the hidden parameters as a fictitious entity into the interpretation of the theory.

The work of Blochinzev and Alexandrov is quite different in its statement of the problem from those discussed before. These authors expressly and from the beginning restrict their objections against the Copenhagen interpretation to the philosophical side of the problem. The physics of this interpretation is accepted unreservedly.

The external form of the polemic, however, is so much the sharper: Among the different idealistic trends in contemporary physics the so-called Copenhagen school is the most reactionary. The present article is devoted to the unmasking of the idealistic and agnostic speculations of this school on the basic problems of quantum physics,' writes Blochinzev in his introduction. The acerbity of the polemic shows that here we have to do not with science alone but with a confession of faith, with adherence to a certain creed. The aim is expressed at the end with a quotation from the work of Lenin: However marvellous, from the point of view of the common human intellect, the transformation of the unweighable ether into weighable material, however strange the electrons lack of any but electromagnetic mass, however unusual the restriction of the mechanical laws of motion to but one realm of natural phenomena and their subordination to the deeper laws of electromagnetic phenomena, and so on – all this is but another confirmation of dialectic materialism.’ This latter statement seems to make Blochinzev’s discussion about the relation of quantum theory to the philosophy of dialectic materialism less interesting in so far as it seems to degrade it to a staged trial i h which the verdict is known before the trial has begun. Still it is important to get complete clarity about the arguments brought for-ward by Blochinzev and Alexandrov.

Here, where the task is to rescue materialistic ontology, the attack is chiefly made against the introduction of the observer into the interpretation of quantum theory. Alexandrov writes: `We must there-fore understand by " result of measurement" in quantum theory only the objective effect of the interaction of the electron with a suitable object.

Mention of the observer must be avoided, and we must treat objective conditions and objective effects. A physical quantity is an objective characteristic of the phenomenon, but not the result of an observation.’

According to Alexandrov, the wave function in con-figuration space characterizes the objective state of the electron. In his presentation Alexandrov overlooks the fact that the formal-ism of quantum theory does not allow the same degree of objectivation as that of classical physics.

For instance, if the interaction of a system with the measuring apparatus is treated as a whole according to quantum mechanics and if both are regarded as cut off from the rest of the world, then the formalism of quantum theory does not as a rule lead to a definite result; it will not lead, e.g., to the blackening of the photographic plate at a given point.

If one tries to rescue Alexandrov’s objective effect' by saying that in reality’ the plate is blackened at a given point after the interaction, the rejoinder is that the quantum mechanical treatment of the closed system consisting of electron, measuring apparatus and plate is no longer being applied. It is the ` factual’ character of an event describable in terms of the concepts of daily life which is not without further comment contained in the mathematical formalism of quantum theory, and which appears in the Copenhagen interpretation by the introduction of the observer.

The introduction of the observer must not be misunderstood to imply that some kind of subjective features are to be brought into the description of nature. The observer has, rather, only the function of registering decisions, i.e., processes in space and time, and it does not matter whether the observer is an apparatus or a human being; but the registration, i.e., the transition from the possible' to the actual,’ is absolutely necessary here and cannot be omitted from the interpretation of quantum theory.

At this point quantum theory is intrinsically connected with thermodynamics in so far as every act of observation is by its very nature an irreversible process; it is only through such irreversible processes that the formalism of quantum theory can be consistently connected with actual events in space and time.

Again the irreversibility is – when projected into the mathematical representation of the phenomena – a consequence of the observer’s incomplete knowledge of the system and in so far not completely `objective.'

Blochinzev formulates matter slightly differently from Alexandrov: In quantum mechanics we describe not a state of the particle in itself but the fact that the particle belongs to this or that statistical assembly. This belonging is.completely objective and does not depend on statements made by the observer.' Such formulations, however, take us very far – probably too far – away from materialistic ontology. To make this point clear it is useful to recall how this belonging to a statistical assembly is used in the interpretation of classical thermodynamics. If an observer has determined the temperature of a system and wants to draw from his results conclusions about the molecular motions in the system he is able to say that the system is just one sample out of a canonical ensemble and thus he may consider it as possibly having different energies. In reality' – so we would conclude in classical physics – the system has only one definite energy at a given time, and none of the others is realized. The observer has been deceived if he considered a different energy at that moment as possible. The canonical ensemble contains statements not only about the system itself but also about the observer’s incomplete knowledge of the system. If Blochinzev in quantum theory tries to call a system’s belonging to an assembly completely objective,' he uses the word objective’ in a different sense from that in classical physics. For in classical physics this belonging means, as has been said, statements not only about the system but also about the observer’s degree ofknowledge of the system. One exception must be made to this assertion in quantum theory. If in quantum theory the assembly is characterized by only one wave function in configuration space (and not, as usual, by a statistical matrix), we meet a special situation (the so-called `pure case ' ) in which the description can be called objective in some sense and in which the element of incomplete knowledge does not occur immediately. But since every measurement would (on account of its irreversible features) reintroduce the element of incomplete knowledge, the situation would not be fundamentally different.

Above all, we see from these formulations how difficult it is when we try to push new ideas into an old system of concepts belonging to an earlier philosophy – or, to use an old metaphor, when we attempt to put new wine into old bottles. Such attempts are always distressing, for they mislead us into continually occupying ourselves with the inevitable cracks in the old bottles instead of rejoicing over the new wine. We cannot possibly expect those thinkers who a century ago introduced dialectic materialism to have foreseen the development of quantum theory. Their concepts of matter and reality could not possibly be adapted to the results of the refined experimental technique of our days.