I don’t think this is necessary.
In a dynamic environment physical processes become probabilistic, but each instant of interaction may still be mathematically deterministic.
Perhaps this is where “superposition” makes it’s entrance.
In a dynamic (chaotic) environment the action may be influenced by the available mathematics at “that moment”, before the condition changes and alters the applicable mathematics.
I believe that is contained in the “theory of relativity”.
Example; The mathematics of the doppler effect result in a difference of observed mathematics, depending on the movement of a travelling source emitting a mathematically unchanging pitch, relative to the POV of the observer.
I think the key statement is “trivially limited”. It is not an argument in my opinion against determinism so much as an argument about the limitations of logic.
In any case your comment is accurate but I’m not so sure that Bohm isn’t saying the same thing only he puts the need for a new mathematics in the future as his theoretical system unfolds new knowledge.
This is complicated stuff and I don’t pretend to understand all of it.
As I understand it, Bohm argued that a particle, instead of possessing a dual potential, may travel as a particle riding a larger universal “pilot wave” that results in a guiding principle in addition to the particle’s trajectory.
In the double slit experiment this would result in identical results and still agree with Schrodingers equation.
The result is the simplification of the particle /wave duality per the Copenhagen Convention, to a travelling particle carried by a larger wave function.
Pilot Wave theory
The de Broglie–Bohm theory, also known as the “pilot wave theory”, Bohmian mechanics, Bohm’s interpretation, and the causal interpretation, is an interpretation of quantum mechanics.
It postulates that in addition to the wavefunction, an actual configuration of particles exists, even when unobserved. The evolution over time of the configuration of all particles is defined by a guiding equation. The evolution of the wave function over time is given by the Schrödinger equation De Broglie–Bohm theory - Wikipedia
It does away with that pesky particle/wave duality that has plagued the Copenhagen Interpretation since its inception.
In Bohmian Mechanics a particle is always a particle and a wave is always a wave. They are two different objects.
And that is where the “Pilot Wave” makes its entrance. AFAIK, the universe expands in a wavelike manner. It is this greater wave that pilots everything in the universe. But “locally” this wave does respond to wave interference.
OTOH, traveling particles have a distinct position at all times, but they are riding a wave that experiences interference, giving the appearance that it is the particle that experiences wave interference while in awavelike state.
There are 2 moving objects (a particle and a wave), instead of one moving object in two different physical states (duality), which is really against standard physics.
Wave-particle duality is the concept in quantum mechanics that quantum entities exhibit particle or wave properties according to the experimental circumstances.[1]: 59
It expresses the inability of the classical concepts such as particle or wave to fully describe the behavior of quantum objects.[2]: III:1-1
Yes well with 10 years of particle physics education maybe I would understand some of this. I will keep at it but I suspect it will never make me better educated than a bright junior high school child.
