On the other hand the Bohm interpretation of quantum mechanics keeps counter-factual definiteness while introducing a conjectured non-local mechanism in form of the ' quantum potential ', defined as one of the terms of the Schrödinger equation.

* Bohm interpretation

An example is the Bohm interpretation of quantum mechanics.

However, until the end of his life de Broglie returned to a direct and real physical interpretation of matter-waves, following the work of David Bohm.

The de Broglie – Bohm theory, also called the pilot-wave theory, Bohmian mechanics, and the causal interpretation, is an interpretation of quantum theory.

He uses this generalized probabilistic interpretation to formulate a relativistic-covariant version of de Broglie – Bohm theory without introducing a preferred foliation of space-time.

Bohm and Hiley have stated that they found their own choice of terms of an " interpretation in terms of hidden variables " to be too restrictive.

Decades later John Bell proved Bell's theorem ( see p. 14 in Bell ), in which he showed that, if they are to agree with the empirical predictions of quantum mechanics, all such " hidden-variable " completions of quantum mechanics must either be nonlocal ( as the Bohm interpretation is ) or give up the assumption that experiments produce unique results ( see counterfactual definiteness and many-worlds interpretation ).

The Madelung equations, being quantum Euler equations ( fluid dynamics ), differ philosophically from the de Broglie – Bohm mechanics and are the basis of the hydrodynamic interpretation of quantum mechanics.

* ( Demonstrates incompleteness of the Bohm interpretation in the face of fractal, differentialble-nowhere wavefunctions.

* 1952 David Bohm propose his interpretation of quantum mechanics

* the Bohm interpretation

Decoherence provides an explanatory mechanism for the appearance of wavefunction collapse and was first developed by David Bohm in 1952 who applied it to Louis DeBroglie's pilot wave theory, producing Bohmian mechanics, the first successful hidden variables interpretation of quantum mechanics.

The currently best-known hidden-variable theory, the " causal " interpretation of the physicist and philosopher David Bohm, originally published in 1952, is a non-local hidden variable theory.

* Bohm interpretation

The alternative realist Bohm interpretation and many-worlds interpretation of quantum mechanics do not make such a revolutionary break with the concepts of classical physics.

In the 1990s Gordon Pask pointed out von Foerster's H and Hmax were not independent and interacted via countably infinite recursive concurrent spin processes ( he favoured the Bohm interpretation ) which he called concepts ( liberally defined in any medium, " productive and, incidentally reproductive ").

The Bohm interpretation preserves realism, hence it needs to violate the principle of locality in order to achieve the required correlations.

Recently, the debate reached the level of a journal publication, interpretation of the Josephson effect here was performed on the basis of the alternative theory of superconductivity as a manifestation of Aharonov – Bohm effect.

Bohm interpretation gives an explanation based on nonlocal hidden variables for the correlations seen in entanglement.

De Broglie – Bohm theory tries to solve the measurement problem very differently: this interpretation contains not only the wavefunction, but also the information about the position of the particle ( s ).

* de Broglie – Bohm – Bell pilot wave formulation of quantum mechanics

Non-locality, however, soon became established as an integral feature of quantum theory ( see EPR paradox ), and David Bohm extended de Broglie's model to explicitly include it.

In the resulting representation, also called the de Broglie – Bohm theory or Bohmian mechanics ,, the wave – particle duality is not a property of matter itself, but an appearance generated by the particle's motion subject to a guiding equation or quantum potential.

The pilot wave model, originally developed by Louis de Broglie and further developed by David Bohm into the hidden variable theory proposes that there is no duality, but rather a system exhibits both particle properties and wave properties simultaneously, and particles are guided, in a deterministic fashion, by the pilot wave ( or its " quantum potential ") which will direct them to areas of constructive interference in preference to areas of destructive interference.

In his later career, de Broglie worked to develop a causal explanation of wave mechanics, in opposition to the wholly probabilistic models which dominate quantum mechanical theory ; it was refined by David Bohm in the 1950s.

As Bohm and Hiley worded it, " the Schrodinger equation for the quantum field does not have sources, nor does it have any other way by which the field could be directly affected by the condition of the particles [...] the quantum theory can be understood completely in terms of the assumption that the quantum field has no sources or other forms of dependence on the particles ".

In Bohm's original papers 1952, he discusses how de Broglie – Bohm theory results in the usual measurement results of quantum mechanics.

Similarly, in the de Broglie – Bohm theory, there are anomalous initial conditions which would produce measurement statistics in violation of the Born rule ( i. e., in conflict with the predictions of standard quantum theory ).

It is in that qualified sense that Born rule is, for the de Broglie – Bohm theory, a theorem rather than ( as in ordinary quantum theory ) an additional postulate.

In Dürr et al., the authors describe an extension of de Broglie – Bohm theory for handling creation and annihilation operators, which they refer to as " Bell-type quantum field theories ".

However, while standard quantum mechanics is limited to discussing the results of ' measurements ', de Broglie – Bohm theory is a theory which governs the dynamics of a system without the intervention of outside observers ( p. 117 in Bell ).

De Broglie – Bohm theory gives the same results as quantum mechanics.

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.

The de Broglie – Bohm theory makes the same ( empirically correct ) predictions for the Bell test experiments as ordinary quantum mechanics.

Bohm's formulation of de Broglie – Bohm theory in terms of a classical-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 1952.

While the ontology of classical mechanics is part of the ontology of de Broglie – Bohm theory, the dynamics are very different.

It extended the original Pilot Wave Theory 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 ).

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.

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.

The de Broglie – Bohm theory of quantum mechanics is a theory by Louis de Broglie and extended later by David Bohm to include measurements.