## Summary

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.

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...

(The entire section is 2111 words.)