A new interpretation of quantum mechanics and its consequences in epistemology

A rather recent interpretation of quantum mechanics, known under the various names of consistent histories, decohering histories, or logical interpretation, has brought interpretation into a standard deductive theory and is now investigated in many places. A key difference with the Copenhagen interpretation is the status of classical physics, now derived completely from quantum principles in both its dynamical and logical aspects. After describing briefly this new interpretation in its essentials, leaving aside technical details, it is shown how its consequences in epistemology differ drastically from the familiar outcomes of the Copenhagen interpretation, leading in particular to a well-defined theory of knowledge. Some more speculative philosophical consequences associated with the unsolved problem of actuality are also mentioned.     

A strange pigeon-hole principle

Using Ramsey theory, we establish the following pigeon-hole type principle: From a large number of random variables (functions, vectors, etc.) one can always select two, X and Y, such that P(X < Y) 1/2. We apply the principle for a poset problem.     

Variations on the theme of repeated distances

We give an asymptotically sharp estimate for the error term of the maximum number of unit distances determined byn points in ^{d, d}4. We also give asymptotically tight upper bounds on the total number of occurrences of the favourite distances fromn points in ^{d, d}4. Related results are proved for distances determined byn disjoint compact convex sets in ².At the time this paper was written, both authors were visiting the Technion — Israel Institute of Technology.     

On the second smallest distance between finitely many points on the sphere

In the following note we investigate the second smallest distance between finitely many points on the sphere. Actually we look for the smallest upper bound for the second smallest distance between n points on the unit sphere. We solve this problem for n=9 and also we give a general, non-trivial upper bound for the second smallest distance of n points with n9.Supported by the Hungarian National Foundation for Scientific Research, Number 1238.     

Interpolatory properties of best rationalL 1-approximations

In this paper the distribution of the zeros of the error function for bestL ₁-approximation by rational functions fromR _n,m is considered. It is shown that the maximal distance between such zeros isO(1/(n–m)), ifn > m.Communicated by Edward B. Saff.     

Characterization of reaction products formed during thin-layer chromatographic detection of thiocarbamate herbicides

The reaction between thiocarbamate herbicides and 2,6-dichlorobenzoquinone-N-chloroimine or 2,6-dibromobenzoquinone-N-chloroimine is suitable for the detection of these herbicides on thin-layer plates with high sensitivity. The reactions were followed by infrared, nuclear magnetic resonance and mass spectrometry. We have established the formation of 2,6-dichlorobenzoquinone-S-alkyl sulphenylimines. In the case of the bromo-derivative, halogen exchange and substitution on the quinone ring took place simultaneously leading to the formation of mixed halogenated 2,6-dihalo- and, in addition, 2,3,6-trihalobenzoquinone-S-alkyl sulphenylimines. The final product of the detection reaction, i.e. 2,6-dichlorobenzoquinone-S-alkyl sulphenylimine was reacted with 2,6-dibromobenzoquinone-N-chloroimine where 2,6-dichloro-3-bromobenzoquinone-S-alkyl sulphenylimine formed as a consequence of the looser bromine-carbon linkage on the 2 and 6 positions of the quinone ring.