Document Type


Publication Date



Feynman, Richard P. (Richard Phillips), 1918-1988, Fourier transformations, Heisenberg uncertainty principle, Quantum theory


Quantum mechanical descriptions in terms of momentum and position are identified as alternatives under the condition of equal complex-vaulted Lebesgue square integrability. While this does not change any of the formal results obtained in quantum mechanics, it does shed a different interpretive light on the steps that lead up to these results. Instead of being independent, even in concept, momentum and position are identified as being the same thing, merely seen from different views. Neither is required to complement the descriptive capability of the other, since each forms a complete alternative in its own right. Apparent complementarity, as well as mutual indeterminacy of codescription, comes about whenever an attempt is made to overlap these two descriptions to form a third codescription which tries to maintain both the terminology and the net integration values of the separate alternatives. Noncommutation of associated operators is a direct consequence of the alternative nature of momentum and position, and the local to global character of the particular map between these alternatives leads to an apparent point-wave duality in their descriptions. It is suggested that challenges to the contemporary interpretation of quantum theory should begin with the assumptions that lead to its formulation involving alternative representations.


Richard C. Heyser prepared this article for submission in the American Journal of Physics.

This item is part of the Richard C. Heyser collection at the College Archives & Special Collections department of