One of the most important interpretative problems of quantum mechanics concerns the so called hidden variables. Sometimes it is said that the Bell's theorem falsifies theories of such variables, but in fact, it falsifies only local ones. This paper deals with David Bohm's interpretation of quantum mechanics, which is a kind of nonlocal hidden variable theory. This theory delivers a full deterministic and realistic description of quantum phenomena and predicts the same results as standard quantum mechanics. It is argued that this interpretation is still worth being investigated, because it remains in the full agreement with the mathematical formalism of this theory and it surpasses the standard interpretation as far as simplicity and lack of arbitrary assumptions are concerned.
One of the most important interpretative problems of quantum mechanics concerns the so called hidden variables. Sometimes it is said that the Bell's theorem falsifies theories of such variables, but in fact, it falsifies only local ones. This paper deals with David Bohm's interpretation of quantum mechanics, which is a kind of nonlocal hidden variable theory. This theory delivers a full deterministic and realistic description of quantum phenomena and predicts the same results as standard quantum mechanics. It is argued that this interpretation is still worth being investigated, because it remains in the full agreement with the mathematical formalism of this theory and it surpasses the standard interpretation as far as simplicity and lack of arbitrary assumptions are concerned.
The de Broglie–Bohm interpretation (Bohmian mechanics, hidden-variables theory, causal interpretation
or pilot-wave theory) is one of the interpretations of quantum mechanics which opposes
to the claim of standard interpretation on the completeness of description of the state of quantummechanical
system, that description in Bohmian mechanics is completed by defining positions of
the particles of the system i.e. hidden variables and their dynamics. These facts are the basis of motivation
for the introduction of a new theory that can describe dubious axiomatic requirements of
standard interpretation. The presented theory is deterministic and explicitly nonlocal. Originators
of Bohmian mechanics were L. de Broglie (1927.) and D. Bohm (1952.) who presented mathematically
more general and conceptual elaborate formulation. Along with the historical overview,
a note is given about the main properties of the theory, such as the issue of nonlocality and hidden
variables. The aim of this paper is to present and explain the main ideas and properties of the
theory as well as to give a systematic overview of present and historical mathematical construction
of the theory and most of all to discuss implications of de Broglie–Bohm theory on the ontology of
quantum-mechanical picture, showcasing examples of the equivalency of the description of a free
particle as a propagation of the plane wave in space or as the ensemble of the trajectories and of
the spreading of the Gaussian wave packet. The main example of the obvious conceptual clashing
of the interpretations is presented: the double-slit experiment, with a detailed examination of the
Bohmian mechanics’ predictions using presented formalism on the two double-slit experiment.
The graphs of trajectories for given examples are obtained.
A brief account of the world view of classical physics is given first. We then recapitulate as to why the Copenhagen interpretation of the quantum mechanics had to renounce most of the attractive features of the clasical world view such as a causal description, locality, scientific realism and introduce a fundamental distinction between system and apparatus. The crucial role is played in this by the Bohr's insistence on the wavefunction providing the most complete description possible for an even individual system. The alternative of introducing extra dynamical variables, called hidden variables, in addition to the wavefunction of the system so as to be able to retain at least some of the desirable features of classical physics, is then explored. The first such successful attempt was that of Bohm in 1952 who showed that a realistic interpretation of the quantum mechanics can be given which maintains a causal description as well as does not treat systems and measuring appeartus differently. We begin with the construction of the Bohm's theory. He introduces particle positions as the hidden variables. The particle positions play a special role in Bohm theory. The particle trajectories are guided by the wavefunction. The Bohm theory is deterministic. The probability enters through a special assumption, ``quantum equilibrium'' hypothesis, for the initial conditions on the ensemble of particle trajectories. The ``wave or particle'' dilemma is resolved by a ``wave and particle'' resolution. The measurements in Bohm theory can be described without mysticism. Bohm's theory is however nonlocal.
Prologue A memorial conference for John Bell, open to the public, was held at Rutgers University around 20 years ago. I gave a short talk there on Bell's views about David Bohm's “hidden variables” formulation of quantum mechanics, a version of quantum mechanics often called the de Broglie–Bohm theory or Bohmian mechanics. This theory was in fact discovered by Louis de Broglie in 1927. In 1952, it was rediscovered and developed by Bohm, who was the first to appreciate its connection to the predictions of standard quantum mechanics. I did not publish the talk. I have decided that it would be appropriate to publish a very lightly edited version of it here, in this volume devoted to the work of Bell on the foundation of quantum mechanics. One reason for doing so is that the connection between Bell and Bohm continues to be somewhat underplayed, with the strength of his advocacy of Bohmian mechanics not properly appreciated. For example, about half of the papers in Bell's collected works on the foundations of quantum mechanics deal with Bohmian mechanics. But in his fine introduction to the revised edition of this great book [1], Alain Aspect mentions this theory in only a single sentence, and parenthetically at that. For several decades after Bell proved his nonlocality theorem, based in part on Bell's inequality, it was widely claimed that Bell had shown that hidden variables – and Bohmian mechanics in particular – were impossible, that they were incompatible with the predictions of quantum mechanics. For example, the great physicist Eugene Wigner, who, unlike most of his contemporaries, was profoundly concerned with the conceptual foundations of quantum mechanics and usually wrote on the subject with great clarity and insight, has written that This [hidden variables] is an interesting idea and even though few of us were ready to accept it, it must be admitted that the truly telling argument against it was produced as late as 1965, by J. S. Bell … This appears to give a convincing argument against the hidden variables theory.
Previously suggested hidden time interpretation of quantum mechanics allows to reproduce the same predictions as standard quantum mechanics provides, since it is based on Feynman many - paths formulation of QM. While new experimental consequences of this interpretation are under investigation, some advantages can be enumerated. (1) The interpretation is much field theoretic - like in classical sense, so it is local in mathematical sense, though quantum (physical) non-locality is preserved. (2) The interpretation is based on one type of mathematical objects, rather than two different (Hilbert space vectors and operators). (3) The interpretation, as it was argued, overcomes the problem of hidden variables in a radically new way, with no conflict to Bell's theorem. Recently an important argument against hidden variables - like formulations of quantum theory was risen - "no protocol" argument. It is argued in the paper, that hidden time interpretation successfully overcomes this argument.
Abstract Nowadays, David Bohm’s hidden variables interpretation of quantum mechanics is one among other possible interpretations of quantum mechanics. In 1952 when he published this interpretation, he could not foresee the complex denouement it would have. I argue that the initial poor reception of Bohm’s proposal, as well as his discouragement in the late 1950s, was related to the prejudices among physicists concerning the hidden variables issues, and its later revival, in the mid-1970s, without any new evidence corroborating it, was related to a new intellectual ambiance concerning interpretational issues. However, even today, there is a persistent misunderstanding about what interpretations may be compatible with quantum mechanics. Lessons from this history for the practice of science are related to the role played by prejudices even in advanced fields of scientific research and the need to overcome them.
An interpretation of Quantum Mechanics published at the International Journal of Quantum Foundations. Abstract: A new interpretation of quantum mechanics is presented in which there is one hidden variable. This could be described as “partial realism” where sometimes quantum variables have real values before we measure and sometimes they don’t. While one hidden variable is insufficient to explain Bell nonlocality, it is allowed by Bell’s inequality. This can help solve the measurement problem and may, in principle, be testable. In addition, a theory of nonlocality emerges directly from this assumption. From the perspective of an outside observer, not correlated with an observed system, we treat all interactions within the system as unitary. However, from the perspective of an “observer” inside the system, we treat all new entanglements as “micromeasurements”, as a projection onto some basis of measurement. One particle can act as a measurement device on another and give the other particle a defined value on one possible measurement axis from an inside perspective. This means that the wave function, from the outside view, will at times describe an objective, fundamentally stochastic uncertainty, at other times a subjective uncertainty that reflects only our lack of knowledge, and at yet other times a combination of both. The standard wave function describes the total uncertainty, the minimal uncertainty that is present for any observer outside of the system, whereas for an “observer” inside the system, only the objective, fundamentally stochastic part of the uncertainty remains, and this can be described by an inner wave function. The hidden variable is invisible to the outside observer.