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Problems viewing this page? For example, measuring position is considered to be a measurement of the position operator. This relationship between physical measurements and Hilbert space operators is, for standard quantum mechanics, an additional axiom of the theory. The de Broglie—Bohm theory, by contrast, requires no such measurement axioms and measurement as such is not a dynamically distinct or special sub-category of physical processes in the theory.
In particular, the usual operators-as-observables formalism is, for de Broglie—Bohm theory, a theorem. In the history of de Broglie—Bohm theory, the proponents have often had to deal with claims that this theory is impossible. Such arguments are generally based on inappropriate analysis of operators as observables. If one believes that spin measurements are indeed measuring the spin of a particle that existed prior to the measurement, then one does reach contradictions.
De Broglie—Bohm theory deals with this by noting that spin is not a feature of the particle, but rather that of the wavefunction. As such, it only has a definite outcome once the experimental apparatus is chosen. Once that is taken into account, the impossibility theorems become irrelevant. There have also been claims that experiments reject the Bohm trajectories  in favor of the standard QM lines.
But as shown in other work,   such experiments cited above only disprove a misinterpretation of the de Broglie—Bohm theory, not the theory itself. There are also objections to this theory based on what it says about particular situations usually involving eigenstates of an operator.
For example, the ground state of hydrogen is a real wavefunction. According to the guiding equation, this means that the electron is at rest when in this state. Operators as observables leads many to believe that many operators are equivalent.
De Broglie—Bohm theory, from this perspective, chooses the position observable as a favored observable rather than, say, the momentum observable. Again, the link to the position observable is a consequence of the dynamics. The motivation for de Broglie—Bohm theory is to describe a system of particles.
This implies that the goal of the theory is to describe the positions of those particles at all times. Other observables do not have this compelling ontological status.
Having definite positions explains having definite results such as flashes on a detector screen. Other observables would not lead to that conclusion, but there need not be any problem in defining a mathematical theory for other observables; see Hyman et al. De Broglie—Bohm theory is often referred to as a "hidden-variable" theory. Bohm used this description in his original papers on the subject, writing: In particular, they argued that a particle is not actually hidden but rather "is what is most directly manifested in an observation [though] its properties cannot be observed with arbitrary precision within the limits set by uncertainty principle ".
Generalized particle trajectories can be extrapolated from numerous weak measurements on an ensemble of equally prepared systems, and such trajectories coincide with the de Broglie—Bohm trajectories. In particular, an experiment with two entangled photons, in which a set of Bohmian trajectories for one of the photons was determined using weak measurements and postselection, can be understood in terms of a nonlocal connection between that photon's trajectory and the other photon's polarization.
The Heisenberg's uncertainty principle states that when two complementary measurements are made, there is a limit to the product of their accuracy. In de Broglie—Bohm theory, there is always a matter of fact about the position and momentum of a particle.
Each particle has a well-defined trajectory, as well as a wavefunction. Observers have limited knowledge as to what this trajectory is and thus of the position and momentum.
It is the lack of knowledge of the particle's trajectory that accounts for the uncertainty relation. What one can know about a particle at any given time is described by the wavefunction. Since the uncertainty relation can be derived from the wavefunction in other interpretations of quantum mechanics, it can be likewise derived in the epistemic sense mentioned above on the de Broglie—Bohm theory.
To put the statement differently, the particles' positions are only known statistically. As in classical mechanics , successive observations of the particles' positions refine the experimenter's knowledge of the particles' initial conditions. Thus, with succeeding observations, the initial conditions become more and more restricted. This formalism is consistent with the normal use of the Schrödinger equation. For the derivation of the uncertainty relation, see Heisenberg uncertainty principle , noting that this article describes the principle from the viewpoint of the Copenhagen interpretation.
De Broglie—Bohm theory highlighted the issue of nonlocality: In the Einstein—Podolsky—Rosen paradox , the authors describe a thought experiment that one could perform on a pair of particles that have interacted, the results of which they interpreted as indicating that quantum mechanics is an incomplete theory.
Decades later John Bell proved Bell's theorem see p. In particular, Bell proved that any local theory with unique results must make empirical predictions satisfying a statistical constraint called "Bell's inequality".
Aspect's results show experimentally that Bell's inequality is in fact violated, meaning that the relevant quantum-mechanical predictions are correct. In these Bell test experiments, entangled pairs of particles are created; the particles are separated, traveling to remote measuring apparatus.
The orientation of the measuring apparatus can be changed while the particles are in flight, demonstrating the apparent nonlocality of the effect. The de Broglie—Bohm theory makes the same empirically correct predictions for the Bell test experiments as ordinary quantum mechanics.
It is able to do this because it is manifestly nonlocal. It is often criticized or rejected based on this; Bell's attitude was: The de Broglie—Bohm theory describes the physics in the Bell test experiments as follows: The particles in the experiment follow the guidance of the wavefunction.
It is the wavefunction that carries the faster-than-light effect of changing the orientation of the apparatus. An analysis of exactly what kind of nonlocality is present and how it is compatible with relativity can be found in Maudlin. Bohm's formulation of de Broglie—Bohm theory in terms of a classically looking version has the merits that the emergence of classical behavior seems to follow immediately for any situation in which the quantum potential is negligible, as noted by Bohm in Modern methods of decoherence are relevant to an analysis of this limit.
See Allori et al. Work by Robert E. Wyatt in the early s attempted to use the Bohm "particles" as an adaptive mesh that follows the actual trajectory of a quantum state in time and space.
In the "quantum trajectory" method, one samples the quantum wavefunction with a mesh of quadrature points. One then evolves the quadrature points in time according to the Bohm equations of motion.
At each time step, one then re-synthesizes the wavefunction from the points, recomputes the quantum forces, and continues the calculation. This approach has been adapted, extended, and used by a number of researchers in the chemical physics community as a way to compute semi-classical and quasi-classical molecular dynamics.
Wyatt and his work on "computational Bohmian dynamics". Bittner 's group at the University of Houston has advanced a statistical variant of this approach that uses Bayesian sampling technique to sample the quantum density and compute the quantum potential on a structureless mesh of points.
There remain difficulties using the Bohmian approach, mostly associated with the formation of singularities in the quantum potential due to nodes in the quantum wavefunction. Various schemes have been developed to overcome this; however, no general solution has yet emerged. These methods, as does Bohm's Hamilton—Jacobi formulation, do not apply to situations in which the full dynamics of spin need to be taken into account. The properties of trajectories in the de Broglie — Bohm theory differ significantly from the Moyal quantum trajectories.
The second issue with Bohmian mechanics may at first sight appear rather harmless, but which on a closer look develops considerable destructive power: These are the components of the post-measurement state that do not guide any particles because they do not have the actual configuration q in their support. At first sight, the empty branches do not appear problematic but on the contrary very helpful as they enable the theory to explain unique outcomes of measurements.
On a closer view, though, one must admit that these empty branches do not actually disappear. As the wavefunction is taken to describe a really existing field, all their branches really exist and will evolve forever by the Schrödinger dynamics, no matter how many of them will become empty in the course of the evolution.
Now, if the Everettian theory may be accused of ontological extravagance, then Bohmian mechanics could be accused of ontological wastefulness. On top of the ontology of empty branches comes the additional ontology of particle positions that are, on account of the quantum equilibrium hypothesis, forever unknown to the observer. Yet, the actual configuration is never needed for the calculation of the statistical predictions in experimental reality, for these can be obtained by mere wavefunction algebra.
From this perspective, Bohmian mechanics may appear as a wasteful and redundant theory. I think it is considerations like these that are the biggest obstacle in the way of a general acceptance of Bohmian mechanics. Many authors have expressed critical views of the de Broglie—Bohm theory by comparing it to Everett's many-worlds approach. Many but not all proponents of the de Broglie—Bohm theory such as Bohm and Bell interpret the universal wavefunction as physically real.
According to some supporters of Everett's theory, if the never collapsing wavefunction is taken to be physically real, then it is natural to interpret the theory as having the same many worlds as Everett's theory. In the Everettian view the role of the Bohmian particle is to act as a "pointer", tagging, or selecting, just one branch of the universal wavefunction the assumption that this branch indicates which wave packet determines the observed result of a given experiment is called the "result assumption"  ; the other branches are designated "empty" and implicitly assumed by Bohm to be devoid of conscious observers.
Dieter Zeh comments on these "empty" branches: David Deutsch has expressed the same point more "acerbically": Everett's many-worlds interpretation is an attempt to demonstrate that the wavefunction alone is sufficient to account for all our observations. When we see the particle detectors flash or hear the click of a Geiger counter , then Everett's theory interprets this as our wavefunction responding to changes in the detector's wavefunction , which is responding in turn to the passage of another wavefunction which we think of as a "particle", but is actually just another wave packet.
For this reason Everett sometimes referred to his own many-worlds approach as the "pure wave theory". Talking of Bohm's approach, Everett says: In the Everettian view, then, the Bohm particles are superfluous entities, similar to, and equally as unnecessary as, for example, the luminiferous ether , which was found to be unnecessary in special relativity. This argument of Everett is sometimes called the "redundancy argument", since the superfluous particles are redundant in the sense of Occam's razor.
These authors claim  that the "result assumption" see above is inconsistent with the view that there is no measurement problem in the predictable outcome i. These authors also claim  that a standard tacit assumption of the de Broglie—Bohm theory that an observer becomes aware of configurations of particles of ordinary objects by means of correlations between such configurations and the configuration of the particles in the observer's brain is unreasonable.
This conclusion has been challenged by Valentini ,  who argues that the entirety of such objections arises from a failure to interpret de Broglie—Bohm theory on its own terms. According to Peter R.
Holland , in a wider Hamiltonian framework, theories can be formulated in which particles do act back on the wave function. De Broglie—Bohm theory has been derived many times and in many ways. Below are six derivations, all of which are very different and lead to different ways of understanding and extending this theory.
De Broglie—Bohm theory has a history of different formulations and names. In this section, each stage is given a name and a main reference. Louis de Broglie presented his pilot wave theory at the Solvay Conference,  after close collaboration with Schrödinger, who developed his wave equation for de Broglie's theory.
At the end of the presentation, Wolfgang Pauli pointed out that it was not compatible with a semi-classical technique Fermi had previously adopted in the case of inelastic scattering.
Contrary to a popular legend, de Broglie actually gave the correct rebuttal that the particular technique could not be generalized for Pauli's purpose, although the audience might have been lost in the technical details and de Broglie's mild manner left the impression that Pauli's objection was valid.
He was eventually persuaded to abandon this theory nonetheless because he was "discouraged by criticisms which [it] roused". An analysis of de Broglie's presentation is given in Bacciagaluppi et al. This sealed the fate of de Broglie's theory for the next two decades.
In , Erwin Madelung had developed a hydrodynamic version of Schrödinger's equation , which is incorrectly considered as a basis for the density current derivation of the de Broglie—Bohm theory. Holland has pointed out that, earlier in , Einstein had actually submitted a preprint with a similar proposal but, not convinced, had withdrawn it before publication. After publishing a popular textbook on Quantum Mechanics that adhered entirely to the Copenhagen orthodoxy, Bohm was persuaded by Einstein to take a critical look at von Neumann's theorem.
It was an independent origination of the pilot wave theory, and extended it to incorporate a consistent theory of measurement, and to address a criticism of Pauli that de Broglie did not properly respond to; it is taken to be deterministic though Bohm hinted in the original papers that there should be disturbances to this, in the way Brownian motion disturbs Newtonian mechanics.
The de Broglie—Bohm theory is an example of a hidden-variables theory. Bohm originally hoped that hidden variables could provide a local , causal , objective description that would resolve or eliminate many of the paradoxes of quantum mechanics, such as Schrödinger's cat , the measurement problem and the collapse of the wavefunction.
However, Bell's theorem complicates this hope, as it demonstrates that there can be no local hidden-variable theory that is compatible with the predictions of quantum mechanics. The Bohmian interpretation is causal but not local. Bohm's paper was largely ignored or panned by other physicists.
Albert Einstein , who had suggested that Bohm search for a realist alternative to the prevailing Copenhagen approach , did not consider Bohm's interpretation to be a satisfactory answer to the quantum nonlocality question, calling it "too cheap",  while Werner Heisenberg considered it a "superfluous 'ideological superstructure' ".
I just received your long letter of 20th November, and I also have studied more thoroughly the details of your paper. I do not see any longer the possibility of any logical contradiction as long as your results agree completely with those of the usual wave mechanics and as long as no means is given to measure the values of your hidden parameters both in the measuring apparatus and in the observe [sic] system.
He subsequently described Bohm's theory as "artificial metaphysics". According to physicist Max Dresden , when Bohm's theory was presented at the Institute for Advanced Study in Princeton, many of the objections were ad hominem , focusing on Bohm's sympathy with communists as exemplified by his refusal to give testimony to the House Un-American Activities Committee. In , Chris Philippidis, Chris Dewdney and Basil Hiley were the first to perform numeric computations on the basis of the quantum potential to deduce ensembles of particle trajectories.
Eventually John Bell began to defend the theory. In "Speakable and Unspeakable in Quantum Mechanics" [Bell ], several of the papers refer to hidden-variables theories which include Bohm's.
The trajectories of the Bohm model that would result for particular experimental arrangements were termed "surreal" by some. Bohmian mechanics is the same theory, but with an emphasis on the notion of current flow, which is determined on the basis of the quantum equilibrium hypothesis that the probability follows the Born rule.
The term "Bohmian mechanics" is also often used to include most of the further extensions past the spin-less version of Bohm. While de Broglie—Bohm theory has Lagrangians and Hamilton-Jacobi equations as a primary focus and backdrop, with the icon of the quantum potential , Bohmian mechanics considers the continuity equation as primary and has the guiding equation as its icon. They are mathematically equivalent in so far as the Hamilton-Jacobi formulation applies, i.
The papers of Dürr et al. Bohm developed his original ideas, calling them the Causal Interpretation. Later he felt that causal sounded too much like deterministic and preferred to call his theory the Ontological Interpretation.
Bohm is clear that this theory is non-deterministic the work with Hiley includes a stochastic theory. As such, this theory is not, strictly speaking, a formulation of the de Broglie—Bohm theory. However, it deserves mention here because the term "Bohm Interpretation" is ambiguous between this theory and the de Broglie—Bohm theory. An in-depth analysis of possible interpretations of Bohm's model of was given in by philosopher of science Arthur Fine.
Pioneering experiments on hydrodynamical analogs of quantum mechanics beginning with the work of Couder and Fort   have shown that macroscopic classical pilot-waves can exhibit characteristics previously thought to be restricted to the quantum realm.
Hydrodynamic pilot-wave analogs have been able to duplicate the double slit experiment, tunneling, quantized orbits, and numerous other quantum phenomena which have led to a resurgence in interest in pilot wave theories. A dissipative system is characterized by the spontaneous appearance of symmetry breaking anisotropy and the formation of complex, sometimes chaotic or emergent , dynamics where interacting fields can exhibit long range correlations.
Stochastic electrodynamics SED is an extension of the de Broglie—Bohm interpretation of quantum mechanics , with the electromagnetic zero-point field ZPF playing a central role as the guiding pilot-wave. Modern approaches to SED consider wave and particle-like quantum effects as well-coordinated emergent systems that are the result of speculated sub-quantum interactions with the zero-point field   .
Researchers performed the ESSW experiment. From Wikipedia, the free encyclopedia. Redirected from Bohm interpretation. Classical mechanics Old quantum theory Bra—ket notation Hamiltonian Interference. Schrödinger's cat Quantum suicide and immortality Stern—Gerlach Wheeler's delayed-choice. Quantum annealing Quantum chaos Quantum computing Density matrix Quantum field theory Fractional quantum mechanics Quantum gravity Quantum information science Quantum machine learning Perturbation theory quantum mechanics Relativistic quantum mechanics Scattering theory Spontaneous parametric down-conversion Quantum statistical mechanics.
Quantum-mechanical probabilities are regarded like their counterparts in classical statistical mechanics as only a practical necessity and not as an inherent lack of complete determination in the properties of matter at the quantum level. David Peat, Infinite Potential: The Life and Times of David Bohm , p. Historical Contingency and the Copenhagen Hegemony discusses "the hegemony of the Copenhagen interpretation of quantum mechanics" over theories like Bohmian mechanics as an example of how the acceptance of scientific theories may be guided by social aspects.
Bohm in and and of J. Vigier in as cited in Antony Valentini; Hans Westman Causality and Chance in Modern Physics.
An ontological interpretation of quantum theory , p. The Quantum Theory of Motion: Hamilton-Jacobi theory and particle back-reaction", Nuovo Cimento B , , pp. Journal of Statistical Physics. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. A video of the electron density in a 2D box evolving under this process is available here. Foundations of Physics Letters.
Conclusions , page Krister; Steinberg, Aephraim M. Journal of Physics A: International Journal of Modern Physics. Retrieved 23 December Retrieved 5 December Speakable and Unspeakable in Quantum Mechanics. Journal of Physics B: Atomic, Molecular and Optical Physics. If one could observe them, one would be able to take advantage of that and signal faster than light, which — according to the special theory of relativity — leads to physical temporal paradoxes.
Wiseman, and Aephraim Steinberg: Quantum weirdness may hide an orderly reality after all , newscientist. Quantum Non-Locality and Relativity: Metaphysical Intimations of Modern Physics. Journal of Optics B. Axiomatics for a Standalone Quantum Mechanics". The solution finds a more natural home in the Everett interpretation.
With a little help from my friends. British Journal for the Philosophy of Science 47, , Many Worlds in Denial? Everett, Quantum Theory, and Reality', Eds. Oxford University Press, , Pp. Nonlocality in microsystems , in: Scale in Conscious Experience:
The distribution of creation events is dictated by the wavefunction. Bohm's formulation of de Broglie—Bohm theory in terms of a classically looking version has the merits that the emergence of classical behavior seems to follow immediately for any situation in which the quantum potential is negligible, as noted by Bohm in
In Bohm's original papers [Bohm ], he discusses how de Broglie—Bohm theory results in the usual measurement results of quantum mechanics.