Part4
Relativity and the Absolute
The Equivalence of Gravity and Acceleration
In special relativity, Einstein's main focus was on observers who move
with constant velocity-observers who feel no motion and hence are all
justified in proclaiming that they are stationary and that the rest of the
world moves by them. Itchy, Scratchy, and Apu on the train do not feel
any motion. From their perspective, it's Martin and everyone else on the
platform who are moving. Martin also feels no motion. To him, it's the
train and its passengers that are in motion. Neither perspective is more
correct than the other. But accelerated motion is different, because you
can feel it. You feel squeezed back into a car seat as it accelerates
forward, you feel pushed sideways as a train rounds a sharp bend, you feel
pressed against the floor of an elevator that accelerates upward.
Nevertheless, the forces you'd feel struck Einstein as very familiar. As
you approach a sharp bend, for example, your body tightens as you brace for
the sideways push, because the impending force is inevitable. There is no
way to shield yourself from its influence. The only way to avoid the force
is to change your plans and not take the bend. This rang a loud bell for
Einstein. He recognized that exactly the same features characterize the
gravitational force. If you're standing on planet earth you are subject to
planet earth's gravitational pull. It's inevitable. There is no way around
it. While you can shield yourself from electromagnetic and nuclear forces,
there is no way to shield yourself from gravity. And one day in 1907,
Einstein realized that this was no mere analogy. In one of those flashes of
insight that scientists spend a lifetime longing for, Einstein realized
that gravity and accelerated motion are two sides of the same coin.
Just as by changing your planned motion (to avoid accelerating) you
can avoid feeling squeezed back in your car seat or feeling pushed sideways
on the train, Einstein understood that by suitably changing your motion you
can also avoid feeling the usual sensations associated with gravity's pull.
The idea is wonderfully simple. To understand it, imagine that Barney is
desperately trying to win the Springfield Challenge, a month long
competition among all belt-size-challenged males to see who can shed the
greatest number of inches. But after two weeks on a liquid diet (Duff
Beer), when he still has an obstructed view of the bathroom scale, he loses
all hope. And so, in a fit of frustration, with the scale stuck to his
feet, he leaps from the bathroom window. On his way down, just before into
his neighbour’s pool, Barney looks at the scale's reading and what does he
see? Einstein was the first person to realize, and realize fully, that
Barney will see the scale's reading drop to zero. The scale falls at
exactly the same rate as Barney does, so his feet don't press against it at
all. In free fall, Barney experiences? the same weightlessness that
astronauts experience in outer space.
In fact, if we imagine that Barney jumps out his window into a large
shaft from which all air has been evacuated, then on his way down not
only would air resistance be eliminated, but because every atom of his
body would be falling at exactly the same rate, all the usual external
bodily stresses and strains-his feet pushing up against his ankles, his
legs pushing into his hips, his arm is pulling down on his shoulders-would
be eliminated as well.'+ By closing his eyes during the descent, Berner
would feel exactly what he would if he were floating in the darkness of
deep space. (And, again, in case you're happier with the nonhuman
examples: if you drop two rocks tied by a rope into the evacuated shaft,
the rope will remain slack, just as it would if the rocks were floating in
outer space.)
Thus, by changing his state of motion-by fully "giving in to gravity Barney
is able to simulate a gravity-free environment. (As a matter of fact, NASA
train astronauts for the gravity-free environment of outer space by hang
them ride in a modified 707 airplane, nicknamed the Vomit Comet, that
periodically goes into a state of free fall.)
Similarly, by a suitable hang in motion you can create a force that is
essentially identical to gravity. For example, imagimeth at Barney joins
astronauts floating weightless in their space capsule, with the bathroom
scale still stuck to his feet and still reading zero. If the capsule should
fire up its boosters and accelerate, things will change significantly.
Barney will feel pressed to the capsule's floor, just as you feel pressed
to the floor of an upward accelerating elevator. And since Barney's feet
are now pressing against the scale, its reading is no longer zero. If the
captain fires the boosters with just the right oomph, the reading on the
scale will agree precisely with what Barney saw In the bathroom. Through
appropriate acceleration, Barney is now experiencing a force that is
indistinguishable from gravity.
The same is true of other kinds of accelerated motion. Should Barney
join Homer in the outer space bucket, and, as the bucket spins, stand at a
right angle to Homer-feet and scale against the inner bucket wall-the
scale will register a nonzero reading since his feet will press against it.
If
the bucket spins at just the right rate, the scale will give the same
reading Barney found earlier in the bathroom: the acceleration of the
spinning bucket can also simulate earth's gravity.
Relativity and the Absolute *All this led Einstein to conclude that the
force one feels from gravity and the force one feels from acceleration are
the same*. They are equivalent Einstein called this the principle of
equivalence.
Take a look at what it means. Right now you feel gravity's influence. If
you are standing, your feet feel the floor supporting your weight. If you
are sitting, you feel the support somewhere else. And unless you are
reading in a plane or a car, you probably also think that you are
stationary-that you are not accelerating or even moving at all. But
according to Einstein you actually are accelerating. Since you're sitting
still this sounds a little silly, but don't forget to ask the usual
question: Accelerating according to what benchmark? Accelerating from whose
viewpoint? With special relativity, Einstein proclaimed that absolute
spacetime provides the benchmark, but special relativity does not take
account of gravity. Then, through the equivalence principle, Einstein
supplied a more robust benchmark that does include the effects of gravity.
And this entailed a radical change in perspective. Since gravity and
acceleration are equivalent, if you feel gravity's influence, you must be
accelerating. Einstein argued that only those observers who feel no force
at all-including the force of gravity-are justified in declaring that they
are not accelerating.
Such force-free observers provide the true reference point for discussing
motion, and it's this recognition that requires a major turnabout in the
way we usually think about such things. When Barney jumps from his window
into the evacuated shaft, we would ordinarily describe him as accelerating
down toward the earth's surface. But this is not a description Einstein
would agree with. According to Einstein, Barney 1s not accelerating. He
feels no force. He is weightless. He feels as he would floating in the deep
darkness of empty space. He provides the standard against which all motion
should be compared. And by this comparison, when you are calling reading at
home, you are accelerating. From Barneys perspective as he freely falls by
your window-the perspective, according to Einstein, of a true benchmark for
motion-you and the earth and all the other things we usually think of as
stationary are accelerating upward. Einstein would argue that it was
Newton's head that rushed up to meet the apple, not the other way around.
Clearly, this is a radically different way of thinking about motion. But
it's anchored in the simple recognition that you feel gravity's influence
only when you resist . By contrast, when you fully give in to gravity you
don't feel it. Assuming you are not subject to any other influences (such
as air resistance), when you give in to gravity and allow yourself to fall
freely, you feel as you would if you were freely floating in empty space-a
perspective which, unhesitatingly, we consider to be unaccelerated.
In sum, only those individuals who are freely floating, regardless of
Whether they are in the depths of outer space or on a collision course with
the earth's surface, justified in claiming that the) are experiencing no
acceleration. *If you pass by such an observer and there is relative
acceleration between the two of you, then according to Einstein, you are
accelerant. *As a matter of fact, notice that neither Itchy, nor Scratchy,
nor Apu, nor Martin was truly justified in saying that he was stationary
during the duel, since they all felt the downward pull of gravity. This has
no bearing on our earlier discussion, because there, we were concerned only
with horizontal motion, motions that unaffected by the vertical gravity
experienced by all participants as an important point of principle, the
link Einstein found between gravity and acceleration means, once again,
that we are justified only in considering stationary those observers who
feel no forces whatsoever.
Having forged the link between gravity and acceleration, instead was
nor ready to take up Newton's challenge and seek an explanation of how
gravity exerts its influence.
warps, Curves, and Gravity
Through special relativity, Einstein showed that every observer cuts up
spacetime into parallel slices that he or she considers to be all of space
at successl1.e instants of time, with the unexpected twlst that observers
moving relative to one another at constant velocity will cut through space
time at different angles. If one such observer should start accelerating,
you might guess that the moment-to-moment changes in his speed and/or
direction of motion would result in moment-to-moment changes In the angle
and orientation of his slices. Roughly speaking, this is what happens.
Einstein (using geometrical insights articulated by Carl Friedrich Gauss,
Georg Bernhard Riemann, and other mathematicians in the nineteenth century)
developed this idea-by fits and starts-and showed that the differently
angled cuts through the spacetime loaf smoothly merge into slices that
are *curved
*but fit together as perfectly as spoons in a silverware tray, an *accelerated
observer carves spatial slices that are warped.*
*Relativity and the Absolute*
With this insight, Einstein was able to invoke the equivalence principle
to profound effect. Since gravity and acceleration are equivalent, Einstein
understood that gravity itself must be nothing but warps and curves in the
fabric of spacetime. Let's see what this means.
If you roll a marble along a smooth wooden floor, it will travel In a
straight line. But if you've recently had a terrible flood and the floor
dried with all sorts of bumps and warps, a rolling marble will no longer
travel along the same path. Instead, it will be p i d e d this way and that
by the warps and curves on the floor's surface. Einstein applied this
simple idea to the fabric of the universe. He imagined that in the absence
of matter or energy --sun, no earth, no stars-space time, like the smooth
wooden floor, has no warps or curves. It's flat. This IS schematically
illustrated in which we focus on one slice of space. Of course, space IS
real) three dimensional, and is a more accurate depiction, but drawings
that illustrate inro dimensions are easier to understand, so we'll continue
to use them. Einstein then imagined that the presence of matter or energy
has an effect on space much like the effect the flood had on the floor.
Matter and energy, like the sun, cause space (and spacetime*) to warp and
curve? And just as a marble rolling on the warped floor travels along a
curved path, Einstein showed that anything moving through warped space-such
as the earth moving in the vicinity of the sun-will travel along a curved
trajectory.
It's as if matter and energy imprint a network of chutes and valleys
along which objects are guided by the invisible hand of the spacetime
fabric. That, according to Einstein, is how gravity). exerts its influence.
The same idea also applies closer to home. Right now, your body would like
to slide down an indentation In the spacetime fabric caused by the earth's
presence. But your motion is being blocked by the surface on which you're
sitting or standing. The upward push you feel almost every moment of your
life-be it from the ground, the floor of your house, the
corner easy chair, or your king size bed-is acting to stop you from sliding
Einstein was able to find equations that do for gravity what Maxwell's
equations did for electromagnetism And by using these equations, Einstein
and many others made for the path that would be followed
by this or that planet, or even by light emitted by a distant star, as it
moves through curved spacetime. Not only have these predictions been
confirmed to a high level of accuracy, but in head-to-head competition
with the predictions of Newton's theory, Einstein's theory consistently
matches reality with finer fidelity.
Of equal importance, since general relativity specifies the detailed
mechanism by which gravity works, provides a mathematical framework for
determining how fast it transmits its influence. The speed of
transmission comes down to the question of how fast the shape of space can
change in time. That is, how quickly can warps and ripples-ripples like
those on the surface of a pond caused by a plunging pebble-race from place
to place through space! Einstein was able to work this out, and the answer
he came to was enormously gratifying. He found that warps and
ripples-gravity, that is-do not travel from place to place instantaneously,
as they do in Newtonian calculations of gravity. Instead, they travel at
exactly the speed of light. Not a bit faster or slower, fully in keeping
with the speed limit set by special relativity. If aliens plucked the moon
from its orbit, the tides would recede a second and a half later, at the
exact same moment we'd see that the moon had vanished. *Where Newton’s
theory failed, Einstein's general relativity prevailed.*
*KR IRS Part4 6724 7724*
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