Criticism and Counterproposals to the Copenhagen Interpretation of Quantum Theory

The Copenhagen interpretation of quantum theory has led the physicists far away from the simple materialistic views that prevailed in 19th century natural science.

These views:

• were intrinsically connected with natural science of that period
• found a systematic analysis in some philosophic systems
• had penetrated deeply into the mind even of common men

This is why many attempts:

• criticized the Copenhagen interpretation
• replaced it by one more in line with classical physics or materialistic philosophy.

These can be divided into 3 different groups:

1. The first group does not want to change the Copenhagen interpretation so far as predictions of experimental results are concerned.

But it tries to change the language of this interpretation to resemble classical physics.

It tries to change the philosophy without changing the physics.

Some restrict their agreement with the experimental predictions of the Copenhagen interpretation to all those experiments that have hitherto been carried out or that belong to normal electronic physics.

Their interpretations cannot be refuted by experiment, since they only repeat the Copenhagen interpretation in a different language.

From a strictly positivistic standpoint, one may even say that we are here concerned not with counterproposals to the Copenhagen interpretation but with its exact repetition in a different language.

Therefore, one can only dispute the suitability of this language.

2. The second group realizes that the Copenhagen interpretation is the only adequate one, if the experimental results agree everywhere with the predictions of this interpretation.

This group tries to change quantum theory in certain critical points.

3. The third expresses its general dissatisfaction with the Copenhagen interpretation and especially with its philosophical conclusions, without making definite counter proposals.

Papers by Einstein, von Laue and Schrodinger belong to this third group which has historically been the first of the three groups.

However, all the opponents of the Copenhagen interpretation do agree on one point.

They want to return to:

• the reality concept of classical physics or the ontology of materialism.
• the idea of an objective real world whose smallest parts exist objectively in the same sense as stones or trees exist, independently of whether or not we observe them.

This, however, is impossible or at least not entirely possible because of the nature of the atomic phenomena.

It cannot be our task to formulate wishes as to how the atomic phenomena should be.

Our task can only be to understand them.

One group of counterproposals works with the idea of hidden parameters.

Since the quantum-theoretical laws determine in general the results of an experiment only statistically, one would from the classical standpoint be inclined to think that there exist some hidden parameters which escape observation in any ordinary experiment but which determine the outcome of the experiment in the normal causal way.

Therefore, some papers try to construct such parameters within the framework of quantum mechanics.

Along this line, for instance, Bohm has made a counter-proposal to the Copenhagen interpretation, which has recently been taken up to some extent also by de Broglie.

Bohm’s interpretation has been worked out in detail. It may therefore serve here as a basis for the discussions.

Bohm considers the particles as `objectively real’ structures, like the point masses in Newtonian mechanics.

The waves in configuration space are in his interpretation `objectively real’ too, like electric fields.

Configuration space is a space of many dimensions referring to the different co-ordinates of all the particles belonging to the system. Here we meet a first difficulty: what does it mean to call waves in configuration space `real'?

This space is a very abstract space.

The word real' goes back to the Latin word res,’ which means ` thing'.

But things are in the ordinary three-dimensional space, not in an abstract configuration space.

One may call the waves in configuration space objective' when one wants to say that these waves do not depend on any observer; but one can scarcely call them real’ unless one is willing to change the meaning of the word.

Bohm goes on defining the lines perpendicular to the surfaces of constant wave-phase as the possible orbits of the particles. Which of these lines is the `real’ orbit depends, according to him, on the history of the system and the measuring apparatus and cannot be decided without knowing more about the system and the measuring equipment than actually can be known.

This history contains in fact the hidden parameters, the `actual orbit’ before the experiment started.

One consequence of this interpretation is, as Pauli has emphasized, that the electrons in the ground states of many atoms should be at rest, not performing any orbital motion around the atomic nucleus.

This looks like a contradiction of the experiments, since measurements of the velocity of the electrons in the ground state (for instance, by means of the Compton effect) reveal always a velocity distribution in the ground state, which is – in conformity with the rules of quantum mechanics – given by the square of the wave function in momentum or velocity space. But here Bohm can argue that the measurement can no longer be evaluated by the ordinary laws. He agrees that the normal evaluation of the measurement would indeed lead to a velocity distribution; but when the quantum theory for the measuring equipment is taken into account – especially some strange quantum potentials introduced ad hoc by Bohm – then the statement is admissible that the electrons ` really' always are at rest.

In measurements of the position of the particle, Bohm takes the ordinary interpretation of the experiments as correct; in measurements of the velocity he rejects it.

At this price Bohm considers himself able to assert: `We do not need to abandon the precise, rational and objective description of individual systems in the realm of quantum theory.'

This objective description, however, reveals itself as a kind of ` ideological superstructure,’ which has little to do with immediate physical reality; for the hidden parameters of Bohm’s interpretation are of such a kind that they can never occur in the description of real processes, if quantum theory remains unchanged.

In order to escape this difficulty, Bohm does in fact express the hope that in future experiments in the range of the elementary particles the hidden parameters may yet play a physical part, and that quantum theory may thus be proved false. When such strange hopes were expressed, Bohr used to say that they were similar in structure to the sentence: `We may hope that it will later turn out that sometimes 2 X 2 = 5, for this would be of great advantage for our finances.'

Actually the fulfillment of Bohm’s hopes would cut the ground from beneath not only quantum theory but also Bohm’s interpretation. Of course it must at the same time be emphasized that the analogy just mentioned, although complete, does not represent a logically compelling argument against a possible future alteration of quantum theory in the manner suggested by Bohm. For it would not be fundamentally unimaginable that, for example, a future extension of mathematical logic might give a certain meaning to the statement that in exceptional cases 2 X 2 = 5, and it might even be possible that this extended mathematics would be of use in calculations in the field of economics. We are nevertheless actually convinced, even without cogent logical grounds, that such changes in mathematics would be of no help to us financially. Therefore, it is very difficult to understand how the mathematical proposals which the work of Bohm indicates as a possible realization of his hopes could be used for the description of physical phenomena.

If we disregard this possible alteration of quantum theory, then Bohm’s language, as we have already pointed out, says nothing about physics that is different from what the Copenhagen interpretation says.

There then remains only the question of the suitability of this language. Besides the objection already made that in speaking of particle orbits we are concerned with a superfluous `ideological superstructure,’ it must be particularly mentioned here that Bohm’s language destroys the symmetry between position and velocity which is implicit in quantum theory; for the measurements of position Bohm accepts the usual interpretation, for the measurements of velocity or momentum he rejects it. Since the symmetry properties always constitute the most essential features of a theory, it is difficult to see what would be gained by omitting them in the corresponding language. Therefore, one cannot consider Bohm' s counterproposal to the