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.
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.
We have learned a lot about quantum mechanics already. We learned it is probabilistic and that it can have indeterminate behavior until measured. The Nobel Prize winner, Richard Feynman, summed this up the best with the following quote from his famous The Feynman Lectures in Physics: “We have implied that in our experimental arrangement (or even in the best possible one) it would be impossible to predict exactly what would happen. We can only predict the odds! This would mean, if it were true, that physics has given up on the problem of trying to predict exactly what will happen in a definite circumstance. Yes! Physics has given up. We do not know how to predict what would happen in a given circumstance, and we believe now that it is impossible-that the only thing that can be predicted is the probability of different events. It must be recognized that this is a retrenchment in our earlier ideal of understanding nature. It may be a backward step, but no one has seen a way to avoid it ⋯ So at the present time we must limit ourselves to computing probabilities. We say ‘at the present time,’ but we suspect very strongly that it is something that will be with us forever-that it is impossible to beat that puzzle-that this is the way nature really is.” Physicists are troubled that this is the way the real world is, but we have come to accept it so we can learn more about the mysteries of the real world. We examine advanced ideas surrounding the Stern-Gerlach experiment and its extensions including delayed-choice experiments, interaction-free experiments, and Bell experiments.
The nature of the problem The quantum world is inexplicable in classical terms. The predictions pertaining to the interaction of matter and light embodied in Newton's laws for the motion of particles and Maxwell's equations governing the propagation of electromagnetic fields are in flat contradiction with the experimental facts at the microscopic scale. A key feature of quantum effects is their apparent indeterminism, that individual atomic events are unpredictable, uncontrollable and literally seem to have no cause. Regularities emerge only when one considers a large ensemble of such events. This indeed is generally considered to constitute the heart of the conceptual problem posed by quantum phenomena, necessitating a fundamental revision of the deterministic classical world view. Some of the principal phenomena, among those discussed in this book, are as follows: ( a ) Self-interference: a beam of electrons sent one at a time through a barrier containing two apertures builds up through a series of localized detection events on a screen an interference pattern characteristic of waves (cf. the frontispiece and §5.1). ( b ) Tunnelling: an α-particle trapped in a nucleus can pass through a potential barrier in a manner forbidden to a classical particle (§5.3). ( c ) The stability of matter: atoms and molecules are found to exist only in certain discrete, or ‘stationary’, energy states. For this reason they do not ‘collapse’, the result predicted by classical electrodynamics. During transitions between stationary states (quantum jumps) an atom exchanges a discrete quantity of energy with the electromagnetic field (§§4.5, 7.6). […]
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.
In previous chapters we presented and discussed the standard, generally accepted Copenhagen interpretation of quantum mechanics according to which there exists in nature at the most fundamental level an irreducible and ineliminable indeterminism. Although we saw that what historically constituted the Copenhagen interpretation of quantum mechanics is difficult to specify with precision, three central commitments do characterize it. (1) In general, no particle trajectories can exist in a space–time background. (2) No deterministic description of fundamental physical phenomena is possible. (3) There exists in the laws of the fundamental physical phenomena of nature an essential and ineliminable indeterminism or probability (unlike the probability of classical physics, that there reflects our ignorance of the finer details of complex physical phenomena). A flavor of these features of the Copenhagen interpretation of quantum mechanics can be gotten from the quotations at the beginning of Part VIII ( Some philosophical lessons from quantum mechanics ). On this view, it is in principle impossible to predict, say, the exact future behavior of an electron (that is, to give its position and velocity as functions of the time). According to the Copenhagen school, there can be no causal description of microphenomena in terms of a continuous space–time background (as there is in classical physics). It is generally believed that a causal interpretation of quantum mechanics is impossible, although no proof of this exists.
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.
One of the aspects of quantum theory which has attracted the most general attention, is the novelty of the logical notions which it presupposes. It asserts that even a complete mathematical description of a physical system S does not in general enable one to predict with certainty the result of an experiment on S, and that in particular one can never predict with certainty both the position and the momentum of S, (Heisenberg’s Uncertainty Principle). It further asserts that most pairs of observations are incompatible, and cannot be made on S, simultaneously (Principle of Non-commutativity of Observations).