An experimental apparatus based on neutron interferometry is is presented which can in principle decide the question whether the empty waves of de Broglie really exist or not.

A brief history of Neutron Interferometry is presented, from a personal perspective. Comments and a message from Professor Sam Werner are included.

If the energy-absorbing radio-frequency spin-flipping device used in perfect crystal neutron interferometry is an intermediate measuring device, then the experimental results contradict the associated wave packet collapse and support the real existence of the de Broglie pilot waves in both arms while the neutron travels in only one.

On the 25th anniversary of Berry’s historic papers on the geometric phase, I discuss here our neutron interferometry experiment in which this phase is clearly separated from the dynamical phase. The connection of this experiment to the observation of the sign reversal of the wave function of a fermion during a 2π precession in a magnetic field by three groups independently in 1975 is discussed.

In 1975, two experimental groups have independently observed the \-symmetry of neutrons’ spin, when passing through a static magnetic field, using a three-blade interferometer made from a single perfect Si-crystal. In this article, we provide a complete analysis of the experiment, both from a theoretical and conceptual point of view. Firstly, we solve the Schrödinger equation in the weak potential approximation, to obtain the amplitude of the refracted and forward refracted beams, produced by the passage of neutrons through one of (...) the three plates of the LLL interferometer. Secondly, we analyze their passage through a static magnetic field region. This allows us to find explicit expressions for the intensities of the four beams exiting the interferometer, two of which will be interfering and show a typical \-symmetry, when the strength of the magnetic field is varied. In the last part of the article, we provide a conceptual analysis of the experiment, showing that a neutron’s phase change, when passing through the magnetic field, is due to a longitudinal Stern–Gerlach effect, and not to a Larmor precession. We also emphasize that these experiments do not prove the observability of the sign change of the wave function, when a neutron is \ rotated, but strongly indicate that the latter, like any other elementary “particle,” would be a genuinely non-spatial entity. (shrink)

Properties sometimes attributed to the “particle” aspect of a neutron, e.g., mass and magnetic moment, cannot straightforwardly be regarded in the Bohm interpretation of quantum mechanics as localized at the hypothetical position of the particle. This is shown by examining a series of effects in neutron interferometry. A related thought-experiment also provides a variation of a recent demonstration that which-way detectors can appear to behave anomolously in the Bohm theory.

Initially Einstein, Podolsky, and Rosen (EPR) and later Bell shed light on the non-local properties exhibited by subsystems in quantum mechanics. Separately, Kochen and Specker analyzed sets of measurements of compatible observables and found that a consistent coexistence of these results is impossible, i.e., quantum indefiniteness of measurement results. As a consequence, quantum contextuality, a more general concept compared to non-locality, leads to striking phenomena predicted by quantum theory. Here, we report neutron interferometric experiments which investigate entangled states in (...) a single-particle system: entanglement is, in this case, achieved not between particles, but between degrees of freedom i.e., between spin, path, and energy degrees of freedom. Appropriate combinations of the spin analysis and the position of the phase shifter in the interferometer allow an experimental verification of the violation of a Bell-like inequality. In addition, state tomography, tomographic analysis of the density matrix of a quantum system, and Kochen-Specker-like phenomena are presented to characterize neutrons’ entangled states and their peculiarity. Furthermore, a coherent energy manipulation scheme is accomplished with a radio-frequency (RF) spin-flipper. This scheme allows the (total) energy degree of freedom to be entangled: the remarkable behavior of a triply entangled GHZ-like state is demonstrated. (shrink)

Using a neutron interferometer and the phase difference calculated from spatial discrete quantum mechanics, a test for discrete quantum theory may implemented by measuring the X spin polarization and its variation with position.

We compare a “Mach-Zehnder interferometer in time” for cold neutrons with its well-known spatial counterpart and demonstrate the intimate connection between space and time for both setups. Further, we outline a combined space-time interferometer, which coherently splits a wavepacket in longitudinal and lateral direction. On the way towards time interferometry “neutron computer holography” seems to be an attractive application. It allows the three-dimensional reconstruction of an object from the scattered intensity, but in contrast to holography with light, there (...) is no need for a reference wave. On the other hand, the possible resolution is worse than in the light case. (shrink)

Neutron matter-wave optics provides the basis for new quantum experiments and a step towards applications of quantum phenomena. Most experiments have been performed with a perfect crystal neutron interferometer where widely separated coherent beams can be manipulated individually. Various geometric phases have been measured and their robustness against fluctuation effects has been proven, which may become a useful property for advanced quantum communication. Quantum contextuality for single particle systems shows that quantum correlations are to some extent more demanding (...) than classical ones. In this case entanglement between external and internal degrees of freedom offers new insights into basic laws of quantum physics. Non-contextuality hidden variable theories can be rejected by arguments based on the Kochen-Specker theorem. (shrink)

In 1974 perfect crystal interferometry has been developed and immediately afterwards the 4π-symmetry of spinor wave-functions has been verified. The new method opened a new access to the observation of intrinsic quantum phenomena. Spin-superposition, quantum state reconstruction and quantum beat effects are examples of such investigations. In this connection efforts have been made to separate and measure various dynamical and geometrical phases. Non-cyclic and non-adiabatic topological phases have been identified and their stability against various fluctuations and dissipative forces has (...) been investigated by means of ultra-cold neutrons. An entanglement between different degrees of freedom of a single neutron system demonstrated the contextuality feature of quantum mechanics. In its continuation this yields to Kochen-Specker theorem like investigations providing a new basis for information processing and for the understanding of quantum physics in general. All investigations show the equivalence of various phase spaces and show how physical phenomena are correlated by quantum laws. Some curiosa occurred during the experiments and some epistemological aspects will be discussed as well. (shrink)

The wave-particle dualism becomes very obvious in matter wave interference experiments. Neutron interferometers based on wave front and amplitude division have been developed in the past. Most experiments have been performed with the perfect crystal neutron interferometer, which provides widely separated coherent beams allowing new experiments in the field of fundamental, nuclear, and solid-state physics. A nondispersive sample arrangement and the difference of stochastic and deterministic absorption have been investigated. In case of a deterministic absorption process the attenuation (...) of the interference pattern is proportional to the beam attenuation, whereas in case of stochastic absorption it is proportional to the square root of the attenuation. This permits the formulation of Bell-like inequalities which will be discussed in detail. The verification of the4π symmetry of spinors and of the quantum mechanical spin-superposition experiment on a macroscopic scale are typical examples of interferometry in spin space. These experiments were continued with two resonance coils in the beams, where the results showed that coherence persists, even if an energy exchange between the neutron and the resonator system occurs with certainty. A quantum beat effect was observed when slightly different resonance frequencies were applied to both beams. In this case, the extremely high energy sensitivity of2.7×10 −19 eV was achieved. This effect can be interpreted as a magnetic Josephson-effect analog. Phase echo systems and experiments with pulsed beams show how interference phenomena can be made visible by a proper beam handling inside and behind the interferometer. All the results obtained until now are in agreement with the formalism of quantum mechanics but stimulate the discussion about the interpretation of this basic theory. (shrink)

A compatible statistical interpretation of a wave packet is proposed. De Broglian probabilities which unite wave and particle features of quantons are evaluated for free wave packets and Jor a superposition of wave packets. The obtained expressions provide a very plausible and physically appealing explanation of coherence in apparently incoherent beams and of the characteristic modulation of the momentum distribution, found recently in neutron interferometry combined with spectral filtering. Certain conclusions about dualism and objectivity in quantum domain are (...) also derived. (shrink)

David Bohm published his “Suggested Interpretation of Quantum Theory in Terms of Hidden Variables” some twenty five years after Louis de Broglie first presented his similar Pilot Wave theory of quantum mechanics. In the following 30 years what became known as the de Broglie–Bohm approach to quantum theory was to a large extent ignored within the physics community. Even David Bohm himself became somewhat disillusioned with the lack of impact of his interpretation of quantum theory and he directed his interest (...) elsewhere. But some 27 years after Bohm had published his interpretation of quantum theory, interest was rekindled in part by new, detailed calculations that demonstrated clearly and graphically, exactly how his interpretation explained quantum phenomena in terms of well defined individual particle trajectories. These computations encompassed two-slit interference, quantum tunnelling, neutron interferometry, Wheeler’s delayed choice experiment, orbital and intrinsic angular momentum, quantum measurement and Einstein–Podolsky–Rosen nonlocal correlations for orbital angular momentum, intrinsic angular momentum and correlated particle interferometry. Since then, the acceptance of the validity of de Broglie–Bohm theory has steadily grown, as has the interest in the consequences of the approach. For my contribution to the current celebratory volume I was asked to provide a personal review specifically of this novel work within its historical context of the last quarter of the twentieth century. (shrink)

The Schrödinger equation for a particle of rest mass $m$ and electrical charge $ne$ interacting with a four-vector potential $A_i$ can be derived as the non-relativistic limit of the Klein–Gordon equation $\left( \Box '+m^2\right) \varPsi =0$ for the wave function $\varPsi $ , where $\Box '=\eta ^{jk}\partial '_j\partial '_k$ and $\partial '_j=\partial _j -\mathrm {i}n e A_j$ , or equivalently from the one-dimensional action $S_1=-\int m ds +\int neA_i dx^i$ for the corresponding point particle in the semi-classical approximation $\varPsi \sim (...) \exp {(\mathrm {i}S_1)}$ , both methods yielding the equation $\mathrm {i}\partial _0\varPsi \approx \left( \frac{1}{2m}\eta ^{\alpha \beta }\partial '_{\alpha }\partial '_{\beta } + m + n e\phi \right) \varPsi $ in Minkowski space–time , where $\alpha ,\beta =1,2,3$ and $\phi =-A_0$ . We show that these two methods generally yield equations that differ in a curved background space–time $g_{ij}$ , although they coincide when $g_{0\alpha }=0$ if $m$ is replaced by the effective mass $\mathcal{M}\equiv \sqrt{m^2-\xi R}$ in both the Klein–Gordon action $S$ and $S_1$ , allowing for non-minimal coupling to the gravitational field, where $R$ is the Ricci scalar and $\xi $ is a constant. In this case $\mathrm {i}\partial _0\varPsi \approx \left( \frac{1}{2\mathcal{M}'} g^{\alpha \beta }\partial '_{\alpha }\partial '_{\beta } + \mathcal{M}\phi ^{(\mathrm g)} + n e\phi \right) \varPsi $ , where $\phi ^{(\mathrm g)} =\sqrt{g_{00}}$ and $\mathcal{M}'=\mathcal{M}/\phi ^{(\mathrm g)} $ , the correctness of the gravitational contribution to the potential having been verified to linear order $m\phi ^{(\mathrm g)} $ in the thermal-neutron beam interferometry experiment due to Colella et al. Setting $n=2$ and regarding $\varPsi $ as the quasi-particle wave function, or order parameter, we obtain the generalization of the fundamental macroscopic Ginzburg-Landau equation of superconductivity to curved space–time. Conservation of probability and electrical current requires both electromagnetic gauge and space–time coordinate conditions to be imposed, which exemplifies the gravito-electromagnetic analogy, particularly in the stationary case, when div ${{\varvec{A}}}=\hbox {div}{{\varvec{A}}}^{(\mathrm g)}=0$ , where ${{\varvec{A}}}^{\alpha }=-A^{\alpha }$ and ${{\varvec{A}}}^{(\mathrm g)\alpha }=-\phi ^{(\mathrm g)}g^{0\alpha }$ . The quantum-cosmological Schrödinger (Wheeler–DeWitt) equation is also discussed in the $\mathcal{D}$ -dimensional mini-superspace idealization, with particular regard to the vacuum potential $\mathcal V$ and the characteristics of the ground state, assuming a gravitational Lagrangian $L_\mathcal{D}$ which contains higher-derivative terms up to order $\mathcal{R}^4$ . For the heterotic superstring theory , $L_\mathcal{D}$ consists of an infinite series in $\alpha '\mathcal{R}$ , where $\alpha '$ is the Regge slope parameter, and in the perturbative approximation $\alpha '|\mathcal{R}| \ll 1$ , $\mathcal V$ is positive semi-definite for $\mathcal{D} \ge 4$ . The maximally symmetric ground state satisfying the field equations is Minkowski space for $3\le {\mathcal {D}}\le 7$ and anti-de Sitter space for $8 \le \mathcal {D} \le 10$. (shrink)

In this paper some topics concerning the possibility of describing phenomena of quantum interference in terms of individual particle spacetime trajectories are reviewed. We focus our attention, on the one hand, on the recent experimental advances in neutron and photon interferometry and, on the other hand, on a theoretical analysis of the description of these experiments allowed by stochastic mechanics. It is argued that, even if no conclusive argument is yet at hand in both the theoretical and the (...) experimental fields, the researches of the last 10 years now seem to favor Einstein's and de Broglie's realistic spacetime description and interpretation of quantum mechanics. (shrink)

For many physicists quantum theory contains strong conceptual difficulties, while for others the apparent conclusions about the reality of our physical world and the ways in which we discover that reality remain philosophically unacceptable. This book focuses on recent theoretical and experimental developments in the foundations of quantum physics, including topics such as the puzzles and paradoxes which appear when general relativity and quantum mechanics are combined; the emergence of classical properties from quantum mechanics; stochastic electrodynamics; EPR experiments and Bell's (...) Theorem; the consistent histories approach and the problem of datum uniqueness in quantum mechanics; non-local measurements and teleportation of quantum states; quantum non-demolition measurements in optics and matter wave properties observed by neutron, electron and atomic interferometry. Audience: This volume is intended for graduate students of physics and those interested in the foundations of quantum theory. (shrink)

This book presents a collection of novel contributions and reviews by renowned researchers in the foundations of quantum physics, quantum optics, and neutron physics. It is published in honor of Michael Horne, whose exceptionally clear and groundbreaking work in the foundations of quantum mechanics and interferometry, both of photons and of neutrons, has provided penetrating insight into the implications of modern physics for our understanding of the physical world. He is perhaps best known for the Clauser-Horne-Shimony-Holt (CHSH) inequality. (...) This collection includes an oral history of Michael Horne's contributions to the foundations of physics and his connections to other eminent figures in the history of the subject, among them Clifford Shull and Abner Shimony. Among the editors and contributors are John Clauser and Anton Zeilinger, recipients of the Nobel Prize in Physics 2022. (shrink)

The new techniques and ideas in quantum interferometry with neutrons, photons, atoms, electrons, and Bose condensates that fluorished in the last two decades have influenced in a decisive way the thinking and the research in the foundations and interpretation of quantum mechanics. The controversies existing among different schools on the reality of matter waves of quantum theory, the postulates of quantum measurement theory, and the (in)completeness of quantum mechanics have to be approached now in a new way. Our argumentation (...) follows the spirit of the Paris school. (shrink)

This paper presents the results of optical interferometry experiments in which the phase of photons in one arm of a Mach-Zehnder interferometer is modified by applying a transverse constriction. An equivalent quantum interferometry experiment using neutron de Broglie waves is discussed in which the observed phase shift is in the spirit of the force-free phase shift of the Aharonov-Bohm effects. In the optical experiments the experimental results are in excellent agreement with predictions.

Isolated neutron stars undergoing non-radial oscillations are expected to emit gravitational waves in the kilohertz frequency range. To date, radio astronomers have located about 1,300 pulsars, and can estimate that there are about 2×108 neutron stars in the galaxy. Many of these are surely old and cold enough that their interiors will contain matter in the superfluid or superconducting state. In fact, the so-called glitch phenomenon in pulsars (a sudden spin-up of the pulsar's crust) is best described by (...) assuming the presence of superfluid neutrons and superconducting protons in the inner crusts and cores of the pulsars. Recently there has been much progress on modelling the dynamics of superfluid neutron stars in both the Newtonian and general relativistic regimes. We will discuss some of the main results of this recent work, perhaps the most important being that superfluidity should affect the gravitational waves from neutron stars (emitted, for instance, during a glitch) by modifying both the rotational properties of the background star and the modes of oscillation of the perturbed configuration. Finally, we present an analysis of the so-called zero-frequency subspace (i.e., the space of time-independent perturbations) and determine that it is spanned by two sets of polar (or spheroidal) and two sets of axial (or toroidal) degenerate perturbations for the general relativistic system. As in the Newtonian case, the polar perturbations are the g-modes which are missing from the pulsation spectrum of a non-rotating configuration, and the axial perturbations should lead to two sets of r-modes when the degeneracy of the frequencies is broken by having the background rotate. (shrink)

A Michelson interferometer with a phase-conjugate mirror (PCM) is described and discussed. The behavior of phase conjugate mirrors is discussed and the result of an experiment with a Michelson interferometer with a phase-conjugate mirror is described and commented. This interferometer has been proposed to be used to test the intrinsic non-locality of quantum mechanics. In this paper a new experimental setup to study the one-way velocity of light is proposed, which uses this new interesting device.

"Elements of Neutron Interaction Theory" is a first-year textbook for graduate students in nuclear engineering, dealing with the interactions of neutrons, photons, and charged particles with nuclei, atoms, and electrons. The aim of the book is to present, as simply as possible, those aspects of neutron interaction theory which follow directly from conservation laws and elementary quantum mechanics. It is intended to be understood by anyone who has obtained the equivalent of a bachelor's degree in physics, chemistry, or (...) one of the engineering disciplines. No mathematical background beyond differential equations and elementary vector analysis and no physics background beyond elementary modern physics is assumed. (shrink)

The first nuclear engineers emerged from the Manhattan Project in the USA, UK and Canada, but remained hidden behind security for a further decade. Cosseted and cloistered by their governments, they worked to explore applications of atomic energy at a handful of national labs. This unique bottom-up history traces how the identities of these unusually voiceless experts - forming a uniquely state-managed discipline - were shaped in the context of pre-war nuclear physics, wartime industrial management, post-war politics and utopian energy (...) programmes. Even after their eventual emergence at universities and companies, nuclear workers carried the enduring legacy of their origins. Their shared experiences shaped not only their identities, but our collective memories of the late twentieth century. And as illustrated by the Fukushima accident seven decades after the Manhattan project began, this book explains why they are still seen conflictingly as selfless heroes or as mistrusted guardians of a malevolent genie. (shrink)

Working in a freely falling frame and starting from the de Broglie and Einstein relations, we calculate the relative phase of monoenergetic Schrödinger radiation in an interferometer at rest in a gravity field.

The ArgumentEinstein's mass-energy relationship was not confirmed experimentally until 1933 when Bainbridge showed that the Cockcroft-Walton experiment afforded a test of it. Earlier, however, it had been used constantly in the analysis of nuclear reactions, as can be seen in those involved in the determination of the mass of the neutron. Chadwick in 1932 was convinced that the neutron mass was about 1.0067 amu (atomic mass units), indicating that the neutron was a proton-electron compound, since that figure (...) was less than the sum of the proton and electron masses. Chadwick's value was challenged in 1933 by Lawrence, who proposed a much lower value of 1.0006 amu, and by Curie and Joliot, who proposed a much higher value of 1.011 amu.Much controversy ensued; eventually, Chadwick and Goldhaber showed in 1934 that the neutron mass was about 1.0080 amu, greater than the sum of the proton and electron masses, proving that the neutron was a new elementary particle (which could decay spontaneously), and providing conclusive experimental support for excluding electrons from the nucleus. These results remained unchanged with further refinements in the last decimal place, the entire pursuit of which provided still further vindication of Einstein's massenergy relationship. (shrink)

ABSTRACT This essay focuses on the history of one of the “atomic patents.” The patent, which described a process to slow down neutrons in nuclear reactions, was the result of experimental research conducted in the 1930s by Enrico Fermi and his group at the Institute of Physics, University of Rome. The value of the patented process became clear during World War II, as it was involved in most of the military and industrial applications of atomic energy. This ignited a controversy (...) between Fermi and U.S. government representatives over royalties to be paid for use of the process during and after the war. The controversy sheds new light on the role that the management of patents played in the context of the Manhattan Project and in the postwar U.S. nuclear program, encompassing issues of power and economic influence in the relationship between scientists, the military, and public administrators. The invention covered by Patent No. 2,206,634 covers the basic process used in the research and development leading up the production of atomic energy and the production of the atomic bomb. Such invention is of continuing importance in the production of fissionable materials and atomic weapons. The Chairman: So Jones might make the greatest invention in the field and be deprived of any award for it? Captain Lavender: If he did not want to accept the award that was offered to him. (shrink)

The discovery of the Higgs boson at LHC confirms that what we experience as empty space should actually be thought as a condensate of elementary quanta. This condensate characterizes the physically realized form of relativity and could play the role of preferred reference frame in a modern Lorentzian approach. This observation suggests a new interpretative scheme to understand the unexplained residuals in the old ether-drift experiments where light was still propagating in gaseous systems. Differently from present vacuum experiments, where anyhow (...) deviations from Special Relativity are expected to be at the limit of visibility, these now acquire a crucial importance and become consistent with the Earth’s velocity of 370 km/s which characterizes the CMB anisotropy. In the same scheme, one can also understand the difference with the other experiments where light propagates in strongly bound systems such as solid or liquid transparent media. This non-trivial level of consistency motivates a new generation of precise laser interferometry experiments which explore the same particle physics vacuum and, in this sense, are complementary to those with high-energy accelerators. (shrink)