The Meaning of Relativiety, with new introduction by Brian Greene ...

INTRODUCTION
by Brian Greene
IN THE course of a single decade, Albert Einstein discovered
special and then general relativity, and in so doing over-
turned the conceptions of space and time that our species had
held for thousands of years. Even so, many of us, at least intu-
itively, still adhere to those disproved conceptions. We imagine
space as an inert stage on which the events of the cosmos take
place. We imagine time being recorded on a universal clock,
ticking away in a identical manner here, and on Mars, and in
the Andromeda galaxy, and everywhere else, regardless of dif-
fering environments and physical contexts. For most of us, the
unchanging eternality of space and time is among the most
basic features of existence. But to hold such beliefs is to hold to
a pre-Einsteinian vision that is not only theoretically untenable
but, as attested to by numerous experiments, demonstrably
wrong.
As a professional physicist, it is easy to become inured to rela-
tivity. Whereas the equations of relativity were once startling
statements fashioned within the language of mathematics,
physicists have now written relativity into the very mathematical
grammar of fundamental physics. Within this framework, prop-
erly formulated mathematical equations automatically take full
account of relativity, and so by mastering a few mathematical
rules one becomes technically fluent in Einstein’s discoveries.
Nevertheless, even though relativity has been systematized
mathematically, the vast majority of physicists would say that
they still don’t “feel relativity in their bones.” I, for one, know
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I N T RO D U C T I O N
how easy it is to slip into familiar Newtonian thinking in which
space and time are incorrectly envisioned as separate, inde-
pendent, and unchanging. But I can also attest to the undimin-
ished feeling of awe I experience each time I pay sufficient at-
tention to details hidden within mathematics streamlined for
relativistic economy, and come face to face with the true mean-
ing of relativity. Space and time form the very arena of reality.
The seismic shift in this arena caused by relativity is nothing
short of an upheaval in our basic conception of reality.
So, what does relativity say?
In 1905, Einstein published what we now call the special the-
ory of relativity in the German Annalen der Physik, with the
unassuming title “On the Electrodynamics of Moving Bodies.”
The paper grew out of an intellectual struggle he’d been en-
gaged with since the age of sixteen regarding the mathematical
description of light’s motion, which was discovered by James
Clerk Maxwell in the 1860s. Briefly put, unlike what one would
expect based on Newton’s equations (and based on common
sense), Maxwell’s equations (when properly interpreted)
showed that whether you run toward or away from an oncom-
ing beam of light, its speed of approach would appear exactly
as it would were you standing still—not one iota faster or
slower. This apparent constancy of light’s speed engaged the
sharpest scientific minds of the late nineteenth and early twen-
tieth centuries because, even though it emerged from the
equations, and even though it was borne out by ever more pre-
cise experimental measurements, it just seemed to make no
sense. How could the speed of light not appear faster if you run
toward an approaching light beam? How could the speed of
light not appear slower if you run away from it? Here’s where
Einstein changed everything. Speed is a measure of distance
traveled divided by duration of the journey, and so is intimately
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I N T RO D U C T I O N
bound up with the concepts of space and time. And, Einstein
claimed, space and time—in contrast to Newton’s intuitively
sensible description—are not fixed and unchanging. Instead,
they’re fluid and malleable. Space and time, he argued, adjust
themselves to keep something else—the speed of light—fixed
and eternal, regardless of the motion executed by the light’s
source or someone observing it.
In practice, this means that if you measure the length of an ob-
ject—a car, a plane, a whatever—that’s in motion, the result
you’ll find is less than if the object were stationary. And if you ob-
serve a clock that is in motion, you’ll find that its rate of ticking is
less than an identical clock that’s stationary. Roughly speaking,
spatial separations shrink and time slows for an object in motion.
These spectacular features of space and time remained fully hid-
den until 1905 because although the effects are real, they’re
miniscule except when the speeds involved approach that of
light. It took the genius of Einstein to see beyond everyday per-
ception and reveal the true character of space and time.
The discovery of general relativity grew out of special relativ-
ity, but took Einstein ten more years to complete. Once again, a
major impetus for Einstein was a blatant conflict he found when
closely examining some of Newton’s earlier insights. In this
case, the focal point was the force of gravity and, in particular,
how quickly gravity can exert its influence. According to special
relativity, nothing—no object, no signal, no information—can
travel from one point in the universe to another at a speed
greater than the speed of light. Yet, as Einstein realized, accord-
ing to Newton’s universal law of gravity, a massive body like the
sun exerts a gravitational pull on other massive bodies, such as
the planets, which is instantaneous. According to Newton, were
the sun to somehow change its mass or its position, we would
immediately become aware of the change because the sun’s
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I N T RO D U C T I O N
gravitational pull on the earth would immediately change. And
an immediate change is one that far exceeds the speed limit set
by light. Einstein’s motivation to seek a new theory of gravity
thus came not from a conflict between Newton’s equations and
experimental data, but from a conflict between Newton’s de-
scription of gravity and Einstein’s own special relativity. To a the-
orist like Einstein, theoretical inconsistency can be as important
as dissonance derived from experimental observations.
The resolution of this conflict was not short in coming. In
1912, after some five years of contemplation, Einstein wrote to
his friend Arnold Sommerfeld that “compared with under-
standing gravity, the special theory of relativity was mere child’s
play.” Nevertheless, Einstein resolutely kept at it. His line of at-
tack was to understand the mechanism by which gravity oper-
ates—after all, how does the sun, some 93 million miles distant,
influence the earth’s motion? The sun never touches the earth,
so how is the force we commonly call gravity communicated
over such vast distances of largely empty space? This is a mys-
tery Newton himself was well aware of, noting in his Principia that
he had been unable to figure out the means by which gravitational
influence is transmitted—and that, henceforth, he was leaving
that problem to the “consideration of the reader.” No doubt,
many a reader read that challenge and read on, but Einstein was
different. He was willing to take on this two-hundred-year-old chal-
lenge in the hopes that if he understood how gravity really works,
he might resolve the conflict between Newton’s description of
gravity and the speed limit set by special relativity.
Einstein’s hope proved well founded. By 1915, Einstein came
up with the general theory of relativity in which he identified
the very fabric of spacetime as the medium that transmits the
force of gravity. Einstein argued that much as a large rock sit-
ting on a trampoline causes the canvas to curve—and in that
way affects the motion of a marble rolling on the trampoline’s
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surface—a large astrophysical body (the sun, the earth, a neu-
tron star) immersed within spacetime causes the fabric of the
cosmos to curve—and in that way affects the motion of other
bodies moving nearby. As the earth orbits the sun, according to
general relativity, it rolls along a valley in the warped spacetime
fabric caused by the sun’s presence.
This is a stunning proposal. With special relativity, Einstein
had shown that the cosmic scaffolding could not be dismantled
into rigid, universally agreed upon struts of space and time.
Now, with general relativity, he argued that the shape of the
cosmic scaffolding responds to the presence of matter or energy—
and, in turn, the shape of spacetime affects how other objects
move. Space and time, according to Einstein, are participants
in the evolution of the universe.
A proposal that so dramatically challenges previous concep-
tions requires dramatic experimental support. Through its un-
derlying mathematical formulation, which owes much to the
nineteenth-century geometrical insights of Bernhard Reimann,
general relativity makes detailed predictions for how objects
move under the force of gravity (i.e., how the curvature of
spacetime affects the motion of objects). When these predic-
tions and those of Newton’s theory of gravity are compared
with experimental observations, Einstein’s are always at least a
little more accurate, vindicating general relativity’s claim to
supplant Newton’s theory. And of prime importance, when
Einstein calculated the speed by which warps and curves travel
through space—the speed of gravity in his new formulation—
the answer he came to was thoroughly gratifying. Unlike in
Newton’s theory in which gravity supposedly exerts its force in-
stantaneously over any distance, in general relativity gravity
travels at exactly the speed of light, fully in keeping with the cen-
tral dictum of the special theory of relativity that nothing can
exceed light speed.
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I N T RO D U C T I O N
Einstein published the general theory of relativity in 1916,
arguably the most important year in our understanding of
space and time. Within general relativity, the special theory was
seen to be a special case—the case in which one considers
space and time in the absence of a background distribution of
matter and energy, i.e., space and time in the absence of grav-
ity. Adding gravity, Einstein discovered, breathes a wholly unex-
pected fluidity and flexibility into spacetime.
* * *
In the century since relativity’s discovery, Einstein’s break-
throughs have been understood more deeply and their implica-
tions for the cosmos appreciated more fully. Here are five high-
lights.
First, much has happened on the experimental front. The
initial experimental tests of relativity were somewhat indirect.
General relativity’s prediction for the bending of starlight pass-
ing by the sun, which was confirmed by two teams of as-
tronomers during the solar eclipse of 1919, is rightly heralded
as the observation that convinced the world that Einstein’s new
theory was correct. However, with relativity’s yielding bizarre
predictions such as motion and gravity being able to affect the
rate of time’s passage, one can’t help longing to see direct veri-
fication. The observational fact that short-lived muon particles
produced in the upper atmosphere by cosmic ray collisions are
able to survive the long journey to Earth’s surface (by moving
quickly, the muons’ internal clocks slow relative to ours, and
hence the moving muons live longer than their stationary
counterparts, allowing them to complete the journey to the
surface of the earth) is a step closer to direct confirmation, but
the disconnect between a muon’s millionth-of-a-second life-
span and time as experienced in everyday life can still make
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I N T RO D U C T I O N
this confirmation of relativity seem remote and theoretical. In
1971, an experiment carried out by Joseph Haefle and Richard
Keating went a long way toward bridging this gap. They strapped
a clock (albeit an atomic clock) into a passenger seat in a Pan
Am jet, and closely monitored it as the plane flew around the
earth. Because the plane was in motion, and also because it ex-
perienced a slightly weaker gravitational field due to its in-
creased distance from Earth’s center, relativity predicts that by
the end of the journey, the onboard clock should differ from
Earthbound stationary clocks by a few billionths of a second.
Indeed, this is just what the experimenters found, thus provid-
ing a direct confirmation of relativity’s conclusion that the pas-
sage of time—real time, the kind of time measured by clocks—
is affected by motion and by gravity.
Second, and relatedly, new experiments are currently under-
way to test some of the more subtle implications of relativity.
Gravity Probe B, a satellite hovering hundreds of miles above
Earth’s surface, is trying to give the first direct confirmation of
relativity’s claim that not only does a massive body warp the
spacetime fabric, but when it turns it drags spacetime into a
whirlpool-like spin. By pointing the most accurate gyroscopes
ever fabricated at a chosen distant star, the experimenters hope
to observe relativity’s prediction that, over the course of a year,
the earth’s rotation will drag spacetime enough to cause the
onboard gyroscopes’ axes to turn by about a hundred-thou-
sandth of a degree. Measuring such a tiny turning angle is a sig-
nificant challenge, but after some forty years of development,
the experimenters believe they have the technological fidelity
to do so. Another difficult but tremendously exciting experi-
ment is the search for gravitational waves. According to general
relativity, when a massive object moves it can cause the fabric of
space to undulate, somewhat like the surface of a pond into
which a pebble has been tossed. Were such a wave of undulat-
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ing space to roll by Earth, all material objects would be
stretched one way, and then the other, as the wave of distorted
space passed. The challenge in detecting these gravitational
waves is that those produced by ordinary phenomena (drop-
ping a cup, two cars colliding, setting off an explosive, etc.) are
too tiny to be seen, while those produced by cataclysmic astro-
physical events (stars going supernovae, black holes colliding,
etc.) are larger but their strength diminishes rapidly as they
spread during their long journey to Earth. Scientists have used
general relativity to calculate that gravitational waves produced
by the most violent of astrophysical events, at typical astronomi-
cal distances, would stretch a one-meter-long rod here on Earth
by less than a millionth of a billionth of a centimeter, making
detection enormously difficult. Nevertheless, in the United
States two gravitational wave detectors are now in operation
(and around the world, a number of others are planned or in
operation) which, at least in principle, have the capacity to
measure such a tiny stretching of matter. This experiment is
particularly important because successfully detecting a gravita-
tional wave would be more than just confirming a remaining
prediction of the general theory of relativity. Because of the in-
trinsic weakness of the gravitational force, gravitational waves
can penetrate realms that are opaque to visible light and elec-
tromagnetic radiation more generally. Thus, the detection of
gravitational waves could very well open up a new field of gravi-
tational wave–based astronomy in which the cosmos is studied
via gravitational—not electromagnetic—radiation. Some physi-
cists are even hopeful that gravitational waves may one day
allow us to peer back to the big bang itself.
A third development stems from the work of Karl Schwarz-
child, a Russian physicist, who shortly after Einstein published
general relativity solved Einstein’s equations to puzzling effect.
Schwarzchild found that if enough matter were crushed into a
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I N T RO D U C T I O N
small enough volume (e.g., were the entire earth crushed into
a one-inch diameter ball), the resulting warpage of spacetime
would become so severe that nothing—not even light—would
be able to escape the resulting powerful gravitational pull.
Einstein was surprised by this solution, and felt that the ex-
treme conditions Schwarzchild was envisioning would never be
attained in the real world. But today, observations using power-
ful Earth- and space-based telescopes have revealed regions suf-
fused with intense gravitational fields in which downward-spi-
raling matter heats up and gives off a spectrum of x-rays that is
precisely in keeping with those expected from matter just be-
fore heading over the edge of one of Schwarzchild’s “dark
stars” (later christened “black holes” by the eminent physicist
John Wheeler). Such data leaves little doubt that black holes
are real, and perhaps even ubiquitous. Astronomers now be-
lieve that many galaxies have a giant black hole sitting at their
center. For example, there is observational evidence that even
our own Milky Way galaxy, at its core, has a black hole weighing
more than three million times as much as the sun. An important
problem, which has resisted resolution for more than twenty-
five years, is to determine what happens in the deep interior of
a black hole. General relativity seems to suggest that time
comes to an end at the black hole’s center, but as yet no one
has figured out what that really means or whether quantum
mechanical considerations might justify the conclusion.
Coming to grips with this problem will likely give deep insights
into the fundamental nature of space and time.
Fourth, gravity is the dominant force when considering the
physics of large agglomerations of matter such as stars and
galaxies. Hence, the grandest possible arena for applying gen-
eral relativity is the largest such agglomeration: the entirety of
the universe itself. Cosmology is the name given to the study of
the origin and evolution of the universe and is a field, not sur-
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prisingly, that general relativity has revolutionized. Before
1916, there had been no shortage of cosmologies proposed by
various of the world’s theologians and natural philosophers.
But with the discovery of general relativity, cosmology entered
the realm of rigorous science. In fact, within just a couple of
years, Einstein realized that the cosmology implied by general
relativity was thoroughly unexpected. The fabric of space, ac-
cording to Einstein’s equations, cannot be static: the universe
can expand or contract, but it can’t stay put. Even Einstein,
maverick thinker that he was, found this conclusion too out-
landish to accept. “Clearly” the universe, on the largest of
scales, is fixed and unchanging. Thus, in 1917, to remedy this
problematic implication of general relativity, Einstein modi-
fied his equations by introducing the so-called cosmological
constant—a uniform energy throughout space that could
exert an outward push and hence balance the inward pull of
gravity, yielding a static cosmos. Some of Einstein’s contempo-
raries—most notably, the Belgian priest Georges Lemaitre and
the Russian mathematician and meteorologist Alexander
Friedmann—were less certain that the universe really was un-
changing, and so during the 1920s they investigated a number
of possible cosmologies emerging from the equations of gen-
eral relativity, both with and without the cosmological con-
stant. All of these theoretical studies came to a head in the wa-
tershed year for cosmology—1929. In that year, Edwin Hubble,
using the 100-inch telescope at Mount Wilson Observatory,
concluded that distant galaxies are rushing away from us with
a speed proportional to their distance, in perfect consonance
with the general relativistic cosmologies—without a cosmologi-
cal constant—that Lemaitre and Friedmann had developed
mathematically. The fabric of space is stretching with time.
Had Einstein been willing to accept the implication of his own
general theory of relativity at face value, he would have pre-
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The Meaning of Relativiety, with new introduction by Brian Greene
Introduction (c) 2005 by Brian Greene

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