This paper attempts to show:(a) The nature of the basic assumptions made either explicitly or implicitly by L. de Broglie in arriving at the fundamental formula, [Formula: see text], of wave mechanics, and that at least some of these assumptions are open to criticism.(b) That it is a little too hasty to regard as demonstrated the non-localization of photons or electrons in motion and the lack of determinism with respect to them.(c) That the presuppositions which lead to the 'relations of incertitude' involve highly arbitrary elements and these 'relations' are read into or arbitrarily imposed upon the physical world rather than really found to be in it.(d) That it is an unwarranted claim that the new mechanics can contribute to the solution of the age-long philosophical problem of free will.(e) That it is possible to render the foundations of wave mechanics logically independent of the theory of relativity.