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A three-dimensional (Euclidean) time had already been introduced by some authors, but still under the «classical» assumption that theonly observable quantity related to any time vectort should be itsscalar amplitudet. See,e.g.,N. S. Kalitzin:Multitemporal Theory of Relativity (Sofla, 1975);P. Demers:Canad. Journ. Phys.,53, 1687 (1975);R. Mignani andE. Recami:Lett. Nuovo Cimento,16, 449 (1976);M. Pavšić andE. Recami:Lett. Nuovo Cimento,19, 273 (1977). See alsoE. A. B. Cole:Nuovo Cimento,40 A, 171 (1977);44 B, 157 (1978).
Very recently, I have got knowledge of a work—P. T. Pappas:Int. Journ. Theor. Phys., to appear (1976)—in which the same transformation as (10) is axiomatically inferred from the non-relativistic hypothesis of a vanishing transversal aberration for light.
On this subject see,e.g.,J. P. Hsu:Found. Phys.,6, 317 (1976);S. Marinov:Found. Phys.,8, 637 (1978).
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Ziino, G. On the theoretical reliability of a three-temporal Lorentz transformation. Lett. Nuovo Cimento 24, 171–174 (1979). https://doi.org/10.1007/BF02725752
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DOI: https://doi.org/10.1007/BF02725752