A Hypothesis: Res Potentia and Res Extensa Linked By Measurement

I wish to explore a hypothesis first put forward clearly by Alfred North Whitehead in his masterwork Process and Reality in 1927. Whitehead proposed that reality consists of two Realms, the Possible and the Actual, in which Actuals give rise to Possibles, which in turn give rise to Actuals. Whitehead built his worldview on events and their relations, not objects.  Heisenberg, one of the major founders of Quantum Mechanics, as I quote below, held much the same view of the reality of the Possible and the Actual.

I think the Feynman formulation of quantum mechanics as a sum over all possible histories, and, roughly, the Copenhagen interpretation of quantum mechanics, may be interpretable to support a scientific interpretation of reality as consisting in ontologically real Possibles, Res Potentia and ontologically real Actuals, Res Extensa, linked by the quantum measurement “process.”  This view, foreshadowed by Heisenberg, may be a new interpretation of quantum mechanics, or not. In its strong form, below, it seems to be a new scientific claim.

Consider first Feynman’s sum over history's formulation of quantum mechanics, held by all to be an equivalent formulation of quantum mechanics. We must, he says, think of a single photon traveling through the two slits of the well know two slit experiment with its famous interference patterns as possibly passing through the left slit and simultaneously possibly not passing through the left slit.

Now consider 19th Century American philosopher C.S. Pierce. Pierce noted that Actuals and Probables obey Aristotle’s Law of the Excluded Middle.  Possibles, he said, do not obey the law of the Excluded Middle.

Here is the Law of the Excluded Middle in logic: The statements “A” or “Not A” are all that can be true; there is nothing in the middle between “A” or “Not A.” The union of the statements “A AND Not A” is a contradiction, always false. The Law of the Excluded Middle applies full force to classical physics, (and to algorithmic Turing Machines). Now think of a probability statement, “The probability of 4,599 heads in 10,000 flips of a fair coin is 0.021”. The statement is either true or false.  There is nothing in the middle. “The probability of 4,599 heads in 10,000 flips of a fair coin IS 0.021.” AND “The probability of 4,599 heads in 10,000 flips of a fair coin IS NOT 0.021.” is a contradiction and always false.

Now consider Feynman’s statement above about the photon “Possibly passing through or simultaneously possibly not passing through the left slit.”  Now consider the union: “The photon possibly does pass through the left slit and simultaneously possibly does not pass through the left slit.” AND “The photon possibly does not pass through the left slit and simultaneously does pass through the left slit.”

This is not a contradiction. Feynman’s statement does not obey the Law of the Excluded Middle.  Feynman’s statement, which is part of a full formulation of quantum mechanics,  is consistent with being a statement about Pierce’s “Possibles.”

Due to superpositions of the solutions of the time reversible linear Schrodinger wave equation, many of the “weird” quantum effects arise. Thus, before measurement occurs, “Schrodinger’s cat is simultaneously possibly dead and possibly alive.”

I therefore think it is of importance to consider Whitehead’s  and Heisenberg’s view again.  I propose as an hypothesis that we consider reality as consisting of two ontological realms, Res Potentia, the realm of the Possible, and Res Extensa, the realm of the Actual. In this view the “unitary propagation of the time reversible Schrodinger equation” lies in Res Potentia. The classical world lies in Res Extensa. The two are linked by the “measurement process” which used to be called, following von Neumann’s axiomatization, “the collapse of the wave function” from quantum to classical.

I quote Shimon Malin, a quantum field theorist, from “Physics and Whitehead” (Ed. T.E. Eastman and H. Keaton):

According to Heisenberg, the interplay between the two modes of quantum systems, being isolated and being measured, is an interplay between potentialities and actualities.

No haste should be made in accepting such a radical view. Outstanding physicists are working on the “measurement problem,” which remains unsolved since 1927.  Theories range from the decoherence of open quantum systems (into their quantum environments) to classicality for all practical purposes, FAPP, to spontaneous collapse, to the Bohm interpretation of quantum mechanics, to objective reduction where R. Penrose hopes to show a link between gravity and measurement, to “modal” interpretations which include possibility statements, but not an ontologically real Res Potentia.  All of these hope to find an account, within quantum mechanics itself, of the  measurement process.  Nothing has worked to general satisfaction so far, but perhaps a way will be found.

The postulate of Res Potentia and Res Extensa linked by the measurement process comes in a weak and a strong version. The weak version remains agnostic about the hoped for success in solving the measurement problem from within quantum mechanics itself. The strong version states that there is no solution to the measurement problem from within quantum mechanics. There may be no logical entailment from a science, Quantum Mechanics before measurement, that is open to interpretation as being about ontologically real Possibles, that, as such, evade the Law of the Excluded Middle, to a science about ontologically real Actuals that, as such, obey the Law of the Excluded Middle, classical mechanics. On this strong version, “measurement” is not a substance or a temporal process, but a becoming: It is the Possible becoming Actual, and “just happens”. Quoting Malin again, “Heisenberg’s interpretation implies that the collapse of a quantum state is not a process in time.” The weak version may at most be a new interpretation of Quantum Mechanics. The strong version is a scientific proposal, which may be true or false.



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