Yoav Ben-Dov

Quantum Theory - Reality and Mystery

Chapter 14

PARTICLES AND WAVES

Reality and contradictions

In previous chapters we reviewed the different attempts to solve the conceptual problems of quantum mechanics in the direction suggested by Einstein: to reject quantum mechanics in its currently accepted version, and to look for a "better" theory. This direction is expressed by the different so-called "interpretations" of quantum mechanics, which try to modify the existing theory in one way or another, so that at least some of the classical properties listed in Chap. 2 would again be satisfied.

As we saw, each one of these interpretations raises difficult problems, and therefore none of them was accepted by the majority of the physicists' community as an viable alternative to the existing theory. Of course, it is always possible that this situation is only temporary, so that in some future, an acceptable and non-problematic Einsteinian interpretation of quantum mechanics would appear - maybe a modified version of one of the existing interpretations, or perhaps a completely novel idea. However, at least for the moment, one can also be justified in claiming that the research plan which tries to re-establish the classical properties in the quantum domain has failed, because it did not achieve its declared goal.

If such is the situation, then it might make sense to examine seriously the opposite approach suggested by Bohr: to accept quantum mechanics as it is, and to look for a conceptual framework in which it would appear as an acceptable theory. Such an examination would be carried out in this and the next chapters. However, an important caveat should be made at this point. Although Bohr talked quite a lot on the need to use clear and unambiguous language, his own formulations were very far from this ideal. Thus, it is almost impossible to give a definite answer to the question whether certain views that might be assigned to him were "really" his own. Therefore, what we try to do here is to reconstruct a coherent philosophical position, which can be supported on the basis of Bohr's writings. Whether this position is identical with Bohr's own views, or whether it differs from it - finally, this question is less important than the question whether it is acceptable, and represents a viable alternative to Einstein's position. Still, in the philosophical and physical literature, there are sometimes descriptions of Bohr's position which are clearly contradictory with his explicit formulations. To avoid such a situation, we shall refer to quotations from Bohr's writings, and try to understand them in their original context.

In philosophical terms, one can say that what Bohr was looking for was not a new physical theory to replace the existing quantum mechanics, but rather a new "epistemology", that is, a new set of ideas and rules which say how a physical theory should look like, what criteria it should satisfy, and what relations are supposed to exist between the theory and physical reality. In this new framework, the existing quantum mechanics would appear as acceptable, notwithstanding the fact that it violates the classical properties. In Bohr's view, the basic conceptual tool of such an epistemology was supposed to be an idea which he called "complementarity". In a rough formulation, according to the idea of complementarity, we should recognize the fact that two (or maybe more) different descriptions of the world, that appear to contradict and exclude each other, can still both be considered as true. When we accept such a situation, we may say that these descriptions "complement" each other to give the complete picture.

At first sight, this idea seems very problematic, because it appears to suggest that we should use a conceptual framework which contains inner contradictions. But to understand Bohr's position, we should first ask why the idea of using contradictory descriptions really disturbs us. Suppose, for example, that we consider the conceptual framework of a certain physical theory. This theory refers to practical situations - that is, it accounts for the results of experiments and observations. Apparently, if our theoretical framework contains contradictions, then in principle it may happen that in some situations, it would give two opposite answers - for example, two contradictory predictions for the results of a single experiment. In such a case, the theory is clearly unsatisfactory, as the results of the actual experiment would necessarily refute at least one of the two predictions.

The question is what happens if we accept a conceptual framework which has contradictions at a general level, but also contains some mechanisms, which ensure that in any particular practical application, it will give only one definite answer. In such a case, the apparent contradiction in the conceptual framework would not be expressed in any practical application, and then we can use our physical theory with no practical problem. This is what Bohr had in mind. In his view, we are allowed to use, in different occasions and different practical contexts, different descriptions of reality which exclude and contradict each other, under the condition that in any specific application, it is clear which one is the valid description for this case. If this is the case, then the apparent contradiction inside the conceptual framework has no practical consequences, so that it should not disturb us.

Is such a position acceptable? Can we be satisfied with a framework that contains contradictions at the general level, as long as they are inconsequential at any particular practical case? The question is, of course, what we expect from the scientific conceptual framework. As we mentioned at the beginning of this book, modern western culture was traditionally formulated in large part around the idea that science is not only an utility to predict experimental results, that we encounter one at a time. Instead, science was also supposed to give a complete and non-contradictory description of "true reality", which exists in an objective manner, that is, independently of our own existence and actions.

It is as if in this view, the "correct" scientific description of the world, that scientific research aims at discovering, was supposed to be a description "from the viewpoint of God", who looks on the world from outside and sees it "as it really is". Still, although it is a description from God's viewpoint, it was assumed that it can be given a complete and non-contradictory formulation in a language accessible to the human mind, such as the language of mathematics and physics. This, in fact, is what lies behind Einstein's references to the Lord and his ways, to support views pertaining to the nature of physical theory. Now, says Bohr, we should give up this metaphysical-theological belief. According to Bohr, the complete picture of physical reality is based on mutually exclusive and contradictory descriptions. Thus, a complete and non-contradictory description of physical reality in a human language, as if from the viewpoint of Einstein's God, is impossible.

As we said, the belief in the existence of a complete and non-contradictory "true" description of objective reality constituted a central belief of the mainstream of modern western culture. Thus, if we give up this belief, this may have consequences which concern not only physics, but other aspects of human culture as well. Therefore, in order to decide whether the idea of complementarity is acceptable, we should examine its consequences not only in physics, but also in other domains. Bohr himself did not refrain from such a comprehensive examination. He tried to apply and examine the idea of complementarity not only within science, but also outside it. As he claimed, such extra-scientific applications of complementarity are not only legitimate, but also welcome, as they may help us to tackle problems that modern western culture has hitherto been incapable of confronting satisfactorily. In this part we shall trace the idea of complementarity, first in physics and then in other domains, in order to decide whether Bohr's position is indeed acceptable. We shall start by examining Bohr's own formulation, in order to understand from them how he saw the idea of complementarity.

Bohr's formulation

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Measurement and definition

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Conceptual steps

From what has been said so far, and later texts by Bohr, one can regard the idea of complementarity in quantum mechanics as based on the following conceptual steps:

1. First, one must recognize that notwithstanding the behavior of quantum objects, the language used by physicists to describe their measurement results must remain a classical language, in which expressions like "the pointer of the measuring apparatus is at rest on the value 3 marked on the scale" have a well-defined meaning. As Bohr insisted, the terms of classical language are the only ones that we have, and they are essential for a clear and non-ambiguous communication of the state of the world. More generally, the language of physics must presuppose that the results of any measurement are objective, that is, they can be described as standing "as they really are": there is a "true" reading of the pointer, which is independent of the question who, if any, is looking at it.

2. On the other hand, as we saw in Heisenberg's example, one cannot define microscopic objects separately from their measurement process. In this example, the need to use at least one photon, or as Bohr puts it elsewhere in the Como lecture, "the individuality of the quantum phenomenon", results in the fact that the question which terms are applicable to the quantum object is dependent on the measurement processes conducted on it. Thus, it is impossible to give a complete description of the quantum phenomena in the classical language, which presupposes that objects can be defined separately from their observation. From this step and the first one, it seems as if the conclusion is that the language of physics cannot give a complete description of the quantum phenomena. But this is obviously absurd, as the quantum phenomena cannot be conceived outside the language of physics.

3. To solve this difficulty, Bohr gives up the relation which existed in the classical framework between the physical language and the phenomena that it describes. As he proposes, physical language should remain a classical language, whose terms refer to an object "as if" it existed by itself. However, this language is to be used to describe a quantum phenomenon only in a given experimental context. Different experimental set-ups lead to different classical descriptions, which would contradict each other if applied all at once. Each one of these descriptions is valid in its specific experimental context, but the complete picture, which comprises all the possible valid descriptions, is outside the scope of any given physical language. Thus, without a specific experimental context, the quantum object cannot be conceived at all. Therefore, physical theory should not aspire to give a complete description of the quantum object as something which exists unto itself. Instead, it should try to exhaust the full scope of all possible descriptions, which stand in a relation of complementarity to each other: they exclude and contradict each other when applied all at once, but together they give the most complete possible picture.

Particle or wave?

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The measurement problem

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Causes and finalities

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Mind and consciousness

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