How Big is Big and How Small is Small
Page 27
We do not classify two objects that appear similar but have radically different histories as the same type. The Mona Lisa, and a perfect forgery, down to the last molecule, are not the same because they have different histories. One was painted by Leonardo da Vinci in about 1500 and the other yesterday. Among plants and animals there are a number of species in the new world and old world that have the same common name because, at least superficially, they look the same, for example the robin and the buffalo. When two species evolve a similar characteristic the process is referred to as convergent evolution or homoplasy; bats have wings, but they are not birds. Whales and dolphins are not fish, a mistake that Linnaeus made, but later corrected.
History and evolution can also be applied to inanimate objects, for example when recognizing what a planet is. In 2006 the International Astronomical Union (IAU) defined a planet as a celestial body that (a) orbits the Sun, (b) is effectively spherical and (c) has cleared its neighborhood. This last criterion is where Pluto fell short. This criterion is more about the history of Pluto than about the fact that it lives in a messy corner of the solar system. Pluto and its orbit were not formed in the normal way a planet forms.
How do we recognize a group of individuals as members of the same category? They should have similar appearance, but that is sometimes hard to quantify. They should be about the same size. They should have been put together in the same way; that is, they should have had a similar history. They should do similar things. In fact for much of the world we can recognize an object by what it is made of and what forces shape it. Galaxies are made of stars. Atoms are made of electrons, protons and neutrons. Planets and stars are both held together by gravity, but the difference is that in stars fusion is at play. In a star, the nuclear, strong and weak forces are at work transforming energy.
So I think that our diagram really does reflect nature and the variety of things in the universe. From quarks and protons to the great walls and voids of galaxies, all of nature is laid out here. Of course there are things missing, but the plot is already cluttered. Still, there is one significant gap. There is a void between 10−14 m and 10−10 m. There is nothing in nature in the interval between the largest nucleus (uranium-235, r = 7.75 × 10−15 m) and the smallest atom (helium, r = 0.31 × 10−10 m). Here is a region of our diagram that is calling out for explanation. Why is it that there is a gap spanning four orders of magnitude?
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Below 10−14 m all the objects of nature are held together by the strong force, above this gap none. The primary or fundamental constituents below the gap are the six types or flavors of quarks: up, down, charm, strange, top and bottom. These are bound together by the strong force and gluons. All of this—the characters and the rules of engagement—are described by quantum chromodynamics.
From this small collection of ingredients all of particle and nuclear physics arises. It tells us how nature builds protons, neutrons and pions, and occasionally more exotic particles such as the omega or charmonia (a combination of a charm and anti-charm antiquark). It also explains the nuclear force as a residual, a little bit of attraction that squeezes between quarks and tethers neighboring nucleons together. The nuclear force is what binds neutrons and protons to form a nucleus, the anchor of the atom.
On our scale of nature diagram, the region dominated by the strong force is well removed from the rest of nature. Only the strong force, living up to its name, is strong enough to bind particles into such a confined region. It also suggest that forces might be a useful organizing principle for the whole diagram.
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The next object above the gap is the atom. Electrons and nuclei are the primary constituents of an atom and they are held together by the electromagnetic force. Much like the strong force in nucleons, the force between electrons and nuclei do not perfectly cancel each other out; they leave a residual, the chemical force. The electromagnetic force not only holds atoms together, it causes all of chemistry. Chemical bonds in turn form molecules, compounds, crystals and metals. It is chemistry that holds together macroscopic objects such as cells, plants and animals. The desk I am sitting at would collapse and those boulders in space we call asteroids would disintegrate if it were not for chemical bonds and the electromagnetic force. From atoms (10−10 m) to that irregular moon of Neptune, Proteus (2 × 105 m) the electromagnetic force and chemistry dominate.
As an aside, the name electromagnetic tells us a bit about how our understanding of this force has changed. At one time scientists viewed the attraction between charged particles and the force between magnets as two separate and unrelated phenomena. But James Clerk Maxwell (1831–1879) saw a symmetry between them and proposed that the two were actually flip-sides of the same coin, two facets of the same force. The magnetic force is caused by charges in motion. It might be electricity in a wire wound around an iron bar in an electromagnet, or an electron in orbit around an iron nucleus in a permanent magnet. This was the first force unification in the history of physics. In recent years one of the holy grails of physics has been to devise a grand unified theory, or GUT. This would be a theory in which the strong, weak and electromagnetic forces are three manifestations of a deeper underlying force. As of this time various GUTs have been proposed, but there is no consensus as to a final GUT.
Beyond GUTs there maybe a theory of everything or TOE, which includes gravity. But there is still a lot of work for physicists to do before either a GUT or a TOE is recognized as describing nature.
Still, we have made progress since Maxwell published his unification in 1865. In the 1970s Abdus Salam, Sheldon Glashow and Steven Weinberg showed that the electromagnetic and weak forces arose from the same set of fields, the electroweak fields. In the process they also predicted the existence of the W and Z bosons, which were experimentally confirmed a decade later. So when I use the term “electromagnetic” instead of “electroweak,” I may sound a bit dated. But I am interested in persistent objects, things that are stable and have structure. We do not know of anything with a structure that depends upon the W or the Z boson.
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The next and last force that sculpts nature is gravity. If we were to take all the moons and asteroids in the solar system and line them up by size, the smallest are simply rocks; even the moons of Mars look like potatoes. But as we look at larger and larger bodies there is a transition from irregular lumps of stone to well-formed spheres. Bodies as big as Miranda, a moon of Uranus (radius of 236 kilometers) or bigger, are spherical. Someplace at about 200 km radius we cross the hydrostatic equilibrium line and gravity is strong enough to pull down the high points and fill in the basins. Gravity has overcome the intrinsic strength of the rock.
To appreciate how, at one scale, chemical bonds can dominate yet at another scale gravity wins, imagine that you are standing on the Royal Gorge bridge, nearly 300 m above the Arkansas River in Colorado. Now take a steel jack chain and start to lower it over the side. Jack chain is actually a pretty weak chain. Each link is made of a piece of wire that is twisted like a figure eight. It keeps its shape because of internal chemical forces. Our chain is #16 gauge, made from wire about 0.16 cm in diameter. So after a 100 m of it have been reeled out there is almost 7 kg of chain hanging from the bridge. The breaking point of this chain is about 18 kg and so we can keep reeling it out. After 200 m, 14 kg hangs below us. Someplace near 250 m we can expect one of the links to straighten and the chain to break. In fact, if the links are identical, and we reel it out smoothly, we would expect the top link to break since it bears the most weight. Gravity has overcome chemistry and most of our chain plunges into the river below. (Most chains would be a few kilometers long before breaking, but bridges are not that high.)
Gravity is the weakest force in nature, yet in the end it is the force that shapes the largest objects: planets, stars, galaxies and even the large-scale structure of the universe. This is because of one unique trait of this force: gravity has only one charge; there is only mass and no anti-mass. Gravity always attract
s. Two quarks with the same color charge repel, two electrons with the same electric charge repel, but particles with mass always attract.
If I had 1 g of hydrogen and I could separate the electrons and the protons into two containers a meter apart there would be a force equal to about a billion tons trying to get them back together. Normally we do not feel that force because the positive protons are paired with the negative electrons on a microscopic level, canceling each other. That sample of hydrogen also has quarks with color charge and tremendous forces between them, but again they cancel on human scales and we are not aware of them. That sample also has mass, a single gram, but the force of that gram, although extremely weak, is felt across the universe.
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On our scales of nature diagram, we can now group things by the force that primarily shapes them (see Figure 15.1). Below the 10−12-m gap the world is dominated by the strong force; from the atom to Proteus is the realm of electromagnetic and chemistry; above that is gravity. Is this significant? Does it point to some deep underlying principle? I do not think so. There are too many exceptions and too many situations where more than one force is important. Why is the tallest tree on Earth, the Hyperion, limited to 115 m? Gravity has limited trees’ height, even though trees are well below the size of spherical moons. Also, black holes exist well below the size of irregular celestial bodies. The limit of the largest stable nucleus, uranium-238, is set because the neutrons and nuclear force can no longer overcome the electric-charge repulsion. In fact the limits of the sizes of different objects is often set by a balance between forces, but combined in a unique way for that situation. This diagram may not reveal anything deep, but it does help us organize what we see.
Figure 15.1 Different forces of nature dominate different scales. The scales of nature diagram, with objects plotted by size from our experimental limit of smallest object, to the edge of the universe. Regions where different fundamental forces dominate are indicated.
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There remains one glaring problem with this size-to-force relationship: we have omitted one of the fundamental forces of nature, the weak force. The weak force is associated with radioactive decay. In its simplest form a neutron decays into a proton as well as an electron and an anti-neutrino. When cobalt or radium undergo a radioactive decay this is exactly what is happening inside the nucleus. In fact, if we were to peer deep inside the neutron we would see that a down quark is decaying into an up quark. These are rare events. The lifetime of a neutron, if it is not bound in a nucleus, is between 14 and 15 min. for comparison, the delta particle decays via strong interaction with a lifetime of 5.58 × 10−24 s.
Perhaps more important in shaping the world as we know it is the reverse but even more difficult process: when a proton decays into a neutron, positron (anti-electron) and neutrino. That reaction does not take place spontaneously like a neutron decay. Because a neutron is heavier than a proton you need to put energy into the system. However, it can happen when two fast-moving protons collide: one proton becomes a neutron, using some kinetic energy and the neutron and the other proton fuse to become a deuteron (see Figure 15.2). This releases more energy than it used, and causes the stars to glow. At the heart of the process that powers stars and lights up the universe, up quarks are changing into down quarks and that is the weak force at work.
After that initial fusing things move faster. The positron and any nearby electrons will collide, annihilate and give up even more energy. The deuteron will combine with hydrogen to form helium-3 and yield even more energy. But what sets the pace for everything is that first step. A proton can bounce around inside a star for a billion years before that occasional weak decay happens at just the right moment.
Figure 15.2 Proton–proton fusion. This process can only happen if one proton decays into a neutron and that transformation is due to the weak force. The weak force sets the rate at which stars burn hydrogen.
The weak force has little to do with the shape and spatial structure of any object in nature. But it has a huge amount to do with the pace at which it evolves. The weak force governs how fast stars burn and stretches their lifetimes out to billions of years. If the combining of two protons to form a deuteron took place via the strong interaction it would happen a quadrillion times faster. It would be reasonable to expect stars to burn hotter and faster. If this were true the universe might still be expanding but it would look a very different place. All the fuel would be used up by now and the stars would be dark.
Since the weak force sets the pace of energy use, our Sun has burned for billions of years and will continue for a few billion more. The weak decay also sets the brightness of our Sun and so the temperature on the surface of our planet. And that, at least from the point of view of humans and life on Earth, is pretty important.
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So again, do we understand the size of the universe or the size of quarks? Can we comprehend the lifetime of a delta particle or the age of the universe? Scientists who spend their lives studying one of these systems can see with their eyes no more than anyone else: a hairsbreadth at the smallest scale and the Andromeda galaxy, if they know where to look, at the largest. But if they truly understand the scale of their subject it means that they know how to manipulate the numbers that are relevant and ignore the ones that are not. The marine biologist who is studying Baleen whales does not worry about the effects of black holes, the physicist looking for glueballs is not concerned with carbon bonds, and the astronomer measuring the distance to the Sloan Great Wall may not be concerned about any of these. When we say that a scientist understands how big or how small something is, it means they know how it relates to other things of similar magnitude that have influence upon their subject, and that they can apply that knowledge successfully.
We stand on a planet 1022 fm or 1041 Planck lengths in diameter, made out of 1052 quarks and we are giants. We live in a universe 1027 m, or human lengths, across and we are insignificant iotas, except for one thing. We can look at stars and cells and atoms and galaxies and, even if our understanding is incomplete, we can comprehend them all. We can take in all the scales of nature and marvel at the world.
Index
A
accelerator, 169
Adam, Jehan, 31
Almagest, 54
analemma, 114
Andromeda galaxy, 16, 218, 219
anemometer, 46
angstrom, 7, 154
Ångström, Anders, 154
antimatter, 175
antiquarks, 175
Arabic numerals, 81
Archimedes, 80, 209
Avogadro’s number, 91
number system, 91
sand in universe, 229
argon dating, 141
Aristarchus of Somos, 86
asteroid belt, 201
astrolabe, 113
astronomical unit (AU), 7, 189, 194
atom, 242
illustrated wavefuctions, 161
size of, 155
spectrum, 122
atomic mass unit (u), 41
Avogadro’s number, 36, 43
Avogadro, Amedeo, 36
B
bacteria, 18
Balaenoptera musculus, 26
baseball, 118
baseline, 87
Beaufort scale, 46
Beaufort, Francis, 46
Bernoulli, Daniel, 68
Bessel, Friedrich, 210
Big Bang, 117, 144, 145, 223, 226
billion, 30
binomial system, 7
black holes, 214
blackbody radiation, 72
Boötes void, 225
Bohr, Niels, 159
Boltzmann’s constant, 71, 73
Boltzmann, Ludwig Eduard, 68, 230
Bradley, James, 210
Brahe, Tycho, 209
Breguet, Abraham-Louis, 130
bristlecone pine, 14
BTU, 102
C
Calculus, the, 236
caloric, 64
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calorie, 102
Cambrian revolution, 141
candle, 220
canonical hours, 128
Cantor, Georg, 236
Capricornus void, 225
carbon-14 dating, 136
cardinality, 236
cards, 230
Carnot cycle, 65
Carnot, Nicolas Léonard Sadi, 65
Carroll, Lewis, 78, 80, 227
Cassini, Giovanni Domenico, 188, 189
cells, 16, 21
Cepheid variables, 218
CERN, 179
cesium-fountain clock, 117
Chapman, Aroldis, 118
chemical
vs. nuclear, 106
bonds, 154, 196
vs. gravity, 244
chemistry, 153–155
Chinese, traditional time, 127
Chuquet, Nicolas, 31
Clausius, Rudolf Julius Emanuel, 66
clocks, 112, 116
clonal colonies, 28
comet, 133
continental drift, 142
Copernicus, Nicolaus, 189, 190
cosmic distances
astronomical unit, 189
candle, 220
Cepheid variables, 218
Hubble’s law, 224
spectral parallax, 213
stellar parallax, 209
Tully–Fisher, 220–221
type Ia supernova, 221
cosmic ladder, 213
Crab nebula, 214–215
crystals, 156
cubit, 3
D
Dalton, John, 36
day, 112, 131
decibels, 58
decimal time, 128
Delambre, Jean Baptiste Joseph, 5, 147
delta particle, 123, 126
delta time, 116
diamond, 156
diatonic, 60
dinosaur
extinction, 141
size of, 26
DNA, 17
Doppler effect, 220, 221
dwarf planet, 201–203
E
Earth
age of, 143
size of, 84