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Cambridge University Press eBooks

The Stern–Gerlach Experiment

Daniel F. Styer

Published Feb 24, 2000• 2 citations
Publisher

Abstract

Measuring magnetic projections What does the previous chapter have to do with quantum mechanics? I have said that the predictions of quantum mechanics are significantly different from those of classical mechanics only when applied to very small objects. How could we make such a tiny compass needle? In fact we don't need to make one, because nature itself supplies one. It is natural to suppose that an atom acts like a tiny magnetic needle because its orbiting electron mimics a current loop. In 1922, physicists Otto Stern and Walther Gerlach decided to test this supposition by measuring the magnetic arrow associated with a silver atom. It is clear that they could not do this by watching an individual atom precess in a uniform magnetic field! Instead, they injected a moving silver atom into a non-uniform field and noticed how the resulting force pushed the atom around. The “Stern–Gerlach apparatus” sketched on the next page thus measures the projection of an atom's magnetic arrow on the vertical axis. What results would you expect from this experiment? Think about this for a moment before reading on. Classical expectations I don't know about you, but here is what I would expect: Once the atom enters the non-uniform magnetic field, its magnetic arrow precesses in such a way that its projection on the vertical axis remains constant. While this precession is taking place, there is also a force on the atom, and the magnitude of that force depends upon the value of the projection. If the atom has a large positive projection, it will experience a large upward force and move up sharply.

DOI
10.1017/cbo9781107050709.004

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A Century Ago the Stern–Gerlach Experiment Ruled Unequivocally in Favor of Quantum Mechanics

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Abstract In 1921, Otto Stern conceived the idea for an experiment that would decide between a classical and a quantum description of atomic behavior, as epitomized by the Bohr–Sommerfeld–Debye model of the atom. This model entailed not only the quantization of the magnitude of the orbital electronic angular momentum but also of the projection of the angular momentum on an external magnetic field – the so‐called space quantization. Stern recognized that space quantization would have observable consequences: namely, that the magnetic dipole moment due to the orbital angular momentum would be space quantized as well, taking two opposite values for atoms whose only unpaired electron has just one quantum of orbital angular momentum. When acted upon by a suitable inhomogeneous magnetic field, a beam of such atoms would be split into two beams consisting of deflected atoms with opposite projections of the orbital angular momentum on the magnetic field. In contradistinction, if atoms behaved classically, the atomic beam would only broaden along the field gradient and have maximum intensity at zero deflection, i. e., where there would be a minimum or no intensity for a beam split due to space quantization. Stern anticipated that, although simple in principle, the experiment would be difficult to carry out – and invited Walther Gerlach to team up with him. Gerlach's realism and experimental skills together with his sometimes stubborn determination to make things work proved invaluable for the success of the Stern–Gerlach experiment (SGE). After a long struggle, Gerlach finally saw, on 8 February 1922, the splitting of a beam of silver atoms in a magnetic field. The absence of the concept of electron spin confused and confounded the interpretation of the SGE, as the silver atoms were, in fact, in a 2S state, with zero orbital and spin angular momentum. However, a key quantum feature whose existence the SGE was designed to test – namely space quantization of electronic angular momentum – was robust enough to transpire independent of whether the electronic angular momentum was orbital or due to spin. The SGE entails other key aspects of quantum mechanics such as quantum measurement, state preparation, coherence, and entanglement. Confronted with the outcome of the SGE, Stern noted: “I still have objections to the idea of beauty of quantum mechanics. But she is correct.”

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A New Interpretation of The Stern-Gerlach Experiment by Classical Physics

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A thorough motion investigation and analysis was conducted again for the original Stern-Gerlach Experiment(SGE). The analysis is still based on the assumption that the atom passing the SG apparatus is a micromagnet due to the spin of its electron, the atoms in the source beam are with an orientation distribution of its angular momentum vectors, while the spin micromagnet is in the precession induced by an inhomogeneous magnetic field. It is the precession that keeps the silver beam with narrower orientation distribution of its angular momentum vectors after passing through the inhomogeneous magnetic field. The motion relativity was introduced in the SGE between the SG apparatus and the silver source beam, which interpreted all the detection phenomena in the multi-stage SGE. The research provided a new and convincing interpretation to the SGE with full satisfaction based on the classical physics without any mysterious or counter intuitive concepts introduced compared to quantum physics.

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We calculate the effects of Larmor precession in the two-state Stern–Gerlach experiment performed with silver atoms. We compare the time constants and Q factors for an oscillating magnetic-dipole moment in free space and in close proximity to an iron magnet. Numerical modelling suggests that the original Stern–Gerlach experiment was too dissipative to have eliminated classical explanations. A recent experiment, also admitting a classical interpretation, is discussed briefly. A new experiment is proposed that should be able to confirm quantum mechanics unequivocally. PACS Nos.: 03.65Bz, 41.20Gz, 32.10Dk

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A detailed analysis of the classic Stern–Gerlach experiment is presented. An analytical simple solution is presented for the quantum description of the translational and spin dynamics of a silver atom in a magnetic field with a gradient along a single z-direction. This description is then used to obtain an approximate quantum description of the more realistic case with a magnetic field gradient also in a second y-direction. An explicit relation is derived for how an initial off center deviation in the y-direction affects the final result observed at the detector. This shows that the “mouth shape” pattern at the detector observed in the original Stern–Gerlach experiment is a generic consequence of the gradient in the y-direction. This is followed by a discussion of the spin dynamics during the entry of the silver atom into the magnet. An analytical relation is derived for a simplified case of a field only along the z-direction. A central question for the conceptual understanding of the Stern–Gerlach experiment has been how an initially unpolarized spin ends up in a polarized state at the detector. It is argued that this can be understood with the use of the adiabatic approximation. When the atoms first experience the magnetic field outside the magnet, there is in general a change in the spin state, which transforms from a degenerate eigenstate in the absence of a field into one of two possible non-degenerate states in the field. If the direction of the field changes during the passage through the device, there is a corresponding adiabatic change of the spin state. It is shown that an application of the adiabatic approximation in this way is consistent with the previously derived exact relations.

Entropy•Apr 25, 2017•14 citations
Measuring magnetic projections What does the previous chapter have to do with quantum mechanics? I have said that the predictions of quantum mechanics are significantly different from those of classical mechanics only when applied to very small objects. How could we make such a tiny compass needle? In fact we don't need to make one, because nature itself supplies one. It is natural to suppose that an atom acts like a tiny magnetic needle because its orbiting electron mimics a current loop. In 1922, physicists Otto Stern and Walther Gerlach decided to test this supposition by measuring the magnetic arrow associated with a silver atom. It is clear that they could not do this by watching an individual atom precess in a uniform magnetic field! Instead, they injected a moving silver atom into a non-uniform field and noticed how the resulting force pushed the atom around. The “Stern–Gerlach apparatus” sketched on the next page thus measures the projection of an atom's magnetic arrow on the vertical axis. What results would you expect from this experiment? Think about this for a moment before reading on. Classical expectations I don't know about you, but here is what I would expect: Once the atom enters the non-uniform magnetic field, its magnetic arrow precesses in such a way that its projection on the vertical axis remains constant. While this precession is taking place, there is also a force on the atom, and the magnitude of that force depends upon the value of the projection. If the atom has a large positive projection, it will experience a large upward force and move up sharply.
Abstract In 1921, Otto Stern conceived the idea for an experiment that would decide between a classical and a quantum description of atomic behavior, as epitomized by the Bohr–Sommerfeld–Debye model of the atom. This model entailed not only the quantization of the magnitude of the orbital electronic angular momentum but also of the projection of the angular momentum on an external magnetic field – the so‐called space quantization. Stern recognized that space quantization would have observable consequences: namely, that the magnetic dipole moment due to the orbital angular momentum would be space quantized as well, taking two opposite values for atoms whose only unpaired electron has just one quantum of orbital angular momentum. When acted upon by a suitable inhomogeneous magnetic field, a beam of such atoms would be split into two beams consisting of deflected atoms with opposite projections of the orbital angular momentum on the magnetic field. In contradistinction, if atoms behaved classically, the atomic beam would only broaden along the field gradient and have maximum intensity at zero deflection, i. e., where there would be a minimum or no intensity for a beam split due to space quantization. Stern anticipated that, although simple in principle, the experiment would be difficult to carry out – and invited Walther Gerlach to team up with him. Gerlach's realism and experimental skills together with his sometimes stubborn determination to make things work proved invaluable for the success of the Stern–Gerlach experiment (SGE). After a long struggle, Gerlach finally saw, on 8 February 1922, the splitting of a beam of silver atoms in a magnetic field. The absence of the concept of electron spin confused and confounded the interpretation of the SGE, as the silver atoms were, in fact, in a 2S state, with zero orbital and spin angular momentum. However, a key quantum feature whose existence the SGE was designed to test – namely space quantization of electronic angular momentum – was robust enough to transpire independent of whether the electronic angular momentum was orbital or due to spin. The SGE entails other key aspects of quantum mechanics such as quantum measurement, state preparation, coherence, and entanglement. Confronted with the outcome of the SGE, Stern noted: “I still have objections to the idea of beauty of quantum mechanics. But she is correct.”
A thorough motion investigation and analysis was conducted again for the original Stern-Gerlach Experiment(SGE). The analysis is still based on the assumption that the atom passing the SG apparatus is a micromagnet due to the spin of its electron, the atoms in the source beam are with an orientation distribution of its angular momentum vectors, while the spin micromagnet is in the precession induced by an inhomogeneous magnetic field. It is the precession that keeps the silver beam with narrower orientation distribution of its angular momentum vectors after passing through the inhomogeneous magnetic field. The motion relativity was introduced in the SGE between the SG apparatus and the silver source beam, which interpreted all the detection phenomena in the multi-stage SGE. The research provided a new and convincing interpretation to the SGE with full satisfaction based on the classical physics without any mysterious or counter intuitive concepts introduced compared to quantum physics.
We calculate the effects of Larmor precession in the two-state Stern–Gerlach experiment performed with silver atoms. We compare the time constants and Q factors for an oscillating magnetic-dipole moment in free space and in close proximity to an iron magnet. Numerical modelling suggests that the original Stern–Gerlach experiment was too dissipative to have eliminated classical explanations. A recent experiment, also admitting a classical interpretation, is discussed briefly. A new experiment is proposed that should be able to confirm quantum mechanics unequivocally. PACS Nos.: 03.65Bz, 41.20Gz, 32.10Dk
Abstract For nearly one hundred years most quantum-mechanics texts have depicted a continuous, spin-direction superposition of the wavefunction of the silver atom traversing a Stern–Gerlach (S–G) magnet. But there are sound scientific arguments which deny that understanding. Schrodinger’s equation for that continuous wavefunction development cannot describe the transfer of energy from the magnetic field to that atom. Modern micro-fabrication techniques now make it possible to implement a simple, accessible experiment testing whether a spin superposition does continue in the magnet. Because the S–G experiment is the prototype for quantum measurement, that observation is crucial to implementing a realistic quantum theory of measurement.
A detailed analysis of the classic Stern–Gerlach experiment is presented. An analytical simple solution is presented for the quantum description of the translational and spin dynamics of a silver atom in a magnetic field with a gradient along a single z-direction. This description is then used to obtain an approximate quantum description of the more realistic case with a magnetic field gradient also in a second y-direction. An explicit relation is derived for how an initial off center deviation in the y-direction affects the final result observed at the detector. This shows that the “mouth shape” pattern at the detector observed in the original Stern–Gerlach experiment is a generic consequence of the gradient in the y-direction. This is followed by a discussion of the spin dynamics during the entry of the silver atom into the magnet. An analytical relation is derived for a simplified case of a field only along the z-direction. A central question for the conceptual understanding of the Stern–Gerlach experiment has been how an initially unpolarized spin ends up in a polarized state at the detector. It is argued that this can be understood with the use of the adiabatic approximation. When the atoms first experience the magnetic field outside the magnet, there is in general a change in the spin state, which transforms from a degenerate eigenstate in the absence of a field into one of two possible non-degenerate states in the field. If the direction of the field changes during the passage through the device, there is a corresponding adiabatic change of the spin state. It is shown that an application of the adiabatic approximation in this way is consistent with the previously derived exact relations.