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Particle trajectories and interference in a time-dependent model of neutron single crystal interferometry
Abstract
The de Broglie-Bohm interpretation of quantum mechanics is shown to provide an explanation of the observed spatial interference in neutron single crystal interferometers in terms of well-defined individual particle trajectories with continuously variable energy.
... The inclusion of the measuring device requires a quantum description that is now necessarily formulated in the configuration space of the whole system that is relevant in this case, particle plus detector. The behaviour of the whole system now depends on the entangled configuration space wave function (20) Ψ(x, z, t) = L (x, t) L (y, t) + R (x, t) R (y, t) where L,R represents the particle, with coordinate x, in the left (L) or right (R) beam and L,R the represents the detector with coordinate y, seeing the particle in the left or right slit. The behaviour of the particle in the two slit experiment, as in Wheeler's variation, now depends on the nature of the detector states. ...
... Extending the numerical integration technique used by Goldberg, Schey and Schwarz [4], and given access to the University of London's mainframe computers, it was quite straightforward, even in 1982, to create computer animated motion pictures showing how de Broglie-Bohm theory (in second order form) accounted for square potential phenomena such as tunnelling, by calculating the quantum potential and trajectories associated with wave packet scattering from square (or indeed any shaped) potentials [19]. This work was extended to include computer generated motion pictures representing a simple model of Mach-Zehnder-type neutron interferometry in 1985 [20]. 5 The simple one dimensional model described above could be extended to describe Mach-Zehnder interference simply by adding an additional wave packet at t = 0 approaching the potential region from the opposite side. The two packets approaching the potential region from either side created a model of the convergence of the beams on the last set of crystal planes. ...
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.
... It is opportune to mention that the geometric potential differs from the quantum potential introduced by Bohm [26] not only in its mathematical deduction but also in its phenomenological meaning. The quantum potential is assumed as a consequence of the non-locally correlated stochastic fluctuations of the Dirac ether [27] and is used to determine the paths followed by the particle in the setup [26,27]. In contrast, the geometric potential is caused by the prepared non-locality, which is a deterministic consequence of the setup configuration, and determines the spatial structuration of the Lorentzian wells in confinement regions. ...
... It is opportune to mention that the geometric potential differs from the quantum potential introduced by Bohm [26] not only in its mathematical deduction but also in its phenomenological meaning. The quantum potential is assumed as a consequence of the non-locally correlated stochastic fluctuations of the Dirac ether [27] and is used to determine the paths followed by the particle in the setup [26,27]. In contrast, the geometric potential is caused by the prepared non-locality, which is a deterministic consequence of the setup configuration, and determines the spatial structuration of the Lorentzian wells in confinement regions. ...
In spite of its accurate prediction of the experimental outcomes of double-hole single particle interference, quantum mechanics does not provide a phenomenological description of the individual realizations of the experiment. By defining a non-locality function and considering the non-paraxial solution of the time-independent Schrödinger equation by the Green’s theorem, we introduce a geometrical potential which leads to an outstanding result. The geometric potential allows the description of spatially structured Lorentzian wells in the volume between the double-hole mask and the detector. The buildup of the interference patterns results from the confined propagation of single particles through these Lorentzian wells. The phenomenological implications of this description are discussed and illustrated by numerical examples, and its compatibility with quantum mechanical predictions is also shown. A further, non-trivial advantage of this model over the conventional formalism, is that the present quantum probability density can be exactly calculated both in the near and far field conditions.
... Some of the results appeared in earlier articles with Phillipides, Hiley (1979) [4] and with Hiley (1982) [5]. In later years, Dewdney developed a computer model of Rauch's Neutron interferometer (1982) [6] and, with Kyprianidis and Holland, models of a spin measurement in a Stern-Gerlach experiment (1986) [7]. He also went on, with Kyprianidis and Holland, to develop computer models of spin superposition in neutron interferometry (1987) [8] and of Bohm's spin version of the Einstein, Podolsky, Rosen experiment (EPR-experiment) (1987) [9]. ...
... The trajectories in a two-pinhole interference experiment with equal widths and equal amplitudes modeled by two-dimensional Gaussian wave-packets with equal widths and equal amplitudes. 6 The causal interpretation based on the Schrödinger is obviously nonrelativistic, but it is more than adequate for the description of the behavior of electrons, protons, neutrons, atoms etc, in a large range of circumstances. Photons, however, are not accurately described by the Schrödinger equation, but by quantum optics which is based on the second-quantized Maxwell equations. ...
The two-slit interference experiment has been modeled a number of times using Gaussian wave-packets and the Bohm–de Broglie causal interpretation. Here we consider the experiment with pinholes instead of slits and model the experiment in terms of two-dimensional Gaussian wave-packets and the Bohm–de Broglie causal interpretation.
... This is an extremely high price to pay for consistency. Fortunately, the existence of the causal interpretation based on which computer models of underlying physical reality can be produced [63][64][65][66][67][68] not only shows that we are not forced to accept this extreme position, but also that it is wrong (though I note that recently, the reality of the trajectories in the causal interpretation has been questioned [69]). As mentioned in Sect.3, not all authors would agree with tenet T4. ...
... Both play an equal part in determining a particles motion, the R-field through the quantum potential Q = −h 2 /(2m)∇ 2 R/R, and the S-field through the guidance formula v = ∇S/m.6 Actually, in computer models of the two-slit experiment[63][64][65][66][67][68] it is seen that trajectories never cross so that a particles path can be theoretically determined with certainty even when their is interference, and irrespective of whether the experiment is of an intermediate type or not. ...
I argue that quantum optical experiments that purport to refute Bohr's
principle of complementarity (BPC) fail in their aim. Some of these experiments
try to refute complementarity by refuting the so called particle-wave duality
relations, which evolved from the Wootters-Zureck reformulation of BPC (WZPC).
I therefore consider it important for my forgoing arguments to first recall the
essential tenets of BPC, and to clearly separate BPC from WZPC, which I will
argue is a direct contradiction of BPC. This leads to a need to consider the
meaning of particle-wave duality relations and to question their fundamental
status. I further argue (albeit, in opposition to BPC) that particle and wave
complementary concepts are on a different footing than other pairs of
complementary concepts.
... Some of the results appeared in earlier articles with Phillipides, Hiley (1979) [4] and with Hiley (1982) [5]. In later years, Dewdney developed a computer model of Rauch's Neutron interferometer (1982) [6] and, with Kyprianidis and Holland, models of a spin measurement in a Stern-Gerlach experiment (1986) [7]. He also went on, with Kyprianidis and Holland, to develop computer models of spin superposition in neutron interferometry (1987) [8] and of Bohm's spin version of the Einstein, Rosen, Podolsky experiment (EPR-experiment) (1987) [9]. ...
The two-slit interference experiment has been modeled a number of times using Gaussian wave-packets and the Bohm-de Broglie causal interpretation. Here we consider the experiment with pinholes instead of slits and model the experiment in terms of two-dimensional Gaussian wave-packets and the Bohm-de Broglie causal interpretation.
... One of his fundamental proposals was to consider that each atomic entity is a real objective physical complex system with a corpuscle, surrounded by a quantum wave. This wave is not an elusive, metaphysical probability wave, as claimed by orthodox quantum mechanics [2], but a real undulatory perturbation, propagating in a subquantum medium and guiding the corpuscle along its trajectory [3]. This piloting or guiding effect may be seen as an information transferring process, where a subtle entity, the pilot-wave, with lesser energetic content, guides the movement of the corpuscle, a much more energetic system in itself. ...
In some situations nonlinearity seems to pervade in nature. Indeed, in adequate conditions, a minor action may give origin to a very large reaction, only apparently providing a gain in output power from a lesser inputted value. Extending de Broglie seminal ideas to a more general pilot-wave theory, we describe the relation between nonlinearity and energy conservation, dismissing any apparent contradiction between the two. We also present what seems to be a possible way to harness energy from the pervading subquantum medium.
... An extended model for a spin-half particle based on the Pauli equation has already been presented in Bohm, Schiller and Tiomno (BST) [27]. Full details of this model have also been discussed in a series of papers by Dewdney et al. [28][29][30][31] and by Holland [32]. This simple model has been applied to neutron diffraction and a single Stern-Gerlach magnet, the results being reported in [29,30]. ...
The claim of Kocsis et al. to have experimentally determined “photon trajectories” calls for a re-examination of the meaning of “quantum trajectories”. We will review the arguments that have been assumed to have established that a trajectory has no meaning in the context of quantum mechanics. We show that the conclusion that the Bohm trajectories should be called “surreal” because they are at “variance with the actual observed track” of a particle is wrong as it is based on a false argument. We also present the results of a numerical investigation of a double Stern-Gerlach experiment which shows clearly the role of the spin within the Bohm formalism and discuss situations where the appearance of the quantum potential is open to direct experimental exploration.
... Bohm and his co-workers are currently trying to give more precise physical and mathematical meaning to the concept of the quantum potential and the causal interpretation of quantum mechanics. A number of technical papers attempt to throw new light on various classical problems in quantum physics, such as the measurement problem (Bohm, Dewdney & Hiley, 1985;Bohm & Hiley, 1976Dewdney, Holland & Kyprianidis, 1986;Hiley, 1985), the role of non-locality (Bohm & Hiley, 1975;Hiley, 1985), quantum interference (Philippidis, Dewdney & Hiley, 1979;Dewdney, 1985), the Aharonov-Bohm effect (Philippidis & Bohm, 1982), barrier penetration (Hiley, 1985), and the relation between classical and quantum levels (Bohm & Hiley, 1985, in preparation;Bohm, Hiley & Kaloyerou,1987). These publications may be considered preliminary results in an ongoing research program aimed at giving mathematical and scientific substance to the many intuitive ontological analogies offered by Bohm, as reviewed in the previous sections. ...
In an attempt to formulate a coherent view of quantum reality, the
theoretical physicist David Bohm has proposed a new concept of order to
supplement the mechanistic Cartesian order of traditional physics. The
"implicate" order is a subtler and deeper order that emphasizes
"unbroken wholeness in flowing movement," in contrast to the coarser and
more superficial, "explicate" Cartesian order of distinct phenomena.
This dissertation attempts to develop a meaning for the idea of
implicate order in the world of human experience. First is offered an
account of some evolutionary episodes in terms of implicate and
explicate order which draws on compatible work in cosmology,
embryogenesis, visual perception, brain memory, decision making and
phenomenology. Two important characteristics of the implicate order are
then identified: in an implicate order, the whole is enfolded (or
represented) in its parts; and all parts render different perspectives
of the whole. Using arguments from decision making, the study of "flow"
in human consciousness, and a model of skill acquisition, it is
suggested that these characteristics manifest themselves in the human
world as the "unity experience" and the "diversity experience,"
respectively. The former is the experience that a given part of one's
life reveals a larger wholeness or unity; the subject-object distinction
is transcended and one becomes absorbed in the flow of whatever activity
is pursued. The latter is a deep appreciation of the diversity of ways
in which people may seek the unity experience. These experiences are
proposed as general values: social and psychological conditions ought to
be such that these experiences are enhanced in all people. A two-by-two
matrix of the two experiences demonstrates the danger of pursuing one to
the exclusion of the other. The experience of unity without diversity
turns into absolutism, the insistence that one's chosen activities or
beliefs are the only right ones. The experience of diversity without
unity becomes relativism, the excessive tolerance of and indifference to
other people's pursuits. The good life lies in the simultaneous
realization of both, unity-in -diversity. Lastly, it is suggested that
this so-called unity-diversity matrix may be used as a personal compass
the meaning of which is negotiated and calibrated in a community of
users.
... where S(r, t) is the phase of the particle wave function Ψ(r, t) = |Ψ(r, t)|e iS(r,t)/ (2) which satisfies the time-dependent Schrdinger equation. Using the method proposed by De Broglie and Bohm, Philipidis et al [13] plotted the trajectories of massive particles in the double slit experiment [13], Dewdney showed trajectories for neutrons inside a (neutron) interferometer [14], and Sanz and Miret-Arts explained the Talbot effect for atoms by plotting their associated trajectories behind a diffraction grating [15]. ...
We present a trajectory-based interpretation of Young's experiment, the
Arago-Fresnel laws and the Poisson-Arago spot. This approach
is based on the equation of the trajectory associated with the quantum
probability current density in the case of massive particles, and the
Poynting vector for the electromagnetic field in the case of photons.
Both the form and properties of the evaluated photon trajectories are in
good agreement with the averaged trajectories of single photons observed
recently in Young's experiment by Steinberg's group at the University of
Toronto. In the case of the Arago-Fresnel laws for polarized
light, the trajectory interpretation presented here differs from
interpretations based on the concept of ‘which-way’ (or
‘which-slit’) information and quantum erasure. More
specifically, the observer's information about the slit that the photons
went through is not relevant to the existence of interference; what is
relevant is the form of the electromagnetic energy density and its
evolution, which will model consequently the distribution of
trajectories and their topology. Finally, we also show that the
distributions of end points of a large number of evaluated photon
trajectories are in agreement with the distributions measured at the
screen behind a circular disc, clearly giving rise to the
Poisson-Arago spot.
In this chapter, we begin by introducing the Schrödinger equation for N spinless particles and discussing its basic properties (particularly the continuity equation). We then introduce the Born rule for position and the concepts of Hilbert space and unitary operator, and review classical mechanics in the form of Newtonian mechanics of N point particles. We discuss the double slit experiment and explain why its outcome agrees with the Schrödinger equation and Born’s rule but disagrees with classical mechanics. We introduce Bohmian mechanics and explain how it treats the double-slit experiment, as well as Wheeler’s delayed-choice experiment.
In this paper we present a series of computer calculations carried out in order to demonstrate exactly how the causal interpretation works in specific cases. In this way we show how the causal interpretation can account for the essential features of single and two particle non-relativistic quantum mechanics, including spin, in terms of well defined individual particle motions.
The invention of neutron interferometry in 1974 stimulated many experiments related to the wave-particle dualism of quantum mechanics. Widely separated coherent beams can be produced within a perfect crystal interferometer, and they can be influenced by nuclear, magnetic and gravitational interaction. The verification of the 4π symmetry of spinor wave functions and of the spin superposition law at a macroscopic scale and the observation of gravitational effects including the Sagnac effect have been widely debated in literature. The coupling of the neutron magnetic moment to resonator coils permitted the coherent energy exchange between the neutron quantum system and the macroscopic resonator. This phenomenon provided the basis for the observation of the magnetic Josephson effect with an energy sensitivity of 10−19eV. Partial beam path detection experiments are in close connection with the development of quantum mechanical measurement theory. The very high sensitivity of neutron interferometry may be used in future for new fundamental, solid-state and nuclear-physics application. A striking spectral modulation effect has been observed by means of a proper post-selection procedure under conditions where the spatial shift of the wave trains greatly exceeds the coherence length of the neutron beams traversing an interferometer. It is shown that Schrödinger-cat-like states are created by the superposition of two coherent states generated in the interferometer. These entangled states exhibit under certain circumstances characteristic squeezing phenomena indicating a highly non-classical behavior. Analogies with light optical experiments are discussed.
In this paper we present a series of computer calculations carried out in order to demonstrate exactly how the causal interpretation works for two-particle quantum mechanics. In particular we show how the causal interpretation can account for the essential features of nonrelativistic, two-particle quantum mechanics in terms of well-defined, correlated, individual particle trajectories and spin vectors. We demonstrate exactly how both quantum statistics and the correlations observed in Einstein-Podolsky-Rosen (EPR) experiments can be explained in terms of nonlocal quantum potentials and nonlocal quantum torques which act on the well-defined individual particle coordinates and spin vectors.
In this contribution we review some calculations in Bohm’s approach to quantum theory. In particular, we discuss the interaction of a quantized cavity scalar field with firstly one and then two particles confined in infinite potential wells.
We show that it is possible to give a causal, continuous and deterministic description of the motion of an individual system undergoing a transition between states using the de Broglie — Bohm interpretation of quantum mechanics.
The purpose of this communication is to discuss the implications of neutron interferometric experiments on the possible interpretation of the quantum formalism. The most recent one, which is a time-dependent double resonance experiment performed by the Vienna experimentalists1 following a suggestion of our group2, has farreaching implications, which, as we hope to show, establish the validity of the causal Stochastic Interpretation of Quantum Mechanics (SIQM) as the most adequate theoretical tool in grasping quantum “paradoxes”. This approach which follows the views of Einstein and de Broglie in their controversy with Bohr and Heisenberg, develops the model of de Broglie’s pilot wave theory3 and Bohm’s quantum potential concept4. This explains why, before we discuss neutron interferometry, we find it useful to expose the basic ingredients of this model for an ordinary double slit situation.
Via the hydrodynamical formulation of quantum mechanics, we propose new boundary conditions to the problem of tunneling through sharp-edged potential barriers with and without dissipation. Above all, these boundary conditions can be matched without assuming continuity of the wave function at a surface sigma where the potential undergoes a, finite jump. Our approach yields a general expression for transmission probability from which tunneling with and without dissipation can be directly correlated to standard discussions found in textbooks.
A brief summarizing review is given of all those neutron interferometric experiments performed hitherto which explicitly use the spin- particle properties of the neutron. It covers topics as the verification of the 4π-periodicity of spinors, the cooperative action of nuclear phase shift and spin-rotation on the neutron wave function, the demonstration of the quantum mechanical principles of fermion spin-state superposition and the more recent double resonance experiments where the two interfering beams propagate through spatially separated oscillatory magnetic fields. Finally a proposal will be presented also for a so-called “late-choice” experiment with polarized neutrons.
Within a perfect crystal interferometer widely separated coherent beams can be produced which can be influenced by nuclear,
magnetic and gravitational interaction. The verification of the 4π-symmetry of spinor wave functions and of the spin superposition
law at a macroscopic scale and the observation of gravitational effects including the Sagnac effect have been widely debated
in literature. The coupling of the neutron magnetic moment to resonator coils permitted the coherent energy exchange between
the neutron system and the macroscopic resonator. This phenomenon provided the basis for the observation of the magnetic Josephson
effect with an energy sensitivity of 10−19 eV. Partial beam path detection experiments are in close connection with the development of quantum mechanical measurement
theory. A striking spectral modulation effect has been observed by means of a proper post-selection procedure under conditions
where the spatial shift of the wave trains greatly exceeds the coherence length of the neutron beams traversing an interferometer.
It is shown that Schrödinger-cat-like states are created by the superposition of two coherent states generated in the interferometer.
These entangled states exhibit under certain circumstances characteristic squeezing phenomena indicating a highly non-classical
behaviour.
Summary In the Bohm theory of quantum mechanics, particles move in well-defined paths. The probability distribution (at a single time)
is exactly what would be computed from the Schrödinger equation. Here we consider two-time probabilities in the Bohm theory,
and compute dipole moment fluctuation spectra for the hydrogen atom. The resulting dipole fluctuations differ from those which
can be obtained from conventional quantum mechanics.
Since the invention of perfect crystal neutron interferometry this technique has become an important tool in the realization of many textbook experiments in quantum mechanics. Widely separated coherent beams of thermal neutrons are produced and superposed by dynamical Bragg diffraction from a properly shaped perfect crystal. The observed interference patterns show the characteristic coherence properties of matter waves which arc influenced by the individual particle and by the properties of the experimental device. The verification of the 4π-periodicity of spinor wavefunctions and the realization of thc spin-superposition experiment on B macroscopic scale has become feasible by this technique. A new kind of a quantum beat effect with an energy sensitivity of 2.7 × 20- eV has been observed in a double coil resonance experiment. The influence of gravity and of the Earth's rotation on the wavefunction become visible at a level of an elementary particle with non-zero mass. All the results are in agreement with the formulation of quantum mechanics but, nevertheless, they stimulate discussion about its interpretation. The particle-wave dualism becomes obvious on a macroscopic scale and with a beam of massive particles.
Contrary to classical mechanics, quantum mechanics does not deal directly with observable events. In order to infer from the knowledge of a quantum state a prediction about an event, it is necessary to call upon the theory of measurement, a complicated system of interpretation of the basic formalism. The Madelung formulation offers seemingly a more direct solution to this problem, since one of its equations of motion assumes a classical form and operates on a local momentum. A critical examination of its limitations leads to the generalization of the Madelung equations. The new local momentum associated to a given state depends on the probability density, the phase of the wave function, and arbitrary quantities. Its spatial average over a finite cell displays the features of the observable momentum. On this ground a model of the observed motion is built up with the help of a minimal set of postulated.
A recent theory of interrupted fluorescence experiments does not make use of collapse, but recognises the orthogonality of different branches of the wavefunction resulting from differences in photon number. However this argument suggests that a single system may, for a substantial period of time, lie in one branch of its many-component wavefunction. It is suggested that hidden variables may help to clarify the situation.
The causal interpretation of the Pauli equation is shown to provide an understanding of spin superposition in neutron interferometry in terms of well-defined individual particle trajectories with continuously variable spin vectors.
A simulation study of a neutron interferometer of Si is carried out. How a wave packet is decomposed into two using the Bragg diffraction was already reported. This paper describes how the divided two parts of a single-neutron wave packet are again superposed. In order for wave packets to be superposed both must belong to the same Hilbert space and a certain physical process to superpose them is necessary. In an interferometer atomic potentials of Si play this role.
In studying the dynamical diffraction effect of neutrons it has been clarified that eigenstates of a quantum system composed of periodic potentials with free spaces on both ends play a crucial role in determining the Bragg reflection, rocking curves, Pendellösung effect, and so on. These eigenstates can be called virtual states, since the occupancy probability within the potential region is significantly modified by the existing potential, even though the energies of concern are much larger than the potential barrier heights.
The authors consider the new adaptations of Einstein's two-slit experiment in terms of recently performed experiments with neutrons, and analyse them in the light of the complementarity principle. They contrast this with the description in terms of the de Broglie-Bohm causal interpretation.
After a presentation of Einstein's and Bohr's antagonistic point of view on the interpretation of Quantum Mechanics an illustration of their conflicting positions in the particular case of Young's double slit experiment is presented. It is then shown that in their most recent form (i. e. time dependent neutron interferometry) these experiments suggest (if one accepts absolute energymomentum conservation in all individual microprocesses) that Einstein was right in the Bohr-Einstein controversy.
Einsteins Materialismus und heutige Tests der Quantenmechanik
Nach einer Darstellung von Einsteins und Bohrs antagonistischen Standpunkten in der Interpretation der Quantenmechanik werden ihre widersprüchlichen Positionen im speziellen Fall des Youngschen Doppelspaltexperiments dargestellt. Es wird dann gezeigt, daß diese Experimente in ihrer neuesten Form (d. h. zeitabhängige Neutroneninterferometrie) Einstein in der Bohr-Einsteinkontroverse recht gaben (wenn man absolute Energie-Impulserhaltung bei allen individuellen Mikroprozessen annimmt).
A brief summarizing review is given of all those neutron interferometric experiments performed hitherto which explicitly use the spin- particle properties of the neutron. It covers topics as the verification of the 4π-periodicity of spinors, the cooperative action of nuclear phase shift and spin-rotation on the neutron wave function, the demonstration of the quantum mechanical principles of fermion spin-state superposition and the more recent double resonance experiments where the two interfering beams propagate through spatially separated oscillatory magnetic fields. Finally a proposal will be presented also for a so-called “late-choice” experiment with polarized neutrons.
It is shown that the quantum potential approach to quantum mechanics, originated by de Broglie and Bohm, can account for the essential features of spatial interference and spin superposition, observed with neutron interferometers, in terms of well-defined individual particle motions.
The realist interpretations of quantum theory, proposed by de Broglie and by Bohm, are re-examined and their differences, especially concerning many-particle systems and the relativistic regime, are explored. The impact of the recently proposed experiments of Vigier et al. and of Ghose et al. on the debate about the interpretation of quantum mechanics is discussed. An indication of how de Broglie and Bohm would account for these experimental results is given.
Following the many-Hilbert-spaces theory of measurement by Machida and Namiki, it is possible to numerically simulate the quantum process of the reduction of wave packets, based on a model plausibly specifying Hilbert spaces. In neutron interferometry experiments such as those done by the Vienna group, each neutron belongs to a Hilbert space. When an interferometer environment is defined and neutrons allowed to interact with it, the degree of visibility degradation is calculated depending on the effectiveness of the interaction. The pile-up of numerous neutrons may or may not make an interfering pattern, depending on whether their interaction with the system is slight enough not to disperse or strong enough to disperse their phase differences after superposition. Thus it is shown that complete disappearance of visibility, i.e., reduction of wave packets, is expected for an infinitely large number of scatterers and/or an infinitely strong interaction, experienced by those neutrons.
In this paper we present a series of computer calculations carried out in order to demonstrate exactly how the de Broglie-Bohm interpretation works for two-particle quantum mechanics. In particular, we show how the de Broglie-Bohm interpretation can account for the essential features of nonrelativistic, two-particle quantum mechanics in terms of well-defined, correlated, individual particle trajectories and spin vectors. We demonstrate exactly how both quantum statistics and the correlations observed in Einstein-Podolsky-Rosen experiments can be explained in terms of nonlocal quantum potentials and nonlocal quantum torques which act on the well-defined individual particle coordinates and spin vectors.
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.
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 the4 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 of2.710
–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.
Bohm 's approach to quantum field theory is illustrated through its application to cavity quantum scalar field dynamics. Specific calculations demonstrate how the evolution of the well-defined scalar field is governed by the nature of its quantum state. The implications of the nonlocality inherent in quantum mechanics and the meaning of the classical limit are discussed in this context.
Interferometry with massive elementary particles combines particle and wave features in a direct way. In this respect, neutrons
are proper tools for testing quantum mechanics because they are massive, they couple to electromagnetic fields due to their
magnetic moment, and they are subject to all basic interactions, and they are sensitive to topological effects, as well. They
play a pionieering role in the development of interferometry with even heavier objects, like atoms, molecules and clusters.
Deterministic and stochastic partial absorption experiments can be described by Bell-type inequalities. Recent neutron interferometry
experiments based on postselection methods renewed the discussion about quantum nonlocality and the quantum measuring process.
It has been shown that interference phenomena can be revived even when the overall interference pattern has lost its contrast.
This indicates persisting coupling in phase space even in cases of spatially separated Schrödinger cat-like situations. These
states are extremely fragile and sensitive to any kind of fluctuations or other decoherence processes. More complete quantum
experiments also show that a complete retrieval of quantum states behind an interaction region becomes impossible in principle.
The transition from a quantum world to a classical one is still an open question and will be tackled by means of dedicated
decoherence experiments. Recent measurements deal with quantum contextuality and quantum state reconstruction. The observed
results agree with quantum mechanical laws and may stimulate further discussions about their interpretations.
Quantum transport through one‐dimensional potential barriers is usually analyzed using either the transmission coefficient (TC) or the Wigner distribution function (WDF) approach. Fast, accurate, and efficient numerical algorithms are developed for each and are compared for (a) calculating current‐field relationships for field‐emission potentials with silicon parameters (and current‐voltage relationships for resonant tunneling diodes), (b) their ability to accommodate scattering, self‐consistency, and time dependence, and for (c) the behavior of their ‘‘particle trajectory’’ interpretations. In making the comparisons, the concern will be on the ability of each method to be incorporated into a larger ensemble‐particle Monte Carlo simulation; it is argued that, in this regard, the WDF approach has significant advantages. Since the TC calculations rely on the Airy function approach, a detailed comparison of this method is made with the widely used Wentzel–Kramers–Brillouin and Fowler–Nordheim approaches for the general problem of field emission from a material into the vacuum.
Since their advent interferometry with X-rays and neutrons have developed steadily. A number of excellent reviews is covering the development up to about five years ago. Advances since then are treated in this review. Topics included are: understanding of angstrom wave interferometers, theory of operation, types, contrast, complementarity, strategies and refinement of measurement, nonlinear Fizeau effect with neutrons, action of gravity and inertia on neutron phase, interferometers with separated crystals, interferometer combining X-ray and optical operation, interferometer combining X-ray and neutron operation.
A new approach to the problem of scattering is presented via the exact invariants of quantum hydrodynamics, where the solution preserves information about the quantum potential which accounts for quantum-wave features such as interference and diffraction effects. Within this formalism, a formula for the transmission coefficient of a steady flux of fluid-particles scattered by an arbitrarily shaped potential well is derived and discussed for some exact and approximate solutions.
An objective account of a Stern-Gerlach experiment performed with spin- particles is developed in which the particles have well-defined and continuous trajectories and spin vectors, through the causal interpretation of the Pauli equation.
The first examples of Bohmian trajectories for photons have been worked out for simple situations, using the Kemmer–Duffin–Harish-Chandra formalism.
We describe a gedanken experiment with an interferometer in the case of pre- and postselection in two different time symmetric ways: We apply the ABL formalism and the de Broglie-Bohm model. Interpreting these descriptions ontologically, we get two very different concepts of reality. Finally, we discuss some problems implied by these concepts.
De Broglie and Bohm successfully showed how the statistical phenomena of nonrelativistic quantum mechanics could be understood as the outcome of individually well defined processes in which physical systems have a corpuscular aspect that pursues a spacetime track. A review is presented of the application of the de Broglie-Bohm method to relativistic boson systems. After summarizing the salient points of the nonrelativistic theory, it is explained why a trajectory interpetation of the Klein-Gordon equation is in general untenable. Then a consistent version of the approach that takes fields as basic variables is presented following a previous analysis based on Bohm's original work. All the formulae needed to apply the theory in the space and normal coordinate representations are given and illustrated through applications to the ground state, the Casimir effect, the number and coherent states, and the classical limit.Emphasis is laid on the nonlocality and noncovariance of the individual processes that underlie the statistical locality and Lorentz covariance of quantum field theory in its canonical formulation. Particular attention is paid to the question of whether it is possible to attribute spacetime trajectories to the quanta of the bosonic field. It is found that this is not possible if the current field-theoretic formalism is adopted unmodified. As an alternative the notion of energy flow lines is investigated and shown to be consistent in classical optics, but only for certain states in quantum optics. The field and energy guidance laws are applied to two-slit interference experiments performed with number and coherent states. Finally, the value of this approach is illustrated through the light it sheds on the problem of interpreting the wavefunction of the universe.
Spin superposition in neutron interferometry, spin measurement, and non-local Einstein-Podolsky-Rosen spin correlations can be understood in terms of well-defined individual particle trajectories with continuously variable spin vectors.
We present the Bohm theory of hydrogenlike atoms, the measurement of orbital angular momentum, and Einstein-Podolsky-Rosen angular momentum correlations. We use the illustrations to discuss the arguments of von Neumann [described in M. Jammer, The Philosophy of Quantum Mechanics (Wiley, New York, 1974)] and Kochen and Specker [J. Math. Mech. 17, 59 (1967)] against hidden variables.
By means of the quantum potential interpretation we show that there is no need for a break or ``cut'' in the way we regard reality between quantum and classical levels.
This MSc dissertation surveys nine interpretations of non-relativistic quantum mechanics. Extensive references are given. The interpretations covered are: the orthodox interpretation, Bohr's interpretation, the idea that the mind causes collapse, hidden variables, the many-worlds interpretation, the many-minds interpretation, Bohm's interpretation and two interpretations based on decoherent histories.
We re-examine the notion of the quantum potential introduced by the Broglie and Bohm and calculate its explicit form in the
case of the two-slit interference experiment. We also calculate the ensemble of particle trajectories through the two slits.
The results show clearly how the quantum potential produces the bunching of trajectories that is required to obtain the usual
fringe intensity pattern. Hence we are able to account for the interference fringes while retaining the notion of a well-defined
particle trajectory. The wider implications of the quantum potential particularly in regard to the quantum interconnectedness
are discussed.
Si riesamina la nozione di potenziale quantico introdotta da de Broglie e Bohm e si calcola la sua forma esplicita nel caso
di un esperimento d'interferenza a due passaggi. Si calcola anche l'insieme di traiettorie delle particelle attraverso i due
passaggi. I risultati mostrano chiaramente come il potenziale quantico produce l'agglomerato di traiettorie che è richiesto
per ottenere l'usuale comportamento di intensità di frangia. Quindi si è in grado di spiegare le frange di interferenza conservando
la nozione di una ben definita traiettoria della particella. Si discutono le più ampie implicazioni del potenziale quantico
particolarmente rispetto all'interazione quantica.
Мы заново исследуем понятие квантового потенциала, введенного де Бройлем и Бомом, и вычисляем его явный вид в случае интерференционного
эксперимента на двух щелях. Мы также вычисляем совокупность траекторий частиц, прошедших через две щели. Полученные результаты
показывают, что квантовый потенциал приводит к группированию траекторий, что требуется для получения обычных интерференционных
полос интенсивности. Следовательно, мы можем объяснитб образование интерференционных полос, сохраняя понятие определенных
траекторий частиц. Обсуждаются следствия квантового потенциала относительно квантовой взаимосвязанности.
The usual interpretation of the quantum theory is self-consistent, but it involves an assumption that cannot be tested experimentally, viz., that the most complete possible specification of an individual system is in terms of a wave function that determines only probable results of actual measurement processes. The only way of investigating the truth of this assumption is by trying to find some other interpretation of the quantum theory in terms of at present "hidden" variables, which in principle determine the precise behavior of an individual system, but which are in practice averaged over in measurements of the types that can now be carried out. In this paper and in a subsequent paper, an interpretation of the quantum theory in terms of just such "hidden" variables is suggested. It is shown that as long as the mathematical theory retains its present general form, this suggested interpretation leads to precisely the same results for all physical processes as does the usual interpretation. Nevertheless, the suggested interpretation provides a broader conceptual framework than the usual interpretation, because it makes possible a precise and continuous description of all processes, even at the quantum level. This broader conceptual framework allows more general mathematical formulations of the theory than those allowed by the usual interpretation. Now, the usual mathematical formulation seems to lead to insoluble difficulties when it is extrapolated into the domain of distances of the order of 10-13 cm or less. It is therefore entirely possible that the interpretation suggested here may be needed for the resolution of these difficulties. In any case, the mere possibility of such an interpretation proves that it is not necessary for us to give up a precise, rational, and objective description of individual systems at a quantum level of accuracy.
In this paper, we propose a physical model leading to the causal interpretation of the quantum theory. In this model, a set of fields which are equivalent in many ways to a conserved fluid, with density |psi|2, and local stream velocity, dxidt=∇Sm, act on a particle-like inhomogeneity which moves with the local stream velocity of the equivalent fluid. By introducing the hypothesis of a very irregular and effectively random fluctuation in the motions of the fluid, we are able to prove that an arbitrary probability density ultimately decays into |psi|2. Thus, we answer an important objection to the causal interpretation, made by Pauli and others. This result is extended to the Dirac equation and to the many-particle problem.
Inverting the spin state of one of the two coherent waves propagating within a neutron interferometer by means of a radio-frequency spin-flip device leads to a nonstationary interference pattern. By using stroboscopic neutron detection one can resolve this to demonstrate the nonclassical behavior of spinor superposition.
The neutron interferometer is a unique instrument that allows one to construct a neutron wave packet of macroscopic size, divide it into two components separated by centimeters, and then coherently recombine them. A number of experiments clearly showing the difference between quantum and classical theory have been performed with it, which are suitable for presentation in elementary quantum courses. This article presents a simple mathematical model of the interferometer, which can be used to illustrate clearly many of the surprising features of quantum systems. For example, one can describe an experiment to determine which component beam the neutron takes (an analog of the two-slit electron experiment). One can then trace in detail the loss of coherence of the wave function, rather than merely invoke the usual "handwaving" uncertainty arguments. The author discusses the effect of gravity on the neutron beam [the classic COW (Colella, Overhauser, and Werner) experiment], including a simple analysis in an accelerated reference frame, and its relation to the equivalence principle, the red shift, and the twin paradox. Also described are the effect of rotation of the neutron by 360° to change its phase, the effect on the wave function of measuring the absence of the particle from a beam ("Dicke's paradox"), and a realizable version of Wheeler's "delayed-choice" experiments, as well as their relation to the problem of "Schrödinger's cat." The treatment is suitable for bright undergraduates and first-year graduate students.
When a series of aluminum slabs are placed in one leg of a perfect-silicon-crystal neutron interferometer, a continuous and significant loss of contrast is observed. This observation is interpreted as being due to the finite length of the neutron wave packets.
A modified version of the time-dependent neutron spinor superposition allows a possible simultaneous detection of neutron paths and intensity self-interference. Previous theoretical doubts are removed and the Einstein-de Broglie version of the wave-particle dualism now seems to be supported by Rauch's experiment.
The quantum potential approach is applied to a 'delayed choice'
experiment considered by Wheeler (1978), and it is shown that there is
no need to conclude that the past has had no existence except insofar as
it is recorded in the present. A simple and intelligible account of a
typical delayed-choice experiment is given. The result indicates that
there is a definable and defined overall process that includes both the
observer-participator and the rest of the universe in one undivided
whole.
The time-dependent scattering of one-dimensional Gaussian wave packets of various energies incident on(1) a square potential barrier and(2) a square well is examined numerically, using the quantum potential introduced by Bohm. The time-dependent quantum potential is calculated in each case, and the results displayed on three-dimensional computer plots. The particle trajectories from different initial positions within the wave packet are also shown, giving a detailed description of reflection and tunneling in terms of individual processes. The wider implications of this analysis are also briefly considered.
Time-dependent spinor superposition in neutron interferometry by means of radio frequency spin flippers enables a possible
simultaneous path and interference detection and provides evidence for the real physical existence of de Broglie « pilot »
waves.
The complementarity principle is shown to conflict with the energy conservation laws in neutron single crystal interferometry. Its shortcomings are revealed in specific performed or proposed neutron interferometry experiments.
- Bohm