I wonder if it would be interesting if anybody had ever thought of whether there was any reason behind born denoting the quantum probability rules as given only by the moduli of the amplitude as opposed to the mod squared. Perhaps not, but I am wondering whether anyone had ever thought of whether there is any relation between this and that perhaps in certain cases,s as if both outcome or rather there two numerical identical particles, there, the chances given only by the mods, such that its as if the outcome probability is given by the multiplicative 'axiom'; as if its probability is multiplied by itself
I doubt it would in many cases,particularly if the values of the moduli can go negative
By this I mean to model the the situation, as if they are there are two numerical identical (or rather qualitatively identical particles) present when there is generally only one; which may be somewhat related to that one gets one gets downward conversion of a single particle into two entangled particles in a singlet state); which may in some (probably not in higher dimension hilbert spaces) explain partly the odd correlations in entanglement; as if they not only came in contact, but where in at one point the same particle, but were downward converted by nature etc, into two bi-particles); or rather perhaps still are the same particle in some odd sense (ie for example, it may partially explain why the probability of any two outcome spin up spin down for particle 1 and particle 2, have a probability of 1/2 (of both occurring) in a singlet state 1/2; as opposed to a 1/4 probability would have ordinarily expected if not correlated.
Likewise, interference in the double slit (again there is a similarity there, but not exactly).
For example, one could say that its akin to using the something like the multiplicative form of additvity, t(echnically not an axiom of probability theory)but where the the interference term (somewhat like the independence terms in said 'axiom') drops out/drop in etc
I am just wondering whether anyone had noticed this odd similarity. Not that endorse it, or believe it would ever work
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