October 12, 2006

Completeness and consistency

How can a fundamental physical theory that is concerned with nothing but statistical correlations between property-indicating events be complete? To show that quantum mechanics is indeed a complete theory, one has to show that it in fact encompasses the property-indicating events. The PIQM does this by showing that the theoretical structure of the theory encompasses the macroworld, and that the macroworld in turn encompasses property-indicating events as unpredictable changes in the values of macroscopic positions. What is incomplete is not quantum mechanics but the spatiotemporal differentiation of the physical world.
Again, no value is possessed unless its possession is indicated — by another value. The PIQM steers clear of the threatening infinite regress by showing that, for all quantitative purposes (rather than merely FAPP), the values of macroscopic positions are self-existent.
Supervenience, manifestation
Erwin Schrödinger: quantum entanglement is the characteristic trait of quantum mechanics. John Archibald Wheeler: the central mystery of physics is the miraculous identity of particles of the same type. Richard Feynman: the double-slit experiment with electrons has in it the heart of quantum mechanics. Henry Stapp: Bell’s proof that the principle of locality is incompatible with quantum mechanics is the most profound discovery in science. According to the PIQM, all of these extraordinary features of quantum mechanics are subsumed and eclipsed by the supervenience of the microscopic on the macroscopic.
The properties of the microword exist only because, and only to the extent that, they are indicated by events in the macroworld. This flies in the face of the twenty-five centuries old atomistic paradigm. It is no longer appropriate to ask: what are the ultimate building blocks, and how do they interact and combine? If we accept Mohrhoff’s suggested identification of the Indian metaphysical concept of Brahman with the single ultimate constituent of the universe, the right question to ask instead is: how does Brahman manifest itself? The answer, in outline: by entering into spatial relations with itself, Brahman gives rise to both matter and space, inasmuch as space is the totality of existing spatial relations, whereas matter is the corresponding (apparent) multitude of relata — “apparent” because the relations are self-relations.
If we experience something the like of which we never experienced before, we are obliged to describe it in terms of familiar experiences. By the same token, what lies “behind” the manifested world can only be described in terms of the finished product — the manifested world. According to the PIQM, quantum mechanics affords us a glimpse “behind” the manifested world at formless particles and non-visualizable atoms, which, instead of being the world’s constituent parts or structures, are instrumental in its manifestation. But it allows us to describe what we “see” only in terms of inferences from macroevents and their quantum-mechanical correlations. Hence the supervenience of the microscopic on the macroscopic.
References and external links
U. Mohrhoff (2000), “What quantum mechanics is trying to tell us”, American Journal of Physics 68, 728–45; a.k.a.
The Pondicherry interpretation of quantum mechanics.
U. Mohrhoff (2001),
Objective probabilities, quantum counterfactuals, and the ABL rule: A response to R. E. Kastner“], American Journal of Physics 69, 864–73.
U. Mohrhoff (2002), [ “Making sense of a world of clicks”], Foundations of Physics 32, 1295–1311.
L. Marchildon (2004), [ “Remarks on Mohrhoff’s Interpretation of Quantum Mechanics”], Foundations of Physics 34, 59–73.
U. Mohrhoff (2004), [ “Do quantum states evolve? Apropos of Marchildon’s remarks”], Foundations of Physics 34, 75–97.
U. Mohrhoff (2004), [ “This elusive objective existence”], International Journal of Quantum Information 2, 201–20.
U. Mohrhoff (2005), [ “The Pondicherry interpretation of quantum mechanics: An overview”], PRAMANA—Journal of Physics 64, 171–85.
U. Mohrhoff (2006), [ “Is the end in sight for theoretical pseudophysics?”], in New Topics in Quantum Physics Research, edited by V. Krasnoholovets and F. Columbus (Nova Science Publishers).
U. Mohrhoff (2006), [ “Quantum mechanics explained”]. This article gives reasons why quantum mechanics should not be interpreted as anything but a generalized probability calculus.
This Quantum World (Mohrhoff’s website)

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