“We are to admit to no more causes of natural things than such as are both true and sufficient to explain their appearances.” — Isaac Newton
In January 8th’s post, I asserted:
Science remains most true to itself and of greatest value to humanity when it assiduously avoids unnecessary assumptions. Over the long arc of history, science has initially embraced — then discarded — most of the following tacit assumptions: dualism, determinism, reductionism, absolute time, absolute space, the principle of locality, materialism, and most recently, realism. In subsequent posts, we’ll examine each …
Today, let’s discuss the notions of absolute space and time.
The publication of Newton’s Principia Mathematica in 1687 paved the way for the Age of Reason. Prior to Newton, there were isolated scientists — Archimedes, Da Vinci, and Galileo, for example — but there was not yet science. In a single stroke, Newton laid solid foundations for scientific methodology by combining inductive reasoning to infer general laws from experimental observations, mathematical formalism to state those laws concisely, logic to deduce new laws, and deductive reasoning to make predictions based upon those laws.
Principia‘s first volume formalizes the science of motion. At the onset, Newton assumes time and space to be absolutes. Regarding time, he writes: “Absolute, true, and mathematical time, of itself … flows equitably without relation to anything external.” Similarly for space. In today’s lingo, we might say that Newton viewed Euclidean space as a fixed stage upon which physical events occur, that time flows the same for every observer, and that time and space are independent.
And so it remained until 1905, when a lowly patent official in Bern Switzerland examined patent applications by day and plotted the overthrow of Newtonian mechanics by night. Albert Einstein, then 26 years of age, noticed something about the nature of light that the titans of physics had overlooked.
In 1862, the principles of electromagnetism had joined Newtonian mechanics in the Pantheon of classical physics. The brainchild of Scottish physicist James Clerk Maxwell, Maxwell’s equations describe the interaction of electricity and magnetism. Because all manner of phenomena — light, electricity, and radio waves among them — are electromagnetic in origin, Maxwell’s equations are astoundingly practical.
Maxwell’s equations take many forms, all equivalent. When they are expressed in so-called Gaussian units, the velocity of light in vacuo, symbolized by c, appears as a universal constant. In this ostensibly innocuous fact, Einstein sensed that the world is not as it seems.
The long-accepted principle of relativity (not to be confused with the theory of relativity) held that the mathematical expressions of physical laws must retain the same form in all inertial frames of reference (that is, in all non-accelerating coordinate systems). However, the appearance of c as a constant in the equations of electrodynamics suggested that the velocity of light must be independent of the reference frame in which that velocity is measured.
Imagine having a peripatetic friend that you frequently encounter during travels. No matter where you meet your friend, he always passes you by at a velocity of, say, 7 mph. Whether you are flying at 600 mph, walking at 3 mph, or biking at 20 mph, you always measure your friend’s velocity at exactly 7 mph in the coordinate system that travels with you. How strange! But that’s how light behaves, albeit at the blazing velocity of 186,000 miles per second.
Familiar moving objects — baseballs, trains, planes, etc. — don’t behave this way. For example, moving sidewalks expedite pedestrian traffic along airport concourses because the velocity of the sidewalk relative to the concourse, say 2 mph, and the velocity of the traveler relative to the sidewalk, say 3 mph, add to yield 5 mph relative to the concourse, a combined rate at which kiosks and sports bars whiz by. But light’s velocity does not add to that of its reference frame.
That the subtler implications of Maxwell’s equations had escaped the notice of virtually all physicists explains their rapt attention to the Michelson-Morley experiment of 1887. Believing that light — like sound — needed a medium in which to propagate, physicists hypothesized the existence of the aether, a weightless, frictionless substance filling the void of space. It was further presumed that the aether remained stationary in an absolute frame of reference, Newton’s absolute space still in vogue. Physicists believed that Michelson and Morley would detect slight differences in the velocity of light measured from different directions (i.e. frames), allowing them to extract from these differences the “aether drift” of the earth, the absolute velocity of the earth relative to the stationary aether.
The experiment failed abjectly. The velocity of light was maddeningly consistent. Measurements taken at differing times of day or year and differing orientations of the apparatus showed no appreciable differences in c. Michelson and Morley concluded tersely, “… the result of the hypothesis of stationary aether is thus shown to be incorrect.”
Through clever thought experiments, Einstein reasoned that the independence of c from its reference frame must imply — astonishingly — the relativity of time: two observers in different frames see one another’s clocks ticking at different rates. The “moving” clock is observed to tick more slowly, and the greater the velocity difference of the frames, the greater the discrepancy in the flow of time.
Relativistic time dilation is ordinarily minuscule, and so it escaped notice until the 20th century when the advent of the cesium clock made possible the measurement of time to 14 digits of precision. Using two such clocks in 1971 — one on earth and one on a round-the-world flight — two physicists, Joseph Hafele and Richard Keating, confirmed the time dilation predicted by Einstein’s theory of relativity.
Time’s relativity implies the relativity of space as well, and the interdependence of space and time. Although Hermann Minkowski, Einstein’s mathematics professor, once characterized his wayward student as a “lazy dog” for cutting classes, he was smitten by the student’s theory. “Henceforth space by itself and time by itself are doomed to fade away into mere shadows,” Minkowski enthused, “and only a kind of union of the two will preserve an independent reality.”
Newton’s assumptions of absolute space and time were reasonable in his era and necessary for the development of classical physics, but relativity forced their abandonment. In the next post, we’ll examine the demise of determinism.