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M. Quack, J. Mol. Struct. 1995, 347, 245-266. The "world game" consists of a game leader who draws tetrahedral dice arbitrarily from two boxes, a) the "de facto" box, where each die has four different faces (denoted S, R, S*, R*) and b) the "de lege" box (four types of die, each one having only one letter on all four faces, say S, or else R, S*, R*). The players are allowed to make just one throw with the selected tetrahedral die and observe the one face of the tetrahedron showing towards them. Then the players, who may be called also the "scientists", must guess from which box the die has been drawn, that is, what are the "rules of the game" (de facto or de lege, there will be a reward for the right guess of the rules of the game, as there might be in science). Now, if the "de lege" box has equal numbers of each die ("S", "R", "S*" and "R*") and if the game leader is a statistically honest person, the statistics are fairly simple and the player does not have much of a winning strategy against other players. If one player knows, however, that the de lege box contains a bias towards one type of die (say 40 % S and 20 % each of the others), he will win with the strategy of guessing "de lege" if he sees an "S" in the single throw and "de facto" if he sees any of the other faces. In fact, however small the known bias is, in the long run he will always win over those who don't know the bias and that is, why it is important to know the bias, also in the analogous physical situation. In our world we observe living matter to be made of S amino acids, and of ordinary matter, not of antimatter, where in the general notation S and R indicate the type of enantiomer and the star indicates antimatter as opposed to ordinary matter (without star). One obvious conclusion concerning the physical situation in biochemical evolution can be drawn from the single observation of an S amino acid world: The bias cannot be 100 % in favor of any combination of R*, R, S*.
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The five competing fundamental hypotheses of chirality that were identified by the time of writing the review[1] are: 1. the classical hypothesis of macroscopic molecular models (basically van't Hoff's description of spontaneous symmetry breaking); 2. the quantum-mechanical hypothesis of de facto symmetry breaking with parity conservation, originally from Hund; 3. the superselection-role hypothesis of Pfeiffer and Primas with spontaneous symmetry breaking caused by the influence of the radiation field; 4. the "environmental" or collison hypothesis of Simonius, Harris, and Stodolsky that induces de facto symmetry breaking in chiral molecules because of interactions with an external medium; 5. the hypothesis of de lege symmetry breaking in chiral molecules because of parity violation. A detailed discussion of these hypotheses can be found in sections 2.1 to 2.5 of ref. [1], where it is also shown how one might distinguish experimentally which hypothesis might be applicable, mostly by using the scheme in Lit. [33].
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z(-t) (T=time) and change from particle to antiparticle (C for charge conjugation). This CPT symmetry was discussed as a general symmetry about 50 years ago by Schwinger, Lueders, and Pauli and since that time has been a fundamental feature of theories in physics(the standard model, but also other fundamental approaches). Violation of CPT symmetry would result in fundamental revisions of our current theories in physics. Simple consequences of CPT symmetry are the exactly equal masses of electron and positron or proton and antiproton or of S enantiomers and R* enantiomers of antimatter (see ref. [93] for further discussion).
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