How Big is Big and How Small is Small: The Sizes of Everything and Why

291 Pages·2014·4.75 MB·English

by  Timothy Paul Smith

HOW BIG IS BIG AND HOW SMALL IS
SMALL
The Sizes of Everything and Why
by
Timothy Paul Smith
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Impression: 1
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Contents
List of Figures
List of Tables
1. From Quarks to the Cosmos: An Introduction
2. Scales of the Living World
3. Big Numbers; Avogadro’s Number
4. Scales of Nature
5. Little Numbers; Boltzmann’s and Planck’s Constants
6. The Sand Reckoner
7. Energy
8. Fleeting Moments of Time
9. Deep and Epic Time
10. Down to Atoms
11. How Small Is Small
12. Stepping Into Space: the Scales of the Solar System
13. From the Stars to the Edge of the Universe
14. A Little Chapter about Truly Big Numbers
15. Forces That Sculpture Nature and Shape Destiny
Index
List of Figures
1.1 The original definition and measurement of the meter.
1.2 Towns embedded in counties, embedded in states, embedded in nations.
2.1 The relationship between surface and volume.
2.2 As towns grow into cities the traffic for supplies must increase.
2.3 A collection of Littorina saxatilis (periwinkle) collected in Scotland.
2.4 Savanna elephant Loxodonta african, Loxodonta catherdralus and Notre
Dame de Paris.
3.1 Loschmidt’s method for determining the size of a molecule.
4.1 The Beaufort and Saffir–Simpson scales and windspeed.
4.2 The Richter scale versus the Mercalli scale.
4.3 The number of hurricanes in the North Atlantic (2003–2012) as a function
of windspeed.
4.4 The Mohs scale versus the absolute hardness of minerals.
4.5 The stars of Orion as reported in the Almagest.
4.6 The frets and related frequencies of a guitar.
5.1 Reversible and nonreversible collisions on a pool table.
5.2 Order as shown with a die and pennies.
5.3 The distribution of light described by Planck’s law.
5.4 The Planck length.
6.1 Eratosthenes’ method for measuring the size of the Earth.
6.2 Aristarchus’s method for measuring the size of the Moon.
6.3 Surveying the distance to unreachable points with angles and baselines.
6.4 Aristarchus’s method for measuring the size of and distance to the Sun.
6.5 The size of a geocentric and a heliocentric universe.
7.1 Energy densities for chemical and nuclear fuels.
7.2 The energy that is released when hydrogen burns, at the molecular level.
7.3 The octane molecule.
7.4 Energy from nuclear fission.
8.1 The analemma, as viewed from New York City.
8.2 The discovery of the omega particle.
9.1 Solar versus sidereal time.
9.2 The decay of carbon-14 used for dating.
9.3 The layers or strata of the Grand Canyon.
9.4 The supercontinent Pangaea about 200–300 million years ago.
10.1 The cross section of a standard meter bar from the 1880s.
10.2 A marching band performs a wheel and demonstrates interference.
10.3 Laser light on a single hair shows an interference pattern.
10.4 Trees in an orchard demonstrate the facets in a crystal.
10.5 The interference pattern of X-rays from a crystal and DNA.
10.6 Wavefunctions of the hydrogen atom.
10.7 The periodic table of the elements.
11.1 Detail from a small part of the table of nuclides.
11.2 The table of nuclides.
11.3 The nuclear force.
11.4 An image of a nucleus made of protons and neutrons with quarks inside of
them.
11.5 A collection of different types of particles made of quarks.
11.6 The interaction between a proton and neutron in terms of pions and quarks.
11.7 The interaction between quarks in terms of gluons and color charge.
11.8 The electric charge distribution of a neutron.
12.1 Kepler’s third law demonstrated by Jupiter’s moons and the planets.
12.2 The transit of Venus as seen by two separate observers.
12.3 Some of the moons in our solar system.
12.4 The rings of Saturn.
12.5 The Titus–Bode law.
13.1 Parallax of a near star.
13.2 The H–R diagram of star color versus luminosity.
13.3 A map of the Milky Way.
13.4 The Andromeda galaxy.
13.5 The Doppler effect in water waves.
13.6 Comparison of the size of galaxies, group, superclusters and the universe.
13.7 The large-scale structure of the universe.
14.1 Everything is small compared to infinity.
15.1 Different forces of nature dominate different scales.
15.2 Proton–proton fusion.
List of Tables
3.1 Names of numbers.
6.1 The symbols and values of numerals in the Roman number system.
6.2 The symbols, values and names of numerals in the Greek number system.
6.3 A comparison of the astronomical measurements of Aristarchus, of
Archimedes and of modern astronomical measurements.
7.1 Comparison of nuclear and chemical forces and bonds.
7.2 Comparison of the four fundamental forces in nature.
8.1 Exotic subnuclear particles; lifetimes, forces and decay.
9.1 Comparison of decimal and standard time.
9.2 Days and years of the planets.
9.3 Present geologic time.
9.4 Supercontinents through the history of the Earth.
12.1 Radius of the orbits of the planets: Copernicus vs modern measurements.
12.2 Some properties of the planets.
12.3 Some properties of the dwarf planets.
13.1 List of nearby stars.
14.1 Examples of sets that have an infinite number of members.
1
From Quarks to the Cosmos:An Introduction
If the meter is the measure of humans, then we are closer to quarks than we are
to quasars. However, if we take the second as the heartbeat of our lives, then we
are closer to the age of the universe than to the lifetime of elementary particles.
There are well over forty-five orders of magnitude between the largest things we
have ever measured—the grand breadth of the universe itself—and our smallest
measurement, the probing of those iotas of matter, quarks, electrons and gluons.
There are also over forty orders of magnitude between the fastest events clocked
and the slowest events, which we continue to watch evolve and unfold.
Somewhere in the middle of these ranges are the scales where we humans spend
our lives, the scales measured in meters and seconds. The breadth of these scales
is truly astonishing and it is a credit to modern science and to our intellectual
capacity that we can write down forty-digit numbers with certainty and a fair
amount of precision.
This book is a guide to understanding and appreciating those numbers, both
the large distances and the small. A concert or an art exhibit may be beautiful
and awe-inspiring, and quarks and the cosmos are awe-inspiring and, I would
argue, beautiful too. But the concert or exhibit may be better appreciated with
program notes or a guide. Likewise, with diligence and a good guide, we can
learn what these vast and infinitesimal numbers mean. We can internalize and
appreciate their beauty.
The universe is about 1027 macross. That is a 1 followed by twenty-seven
zeros: 1,000,000,000,000,000,000,000,000,000 m. At the other extreme, we have
probed neutrons and protons. We know that they contain quarks and we know