## Thursday, June 1, 2017

### Bell’s inequality and causality

 Niels Bohr
Quantum Mechanics took shape about ninety years ago. During the twenties, Niels Bohr and Werner Heisenberg formulated the Copenhagen interpretation, which added to the mathematical formulation some additional considerations such as the following:
• Physical systems with properties that can take concrete and opposing values ​​(such as direction of polarization or spin) in certain circumstances can be in a state where those properties do not take a defined value, but keep all the possibilities simultaneously open. For example, the direction of polarization of a photon can be simultaneously north-south and east-west. The spin of a particle can be both up and down.
• The act of measuring one of these properties causes the collapse of the wave function, which means that the result of the measurement can only be one of the possible values. The wave function gives us the probability of obtaining each value.
• It is possible to build a physical system formed by two or more interlaced particles with respect to some property, which means that if one of the particles collapses with a certain value, the other particle has no choice but to collapse with the other.
During the 1930s, Einstein, Podolsky, and Rosen formulated the EPR paradox, a mental experiment that indicated that the Copenhagen interpretation of quantum mechanics implies that causality may not be local. In simpler words: there could be causes that would cause instantaneous effects at a great distance. Let’s look at a simplified version of the experiment:
According to the Copenhagen interpretation of quantum mechanics, you can build a physical system made up by two photons, one with north-south polarization and the other east-west. One of these photons stays in our lab, while the other is sent a light-year away. Then we measure the polarization of the first photon and find that it is north-south. We will automatically know that the other has collapsed with the east-west polarization, at the very moment when we measured the first. For that to happen, an instantaneous effect would have to take place at a distance of one light-year. Thus causality would not be local.
 John Stewart Bell
For thirty years, the EPR experiment remained mental. But in 1964 John Stewart Bell formulated a mathematical expression (Bell’s inequality) whose result would be different starting from Einstein’s local causality, or from the Copenhagen interpretation. This made it possible to perform experiments that measure the value of that expression, thus automatically transforming the EPR mental experiment into a physical experiment.
Bell’s inequality has been measured in numerous experiments carried out from 1972 to the present. In all cases the prediction of the Copenhagen interpretation has been confirmed, as against Einstein’s.

Let’s look at some typical errors regarding Bell's inequality:

1. Bell’s inequality shows that there are causeless effects. This is false. What it proves is a successful prediction of the Copenhagen interpretation of quantum mechanics. Consequently, if this interpretation is true, instantaneous effects may occur at a distance (that is, causality would not be local). In these experiments there is always a cause: the measurement of the property in question.
2. Bell’s inequality shows that the Copenhagen interpretation is true. This is also false. It proves that this interpretation has made a correct prediction, therefore throws down an attempt to prove it false. But, like any physical theory, it could be overthrown by another experiment.
What would happen if the Copenhagen interpretation turned out to be wrong? In fact, other interpretations have been formulated, although at the moment they are followed by a minority. In such a case, Bell’s inequality would have to be reinterpreted, and the conclusion may not follow that causality may not be local.

That is, there are many questions to be solved, as usually happens in science. What can be said is that the conclusions some attempt to draw from this inequality to favor their materialist ideology have no basis.

Manuel Alfonseca