Gyroscopic motion is used to explain why it is that there is maintenance of same or opposite axis of rotation orientation, by electron particles produced as a pair. Important for answering two important questions. Why can pairs of particles separated by large distances act as if they are coordinating their responses to tests? The proposed answer making faster than light communication between particles unnecessary. It also explains the strange semi permanence of propensity to give particular state outcomes for a repeated same test, that is lost when there is an intermediate different test. Two famous examples of supposed quantum strangeness.
Gyroscopic motion is used to explain why it is that there is maintenance of same or opposite axis of rotation orientation, by electron particles produced as a pair. Important for answering two important questions. Why can pairs of particles separated by large distances act as if they are coordinating their responses to tests? The proposed answer making faster than light communication between particles unnecessary. It also explains the strange semi permanence of propensity to give particular state outcomes for a repeated same test, that is lost when there is an intermediate different test. Two famous examples of supposed quantum strangeness.
It is suggested that a thorough treatment of electron spin has advantages as a method of presenting many of the concepts and techniques of intermediate quantum mechanics. The starting point is the Stern-Gerlach experiment, from which the anticommutation relations for the spin operators may immediately be deduced. The commutation relations, which demonstrate that the spin is an angular momentum, are derived from these and it is shown that the anomalous gyromagnetic ratio is a natural consequence of the properties of the spin operators. The Pauli theory, which is the simplest example of the use of matrices in quantum mechanics, is briefly summarised, and employed in an analysis of the double Stern-Gerlach experiment. This example of a change of representation is used to introduce Dirac's transformation theory which, together with a variant of the double Stern-Gerlach experiment, is made use of in a discussion of the EPR paradox, Bell's inequality and hidden-variable theories. It is emphasised that the quantum mechanical description of these phenomena is consistent and that, from the viewpoint of quantum theory, no action-at-a-distance is required to explain them.
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.
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.”
Abstract We analyze idealized sequential Stern–Gerlach (SG) experiments with higher spin particles. This analysis serves at least two purposes: the widely discussed spin-1/2 case leads to some misunderstandings since the probabilities are always evenly distributed for the sequential orthogonal magnets, which does not generalize to higher spins. A detailed discussion of the higher spin case, as is done here, is highly useful. Secondly, the Wigner rotation matrices for generic spins become conceptually more transparent with this physical example. We also give compact formulas for the probabilities in terms of the angle between the sequential SG apparatus for generic spins. We work out the spin-1/2, spin-1 cases explicitly. Since there are some confusing issues regarding the actual experiment, we also compile a ‘facts and fiction’ section on the SG experiments.
Entanglement is the superposition of two or more particles in multiple states. An example is given for the double-well potential; another involves particles with spin 1/2. Measurement of spin is carried out by a Stern–Gerlach apparatus, using the deflection of a spin by a magnet. Entangled spin-1/2 states, namely triplet states having total spin 1, and the singlet state, with spin 0, are also examined; the latter state appears in same form when expressed in spin up/down along any Cartesian coordinate. The determination of one of the spins in an entangled singlet state immediately determines the other, resulting in a “spooky action at a distance.” Einstein, Podolsky, and Rosen (EPR) claimed to show, on the basis of local realism, that quantum mechanics must be incomplete because of this feature. Their logic suggests that one might explain the instantaneous results by invoking “hidden variables” not contained in a quantum treatment.
The Stern–Gerlach experiment can play an important role in teaching the formalism of quantum mechanics. In the context of a finite-dimensional Hilbert space students can learn how to prepare a specific quantum state starting from an arbitrary state, issues related to the time evolution of the wave function and quantum measurement. The Stern–Gerlach experiment can also be used to teach the distinction between the physical space where the experiment is performed and the Hilbert space where the state of the system lies, and how information about the state of the system in the Hilbert space can be exploited to interpret the possible outcomes of the experiment in physical space. Students can learn the advantages of choosing an appropriate basis to make predictions about the outcomes of experiments with different arrangements of Stern–Gerlach devices. The latter can also help students understand that an ensemble of identically prepared systems is not the same as a mixture. We discuss student difficulties with the Stern–Gerlach experiment based on written tests and interviews with advanced undergraduate and graduate students in quantum mechanics courses. We also discuss preliminary data which suggest that the Quantum Interactive Learning Tutorial on the Stern–Gerlach experiment is helpful in improving student understanding of these concepts.