*Part5*
General Relativity and the Bucket
Beyond giving the world, a mathematically elegant, conceptuaI1y powerful,
and, for the first time, fully consistent theory of gravity, the general
theory of relativity also thoroughly reshaped our view of space and time.
In both Newton's conception and that of special relativity, space and time
provided an unchanging stage for the events of the universe. Even though
the slicing of the cosmos into space at successive moments has a
flexibility in special reality unfathomable in Newton's age, space and time
do not respond to happenings in the universe. Spacetime-the loaf, as we've
been calling it is taken as a given, once and for all. In general
relativity, all this changes. Space and time become players in the evolving
cosmos.
They come alive. Matter here causes space to warp there, which causes
matter over there to move, which causes space way over there to warp even
more, and so on. General relativity provides the choreography for an
entwined cosmic dance of space, time, matter, and energy. { KR I really
cannot find any warping and weaving in the sky;it all arose from the theory
of SDINGULARITY; but imagine the swimming pull as the space; you are in
moving; how?; pull and push your legs; warp and weave side ways or fromt
and back; so too Einstein predicted that if the matter were to travel at
such speed, force must come either by matter swimming or the swimming pool
space swimming pulling and pushing at every level} This is a stunning
development But we now come back to our central theme: What about the
bucket? Does general relativity provide the physical basis for Mach's
relations ideas, as Einstein hoped it would?
Over the years, this question has generated much controversy. Initially,
Einstein thought that general relativity fully incorporated Mach's
perspective, a viewpoint he considered so important that he christened it
Mach's principle. In fact, in 191 3, as Einstein was furiously working to
put the final pieces of general relativity in place, he wrote Mach an
enthusiastic letter in which he described how general relativity would
confirm Mach's analysis of Newton's bucket experiment. And in 1918, when
Einstein wrote an article enumerating the three essential ideas behind
general relativity, the third point in his list was Mach's principle. But
general relativity is subtle and it had features that took many years for
physicists, including Einstein himself, to appreciate. All these aspects
were better understood, Einstein found it increasingly difficult to fully
incorporate Mach's principle into general relativity. Little by little, he
grew disillusioned with Mach's ideas and by the later years of his life
came to renounce them. With an additional half century of research and
hindsight, we can consider anew the extent to which general relativity
conforms to Mach's reasoning. Although there is still some controversy, I
think the most accurate statement is that in some respects general
relativity has a distinctly Machian flavour, but it does not conform to the
fully relationist perspective Mach advocated. Here's what I mean.
Mach argued that when the spinning water's surface becomes concave, or when
you feel your arms splay outward, or when the rope tied between the two
rocks pulls taut, this has nothing to do with some hypothetical -and, in
his view, thoroughly misguided - notion of absolute space (or absolute
spacetime, in our more modern understanding). Instead, he argued that it's
evidence of accelerated motion with respect to all the matter that's spread
throughout the cosmos. Here there no matter, there'd be no notion of
acceleration and none of the enumerated physical effects (concave water,
splaying arms, rope pulling taut) \vould happen.
What does general relativity say! According to general relativity, the
benchmarks for all motion, and accelerated motion in particular, are freely
falling observers-observers who have fully given in to gravity and are
being acted on by no other forces.
Now, a key point is that the gravitational force to which a freely falling
observer acquiesces arises from all the matter (and energy) spread
throughout the cosmos. The earth, the moon, the distant planets, stars, gas
clouds, quasars, and galaxies all contribute to the gravitational field (in
geometrical language, to the curvature of spacetime) right where you're now
sitting.
Things that are more massive and less distant exert a greater gravitational
influence, but the gravitational field you feel represents the combined
influence of the matter that's out there." The path you'd take were you to
give in to gravity fully and assume free-fall motion-the benchmark you'd
become for judging whether some other object is accelerating-would be
influenced by all matter in the cosmos, by the stars in the heavens and by
the house next door. Thus, in general relativity, when an object is said to
be accelerating, it means the object is accelerating with respect to a
benchmark determined by, matter spread throughout the universe. That's a
conclusion which has the feel of that Mach advocated. So, in this sense,
general relativity does incorporate some of Mach's thinking.
Nevertheless, general relativity does not confirm all of Mach's reasoning,
as we can see directly by considering, once again, the spinning bucket
in an otherwise empty universe. In an empty unchanging universe-no
stars, no planets, no anything at all-there is no gravity." And without
gravity, spacetime is not warped-it takes the simple, uncurved shape
and that means we are back in the simpler setting of special relativity. If
we now introduce the bucket into this empty universe, it has such a tiny
mass that its presence hardly affects the shape of space at all. And so the
discussion we had earlier for the bucket in special relativity applies
equally well to general relativity).. In contradiction to what Mach would
have predicted. general relativity comes to the same answer as specla1
relativity, and proclaims that even in an otherwise empty universe, you
will feel pressed against the inner wall of the spinning bucket; in an
otherwise empty universe, your arms will feel pulled outward if you spin
around; in an otherwise empty universe, the rope tied between two twirling
rocks will become taut. The conclusion we draw is that even in general
relativity, empty spacetime provides a benchmark for accelerated motion.
Hence, although general relativity incorporates some elements of
Mach's thinking, it does not subscribe to the completely relative concept
of no motion Mach advocated." Mach's principle is an example of a
provocative idea that provided inspiration for a revolutionary discovery.
even though that discovery ultimately failed to fully embrace the idea that
inspired it.
Spacetime in the Third Millennium
The spinning bucket has had a long run. From Newton's absolute space
and absolute time, to Leibniz’s nd then Mach's relational conceptions,
Relativity and to Einstein's realization in special relativity that space
and time are relative and yet in their union fill out absolute spacetime,
to his subsequent discovery). In general relativity that spacetime is a
dynamic player in the unfolding cosmos, the bucket has always been there.
Twirling in the back of the mind, it has provided a simple and quiet test
for whether the invisible, the abstract, the untouchable stuff of space-and
spacetime, more generally-is substantial enough to provide the ultimate
reference for motion. The verdict? Although the issue is still debated, as
we've now seen, the most straightforward reading of Einstein and his
general relativity is that spacetime can provide such a benchmark:
spacetime is a something. *' Notice, though, that this conclusion is also
cause for celebration among supporters of a more broadly defined
relationist outlook. In Newton's view and also that of special relativity,
space and spacetime were invoked as entities that provide the reference for
defining accelerated motion. And since, according to these perspectives,
space and spacetime are absolutely unchangeable, this notion of
acceleration is absolute. In general relativity, though, the character of
spacetime is completely different.
Space and time are dynamic in general relativity: they are mutable;
they respond to the presence of mass and energy; they are not absolute.
Spacetime and, in particular, the way it warps and curves, is an embodiment
of the gravitational field. Thus, in general relativity acceleration
relative to spacetime is a far cry from the absolute, staunchly unrelation
conceptional invoked by previous theories. Instead, as Einstein argued
eloquently a few years before he died," acceleration relative to general
relativity's spacetime is relational. It is not acceleration relative to
material objects like stones or stars, but it is acce1ertlon relative to
something just as real, tangible, and changeable: a field-the gravitational
field." In this sense, spacetime-by being the incarnation of gravity is so
real in general relativity that the benchmark it provides is one that many
relationists can comfortably accept.
Debate on the issues discussed in this chapter will no doubt continue
as we grope to understand what space, time, and spacetime actually are.
With the development of quantum mechanics, the plot only thickens. The
concepts of empty space and of nothingness take on a whole new meaning when
quantum uncertainty takes the stage. Indeed, since 1905, Einstein did away
with the luminiferous aether, the Idea that space is filled with invisible
substances has waged an ingenious comeback. Moreover, as we will now see,
the most basic role that space plays in a classical universe-as the medium
that separates one object from another, as the intervening stuff that
allows us to declare definitively that one object is distinct and
independent from another-is
thoroughly, challenged by startling quantum connections.
{FABRIC OF THE COSMOS BY GREENE}
K Rajaram IRS 7724 8724 completed THE END part5
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