Abstract
This chapter illustrates some of the characteristic features by which quantum mechanics differs from classical theories. In Section XIII.1, using a gedanken experiment with the Stern-Gerlach apparatus it is shown that a polarized beam (a pure state) cannot be split by the magnetic field, and that the splitting of such a beam is a consequence of the measurement. In Section XIII.2 we derive the predictions of quantum mechanics for spin correlation measurements in the singlet state of pairs of spin-2 particles. In Section XIII.3 these predictions are confronted with Bell’s inequalities, which follow from a hypothesis first proposed by Einstein, Podolsky, and Rosen. We conclude with a short discussion of hidden-variables theories.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
We are again using units where h ≡ 1.
The Maxwell equation O• B = B;/ax; = 0 tells us that the variation of B1 with x is just as great as the variation of B3 with z. We shall return to the subject of this approximation in the appendix to this section.
The original Stern-Gerlach experiment (1922) used silver atoms rather than hydrogen atoms. For other arrangements of a Stern-Gerlach experiment, see Myer Bloom and Karl Erdman, Can. J. Phys. 40, 179 (1962).
We assume here that the particles are not identical. If the particles are identical one arrives at the same results by a somewhat more complicated calculation.
This is only true if the spin and the magnetic moment are antiparallel as for the electron; otherwise the roles of the two counters must be interchanged. A factor 2 is included here in the definition of “spin components.”
The cautious reader might notice already, however, that from the point of view of quantum mechanics this hypothesis looks not so “ natural” after all, since it ascribes simultaneously fixed values to noncommuting observables.
This is the “reproducibility assumption “ of science : If an experiment is repeated it must reproduce the same result. (We neglect statistical fluctuations, which is justified for sufficiently large N.)
J. S. Bell, Physics 1, 195 (1964). Various forms of Bell’s inequalities are discussed in the review by J. F. Clauser and A. Shimony, Rep. Prog. Phys. 41, 1881 (1978).
See also A. Peres, Am. J. Phys. 46, 745 (1978).
N. F. Mott and H. S. W. Massey. The Theory of Atomic Collisions, 3rd ed., Section IX.2. Clarendon Press, Oxford, 1965.
M. Lamehi-Rachti and W. Mittig, Phys. Rev. D 14, 2543 (1976).
A. Aspect, P. Grangier, and G. Roger, Phys. Rev. Letters 49, 91 (1982)
A. Aspect, J. Dalibard, and G. Roger, Phys. Rev. Letters 49, 1804 (1982).
“No elementary quantum phenomenon is a phenomenon until it is an observed phenomenon.” (J. A. Wheeler.)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1986 Springer Science+Business Media New York
About this chapter
Cite this chapter
Bohm, A. (1986). Some Fundamental Properties of Quantum Mechanics. In: Quantum Mechanics: Foundations and Applications. Texts and Monographs in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-01168-3_13
Download citation
DOI: https://doi.org/10.1007/978-3-662-01168-3_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-13985-0
Online ISBN: 978-3-662-01168-3
eBook Packages: Springer Book Archive