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Last Updated on May 6, 2015, by eNotes Editorial. Word Count: 2111

Roland Omnès is a specialist in quantum mechanics and a professor of physics at the University of Paris XI. Omnès thinks deeply and writes clearly about the conceptual framework of physical science. He has received high recognition for his books: The Interpretation of Quantum Mechanics (1994), a book for specialists, and Understanding Quantum Mechanics (1999), a text for beginning science students, experienced physicists, mathematicians, and philosophers. Omnès also wrote Introduction to Particle Physics (1971) and coauthored Mandelstam Theory and Regge Poles: An Introduction for Experimentalists (1963) with Marcel Froissart.

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Omnès separates the contents of Quantum Philosophy into four major parts. Part 1 reviews key individuals and ideas in the historical development of classical logic, physics, mathematics, and the philosophy of knowledge. By retracing the establishment of past foundations, an appreciation can be developed for the evolution of scientific knowledge. Furthermore, with this approach, Omnès hopes to clear up the difficulties in understanding and interpreting contemporary science. In part 2, Omnès documents the historical break between classical, commonsense physics and formal, mathematically based physics. This fracture continues to haunt science to this day and contributes to an unfortunate cleavage of our culture in a time when many of the possible applications of science require the enlightened judgment of the public. Therefore, in part 3, starting from the fundamental principles of quantum physics, Omnès builds a bridge from the formal mathematical formulation to the real, visible world. Part 4 then briefly explores some possible directions that may be taken to bring logic and reality closer together and to open up new domains of knowledge. Although the amount of redundancy in this book may be viewed as a weakness, it is also a strength for the general reader, providing the repetition necessary to understand some unfamiliar, formal, and quite difficult scientific points.

Omnès points out that the first individuals to use logic and mathematics to infer a representation of the world were the Pythagoreans. In particular, Pythagoras observed that there is a harmony in nature that is commanded by numbers. He became convinced that the basic objects in nature, including the sun, the moon, and the stars, are controlled by basic harmonies that can be described mathematically. By using numbers and geometric shapes to analyze the world, Pythagoras and his followers hoped to understand its nature and interrelationships. Math was born. Proof by reasoning became established.

During the 1500’s, classical physics was rapidly developing. Aristotle’s concept of an earth-centered universe started to crumble when Nicolaus Copernicus suggested a new system that placed the earth and the planets in orbits around the sun. Johannes Kepler’s description of planetary motion, deduced from Tycho Brahe’s data, demonstrated that empirical rules could be cast into mathematical form. Subsequently, with the aid of the telescope, Galileo helped usher in the modern scientific method: Pose hypotheses, design experiments, build the apparatus, make observations, and expose conclusions to peer review by publishing the results. Omnès reviews the continuing evolution of classical physics by recounting how Galileo used experiments with balls and inclined planes to represent reality visually in a way fully understood by intuition. He also relates the introduction of the inductive method by Francis Bacon, in which observations of many specific examples are generalized into the laws of nature.

According to Omnès, the pinnacle of science was reached by Sir Isaac Newton. Newton’s greatest contribution was the ability to see the world in a new way. Falling bodies, planetary motions, and collisions were all described using universal principles that were expressed in terms of logical mathematics. His laws could predict the future of each body in a decisive, deterministic way.

However, Newton’s extensive use of mathematics began the unfortunate removal of the ideas of science from the reach of the layperson, who was almost always unversed in that esoteric language. For example, Newton’s universal law of gravitation required a mathematical device in order to calculate the gravitational force. The idea of an instantaneous force acting at a distance, a purely mathematical construct, was introduced. Omnès calls this construct the first step in moving from a conceptual to a formal description of science.

The next major step in the development of science was introduced in an attempt to understand and describe light. According to the experiments and analysis of Thomas Young and Augustin-Jean Fresnel, light behaves as a wave. In order to describe the propagation of light through a vacuum, an immaterial, all-pervasive medium known as the ether was fabricated. Omnès states that this disturbing ether, which was later discounted, further increased the gap between scientific interpretation and reality.

The gap between classical and formal physics widened further in the 1860’s when James Clerk Maxwell formulated a mathematical theory for the laws governing the interconnectedness of electricity and magnetism. These four physical laws, Maxwell’s laws of electromagnetism, were consistent with all the existing empirical data and rules, but they were purely mathematical equations that described the dynamics of a system of electrical and magnetic fields. The concept of an electromagnetic field could be described only by mathematical language. With formal mathematical concepts being used more frequently by scientists, Omnès suggests that intuition was gradually going blind. However, welcome or not, the mathematical description was unavoidable. Toward the end of the 1800’s, mathematics was quickly becoming the universal language of science. The relationships between things had become more important than the nature of things.

At this juncture, Omnès poses some profound, far-reaching questions: What is the meaning of understanding? Philosophers represented the world with mental images constructed by reasoning and ordinary language. Is the mind limited to exploiting the observed facts, as suggested by philosopher David Hume, or can knowledge be expanded by further investigation into the origins of the laws of nature? Omnès then asks how understanding is even possible. In contrast with Immanuel Kant, Omnès concludes that a new philosophy is imperative and that reason must be complemented by logic and reality. Omnès points out that the world is really quite different from the way it is generally perceived. Nature is governed by laws whose form is mathematical. However, mathematics has no meaning by itself. Although mathematics is an integral part of an all-encompassing philosophy of knowledge, its meaning must be found in the science itself.

By the end of the nineteenth century, a major problem existed: The mathematical formulation of the laws of science seemed incomprehensible to the classical philosopher. The more scientists proclaimed to know, the less seemed to be understood. Mathematics appeared to be only a game of relations that tried to accommodate everything. This eventually led to the complete fracture between classical and formal science in the early 1900’s, when the mathematical formalisms developed by Albert Einstein to explain the theory of special relativity and the relativistic theory of gravitation developed by Werner Heisenberg and Erwin Schrödinger to explain the phenomenon of the microscopic world in terms of quantum mechanics was introduced. Omnès looks for a way to build a bridge to reality and formulates the last half of his book on the premise that physical reality is governed by the laws of quantum physics. Although quantum mechanics is a formal, unfamiliar language to most, all of physics and chemistry depend on it. Quantum mechanics most deeply penetrates the whole set of scientific laws.

Omnès describes quantum theory as a set of rules that interrelate the facts of nature. With quantum mechanics, the atoms of an object are replaced by a wave function, a blurry cloud of probabilities. Matter can behave as a wave or a particle but not both at the same time. Quantum physics is a set of propositions that can be expressed in ordinary language, but due to the underlying formalism, the meaning is very obscure. Heisenberg’s uncertainty principle is a direct consequence of the basic principles of quantum theory. Omnès suggests that Niels Bohr made a mistake in concluding that there are two distinct categories of laws, the classical and the quantum. Omnès then chooses to recover the classical, visual representation of the world from the formal quantum representation.

Because physical science had become mired in the formalism of unfamiliar mathematics, Omnès looks to regain a real image of the world by following a reverse path to the historical development of physical science. His course starts with the quantum world and proceeds to an understanding of the classical world. Deduce common sense from quantum premises, he urges. In other words, instead of explaining reality in terms of a mental representation of it, explain it in terms that account for both the mental and the intuitive. Reason must be deduced from the underlying scientific principles of the world as opposed to determining those principles through the ordinary language of reason.

Omnès proceeds from the foundation of quantum physics by recounting the concept of “consistent histories” that was introduced by Robert Griffiths in 1984 and expounded upon by Omnès, Murray Gell-Mann, and James Hartle in the late 1980’s. A history is a sequence of various properties that take place at different times. After specifying the time of each event, the history can be rewritten by using appropriate mathematical operators called “projectors.” Wave function probabilities are just numbers assigned to events that predict the probability of a given history. Only histories that can be assigned a probability are consistent and meaningful.

Omnès explains that by using the concept and language of consistent histories, the quantum world can be described. By defining an object as a collection of wave functions, consistent histories translate quantum words into classical terms. The description of a physical system is constructed from the propositions belonging to a unique, consistent quantum logic which is supported by implications that can be demonstrated. The fracture between the classical and formal descriptions of science closes, and a commonsense, intuitive representation of the world emerges. Schrödinger’s formulation of quantum mechanics that describes the microscopic world becomes Newton’s classical mechanics in the macroscopic world. As Omnès points out, the laws of reality are ultimately quantum and formal, but the logic of consistent quantum histories reconstructs a commonsense representation of the classical world.

In direct contrast with traditional epistemology, Omnès suggests that common sense is merely the result of the basic laws of nature. Although Bohr wanted to use classical physics as the unique reference point, Omnès demonstrates that the correct starting point is the deeper quantum principles that govern the world. Omnès clarifies some of the possible contradictions of the consistent histories approach by explaining the concept of decoherence. For example, the old legend of Schrödinger’s mythical cat, that a cat might be both dead and alive at the same time, results from the assumption that wave functions typically interfere on the macroscopic level. However, decoherence is a physical effect that quickly suppresses quantum interference at the macroscopic level. Quantum paradoxes, such as Schrödinger’s cat, are resolved without any mysterious action-at-a-distance, and the conclusion makes good sense out of quantum measurements. From the concept of consistent quantum histories governed by decoherence and the principle of inertia, the quantum world disguised by wave function probabilities emerges into ordinary reality, the three-dimensional world envisioned by the Greeks.

According to Omnès, the reconstruction of the macroscopic world from the theoretical model of quantum mechanics exhibits every characteristic of reality except for uniqueness of the facts. Omnès refers to this problem as the chasm between quantum and classical descriptions of the world. The problem arises because the probabilistic nature of a wave function is still manifest even at the macroscopic level. However, the present interpretation of quantum mechanics through the use of consistent histories is perfectly compatible with the uniqueness of reality. Uniqueness is not predicted, but it is not contradicted. Consistent histories may not succeed totally in reaching realism, but their primary goal is only to provide a method of interpretation. The uniqueness of reality must come from philosophy or metaphysics and not from science.

In the last part of the book, Omnès superficially explores future directions that science might take to find the source of the order of all things or even a new philosophy of knowledge. A fully consistent form of quantum theory still needs to be developed, one that includes its relativistic counterparts. Can science organize reality from the smallest to the largest scale? Can science give rise to its own philosophy? These questions are profound and difficult to address, but Omnès is optimistic about a positive outcome.

Sources for Further Study

Booklist 95 (April 15, 1999): 1495.

Library Journal 124 (August, 1999): 133.

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