5 Conclusions.

Significant tests of quantum mechanics that can be performed at Dane are proposed. They consist of measuring the amplitude of interference effects and comparing it to the predicted value. They may reach the relative accuracy of 10. The tests of Sect. 3.2 and, maybe, the one of Sect. 3.3 can be conducted with the KLOE detector as is. They only require a specific analysis of data that will be collected anyhow. These tests of Sect. 3.2 are valid regardless of the Weisskopf-Wigner approximation, [12], because the probability for the two kaons to decay at the same time into the same mode can be shown to be zero just regardless of the time evolution operator , [13].

Tests of quantum mechanics in kaon physics were proposed already in Ref. [1]. One of the motivations was to look for possible spontaneous wave-function collapses not involving an observer, because such effects would induce decoherence. That motivation is still valid. Differential equations for the time evolution of the density matrix in presence of a decoherence mechanism were developed in Ref. [14]. In Ref. [15], that kind of evolution was considered relevant to particles in the vicinity of black holes, therefore to string theory. Guesses at how strong this effect could be in kaon physics are given in Ref. [16]. A more detailed analysis is made in Ref. [9] and expressions relevant to two-kaon states are given in Ref. [10]. The latest theory assumes strangeness conservation in the decoherence mechanism and does not require ``completeness''. However, it is our opinion that it is better to keep as broad a perspective as possible and to perform all the tests proposed here, which test all the above theories, rather than only those that have the best chance to reveal a violation of quantum mechanics in the context of the theory of Refs. [9], [10], and [16]. Acknowledgments The author is indebted to N.E. Mavromatos for several very useful discussions in Frascati in April 1994.