  It is shown that the conventional approach to microcosm investigations uses
an incorrect supposition (incorrect space-time model) whose incorrectness is
compensated by means of additional hypotheses, known as quantum mechanics
principles. Such a conception reminds the Ptolemaic doctrine of celestial
mechanics. Alternative research program, which uses a more correct space-time
model and does not need additional hypotheses (quantum principles) for free
explanations of quantum effects, is suggested. If the more correct space-time
model were known in the beginning of XXth century, when research of microcosm
started, quantum mechanics could develop in other way. The alternative research
program appeared with a secular delay, because all this time the necessary
mathematical technique was not available for researchers. Absence of necessary
mathematical technique is connected with some prejudices which have been
overcame at the construction of new conception of geometry and that of
statistical description. Basic statements of the new mathematical technique and
principles of its application in alternative research program are presented in
the paper.
