2.2.2  The Quantum Precepts

The history of how it was determined that the quantum theories do not follow the classical precepts, is registered in many books. It is still a topic under discussion. Even in our days, books and articles are written. Experiments are performed. And the physicists discuss. It is a history not closed. The student can find a lot of material to study and a branch for research in these themes. There is a lot to investigate in this field; specially from the approximation called experimental philosophy. To start the student can read the book of F. Selleri. See References.

We will describe briefly the beginning of that story. And the form in which the problem has been cleared up. And we will mention the most recent results.

Even A. Einstein, that substantially contributed to quantum theory, never accept it as the definite theory which describes the nature. For him, a physical theory must have the characteristics of a classical theory in order to represent the physical reality.

In 1935 he defined the physical reality: He published, in collaboration with B. Podolsky and N. Rosen, the article Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?

First he pointed out clearly that the elements of physical reality can not be determined a priori by philosophical considerations, but they must be found experimenting and measuring. Second, he defined the physical reality. In his definition he wrote:

If, without 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.

The idea of physical reality, as in the above paragraph, agrees with the classical and quantum idea of physical reality. It is know as local realism.

Using his criterion of physical reality, Einstein showed that the quantum mechanics is not complete. This is, quantum mechanics does not give a complete description of the external world. In his own words:

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.

The realism described by Einstein in his article of 1935 is known as local realism. Apparently the nature does not behave according to this realism. The experiments to show this realism we call them experiments type Einstein-Podolsky-Rosen (EPR).

In an article called in the same way, N. Bohr answered. And based on his principle of complementarity, he refuted Einstein and collaborators paper conclusions. According to Bohr, quantum mechanics offers the last word in the description of the physical reality.

But the discussion, to be a physical discussion must be based on experimental evidences. The last word must be provided by the experiment. Bell theorem changed the discussion completely and put the debate on the possibility of experimental test. This is, under the correct way of physics.

In 1964 J. S. Bell, taking the paper of A. Einstein on physical reality, wrote algebraic predictions. The inequality is known as Bell's inequality. This inequality is contradicted by the quantum mechanical measurements in an experiment type EPR. That is, if performing and experiment type EPR one finds that Bell inequality is violated, then the local realism of Einstein is not the way the nature conducts herself.

In an experiment of two polarizers, as in the ideal case of an experiment type EPR, A. Aspect and co-workers showed that the Bell inequality is violated. This agreement with the quantum mechanics was established experimentally far away than ten standard deviations. Therefore the local realism is not the way the nature carries herself.

The violation of the Bell inequality, in an strict relativist separation for the performed measurements, means that experimentally is not possible to maintain a reality à la Einstein. In a reality à la Einstein the correlations are explained by the common properties determined in the common source. These properties are transported by the correlated physical systems. Let's consider an instance.

For example:

According to the experiment a pair of decades ago, the possibility of constructing a muon collider was remote; now there is the project to construct it at Fermilab USA. The project involves more than 100 physicists from 27 institutions from all over the world. For the muon decays into $e\nu_e \nu_{\mu}$ after $2.2 \times 10^{-6}$ seconds, in the acceleration process to take the muons and antimuons at velocities close to $c$ many muons will be lost. The muons and antimuons that reach velocities close to $0.9999985c$ will live in the collider close to $1.27 \times 10^{-3}$ seconds, according to the observer in the laboratory. This time is enough to experiment with the muons and the yields from the muon collisions.

The muon collider was proposed, in the 1970's, by Skrinsky and Neuffer. But it was up to the decade of 1990 that significative advances in capturing and cooling muon techniques made that the idea were taken seriously. Now it is possible to achieve luminosities, in the muon collider, comparable to those obtained in the proton-antiproton colliders or in the electron-positron colliders. See Figure 2. The responsible group of exploring the muon collider possibility, of high energy and high luminosity, is leaded by R. B. Palmer. The physics that could be studied in the muon-antimuon collider could be very similar to that studied in the electron-positron collider. The family of the muon and the family of the electron is the same. Both particles are leptons. The muon is like a massive electron. Close to two hundred times more massive than the electron. For its great mass, the muons produce much less synchrotonic radiation.

There are some advantages in using muons instead of electrons in the colliders, these are: The muons can be accelerated and stored in circular accelerators, like the protons, at energies of $250~Gev$ or higher. The electrons must be accelerated in linear accelerators. In circular accelerators they lose too much energy. The muons lose less energy than the electrons by stopping effect. This radiation form is known as bremsstrahlung radiation. Their spectrum of energy is less wide. There are more produced particles per bunch. The luminosity is higher. The channel $s$ of Higgs bosons production is increased, because the coupling of any Higgs boson is proportional to the muon mass.

The student can check in any advanced textbook of high energy physics, if he or she requires an explanation about the before mentioned techniques and concepts.

The effective energy in the collision of puntual particles, like the muons, the electrons or the gamma rays, is about 10 times greater than the energy from the proton collisions. For that, a circular muon collider will be a factor of ten more small than the equivalent proton collider. For example, a muon collider, of $4~TeV$ of energy in the center of mass, of 6 kms of circumference, will have an effective energy -a physical potential for physical discoveries- akin to that would have the 80 kms of circumference superconducting supercollider. Also will be more small than the conventional linear collider of electrons of the same energetic capacity. This linear collider must be 50 kms long.

There are many difficulties in the construction of the muon collider. There is no guarantee that it will be cheaper. Nor guarantee that it will have the required luminosity. The most serious problem is the generated by the muon decay into electrons and neutrinos. This will produce a great amount of radiation. The design must have to take into account those problems. The collider design must solve them.

We will show, with other example, the process of experimentation in the next section.

Figure 1:Muon collider.