5. The Einstein-Podolsky-Rosen paradox

The debate between physicists of opposite tendencies focused on an article, published in 1935 by A. Einstein, B. Podolsky and N. Rosen, titled: Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?

In this article the authors, after an epistemological introduction on the cognitive power of Physics, proposed a mental experiment (Gedankenexperiment) from which, they said, one can deduce that, in the description of single particles, Quantum Mechanics leads to contradictory results.

This article, extremely effective also from the literary point of view for it sharp and clear concision with regard to the complexity of the argument, is practically impossible to reassume. We transcribe here only few excerpts, the most important to give the methodological point of view of the authors.

Any serious consideration of a physical theory must take into account the distinction between the objective reality, which is independent of any theory, and the physical concepts with which the theory operates. These concepts are intended to correspond with the objective reality, and by means of these concepts we picture this reality to ourselves.
In attempting to judge the succes of a physical theory, we may ask ourselves two questions: (1)"Is the theory correct?" and (2)Is the description given by the theory complete?"

The correctness of the theory is judged by the degree of agreement between the conclusions of the theory and human experience.
This experience, which alone enables us to make inferences about reality, in physics takes the form of experiment and measurement.

Whatever the meant assigned to term complete, the following requirement for a complete theory seems to be a necessary one: every element of the physical reality must have a counterpart in the physical theory.

The second question is thus easily answered, as soon as we are able to decide what are the elements of the physical reality.
The elements of the physical reality cannot be determined by a priori philosophical considerations, but must be found by an appeal to results of experiments and measurements.
A comprehensive definition of reality is, however, unnecessary to our purpose. We shall be satisfied with the following criterion, which we regard as reasonable.
If, whitout in any way disturbing a system, we can predict with certainty (i.e. with probability equal to unity) the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity.

We find here enunciated the basic epistemological assumptions of Einstein and the core of its critic to the Copenhagen School.

In synthesis:

  1. To know is to know something that exists independently from the observer and its theories. Therefore the authors refuse the Berkeley's principle Esse est percipi which, in their opinion, is the basis of the Copenhagen School, and assert the existence of an objective reality.
  2. The knowledges of this reality are organized in theories, which are a pure product of the human intellect; these theories must control their adequacy interacting with the objective reality through experiments and measurements.
  3. A theory must be not only adequate, but also complete; it is complete only if every element of the reality has a counterpart in the theory.
  4. Criterion of reality: a quantity corresponds to an element of reality only if we can preview its value without direct interaction with the same element, that is without the element is observed by anyone.

Einstein and his associates in the body of the article contest the completeness of the Quantum Mechanics, traying to demonstrate that its theoretical elements do not succeed in explicating properties that, according to their criterion of reality, must be thought objective and conclude theirs written saying:

While we have thus shown that the wave function does not provide a complete description of the physical reality, we left open the question of whether or not such a description exists. We believe, however, that such a theory is possible.

Instead reporting the mental experiment described in the article, which can cause some difficulty for the not specialist ones, we transcribe another analogous argument proposed by Einstein in the 1942.

We consider as a physical system, in the first instance, a radioactive atom of definite average decay time, which is practically exactly localised at a point of the coordinate system.
The radioactive process consists in the emission of a (comparatively light) particle. For the sake of simplicity we neglect the motion of the residual atom after the disintegration process. Then it is possible for us, following Gamow, to replace the rest of the atom by a space of atomic order of magnitude, surrounded by a closed potential energy barrier which, at a time t = 0, encloses the particle to be emitted.
The radioactive process thus schematised is then, as is well known, to be described - in the sense of elementary quantum mechanics - by a Psi-function in three dimensions, which at the time t= 0 is different from zero only inside of the barrier, but which, for positive times, expands into the outer space.
This Psi-function yields the probability that the particle, at some chosen instant, is actually in a chosen part of space (i.e., is actually found there by a measurement of position).
On the other hand, the Psi-function does not imply any assertion concerning the time instant of the disintegration of the radioactive atom.
Now we raise the question: Can this theoretical description be taken as the complete description of the disintegration of a single individual atom? The immediately plausible answer is: No. For one is, first of all, inclined to assume that the individual atom decays at a definite time; however, such a definite time-value is not implied in the description by the Psi-function.
If, therefore, the individual atom has a definite disintegration time, then as regards the individual atom its description by means of the Psi-function must be interpreted as an incomplete description.
In this case the Psi-function is to be taken as the description, not of a singular system, but of an ideal ensemble of systems.
In this case one is driven to the conviction that a complete description of a single system should, after all, be possible, but for such complete description there is no room in the conceptual world of statistical quantum theory.

From Albert Einstein: Philosopher-Scientist,
Einstein's Reply to Criticisms
Published by Cambridge University Press, 1949.