# The criterion of minimal loss

If we have a conflict between physical principles, we need some criteria or metaprinciples to decide which of the two principles is worth to be preserved. Once principles usually do not have empirical content themself, we cannot use Popper's criterion of empirical content themself to decide between them. Nonetheless, there is a quite similar criterion which can be used to replace it: Last but not least, even if this does not lead to testable physical predictions, physical principles restrict the theories which conform to them. This is the most important property of a physical principle. A principle which does not restrict, in some way, the physical theories is not a physical principle, but, at best, an esthetical one. The restrictions coming from the different physical principles lead to restrictions for the physical theories following them, and these restrictions already lead to nontrivial empirical content.

Similar to Popper's criterion of empirical content, we should prefer those principles which give more serious restriction. Thus, in case of conflict between two principles, we should prefer the principle which restricts the theories in a more severe way. We can formulate this in form of the following criterion of minimizing the loss of restrictive power:

If, in case of conflict between two principles A and B, giving up principle A leads to a more severe loss of restrictive power in comparison with giving up principle B, we should give up principle B.

Of course, usually it is hard to compare which of the two restrictions are more severe. In these cases, all what the criterion gives is some point we have to care about – the restrictive power of a principle. In particular, it is helpful to understand that the restrictive power of a physical principle is something positive, therefore, that giving up a restrictive principle without sufficient reason is no good.

Nonetheless, there are, strangely, some particular cases where this criterion gives a strong unique answer. Moreover, two examples of this type are important in our discussion.

## Application to the conflict between realism and realistic Einstein causality resp. realistic relativistic symmetry

The situation where the criterion of minimal loss gives a unique answer is one where the two principles in conflict are nonetheless connected in some way, so that giving up one of them, say A, requires a modification – in particular, a weakening – of the other principle, say B, too. If the weakened principle B', which we obtain, as a consequence, is no longer in conflict with the principle A, then there is no reason to give up principle A – to replace B by B' is necessary anyway.

This situation seems to be a very artificial one, it seems, in this case nobody would propose to give up A. But this is, exactly, the situation we meet if we consider Bell's inequality. One of the ingredients we need in the proof is a realistic version of Einstein causality, a version, which does make sense only in a realistic context. Thus, if we give up realism, we automatically have to weaken the realistic version of Einstein causality as well. It becomes a weak version of Einstein causality, applicable only to observable effects, whose reality is unquestionable. But this weaker version of Einstein causality is not in conflict with realism – realism, together with weak Einstein causality, are not sufficient to derive Bell's inequality, thus, their combination is not falsified by the violation of Bell's inequalities.

Thus, we have a situation, where giving up realistic Einstein causality, replacing it by weak Einstein causality, clearly minimizes the loss of restrictive power, because this weakening has to be done anyway, even if we give up realism:

The loss of restrictive power is lower for replacing realistic Einstein causality by weak Einstein causality, in comparison with giving up realism. Therefore, the criterion of minimal loss requires to give up realistic Einstein causality.

The same argumentation can be applied to the corresponding realistic version of relativistic symmetry as well. This version, applied to the notion of causality, leads to the realistic version of Einstein causality, which is in conflict with realism. But, if we give up realism, it reduces to a weaker version, which is restricted to observables, as well.

The loss of restrictive power is lower for replacing the realistic version of relativistic symmetry by the weak version of relativistic symmetry, in comparison with giving up realism. Therefore, the criterion of minimal loss requires to give up the realistic version of relativistic symmetry.

Given these two results, one could ask if there is a way to circumvent this argumentation. There is: One should use another, even more restrictive principle, which is in conflict with realism (because it allows to derive, if applied to causality, realistic Einstein causality), but does not reduce to observable effects only if we reject realism. Such a principle of relativistic symmetry is known, it is the principle of manifest relativistic symmetry. This principle rejects all structures in a theory, even those which remain unobservable, which do not have relativistic symmetry.

Therefore, taking into account the criterion of minimal loss, we find that the only conflict not solved by this criterion is the conflict between realism and the principle of manifest relativistic symmetry.