Foundations of Physics, Vol. 7, Nos. 5/6, 1977 Momentum Conservation Decides Heisenberg's Interpretation of the Uncertainty Formulas Th. D. Angelidis 1 Received March 24, 1975 The present thesis considers, in the light of Heisenberg's interpretation of the uncertainty formulas, the conditions necessary for the derivation of the quanti- tative statement or law of momentum conservation. The result of such con- siderations is a contradiction between the formalism of quantum physics and the asserted consequenees of Heisenberg's interpretation. This contradiction decides against Heisenberg's interpretation of the uncertainty formulas on upholding that the formalism of quantum physics is both consistent and complete, at least insofar as the statement of momentum conservation can be proved within this formalism. A few comments are also included on Bohr's "complementarity interpretation" of the formalism of quantum physics. A suggestion, based on a statistical mode of empirical test#~g of the "uncerta#~ty" formulas, does not give rise to any such contradiction. 1. INTRODUCTION A deductive theory is consistent a) if of any two contradictory statements at least one cannot be derived or proved in this theory; two statements of which one is the negation of the other are called contradictory. A deductive theory is complete if of any two contradictory statements formulated in the terms of this theory at least one statement can be derived or proved in this theory. Hence, a deductive theory is inconsistent if there are two contradictory statements which can both be proved within this theory. A deductive theory is incomplete if there are two contradictory statements formulated in the terms of this theory neither of which can be proved within this theory. Momentum conservation is an empirical fact. The quantitative statement or formula whose physical reference is the empirical fact of momentum con- o University College London, London, England. 431 © 1977 Plenum Publishing Corp., 227 West 17th Street, New York, N.Y. 10011. To promote freer access to published material in the spirit of the * 1976 Copyright Law, Plenum sells reprint articles from all its journals. This availability underlines the fact that no part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming, recording, or otherwise, without written permission of the publisher. Shipment is prompt; rate per article Js $7.50.