Recently much attention has been paid to the discovery of Hubble's law -the linear relation between the rate of recession of the distant galaxies and distance to them.Though we now mention several names associated with this law instead of one, the motivation of each remains somewhat obscure. As it is turns out, two major contributors arrived at their discoveries from erroneous reasoning, thus making a case for a Type III error.It appears that Lemaitre (1927) theoretically derived Hubble's Law due to his choice of the wrong scenario of the Universe's evolution. tested the linearity law not based on Lemaitre's non-static model, but rather a cumbersome extension of de Sitter's static theory proposed by Weyl (1923) and Silberstein (1924).
Friedmann, who died young in 1925, deserves to be called the father of Big Bang cosmology. But his seminal contributions have been widely misrepresented and undervalued.
Higher-order extrema with topological indices greater than unity are discussed. Explicit constructions are given for their wave functions, and simple geometric rules are presented for analysis of their topological indices. Experimental means for verifying the theory with use of Gaussian laser beams are considered, unusual properties of optical vortices constructed from this new type of critical point are described, and applications to topologically based optical arithmetic are suggested.
From the extant statistical data, the paper reconstructs several episodes in the history of the Royal Mint during Isaac Newton's tenure. We discuss four types of uncertainty that are embedded in the production of coins, extending Stephen Stigler's work in several directions. The jury verdicts in trials of the pyx for 1696-1727 allow judgement on the impartiality of the jury at the trials. The verdicts, together with several remarks by Newton in his correspondence with the Treasury, allow us to estimate the standard deviation σ in weights of individual guineas coined before and during Newton's Mastership. This parameter, in turn, permits us to estimate the amount of money that Newton saved Britain after he put a stop to the illegal practice by goldsmiths and bankers of culling heavy guineas from circulation and recoining them to their advantage; a conservative estimate of savings to the Crown is £41510, and possibly three times as much. The procedure by which Newton probably improved coinage gives historical insight on how important statistical notions-standard deviation and sampling-came to the forefront in practical matters: the former as a measure of variation of weights of coins, and the latter as a test of several coins to evaluate the quality of the entire population. Newton can be credited with the formal introduction of testing a small sample of coins, a pound in weight, in the trials of the pyx from 1707 onwards, effectively reducing the size of admissible error. Even Newton's 'cooling law' could have been contrived for the purpose of reducing variation in the weight of coins during initial stages of the minting process. Three open questions are posed in the conclusion.
We consider the EPR experiment in the energy-based stochastic reduction framework. A gedanken setup is constructed to model the interaction of the particles with the measurement devices. The evolution of particles' density matrix is analytically derived. We compute the dependence of the disentanglement rate on the parameters of the model, and study the dependence of the outcome probabilities on the noise trajectories. Finally, we argue that these trajectories can be regarded as nonlocal hidden variables.
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