The Copenhagen interpretation is the standard interpretation of quantum mechanics drawn up essentially by Niels Bohr in 1927 from results obtained by Werner Heisenberg and Max Born for the interpretation of the Born-Heisenberg-Jordan matrix mechanics, and De Broglie-Schrödinger wave mechanics.

Bohr was the director of the Danish Institute of Physics in the city of Copenhagen where multiple discussions took place between the founders of quantum mechanics, and the interpretation took its name from the city.

It is based on the Bohr principle of complementarity. This principle was inspired by the example of the theory of relativity in which the solution to contradictions of Newtonian mechanics with Maxwell's electromagnetism consisted in questioning the existence of absolute time and the independent existence of space and time. From the lack of measurement of absolute movement and the existence of a speed limit for all causal signals in the universe, it was deduced that the concept of absolute movement was meaningless, and space and time had to be merged in Minkowski space-time. geometry

According to Bohr, the fact that physics describes first and foremost what is observable should not be forgotten, which does not mean, as some have believed, that this was a positivist profession of faith by Bohr. He himself, like Heisenberg, actually refused to be considered to be a positivist. Simply stated, physics is at least this, even though it cannot be reduced to this.

From this idea, the contradictions between the wave and particle points of view to describe the behaviour of light, matter and their interactions are resolved in the following way.

The physicist uses classical measuring instruments, which give classical measurements that can be interpreted, by their very nature, in the language of waves and particles. But in reality there are neither waves nor particles! Quanta are simply other; they are not classical objects in space and time.

Just as there is no absolute time or space, there are no subtly associated but nevertheless classical absolute particles or waves. This therefore leads to another use of waves and particle concepts to describe the experiments related to the quantum world. But because of the very structure of the quantum mechanics equations, a quantum phenomenon using completely classical concepts can never be measured or described, not because the laws of nature are prevent from knowing whether a particle or a wave really exists on a quantum level, but because there is no such thing!

## This is the exact physical content of the famous Heisenberg inequalities.

Bohr's principle of complementarity is therefore an injunction to classical physicists to rid themselves of the idea that the objects in the atomic world should be conceived in classical terms, and to see clearly that the measurement of a phenomenon is something much subtler than in classical physics. The transition between the raw appearance of things and an adequate conception of their real nature is much more indirect and can be a source of errors and contradictions.

The other aspect of the Copenhagen interpretation concerns the status of probability calculations and quantum mechanical causality. According to Bohr, Heisenberg, Pauli, Jordan, Born and Dirac, the wave function, or rather Schrödinger's state vector, expresses an intrinsic element of chance at play in the quantum world, and in no way a limit to our knowledge of the parameters determining the state of a mechanical system, as in the kinetic theory of gases and especially its extension, statistical mechanics. The field of application of causality is therefore considerably limited.

The Schrödinger state vector most often develops deterministically but because of the probabilities associated with obtaining a measurement there is always an element of chance that cannot be eliminated.

To summarise, in answer to the following questions:

1) **Do the fundamental entities of atomic physics such as electrons, photons, etc. really exist, independently of any observations made by physicist?**

2) **If the answer to the previous question is yes, is it possible to understand the structure and development of atomic objects and processes as images in space-time related to their associated reality?**

3) **Can the laws of physics be formulated in such a way that one or more causes can be attributed to the observed effects?**

The upholders of the Copenhagen interpretation reply: **NO**!

Neither Einstein, nor Schrödinger, De Broglie and Planck were satisfied with this position. During the following years the first two of these performed many thought experiments such as Einstein's box, Schrödinger 's cat and the famous EPR paradox, to prove that the Copenhagen interpretation was wrong!

De Broglie and then David Bohm proposed a non-linear theory to replace the wave equation for a particle of matter, a special case of Schrödinger' equation, to escape from the Copenhagen interpretation. This theory has up to now only worked in the non-relativistic case, and the problems faced in attempting to take account of special relativity are for the moment insurmountable.

It is, however, worthy of note that these theories produced a counter-example to a von Neumann theorem which was based on assumptions that were too restrictive, and which appeared to be an obstacle to modifying the equations and principles of Copenhagen quantum mechanics.

Will it be the same for the famous John Bell inequalities violated by Aspect's experiment in 1982 and giving strong support to the standard interpretation of quantum mechanics? This is highly unlikely but doubtless not impossible if the effects of quantum gravitation come into play as Roger Penrose, the Nobel prize winner Gerard ‘t Hooft and others believe.