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CRC Press eBooks

Spin

Jonathan Allday

Published Mar 3, 2009• 0 citations
Publisher

Abstract

We have a couple of loose ends lying around. For one thing, I have yet to explain why it is that an electron passing through an S-G magnet can take only two paths. Up to now I have assumed that there’s some physical property belonging to the electron that determines which path it will take through the S-G magnetic eld. Of course this is a quantum mechanical property and so we have seen how the behavior of the electron depends on the context of the experiment as well.

DOI
10.1201/9781584887041-17

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We have a couple of loose ends lying around. For one thing, I have yet to explain why it is that an electron passing through an S-G magnet can take only two paths. Up to now I have assumed that there’s some physical property belonging to the electron that determines which path it will take through the S-G magnetic eld. Of course this is a quantum mechanical property and so we have seen how the behavior of the electron depends on the context of the experiment as well.
Since all experiments are subjected to the laws of quantum mechanics, the invalidity of the law of causality is definitively proved by quantum mechanics. (Heisenberg, 1927, p. 197, trans. in Stern, 1969, p. 132) THE PROBLEM OF INDETERMINISM If quantum mechanics is correct, on whatever interpretation, there are experimental setups such that no amount of observational knowledge of the initial system could possibly predict the outcome. An electron goes through a magnetic field in the Stern-Gerlach experiment in a superposed spin state | up > + | down >. It will take an upward or downward path through the magnetic field, and if quantum mechanics is correct, no observation of its physical configuration prior to the performance of this kind of experiment can possibly reveal which it will be. The standard indeterministic interpretation of quantum mechanics has it that not only can no observation of the prior physical properties of the system, including of the electron, allow us to predict the outcome of the experiment, but that the system lacks any physical properties, observable or not, such that were they known ahead of time, we would know what the outcome is. In other words, on this interpretation, two quantum mechanical systems that start with exactly the same intrinsic properties can behave in different ways. This is indeterminism. It is seen as challenging the PSR for exactly the reason libertarian free will is, but more deeply because the defender of libertarian free will can allow for indeterministic explanations involving the reasons for one action rather than another.
Models for the Helium Atom.---(1) Bohr's model is unsatisfactory because it gives too great a value for the ionizing potential and is not in accord with the optical and magnetic properties of helium. Now the chemical evidence suggests that each electron in an atom has its own separate orbit, and that these orbits are closely interrelated. Accordingly two new models are considered. (2) In the double circle model the two electrons are assumed to move in two separate, parallel, circular orbits. The model, however, is unstable, for the ionizing potential, computed by applying the quantum theory, comes out negative. Another objection is that the magnetic moment is not zero. (3) In the semi-circular model each electron is assumed to oscillate back and forth along an approximately semi-circular path in accord with classical mechanics, each being brought to rest at the end of its path by the repulsion of the other. Assuming the maximum angular momentum of each equal to $\frac{h}{2\ensuremath{\pi}}$, the absolute dimensions of the model were computed. The total energy comes out less than for the Bohr model, and the ionizing potential, 25.62 volts, agrees closely with the experimental value. The magnetic moment is zero.Application of the Quantum Theory to Coupled Electrons.---The success of the semi-circular model in giving the correct value for the ionizing potential of helium suggests that in the case of coupled electrons the quantum theory should be applied not to the momentum of the individual electrons according to the relation $\ensuremath{\int}\mathrm{pdq}=\frac{h}{2\ensuremath{\pi}}$, but rather to the momentum which, by being relayed from one electron to another, passes in each direction around the nucleus.
Models for the Helium Atom.---(1) Bohr's model is unsatisfactory because it gives too great a value for the ionizing potential and is not in accord with the optical and magnetic properties of helium. Now the chemical evidence suggests that each electron in an atom has its own separate orbit, and that these orbits are closely interrelated. Accordingly two new models are considered. (2) In the double circle model the two electrons are assumed to move in two separate, parallel, circular orbits. The model, however, is unstable, for the ionizing potential, computed by applying the quantum theory, comes out negative. Another objection is that the magnetic moment is not zero. (3) In the semi-circular model each electron is assumed to oscillate back and forth along an approximately semi-circular path in accord with classical mechanics, each being brought to rest at the end of its path by the repulsion of the other. Assuming the maximum angular momentum of each equal to $\frac{h}{2\ensuremath{\pi}}$, the absolute dimensions of the model were computed. The total energy comes out less than for the Bohr model, and the ionizing potential, 25.62 volts, agrees closely with the experimental value. The magnetic moment is zero.Application of the Quantum Theory to Coupled Electrons.---The success of the semi-circular model in giving the correct value for the ionizing potential of helium suggests that in the case of coupled electrons the quantum theory should be applied not to the momentum of the individual electrons according to the relation $\ensuremath{\int}\mathrm{pdq}=\frac{h}{2\ensuremath{\pi}}$, but rather to the momentum which, by being relayed from one electron to another, passes in each direction around the nucleus.