The Ontological Interpretation

It is noted that a system of particles reaches equilibrium when the resulting forces on them are zero, and hence the quantum force on a free particle must be perceived to vanish. This requires the quantum potential to be either zero or a constant, independent of position. The first condition relates to a classical particle, whereas the second condition implies 

In terms of the quantum-potential formulation particle trajectories can be associated with the quantum HJ equation (6) in exactly the same way as in the classical case [34, 35]. As before, particle trajectories associated with the phase S may be obtained by constructing the normals to S, each one distinguished by its initial coordinates. By this procedure Bohm managed to revive the pilot-wave model of De Broglie. It means that a point particle of mass m on a trajectory x = x(t), is now associated with the physical 

The particle is now separate from the quantum field that affects it. This field is given by 

Although is a field as real as Maxwell s fields, it does not show up immediately as the result of a single measurement, but only in the statistics of many measurements. It is the De Broglie-Bohm variable x that shows up immediately each time. The particle has an equation of motion (T3.2) 

This equation shows that in addition to the classical force — W acting on the particle there is also the quantum force —Wq. 

---

Bohmian mechanics refers to the ontological interpretation of quantum theory pioneered by Bohm [4]. The mathematical structure of the theory is not affected by the different interpretation and the same formalism adopted before [7] will be used here. 

No record of any discussion of radiation damping based on the ontological interpretation could be found. One major simplification would be that in terms of this approach electrons in real stationary states have no kinetic energy and will be accelerated from rest. 

The chemistry community, understandably, failed to respond at all, even though Bohmian mechanics probably holds the key to the development of a theory of chemistry, soundly based on quantum theory and relativity. The problem with molecular structure is resolved by the ontological interpretation of quantum-mechanical orbital angular momentum and the key to chemical reactivity and reaction mechanism is provided by the quantum potential function. 

D. Bohm and B.J. Hiley, The undivided universe. An ontological interpretation of quantum theory, Routledge, London, 1993. 

In his latest works Vernadsky tries to do it by means of the four basic notions natural body, duration, symmetry and entropy. It is not the way to solve the double-temporality problem completely, but it is the way to take the problem out of the biosphere and consequently out of the domain of phenomena Vernadsky mainly deals with. The hypothetical methodological ground of this approach could be interpreted in the following way assume that in the frame of the bio here there are some fundamentally different kinds of natural bodies and fundamentally different kinds of processes in which they participate. Then reduce the times to the properties of these natural bodies. Doing so, we could define the peculiarities of the different times . The ontological consequences of this step will be for now ignored. 

The meta-interpreter in our framework is constructed for reasoning with the metaprograms MPs, MMPs, and AMPs. It is defined by a demo predicate of the form demo (A). With this predicate we can infer the answer A from the meta-programs. Our meta-interpreter adapts the Vanilla meta-interpreter in [12] in order for reasoning with the meta-programs transformed from ontologies and rules where we have defined three kinds of meta-level statements (1) statement (A B) for the object-level of an ontology, (2) meta statement (A B) for the... 

If we would try to find an ontological interpretation of the Bom-Oppenheimer hierarchical type of quantization, surely the concept of quantization of atomic centers would be more adequate description than the concept of quantization of nuclei motion. The question arises how to retrace the simultaneous quantization of the unit system of electrons and nuclei. The author solved this problem in his... 

The second part of the answer to the difference between a formal verification and a safety case is that a formal verification generally takes the formalized premises and conclusion as given and is focused on the demonstration that the latter follows from the former. A safety case will add to this careful justification that the premises are true of the system concerned, and that the formal conclusion does indeed support the real-world interpretation required of it. An instructive illustration of these differences between a formal verification and a case is provided by formal verification of the Ontological Argument [10] this is a formally correct proof of the existence of God—a claim that will cause most readers to examine its premises and the formalization of its conclusion with especial interest. 

---