"According to D. Bohm's interpretation of quantum mechanics, a particle always has a well-defined spatial trajectory... According to Bohm's theory, particles have definite positions and velocities at all times."
This isn't well-stated. A particle always has a well-defined position. But it's problematic either way because Bohmian mechanics arguably isn't really a mechanics at all:
"Since Bohmian mechanics is not about measurements but about ontology, namely particles, it has no measurement problem. However, since quantum mechanics does have the measurement problem, one may wonder whether Bohmian mechanics might not have another problem, namely that it is not a correct description of nature." p. 173
It has no measurement problem because it doesn't deal with empirical results. Only the formalism. As an ontological framework, Bohmian physics isn't "Bohmian mechanics" but something quite different.
Bohmian mechanics assumes point-particles that are waves (or governed by wave dynamics; how Bohm formulated his theory grew more nuanced over time as well as more philosophical). Bohm takes quantum mechanics and this assumption and says "here's what we can say." The problem is that this doesn't really say much of anything and Bohm knew this. Those who follow Bohm know this:
"Bohmian mechanics is about particles guided by a wave. This is new, but not revolutionary physics. This chapter will now present a paradigm shift. It is about how nature is, or better, it is about how any theory which aims at a correct description of nature must be. Any such theory must be nonlocal. We do not attempt to define nonlocality...but simply take it pragmatically as meaning that the theory contains action at a distance in the true meaning of the words, i.e., faster than light action between spacelike separated events."
Bohmian mechanics is deterministic only in the sense that it takes as given particles exist and then says the deterministic wave equations which don't describe particles (but waves) do describe particles in ways that we don't know and that are indeterministic in unknown senses:
"Nevertheless, independently of the specific proposals that we have made here, the essential point with regard to the question of mechanism is that the fluctuations should come from qualitatively new kinds of factors existing in a new domain.
Within the new domain described above, we would naturally expect that new kinds of laws would operate, which may include new kinds of causal laws as well as new kinds of laws of chance. Of course, if one were now to make the assumption that these new laws would surely be nothing more than purely causal laws, one would then fall back into deterministic mechanism, while the similar assumption that they were surely nothing more than laws of probability would throw one back into indeterministic mechanism. On-the other hand, we have in the proposals made in this chapter avoided both these dogmatic and arbitrary extremes, since we have considered, as the situation demanded, the possibility that there are new features to the causal laws (a quantum force not appearing at higher levels) as well as to the laws of chance (random fluctuations originating in the sub-quantum mechanical level)"
"sub-quantum mechanical level" == "hidden variables". But Bohm regards it as fundamentally "hidden." In fact, Bohm is critical of mechanics itself (he calls it unscientific).
"Bohm here seems to presume that a hidden-variables theory will attempt to restore a picture of particles with definite positions and momenta..."
Bohm-proponents, from Bell to P. T.I. Pylkkänen, have universally recognized that his theory is nonlocal. If particles exist, then they must be (by definition) defined by precise positions. This cannot explain empirical results. Ergo, something determines their position which does not obey any laws we know of and cannot. Perhaps it's faster-than-light-travel, perhaps it's incoming waves, perhaps it's conscious observation, perhaps it is that all matter is both wave and particle all the time (and thus is always and forever both deterministic and indeterministic; on this and how it features centrally in Bohm's interpretation as well as in its relevance today see Mind, Matter, and the Implicate Order by Pylkkänen). But the point is that formally, Bohmian mechanics is simply a spin-off of the Copenhagen interpretation in which the collapse of the state vector is removed but not really replaced, and classical physics doesn't emerge from it. It describes a quantum realm in which particles are defined locally in ways that cannot be used to recover the world we experience, our observations, or anything at all (hence the "it's not about measurement" bit, which is essentially equivalent to saying it isn't physics). As a conceptual model, we have something else altogether.
And despite the fact that most critiques of (and supportive sentiments of) Bohmian mechanics stem from this idea that the Bohm interpretation (or Boglie-Bohm interpretation) is deterministic, Bohm doesn't exactly make it difficult to realize that his interpretation is wholly, completely, and clearly not a deterministic one:
"So, in terms of this notion, the idea of a separately and independently existent particle is seen to be, at best, an abstraction furnishing a valid approximation only in a certain limited domain. Ultimately, the entire universe (with all its particles, including those constituting human beings, their laboratories, observing instruments, etc.) has to be understood as a single undivided whole, in which analysis into separately and independently existent parts has no fundamental status." p. 221
Bohm's Wholeness and the Implicate Order (Routledge; 1980)
Yes. I've just never understood it's prevalence. Here's a guy who cites everybody from von Mises to Piaget, who has written accessible books and whose essays have been put together by others (if memory serves, with a preface by the Dalia Lama), and who has much more potential to be misunderstood by mystics and other esoteric approaches to reality than most "quantum mysticism" published for mainstream readers, yet a few papers and a textbook have so dominated how Bohm is understood. His work on causation was written in '57. The quote immediately above is from a book published in 1980. It's not like the guy was keeping himself quiet. It's just that he had a deep and abiding interest in philosophy of a type that used to define physics and sciences in general yet has faded almost everywhere (unfortunately). So much of what he wrote is ignored. Your 2nd quote, for example, is almost identical to a line in one of the two papers by Bohm that are generally cited in the physics literature, "A Suggested Interpretation of the Quantum Theory in Terms of "Hidden" Variables. II". Yet it contains a subtle distortion: "In our interpretation, however, we assert that the at present "hidden" precisely definable particle positions and momenta determine the results of each individual measurement process". Given that Bohm refers in this same paper to "forces [that] may be said to transmit uncontrollable disturbances instantaneously from one particle to another" and his repeated references to a "conceptual model", why it is not understood that his physical interpretation of "particles" is simply to assume they exist (and therefore necessarily have a position, even if it is "continuously varying", quantifiable only to a limited degree, and necessarily located in space only via superluminal forces which determine it's dynamics) is beyond me.
and that Bohm's is one such
is also pretty common amongst proponents of the KA/CA
In my experience, most proponents of the KA/CA arguments only know it through distilled, simplified versions (usually supplied thanks to Craig, who apparently doesn't mind simplifying his own work to be indefensible if it means we have legions of theists who are supplied with half-baked versions of Craig's own arguments and his abuse to Plantiga's). You're the first I've read here who defended classical causality by referencing so-called deterministic interpretations of QM.
In any event, it doesn't really matter as you aren't defending the proposition so much as saying that it doesn't matter even if it were true.
