The bulk of experiments and observations that lined the path to quantum mechanics amounted to a backlog of data in need of explanation. A notable exception was the Stern-Gerlach experiment (SGE) designed to test the predictions of the Old Quantum Theory as embodied by the 1913-1916 Bohr-Sommerfeld-Debye atom model. After its initial triumphs, such as the explanation of the astrophysically observed spectrum of He+, this model was frowned upon in some quarters, mainly because of its ad hoc nature. Otto Stern (1888-1969) – and his close colleague and friend, Max von Laue (1879-1960) – even took a vow: “If this nonsense of Bohr should, in the end, prove to be right, we will quit physics.” Stern would go further yet and, in 1920, devise an experiment – the SGE – to disprove Bohr’s model. However, contrary to Stern’s expectations, the SGE ruled unequivocally in favor of the model and its amendments. Wolfgang Pauli (1900-1958) quipped: “That should convert even the non-believer Stern.” And it did: Confronted with the outcome of the SGE, Stern noted in 1961: “I still have objections to the idea of beauty of quantum mechanics. But she is correct.” Ironically, the SGE would epitomize quantum mechanics as we know it: whether quantum measurement, state preparation, coherence, or entanglement – apart from the quantization of angular momentum and its spatial projections – the SGE has it all. The descendants of the SGE include transformative techniques for the study of the quantum properties of nuclear, atomic, molecular, and condensed-matter systems, with Magnetic Resonance Imaging (MRI) being among the most widely used.
The bulk of experiments and observations that lined the path to quantum mechanics amounted to a backlog of data in need of explanation. A notable exception was the Stern-Gerlach experiment (SGE) designed to test the predictions of the Old Quantum Theory as embodied by the 1913-1916 Bohr-Sommerfeld-Debye atom model. After its initial triumphs, such as the explanation of the astrophysically observed spectrum of He+, this model was frowned upon in some quarters, mainly because of its ad hoc nature. Otto Stern (1888-1969) – and his close colleague and friend, Max von Laue (1879-1960) – even took a vow: “If this nonsense of Bohr should, in the end, prove to be right, we will quit physics.” Stern would go further yet and, in 1920, devise an experiment – the SGE – to disprove Bohr’s model. However, contrary to Stern’s expectations, the SGE ruled unequivocally in favor of the model and its amendments. Wolfgang Pauli (1900-1958) quipped: “That should convert even the non-believer Stern.” And it did: Confronted with the outcome of the SGE, Stern noted in 1961: “I still have objections to the idea of beauty of quantum mechanics. But she is correct.” Ironically, the SGE would epitomize quantum mechanics as we know it: whether quantum measurement, state preparation, coherence, or entanglement – apart from the quantization of angular momentum and its spatial projections – the SGE has it all. The descendants of the SGE include transformative techniques for the study of the quantum properties of nuclear, atomic, molecular, and condensed-matter systems, with Magnetic Resonance Imaging (MRI) being among the most widely used.
ABSTRACT The bulk of experiments and observations that lined the path to quantum mechanics amounted to a backlog of data in need of explanation. A notable exception was the Stern–Gerlach experiment (SGE) designed to test the predictions of the old quantum theory as embodied by the 1913–1916 Bohr–Sommerfeld–Debye atom model. After its initial triumphs, such as the explanation of the astrophysically observed spectrum of , this model was frowned upon in some quarters, mainly because of its ad hoc nature. Otto Stern (1888–1969)—and his close colleague and friend, Max von Laue (1879–1960)—even took a vow: “If this nonsense of Bohr should, in the end, prove to be right, we will quit physics.” Stern would go further yet and, in 1920, devise an experiment—the SGE—to disprove Bohr's model. However, contrary to Stern's expectations, the SGE ruled unequivocally in favor of the model and its amendments. Wolfgang Pauli (1900–1958) quipped: “That should convert even the non‐believer Stern.” And it did: Confronted with the outcome of the SGE, Stern noted in 1961: “I still have objections to the idea of beauty of quantum mechanics. But she is correct.” Ironically, the SGE would epitomize quantum mechanics as we know it: whether quantum measurement, state preparation, coherence, or entanglement—in addition to the quantization of angular momentum and its spatial projections—the SGE has it all. It now seems that the SGE may even impact future studies of the relationship of quantum theory to other pillars of physics, most notably, general relativity. The descendants of the SGE include transformative techniques for the study of the quantum properties of nuclear, atomic, molecular, and condensed‐matter systems, with magnetic resonance imaging being among the most widely used. Key Points Edward Pickering; Williamina Fleming; Pickering series; Bohr‐Sommerfeld‐Debye model of the atom; Otto Stern; Stern‐Gerlach experiment; Bohr magneton; Old Quantum Theory; Spin; nuclear magneton; magnetic dipole moment of the proton; matter‐wave duality; Quantum Mechanics.
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.”
The Stern-Gerlach experiment (SGE) has been known for decades, but a complete theory that explains all facets of it remains enigmatic. In its classic realization, each spin state of an atom follows a unique path or trajectory in an SGE. The enigmatic part is the final output of SGE. Feynman envisaged the outcome to be an entangled state, a superposition of $|\text{spin}\phantom{\rule{4.pt}{0ex}}\text{state}\ensuremath{\rangle}\ensuremath{\bigotimes}|\text{corresponding}\phantom{\rule{4.pt}{0ex}}\text{path}\ensuremath{\rangle}$. Later works described the final state of SGE as a mixed state, a weighted average of states belonging to separate beams or trajectories. Notably, Schwinger, Englert, and Scully compared the difficulty of obtaining a coherent output (a pure state) to ``putting together Humpty Dumpty'' again. Yet recent experiments using Bose-Einstein condensates indicate the emerging beams are partly coherent, favoring Feynman's description. In this work, we revisit SGE using a recent version of the quantum master equation. We show that both outcomes are probable depending on the time of flight and the timescale of the environmental fluctuations. We predict the output is initially coherent and grows gradually into a mixed state. Moreover, we also estimate how the magnetic-field gradient helps broaden the beam waist. Moreover, our treatment implies that the wave function of an atom passing through a Stern-Gerlach device does not undergo an instantaneous collapse; rather, a gradual decay of coherences results in a mixed state, resulting in an irreversible process.
While the Stern–Gerlach experiment is an old and familiar problem, no analysis of this experiment is presented in the pedagogical literature using modern quantum mechanical techniques. Expositions of the Stern–Gerlach experiment are usually based on ‘‘old quantum theory,’’ i.e., semiclassical Bohr–Sommerfeld quantum mechanics. The experiment is also a popular one in discussions of the postulate of quantum measurement, which asserts that the process of measuring an observable forces the state vector of the system into an eigenvector of that observable, and the value measured will be the eigenvalue of that eigenvector. The most enduring of the philosophical arguments associated with quantum mechanics ultimately revolves around the mechanism of quantum measurement. Since the postulate of quantum measurement is expressed in terms well outside the realm of the old quantum mechanics, the traditional analysis of the Stern–Gerlach experiment cannot reveal any information about the relationship between dynamics and measurement. Therefore, a modern analysis of the Stern–Gerlach experiment must be made if this experiment is to reveal any information about the relationship between dynamics and the mechanism of quantum measurement. This paper presents such an analysis, and develops some of the implications for the theory of quantum measurement.
Abstract Motivated by his interest in thermodynamics and the emerging quantum mechanics, Otto Stern (1888–1969) launched in 1919 his molecular beam method to examine the fundamental assumptions of theory that transpire in atomic, molecular, optical, and nuclear physics. Stern’s experimental endeavors at Frankfurt (1919–1922), Hamburg (1923–1933), and Pittsburgh (1933–1945) provided insights into the quantum world that were independent of spectroscopy and that concerned well-defined isolated systems, hitherto accessible only toGedankenexperiments. In this chapter we look at how Stern’s molecular beam research came about and review six of his seminal experiments along with their context and reception by the physics community: the Stern-Gerlach experiment; the three-stage Stern-Gerlach experiment; experimental evidence for de Broglie’s matter waves; measurements of the magnetic dipole moment of the proton and the deuteron; experimental demonstration of momentum transfer upon absorption or emission of a photon; the experimental verification of the Maxwell-Boltzmann velocity distribution via deflection of a molecular beam by gravity. Regarded as paragons of thoroughness and ingenuity, these experiments entail accurate transversal momentum measurements with resolution better than 0.1 atomic units. Some of these experiments would be taken up by others where Stern left off only decades later (matter-wave scattering or photon momentum transfer). We conclude by highlighting aspects of Stern’s legacy as reflected by the honors that have been bestowed upon him to date.
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.