David Bohm:
"Causality and Chance in Modern Physics" (1957)

(Copyright © 2014 Piero Scaruffi | Legal restrictions )
I suspect that very few people have actually read this frequently cited book. It is an extremely difficult book because it deals with philosophy of science and it is written in the worst possible combination of scientific and philosophical language: technical like science but vague and obscure like philosophy.

Most of the book simply summarizes development in Physics that led to a critique of Newton's determinism: Electromagnetism, Thermodynamics and Quantum Mechanics changed the Newtonian worldview that the world is made of (lcalized) bodies and bodies interact via forces. There are different levels of description. What appears to be a deterministic law can be shown to be just a statistical regularity of chaotic processes when observed from a lower level. On the other hand, chaotic motion can be shown to be caused by deterministic laws at an even lower level. And so forth. One is not entitled to assume that a deterministic description works in all possible contexts (that even the apparently random fluctuations will be reduced to deterministic laws), nor that a probabilistic description works in all possible contexts. Deterministic description and probabilistic description coexist and complement each other. Each side gives an approximate description of reality. It so happens that subatomic physics is statistical in nature (we can only know probabilities), but that does not mean that this is the end of the story. Based on this philosophy, Bohm argues (with no empirical evidence) that Quantum Mechanics too is only an approximation of a broader theory will would turn out to be deterministic and continuous. Bohm has faith in a level below quantum mechanics that is more fundamental. Quantum theory is not complete and is only an approximation, just like Brownian motion can be explained if one could go to the atomic level. One could imagine, for example, oscillations described by nonlinear equations for which only some discrete stable frequencies of oscillation exist, such that if the oscillations are moved away from one frequency they will quickly fall into another stable frequency, yielding the impression that there was a discrete jump from one state to another and no continuous change, when in reality they transitioned very rapidly through the unstable regions. Bohm doesn't view Heisenberg's indeterminacy principle as a fundamental law of nature but as a simple fact of the subatomic level: an accurate definition of the position requires light of short wavelengths, i.e. a large momentum; and an accurate measurement of momentum requires light of very low momentum, i.e. long wavelengths (Einstein's formula E=hv can be expressed also as a proportionality between momentum and wavelength). Von Neumann thought he had proved that the indeterminacy principle constitutes an unassailable limit, no matter what refinement can come in the future, that a science in which classical causality applies cannot possibly exist, but Bohm argues that Von Neumann cheated: Von Neumann assumed that at all levels of the universe behave like the quantum level, in probabilistic fashion. Bohr interpreted the indeterminacy principle as saying that the measuring apparatus and the observed object constitute one indivisible whole whose parts cannot be analyzed separately, and Bohm sees this as a more legitimate approach. Bohm thinks that quantum mechanical effects arise from a sub-stratum of continuous motion and continuous degrees of energy, a substratum whose laws generate the laws of Quantum mechanics at the higher level of the subatomic world. Bohm sees evidence of this substratum in the fact that Quantum Mechanics runs into trouble at very short distances at very high energy (infinite values appear that physicist have to "normalize"). Bohm's explanation for those difficulties is that there is a subquantum process that is continuous but is also very fast, happening at such very high frequency (E=hv) that at the quantum level it appears to be discrete jumps. This idea that Quantum Mechanics needs to be "completed" at a lower level was predated by French physicist DeBroglie ("On the role of continuous waves in wave mechanics", 1927) and by Soviet physicists Dmitri Blokhinzhev ("Criticism of the Philosophical Views of the Copenhagen School", 1951). Bohm was not aware of them when he first formulated it ("A Suggested Interpretation of the Quantum Theory in Terms of Hidden Variables", 1952).

The most daring part of the book comes at the end. Everything in the universe changes all the time and the parameters required to fully determine it are infinite in number. Things are maintained in existence by a balance of the processes tending to change them. Everything changes all the time, which implies that everything has to change all the time in order to adapt to everything that has changed around it. The ability to change and become something else is a fundamental property of things, otherwise they wouldn't be. A thing always becomes something else, and something that was not contained in the original concept of that thing. All things undergo qualitative transformations. All things become other kinds of things, and influence each other's transformations. Nothing can be defined by a finite number of parameters.
Because of this "qualitative infinity of nature", there is potentially an infinite number of theories that explain other theories . Whenever we examine a thing, we are limiting ourselves to the parameters that are useful in our context, but that thing actually has an infinite number of parameters that could become important in other contexts. A thing cannot be defined by an immutable and finite set of parameters. A thing has an infinite number of parameters in common with what it was before, but also an infinite number of parameters that are different from the ones it had before. We can talk about a thing by considering some of the parameters that are in common at different moments. Laplace's determinism is impossible because we can never know all the initial conditions, which are infinite in number But that does not exhaust the set of parameters that truly define that thing. A different context will require a different theory to study that thing, a theory that takes into account some of the parameters that we initially ignored. Since there is an infinite number of parameters in the "qualitative infinity of nature", there is an infinite number of theories.
On the other hand, the process of becoming is not arbitrary: we can always explain why something happened, we can always trace back its origin. What we cannot do is to foretell the future because the number of possible influences is infinite. We can figure out which (finite) causes caused something, but we cannot calculate all the (infinite) possible effects on something by everything else. What happens next depends on a potentially infinite number of parameters. a thing is just an abstraction from a unitary process of becoming: everything is related to everything else. We can abstract an individual thing by ignoring most of the parameters that define it (most of the influences from other things) but it is only an abstraction. Any theory about that individual thing, or a set of individual things, is an approximation of the total reality, which is infinitely complex. Anything is in principle knowable, and we can keep refining and improving our knowledge of the whole, but the whole of reality is infinitely large, which means that no matter how many millions of years we study the universe we will never completely know it. The number of abstractions that we can extract from this totality is infinite, and therefore we can form an infinite number of theories, each of which is only an approximation of the complete truth. We get to know more and more of the absolute by studying the relative.
The problem with Bohm's discussion is (ironically for a physicist) terminology. We never get a clear-cut definition of "qualitative infinity of nature": why "qualitative" and not simply "Infinity"? What happens if i drop the "qualitative"? The title of the book is "Causality and Chance". We get a thorough discussion of causality, but what he means by "chance" remains a bit obscure. Is it just another word for "probability"? Bohm repeatedly mentions "laws of chance": if there is a law, then it is not chance.

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