Theories of Space and Time from Aristotle to Einstein (Part II): From Newton to Einstein and Beyond

Vishnya Maudlin, Ph.D. Professor
New York University, USA

For centuries, philosophers and mathematicians had tried to work out the rules that governed the motion of material objects, but they were always hampered by unspoken assumptions – ideas about the way the world is that are so powerful and apparently so obvious that they were never questioned. As we have seen, for example, philosophers felt that celestial objects had to move on circular orbits, or at best on circles rolling within circles. Planetary orbits had to conform to heavenly perfection, and the only perfect eternal motion was uniform circular motion. It took the genius of Kepler to look at the data honestly and show that orbits, in fact, are ellipses. Newton opened Book I of the Principia with a lengthy scholium on the nature of relative and absolute spaces. Newton’s laws of motion together with his Law of Gravitation opened up an entirely new vista on how the solar system operates. The Universal Law of Gravitation unified earthly and heavenly phenomena contrary to the Aristotelian division into two separate physics, physics on the Earth and celestial physics. Newton felt that absolute space was a logical and ontological necessity, required even for the validity of his first law of motion (the law of inertia). The basic issue between Newton and Leibniz was the distinction of physical space from mathematical space. The relevant question for physics became whether or not physical space has an existence of its own independent of the matter in it. Aside from any physical reality, one can mentally and logically construct an entity referred to as Euclidean space. As Gauss and Riemann realized in the 19th century, one can also logically and consistently construct other types of mathematical spaces. Is the choice between these spaces in physics empirical or conceptual? That was a matter of debate. With Einstein, we have a major revolution in our notions of space and time. The problem of the asymmetry of explanations in electromagnetic theory led Einstein to his theory of relativity. In this case, no new observational fact led to a new theory, but a new theory is conceived through careful conceptual thinking.