You can't say you are describing the system completely if you can only make a vague prediction.
That is because the unverse is not a static condition. These are some of the problems Bohmian Mechanics solves,
locality and
entanglement at great distances.
He saw the universe as a dynamic Wholeness, where if one thing happens in one place it affected something else, regardless where in the universe, i.e. Looking at it from that perspective the "Wholeness" presents some "hidden variables", which are in conflict with the Standard Model.
A very simplified example of a deterministic probability ; Assume 2 hydrogen atoms millions of miles apart from an oxygen atom.
Each atom is following a path that creates a probability they will intersect with the other two in the future. Pure determinism would bring these atoms together and form a water molecule. But these deterministic paths are dependent on absolute straight lines for the atoms to meet at the deterministic point.
But suppose somewhere else a star goes nova and creates a wave function which interferes with one of the atoms and shifts its path so that it will no longer intersect with the other two. Result, no water molecule at the original intersection.
Thus while the bonding of H2O is a deterministic process, the chance of meeting of the individual parts is probabilistic.
This led Bohm to the concept of
hidden variables, which is actually the only real deviation from the standard madel. He called this the Guiding Equation, which does not exist in the Standard Model.
Can we say that when those atoms were far apart from each other there was a % probability of meeting. Probabilities are not fixed and deterministic in and of themselves. There is a range of probabilistic events, from 100% certainty (purely deterministic), to possible but with a .000000000001% low level of probability and certainly not deterministic to a specific result at a specific time.
Robert Hazen explained this in his presentation of the probability of life evolving from bio molecules, which would require the exact necessary conditions which make this possible. Hazen called it the
bottleneck, where conditions must be just right to
allow for such an event to happen. Start the clip @ 25:25 to avoid a lenghty introduction.
Thus, IMO, determinism rests on probability, which rests on possibility, which rests on potential, which rests on mathematical values and functions.
A hierarchy of orderings, which may or may not result in a specific event.
During the early time of inflation, the Wholeness was in a compressed state and just after the Inflationary Epoch, probabilistic events were common, the potential for particle interaction had a very high probability of deterministic events. But as the universe expanded and continous to expand dynamically the potential for interaction persists, but the range of probabilities goes down.
One can argue that Determinism means something must happen precisely as the original state would indicate. But I don't believe this is the case. In a dynamic environment there are just to many variables to assure deterministic results every time and this gave rise to
locality in the Standard Model which of course is easier to measure.
But look at a a piece of flotsam in the middle of the ocean. Can we possibly predict where it will make landfall, if ever?
Or look at a cloud, the dynamics in such environments are so complicated that, while we know something will happen (will eventually become deterministic in some way), there is no possibility to accurately predict what, where, and when something will happen.
Thus weather forecasts can only be made in very short increments, based on available information, and even then are "best guesses". That's why weather forecasters speak in terms of "chance of rain", or "expected to develop into a hurricane".
I'll readily admit that this is my "best understanding (guess)" of Bohmian Mechanics. Bohm had the maths to back up his claims, I don't.....
