Part 3
Carving space and time
To see this, imagine that Marge and Lisa, seeking some quality together
time, enrol in a Burns Institute extension course on urban renewal. For
their first assignment they are asked to redesign the street and avenue
layout of Springfield, subject to two requirements: first, the street
avenue grid must be configured so that the Soaring Nuclear Monument is
located right at the grid's center, at 5th Street and 5th Avenue, and,
second, the designs must use streets 100 meters long, and avenues, which
run perpendicular to streets, that are also 100 meters long. Just before
class, Marge and Lisa compare their designs and realize that something is
terribly wrong. After appropriately configuring her grld so that the
Monument lies in the center, large finds that Kwik-E-Mart is at 8th Street
and 5th. Avenue and the nuclear power plant is at 3rd Street and 5th
Avenue. But in Lisa's design, the addresses are completely different: the
Kwik-E-Mart is near the corner of 7th Street and 3rd Avenue, while the
power plant is at 4th Street and 7th Avenue. Clearly, someone has made a
mistake.
After a moment's thought, though, Lisa realizes what's going on. There are
no mistakes. She and Marge are both right. They merely chose different
orientations for their street and avenue grids. Marge's streets and avenues
run at an angle relative to Lisa's; their grids are rotated relative to
each other; they have sliced up Springfield into streets and avenues in two
different ways ! The lesson here is simple, yet important.
There 1s freedom in how Springfield-a region of space-can be organized
by streets and avenues. There are no "absolute" streets or "absolute"
avenues. Marge's choice is as ! valid as Lisa's-or an!, other possible
orientation, for that matter.
Hold this idea in mind as we paint time into the picture.
Einstein's unexpected answer is that they both are. Although the
conclusions of our two referees differ, the observations and the reasoning
of each are flawless. Like the bat and the baseball, they simply have
different perspectives on the same sequence of events. The shocking thing
that Einstein released is that their different perspectives yield different
but equally valid claims of what events happen at the same time. Of course,
at everyday speeds like that of the train, the disparity is small-Martin
claims that Scratchy got the light less than a trillionth of a second
before Itchy-but were the train moving faster, near light speed, the time
difference would be substantial.
Think about what this means for the flip-book pages slicing up a
region of spacetime. Since observers moving relative to each other do not
agree on what things happen simultaneously, the way each of them will slice
a block of spacetime into pages-with each page containing all
events that happen at a given moment from each observer's perspective will
not agree, either. Instead, observers moving relative to each other cut a
block of spacetime up into pages, into time slices, in different but
equally valid ways. What Lisa and Marge found for space; Einstein found
for spacetime. Angling the Slices The analogy between street avenue grids
and time slicing can be taken even further.
Imagine that Itchy and Scratchy have reconciled. Instead of trying to
shoot each other, they just want to ensure that clocks on the front and
back of the train are perfectly synchronized. Since they are still
equidistant from the gunpowder, they come up with the following plan. They
agree to set their clocks to noon just as they see the light from the
faring gunpowder. From their perspective, the light has to travel the same
dis-Relativity and the Absolute trance to reach either of them, and since
light's speed is constant, it will reach them simultaneously. But, by the
same reasoning as before, Martin and anyone else viewing from the platform
\rill say that Itchy 1s heading toward the emitted light while Scratchy 1s
moving away from it, and so Itchy will receive the light signal a llttle
before Scratch) does Platform observers wdl therefore conclude that Itchy
set his clock to 12 00 before 1 Scratchy and will therefore claim that
Itchy's clock is set a blt ahead of Scratchy's. For example, to a piatform
observer like Martin, when it's
12:06 on Itchg's clock, it may be only 12.04 on Scratchy’ s
Yet, from the viewpoint of Apu and I eloquent on the tram, Itchy and
Scratchy performed the synchronization perfectly. Again, although it's hard
to accept at a gut level, there is no paradox here. observers in relative
motion do not agree on simultaneity-they 1 do not agree on what thzngs
happen at the same time.
A single page from the perspective of those on the train contains events
that lie on earlier and later pages of a platform observer.
If Newton's conception of absolute space and absolute time were correct,
everyone would agree on a single slicing of spacetime. Each slice would
represent absolute space as viewed at a given moment of absolute time. But
this is not how the world works; and the shift from rigid Newtonian time to
the newfound Einsteinian flexibility inspires a shift in our metaphor.
Rather than viewing spacetime as a rigid flip
Sometimes it is useful to think of it as a huge, fresh loaf of bread. And in
place of the fixed pages that make up a book-the fixed Newtonian time
slices-think of the varlet> of angles at which you can slice a loaf into
parallel pieces of bread, each piece of bread represents
space at one moment of tinier from one observer's perspective.
slicing up a loaf of bread in two different ways, there is still something
that we would fully agree
upon:
How could it be otherwise? We both imagined cutting up the same loaf.
Different observers slice up a region of spacetime in different ways, but
the region itself, like the loaf of bread, has an independent existence.
Thus, although Newton definitely got it wrong, his intuition that there was
something absolute, something that everyone would agree upon, was not fully
debunked by special relativity.
Absolute space does not exist. Absolute time does not exist. But
According to special relativity, absolute spacetime does exist. With this
observation, let's visit the bucket once again.
In an otherwise empty universe, with respect to *what *1s the bucket
spinning? According to Newton, the answer is absolute space. According
to Mach, there is no sense in which the bucket can even be said to spin.
According to Einstein's special relativity, the answer is absolute
spacetime.
To understand this, let's look again at the proposed street and avenue
layouts for Springfield. Remember that Marge and Lisa disagreed on the
street and avenue address of the Kwik-E-Mart and the nuclear plant
because their grids were rotated relative to each other. But regardless of
how each chose to lay out the grid, there are some things they definitely
still agree on. For example, if in the interest of increasing worker
efficiency during lunchtime, a trail is painted on the ground from the
nuclear plant straight to the Kwik-E-Mart, large and Lisa will not agree on
the streets and avenues through which the trail passes, as you can see
Einstein realized that something similar holds for spacetime.
Now, even though different observers slice up the spacetime loaf at
different angles and thus will not agree on how much time has elapsed or
how much distance is covered between various points on a trajectory, such
observers will, like Marge and Lisa, still agree on whether a trajectory
through spacetime is a straight line. Just as the geometrical
shape of the painted trail to the Kwik-E-Mart is independent of
the street avenue slicing one uses, so the geometrical shapes of
trajectories in spacetime are independent of the time slicing one uses.'0
This is a simple yet critical realization, because with it special
relativity
provided an absolute criterion-one that all observers, regardless of
their constant relative velocities, would agree on-for deciding whether
or not something is accelerating
Spacetime provides the backdrop with respect to which something, like a
spinning bucket, can be sad to accelerate even in an otherwise empty
universe. With this insight, the pendulum swung back again: from Leibniz
the relationist to Newton the absolutist to Mach the relationist, and now
back to Einstein, whose special relativity showed once again that the arena
of reality-viewed as spacetime, not as space-is enough of a something to
provide the ultimate benchmark for motion.
At this point you might think we've reached the end of the bucket
story, with Mach's ideas having been discredited and Einstein's radical
updating of Newton's absolute conceptions of space and time ha\,ing won the
day.
The truth, though, is more subtle and more interesting. But if you're new
to the ideas we've covered so far, you may need a break before pressing on
to the last sections of this chapter. In Table 3.1 you'll find a summary to
refresh your memory when you've geared up to reengage.
Okay. If you're reading these words, I gather you're ready for the next
major step in spacetime's story, a step catalyzed in large part by none
other than Ernst Mach. Although special relativity, unlike Mach's theory,
concludes that even in an otherwise empty universe you would feel pressed
against the inside wall of a spinning bucket and that the rope tied between
two twirling rocks would pull taut, Einstein remained deeply fascinated by
Mach's ideas. But he realized that serious consideration of these ideas
required significantly extending them. Mach never really specified a
mechanism whereby distant stars and other matter in the universe might play
a role in how strongly your arms splayed outward when you spin or how
forcefully you feel pressed against the inner wall of a spinning bucket.
Einstein began to suspect that if there were such a mechanism it might
have something to do with gravity. This realization had a particular allure
for Einstein because in Special relativity, to keep the analyses actable,
he had completely ignored gray-Newton Space is an entity; accelerated
motion is not relative; absolutist position.
The experimental success of Newton’s law notwithstanding, Einstein realized
that according to Newton, gravity exerts its influence from place to place,
from the sun to the earth, from the earth to the moon, from any-here to
an!,-there, ~instantaneously, in no time at all, much faster than light.
And that directly contradicted special relativity.
Newton's law predicts that the water would start to recede from high tide,
because of the loss of the moon's gravitational pull, about a second and a
half before you saw the moon disappear from the sky. Like a sprinter
jumping the gun, the water would seem to retreat a second and a half too
soon.
The reason is that, according to Newton, at the very moment the
the moon disappears, its gravitational pull be instantaneous? Disappear
too, and without the moon's gravity, the tides would immediately start to
diminish. Yet, since it takes light a second and a half to travel the
quarter million miles between the moon and the earth, you wouldn't
immediately see that the moon had disappeared; for a second and a half, it
would seem that the tides &,ere receding from a moon that was still shining
high overhead as usual. Thus, according to Newton's approach, gravity can
affect us before light-gravity can outrun light-and this, Einstein felt
certain, was wrong."
And so, around 1907, Einstein became obsessed with the goal of formulating
a new theory of gravity, one that would be at least as accurate as Newton's
but would not conflict with the special theory of relativity. This turned
out to be a challenge beyond all others. Einstein's formidable intellect
had finally met its match. His notebook from this period is filled with
half-formulated ideas, near misses in which small errors resulted in long
wanderings down spurious paths, and exclamations that he had cracked the
problem only to realize shortly afterward that he'd made another mistake.
Finally, by 1915, Einstein emerged into the light.
Although Einstein did have help at critical junctures, most notably from
the mathematician Marcel Grossmann, the discovery of general relativity
was the rare heroic struggle of a single mind to master the universe. The
result is the crowning jewel of pre-quantum physics.
Einstein's journey toward general relative began with a key question
that Newton, rather sheepishly, had sidestepped.
How does gravity exert its influence over immense stretches of space?
The sun doesn't touch the earth, so how does it do that? In short, how does
gravity get the job done? Although Newton discovered an equation that
describes the effect of gravity with great accuracy, he fully recognized
that he had left unanswered the important question of how gravity actually
works. In his *Principia, *Newton wryly wrote, "I leave this problem to the
consideration of the reader."13 As you can see, there is a similar between
this problem and the one Faraday and Maxwell solved in the 1800s, using the
Idea of a magnetic field, regarding the way a magnet exerts influence on
things that it doesn't literally! touch. So, you might suggest a similar
answer: gravity exerts its influence on another field, the gravitational
field broadly speaking, this is the right suggestion. But realizing this
answer in a manner that does not conflict with special relativity is easier
said than done.
What is equally dazzling, the story comes full circle because Einstein's
key breakthrough was tightly linked to the very issue Newton highlighted
with the bucket: What is the true nature over accelerated motion?
KR IRS part3 57246724
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