Posted: 01/09/2013 2:08 pm
Former NASA researcher;
computational scientist; emeritus professor of mathematics, James
Madison University; author, 'Reason and Wonder'
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 2nd'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.
(This article is adapted from Chapter 6 -- "A Wrinkle in Time" -- of the author's recent book
Reason and Wonder.)
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