QM and Copenhagen Interpretation

Copenhagen interpretation is the widely accepted interpretation of quantum mechanics. It has many reasonable elements. Thus studying the relation between the theory of quantum motion and Copenhagen interpretation will undoubtedly be helpful for the understanding of quantum motion. In addition, it will also make people grasp Copenhagen interpretation more easily. Here we will give a detailed analysis of their relations.

According to Primas (1981)'s summary, Copenhagen interpretation can be outlined as follows.

  1. The theory is concerned with individual objects.
  2. Probabilities are primary.
  3. The frontier separating the observed object and the means of observation is left to the choice of the observer.
  4. The observational means must be described in terms of classical physics.
  5. The act of observation is irreversible and it creates a document.
  6. The quantum jump taking place when a measurement is made is a transition from potentiality to actuality.
  7. Complementarity properties cannot be observed simultaneously.
  8. Only the results of a measurement can be taken to be true.
  9. Pure quantum states are objective but not real.

In the following, we will analyze the above summary of Copenhagen interpretation one by one. The first item, i.e., that quantum mechanics is concerned with individual objects, clearly states that quantum mechanics is not a theory about the ensemble comprising a large number of particles, but a theory about individual objects. Thus Copenhagen interpretation excludes the possibility of an ensemble interpretation of quantum mechanics. This is consistent with the theory of quantum motion, according to which what quantum mechanics describes is the RDM of individual objects. Furthermore, the theory of quantum motion also provides a convincing exemplification for the first item of Copenhagen interpretation.

Concerning the second item, i.e., that probabilities are primary, it means that the probabilities appearing in quantum mechanics don't result from the ignorance of the observer or the inability of the theory, but must be regarded as an essential character of Nature. Moreover, when quantum mechanics is able to predict these probabilities, it should be accepted as a complete theory. No doubt it is extremely difficult or even impossible to understand this item within Copenhagen interpretation. As a result, people always resort to the law of causation to reject this item, and further get back the classical deterministic picture by introducing the so-called hidden variables. Then they naturally regard the appearance of probabilities in quantum mechanics as an indication of the incompleteness of the theory. Which of these two viewpoints is correct cannot be determined before we find the real motion in quantum world. In fact, it has been a vexed problem since the founding of quantum mechanics. Now in the light of the theory of quantum motion, the probabilities appearing in quantum mechanics result from the actual quantum motion of particles, which is essentially discontinuous and random. Accordingly the theory of quantum motion provides a real physical explanation of the second item of Copenhagen interpretation.

The third item, i.e., that the frontier separating the observed object and the means of observation is left to the choice of the observer, is evidently unsatisfactory. It does not give a quantitative physical description to determine the border and further distinguish between the observed object and the measuring apparatus. Although Bohr evaded this difficulty by regarding the observed object and the measuring apparatus as an indivisible whole, his opinion may be inconsistent. The macroscopic measuring apparatus is regarded as one kind of independent existence, while a macroscopic measuring apparatus is composed of a large number of microscopic particles, thus it must be an ad hoc prescription not to regard the microscopic particles as one kind of independent existence. In fact, there should exist an objective physical border between the microscopic particles and the macroscopic measuring apparatus, and we must give an accurate quantitative description of this border. However, such description is missing in quantum mechanics and its Copenhagen interpretation. Now the theory of quantum motion provides a quantitative physical description of the border, and objectively explains the wavefunction collapse resulting from the interaction between the microscopic particles and the macroscopic measuring apparatus. Especially it gives a uniform realistic description of the microscopic and macroscopic worlds. Thus the theory of quantum motion is more satisfactory than Copenhagen interpretation.

The fourth item, i.e., that the observational means must be described in terms of classical physics, means that although the observed microscopic objects are so peculiar that classical physics can no longer provide a consistent explanation of their displays, our observational means must still be described in terms of classical physics, and we can only use classical concepts to describe the experimental facts. This conclusion has been widely accepted. But as we think, all concepts are only free inventions of human being, and their validity and applicability must be verified at any moment. Especially when there appears a new experimental fact that cannot be consistently explained by the existing concepts, this kind of examination is more indispensable. Thus we must examine and validate the validity and completeness of the classical concepts. On the other hand, even if we still use the existing classical concepts, we must be ready to renewedly understand their meanings in face of new experience. The fact is always that we don't really understand the concepts invented by us in the beginning, and this kind of understanding becomes deeper and deeper only when more and more experience is accumulated. Now the universal existence of quantum motion makes people see the limitations of classical concepts more clearly. Even for the observational means and the macroscopic phenomena they are only approximate descriptions, and their existence cannot prevent us from finding the description which is closer to reality.

The fifth item, i.e., that the act of observation is irreversible and it creates a document, holds true for both the observation on the microscopic systems and that on the macroscopic systems. Moreover, the irreversible process can be explained only in terms of classical physics. Thus the irreversible process during an observation is actually irrelevant to the peculiar properties of quantum measurement. Now quantum motion and its law further confirm this conclusion. 

The sixth item, i.e., that the quantum jump taking place when a measurement is made is a transition from potentiality to actuality, explicitly asserts the objective existence of instantaneous wavefunction collapse during a measurement. Furthermore, Copenhagen interpretation acknowledges that the quantum jump or instantaneous wavefunction collapse is a new physical process, and cannot be accounted for by quantum mechanics. As we think, it is just the absence of the description of this process that results in the physical incompleteness of the existing quantum theory. Owing to this absence, Copenhagen interpretation is not a complete interpretation either. Now the theory of quantum motion provides an objective description of the wavefunction collapse process. It is a complete quantum theory, and naturally includes a complete interpretation.

The seventh item, i.e., that complementarity properties cannot be observed simultaneously, is the core of Copenhagen interpretation (cf. Bohr 1927). But as we think, it is also the most obscure part of the interpretation. Although this assertion is correct, its demonstration given by Copenhagen interpretation is by no means complete. On the one hand, Copenhagen interpretation regards this assertion as an inevitable result of the measurement disturbance. However, it never provides a clear explanation of this disturbance, and its demonstration is always a mixture of classical part and quantum part. In fact, in order to understand the measurement process, we must deal with the quantum entanglement process and the wavefunction collapse process during the measurement. On the other hand, Copenhagen interpretation overemphasizes the influence of the measurement disturbance, and disregards the possibility that the objective motion state of the observed object may be the main physical cause. The fact that complementarity properties cannot be observed simultaneously may actually reflect the peculiarity of the motion state of the observed object. Since Copenhagen interpretation denies the existence of the objective motion of microscopic particles, its demonstration of the above assertion cannot be complete.

Now the theory of quantum motion will provide a clear and complete physical explanation for the above assertion. Here as an example we discuss the observation on the complementarity properties position and momentum. First, concerning any quantum motion state of a particle, the standard deviations of the distributions of position and momentum all satisfy Heisenberg’s uncertainty relation. Concretely speaking, as to the motion state in which the position of the particle is more definite, the momentum distribution of the particle will be closer to an even distribution, i.e., the momentum of the particle will be more indefinite, or vice versa. Then there exists no a motion state in which the position and the momentum of the particle are both definite in reality. Moreover, according to the reasonable assumption that measurement truly reflects the observed state, this kind of quantum motion state will further require that the position and the momentum of a particle cannot be observed simultaneously. It should be noted that, whereas the position and the momentum of a particle cannot both be in a definite state in reality, it may be improper to say that the position and the momentum of a particle cannot be observed simultaneously, since this statement seems to imply that the position and the momentum of the particle can both be in a definite state before measurement. Secondly, when considering the measurement process, the position measurement of a particle will result in the wavefunction collapse process, and the motion state of the particle will collapse to one of its position eigenstates, in which the momentum distribution of the particle is an even distribution, according to the law of quantum motion. This conclusion is the same for the momentum measurement of a particle. Thus the above assertion given by Copenhagen interpretation can be physically explained by the theory of quantum motion.

As to the last two items, i.e., that only the results of a measurement can be taken to be true, and pure quantum states are objective but not real, they mean that there exists no any realistic picture for the microscopic objects. This is an astonishing assertion. In the following, we will give a critical analysis of this assertion.

As we know, Bohr repeatedly stressed that any elucidation of the microscopic phenomena must resort to complementarity principle. Concretely speaking, the information obtained by the measurements under different experimental conditions will exhaust all definable knowledge about the observed microscopic object, but at the same time, when we try to unite the information in a realistic picture it appears to be incompatible. Then any single realistic picture cannot provide an exhaustive account of the microscopic phenomena, instead we can only provide a complementary account of the microscopic phenomena using incompatible classical pictures. Accordingly Copenhagen interpretation asserts that there exists no any realistic picture for the microscopic objects, and we can only use the complementary classical pictures to describe them.

It can be seen that the essential reason why Copenhagen interpretation rejects the realistic picture of the microscopic objects is that the information obtained by the measurements under different experimental conditions is incompatible when being united in a single realistic picture. Then why is the information incompatible when being united in a single realistic picture? Which picture is the realistic picture in which the information is incompatible? The answer of Copenhagen interpretation is that the information is incompatible when being united in a single picture of classical corpuscular or classical wave. The information obtained by the measurements under some experimental conditions shows that the display of a microscopic object resembles that of classical corpuscular, while the information obtained by the measurements under other experimental conditions shows that the display of a microscopic object resembles that of classical wave. Thus the realistic pictures rejected by Copenhagen interpretation are simply the pictures of classical corpuscular and classical wave. Then are there any further reasons to reject all the other possible realistic pictures? No! If there is one reason, it is only the prejudice unconsciously hold by most people including Bohr and Einstein, i.e., that the pictures of classical corpuscular and classical wave are the only possible realistic pictures, in other words, continuous motion is the only possible form of motion.

It should be acknowledged that the pictures of classical corpuscular and classical wave are indeed helpful for describing the microscopic objects. But how can we prove that this kind of description is the only possible description? And why must we still use the macroscopic classical pictures to describe the microscopic processes? The picture of continuous motion directly comes of our macroscopic experience, and the theory of continuous motion, namely classical mechanics, had gained some successes. But as we know, continuous motion is no longer suitable for describing the microscopic objects, then whereby do we think continuous motion is the only possible motion? And whereby do we assert that the single realistic picture of the microscopic objects does not exist?

In fact, the appearance of quantum mechanics has strongly implied that there exists a new kind of motion which is different from the familiar continuous motion. The new motion will provide a single realistic picture for the microscopic objects, and can naturally display the complementarity properties which are mutually exclusive in the framework of classical physics. Quantum mechanics does not prevent us from finding the new motion. What block us are only ourselves, our prejudice, our arrogance and our ignorance. Now the existence of quantum motion clearly reveals the limitations of complementarity principle. At the same time, it makes people have to painfully reject the prejudice of the uniqueness of continuous motion. The pain is transitory, while the happiness brought by the understanding of reality is permanent.

In a word, owing to the absence of a realistic picture of the microscopic objects, the above essentials of Copenhagen interpretation can hardly be convincing, and the intrinsic connections between them can hardly be established either. Moreover, complementarity principle, which is the core of Copenhagen interpretation, also proves to be trustless. By comparison, the theory of quantum motion provides a real picture of microscopic reality, and can establish the intrinsic connections between the valid essentials of Copenhagen interpretation. But accordingly Copenhagen interpretation no longer exists, and will be replaced by the new realistic interpretation in terms of quantum motion.