Picture This!: Grasping the Dimensions of Time and Space

205 Pages·2016·21.996 MB·English

by  Michael Carroll (auth.)

Grasping the Dimensions of Time and Space
Michael Carroll
Picture This!
Grasping the Dimensions of Time and Space

Picture This!
Grasping the Dimensions of Time and Space
By Michael Carroll, with original illustrations by the author
Michael Carroll
Littleton , CO , USA
ISBN 978-3-319-24905-6 ISBN 978-3-319-24907-0 (eBook)
DOI 10.1007/978-3-319-24907-0
Library of Congress Control Number: 2016936414
© Springer International Publishing Switzerland 2016
T his work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the
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not imply, even in the absence of a specifi c statement, that such names are exempt from the relevant protective
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Cover image by the author
Printed on acid-free paper
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The registered company is Springer International Publishing AG Switzerland
Prefa ce
THE LONG AND SHORT OF IT
As we have become aware of our place in the universe, and its true scale,
we are forced to use larger and larger numbers. Our neighborhood has
expanded from the homes in our village to the planets in our Solar
System to the galaxies in our local group. In our modern, technological
culture, we throw around some big numbers. We have to. Our complex
everyday lives necessitate it. Take, for example, our transportation. Maybe
you drive a mid-sized hybrid car. Its engine turns out about 90 horse-
power. If we run the clock back a century to a family similar to yours, one
or two horses typically served that family’s transportation needs, and
perhaps a few more if they used farming equipment. What could they
have done with 90 horses?
I f you climb aboard a mid-sized civilian airliner, like an Airbus A320,
each of its engines has power equivalent to roughly 1600 cars or 16,000
horses.1 In a single, modest commercial airliner, we have half as many
horses as were employed by the entire combined armies of Genghis Khan.
The numbers we use in our everyday lives have multiplied over time. We
know more. We know how small we are.
This knowledge did not come easily. The Greek scholars Aristarchus
and Hipparchus were among the fi rst who attempted to fi gure out the dis-
tance from our own world to the Moon. Aristarchus assumed – correctly –
that when the Moon was exactly half illuminated, it formed a right angle
between the Sun and Earth. By fi guring the angle between the Sun and
Moon, he could then assume a triangle with the three cosmic objects. The
measure of this triangle provided him with an estimate of the distances
1. C alculated from Airbus
between Earth and the Sun and Earth and the Moon. In the second century A320’s IAE V2500 engine
thrust of 155 kN.
B. C., Hipparchus used similar methods to those used by Aristarchus a cen-
2. H ipparchus actually
tury before. He agreed with Aristarchus that the Earth-Moon distance was
estimated the distance from
roughly 59 times the radius of Earth, 2 and the range to the Sun at 1200 Earth to the Moon at 67
Earth radii.
times that of Earth’s radius. He was off by 23,250 times.
v
vi
PREFACE
Astronomers continued to refi ne their observations and math skills,
gathering insights into just how large an affair the vault of the heavens
truly is. Two sixteenth-century astronomers, Christiaan Huygens and Jean-
Dominique Cassini, independently determined the distance to the Sun
from Earth. Huygens used a very clever geometric method. Like all good
telescope observers of the day, he knew that Venus exhibited phases just
like the Moon does. He also realized that the phase of Venus depended on
the angle between it, the Sun and Earth, just as Hipparchus had done with
the Moon and Earth. So, for example, when Venus, the Sun, and Earth
form a right angle, Venus looks half lit, like a half Moon. By measuring two
inside angles in a triangle, you can also measure the length of one side, if
you know how big the other side is. Unfortunately, he had to guess at this
number. He was not far off. Cassini came along and, armed with a newly
calculated distance to Mars using parallax, was able to estimate the Sun’s
distance at 140,000 km.
Using even more math, German mathematician/astrologer Johann
Kepler3 described the laws of motion, enabling observers to estimate the
distance of planets from the Sun by the way they moved in their orbits. The
Solar System turned out to be a surprisingly large affair. Space beyond was
even more vast (see Chap. 6 ) .
H ow do we get our minds around such concepts? We fi nd astronomi-
cal numbers baffl ing. The human brain can visualize a few tens of objects
on a table, but beyond that point, it begins to generalize in an effort to
make comprehension manageable. The stars visible in the night sky, away
from light pollution, number approximately 6000 to the naked eye. But
this number is a fairly abstract one, understandable on an intuitive level
only as a visual experience or impression.
However, we c an understand by analogy and comparison. When we
are told that a million Earths would fi t inside the Sun, we are impressed,
but a bit mystifi ed. But when we use the comparison of a basketball next to
the head of a pin, we can comprehend that relationship. P icture This! takes
us on such a journey. By using objects and landmarks familiar to us, we
will delve into the sizes, shapes, and relationships of cosmic objects that
boggle the mind, humble the heart, and inspire the spirit.
It is a daunting challenge. Take, for example, the Solar System. With a
basketball Sun nestled in the center, the span of our planetary system – out
to Pluto – stretches 24 m across. With our pinhead-sized Earth, it is a big
neighborhood. But we have only begun. The scales of our cosmic sur-
roundings become ever more diffi cult to comprehend. Demonstrating the
distance to the nearest star is nearly impossible, even on this diminutive
3. Kepler, who lived from 1571 scale. The nearest sun resides a substantial way across the continental
to 1630, played a key role in
United States. Only a handful of stars would fi t within the entire globe of
the seventeenth-century
“scientifi c revolution.” His Earth. To comprehend, we must “jump scales” to something larger, shrink
work served as part of the
the Sun farther down, and compress distance into something manageable.
foundation for Isaac
Newton’s laws of physics. “You have to do all these little tricks,” says astrophysicist/educator Jeff
vii
PREFACE
Bennett. “Anything you do to try to get your head around them works for
only so long. For example, we’ll usually start out with the Earth-Moon
system. The Moon is 30 Earth diameters away, and it is about a third the
size of Earth, but then when you try to put the Sun in, you can’t do it. So
you have to change scale. You come up with this new scale. You can jump
scale and put the galaxy on a football fi eld, for example, but it becomes
meaningless to most people. The numbers become mind numbing. So
instead, I like to use counting. Counting to 100 billion takes you 3000 years.
That’s something you can understand.”
It is diffi cult and often confusing to communicate relative size using
the written word. For example, in 2005, the small asteroid 2005YU55
passed within 201,700 miles of Earth – closer than the Moon. Astronomers
imaged the cosmic stone potato with radar, and the press described the
object as being “as long as an aircraft carrier.” The problem with this
description is that it only involves one dimension: length, while the object
is a three-dimensional one. This book depends upon visual analogies, so
the best way to show the size of 2005YU55 was to place the entire object, or
an approximation of it, next to an aircraft carrier. First, we place a photo of
an aircraft carrier at the bottom of the frame, with a wake and a sky painted
in. The photo used is the Nimitz-class aircraft carrier U SS Ronald Reagan.
Next, we place the radar image of the asteroid above the ship, with a
shadowed side and color fi lled in.

Fig. P.1 Asteroid 2005YU55 next to an aircraft carrier (Photo by Mass Communication Specialist 2nd Class Joseph M. Buliavac, courtesy
of the U. S. Navy, ID 090608-N-3659B-059. Radar image Courtesy of NASA/JPL/Caltech.)
viii
PREFACE
To provide a three-dimensional relationship between the fl oating
rock and the surface, we drop in a shadow across the ocean and the carrier.
In the radar image, craters are not visible, but they are subtly implied, and
bodies of this size often seem to have them, so craters are artistically draped
over the sunlit surface.
To complete the effect, refl ected light from the ocean is rendered on
the shadowed side. Now, we have a view of asteroid 2005YU55 in a setting
that is understandable on an intuitive level.

Fig. P.2 A shadow presumably from a crater and crater texture are added to make the rock more realistic (Art by the author.)
Fig. P.3 The fi nal result
(Art by the author.)
ix
PREFACE
A s we explore scales of various sizes, we notice echoes in patterns of
varying sizes. For example, the spiral of a hurricane reminds us of the spi-
ral arms of a galaxy’s stars or the spirals found in certain biological struc-
tures. The ancient Greeks noticed these parallels millennia ago. They
coined the term “golden mean” or “golden ratio” to describe a repeating
proportion found in many natural forms. Greek philosophers believed
that beauty contained three essential elements: symmetry, proportion, and
harmony. To describe the natural proportion of forms in nature, Greek
mathematicians established the golden ratio. If two objects – compared to
each other – had an identical ratio to the sum of those objects compared to
the larger of the two original objects, the objects were defi ned as being in
the golden mean. Like a computer program’s fractals, the shapes repeat, no
matter the scale. As a modern example, in 2010, the journal Science reported
that the golden ratio is present at the atomic scale in the magnetic reso-
nance of spins in cobalt niobate crystals.
A more mathematically advanced approach to the spiral forms found
in nature, especially those found in biological forms such as the organiza-
tion of leaves in an aloe plant (called phyllotaxis), the confi guration of an
artichoke’s plates, or the arrangement of a pinecone’s petals. This approach
can be summed up by a relationship called Fibonacci sequence. The fi rst
two numbers in the Fibonacci sequence are 1 and 1.4 Each succeeding
number is the sum of the previous two (so the sequence begins as 1, 1, 2, 3,
5, 8, 13, and so on). Sunfl owers famously display two superimposed oppo-
site spirals in the fl orets outside of the seed head, one spiral of 34 and the
other of 55 fl owers. The Fibonacci sequence even shows up in the family
tree of honeybees. If an unfertilized female bee lays an egg, that egg will
hatch a male, or drone, bee. But if the female has mated, her egg will
become a female. This means that any male bee always has one parent, 2
grandparents, 3 great-grandparents, 5 great-great-g randparents, etc.
Fibonacci numerical sequence presents on many varied levels, including
physics, chemistry, biology, and mathematics. For example, a physicist will
tell us that the spiral is the lowest energy form that arises through self-
organizing processes. The biologist sees the spiral of leaves as the most
effi cient use of space for leaves to gather light in photosynthesis. Structure
echoes purpose.
These spiral forms follow the shape they do, in part, because their
structure follows their purpose. In the same way, the spiral form of a galaxy
issues from its nature: density waves move throughout the stars at its disk,
resulting in its grand spirals of stars. The rings of Saturn, actually a vast
spiral around the planet, are also triggered by density waves.
T he concept of structure echoing purpose originally came from
architecture. The early twentieth-century architect Louis Sullivan champi-
oned the idea, which he put in this way: “Form follows function.” In 1896,
4. S ome applications begin
he wrote, the sequence at 1 and 0.