Then in 1928, Hubble offered evidence that distant galaxies were receding and the whole universe was expanding. At that point, almost every physicist would have been more than happy to throw out the cosmological constant, as unnecessary. Unfortunately, like a fairy-tale evil spirit, ? proved much easier to raise than to banish. No one could prove that ? was necessarily equal to zero. It was known that ? must be small, since a non-zero ? produces a "pressure" in space-time, encouraging the expansion of the universe regardless of the presence of matter. Thus the rate of expansion of the universe sets an upper limit on the possible value of ?.
Even so, the cosmological constant was felt to be somehow "unphysical." Kurt Gödel, the famous logician, added weight to that idea. He became interested in general relativity when he was Einstein's colleague at the Princeton Institute for Advanced Study, and in 1949 he produced a strange solution of the Einstein field equations with a non-zero ?. In Gödel's solution the whole universe has an inherent rotation, which the real universe according to all our measurements does not. This was regarded as evidence that a non-zero cosmological constant could lead to weird results and was therefore unlikely.
However, weirdness for the universe is certainly permitted. We have seen enough evidence of that on the smallest scale, in the quantum world. And now we have the possibility that remote galaxies, flying apart from each other faster and faster under the pressure of a non-zero ?, offer evidence on the largest scale that once again, in the words of J.B.S. Haldane, "the universe is not only queerer than we suppose, it is queerer than we can suppose."
TABLE 4.1
Event
time, t
Gravity decouples
10-43 seconds
Inflation of universe
10-35 seconds
Nuclear matter density
0.0001 seconds
Neutrinos decouple
1 second
Electron/positron pairs vanish
30 seconds
Helium nuclei form
3.75 minutes
Atoms form
1 million years
Galaxy formation begins
1 billion years
Birth of solar system
10 billion years
Today
15 billion years
TABLE 4.2
T=log(t/tN), where tN is chosen as 15 billion years.
Event
T
Big Bang
-infinity
Gravity decouples
-60.7
Inflation of universe
-52.7
Nuclear matter density
-21.7
Neutrinos decouple
-17.7
Electron/positron pairs vanish
-16.2
Helium nuclei form
-15.3
Atoms form
-4.2
Galaxy formation begins
-1.2
Birth of solar system
-0.2
Today
0
TABLE 4.3
Tc=log(t/log(C-t))
Event
Tc
Big Bang
-infinity
Gravity decouples
-61.31
Inflation of universe
-52.31
Nuclear matter density
-22.31
Neutrinos decouple
-18.31
Electron/positron pairs vanish
-16.83
Helium nuclei form
-15.95
Atoms form
-4.81
Galaxy formation begins
-1.81
Birth of solar system
-0.74
Today
-0.52
"Halfway" point (32.5 billion yrs)
0
Helium dissociates
+15.95
Electron/positron pairs form
+16.83
Neutrinos couple
+18.31
Gravity couples
+61.31
End point (65 billion years)
+infinity
TABLE 4.4
Closed Universe.
Event
t (billions of years)
Today
0
Sun becomes red giant
5
Halfway point, expansion ceases
17
Most dwarf stars cease to shine
30
Big Crunch
50
TABLE 4.5
Open Universe, Unstable Proton.
Event
t (years)
Today
0
Sun becomes red giant
5 billion
Most dwarf stars cease to shine
30 billion
All stellar activity ceases
1014
Stellar remnants become black holes
1030-1036
Black holes evaporate
1064
Radiation only
1080
TABLE 4.6
Open Universe, Stable Proton.
Event
t (years)
Today
0
Sun becomes red giant
5 billion
Most dwarf stars cease to shine
30 billion
All stellar activity ceases
1014
Stars are iron neutron stars
101600
Neutron stars form black holes
>10 to the 1026
Radiation only
10 to the 1076
CHAPTER 5
The Constraints of Chemistry
There is another way to distinguish physics from chemistry. Physics is needed in describing the world of the very small (atoms and down) and the very large (stars and up). Chemistry works with everything in between, from molecules to planets. So although physics is vital to us (where would we be without gravity and sunlight?), chemical processes largely control our everyday lives.
An exception to this rough rule has been created in the last century, as a result of human activities. Lasers, nuclear power, and all electronics from computers to television derive from the subatomic world of physics.
5.1 Isaac Asimov and the Timonium engine. Isaac Asimov was a famous science fiction writer, justly proud of the breadth of his knowledge. He wrote books on everything that you can think of, inside and outside science.
In the nineteenth century, the following jingle was made up about Benjamin Jowett, a famously learned Oxford Don:
"I am Master of this college,
What I don't know, isn't knowledge."
About Asimov, we might offer this variation:
"I am science fiction's guru,
What I don't know, don't say you do."
This doesn't actually rhyme, but it makes a point. Asimov knew lots. So when he, on a panel at a science fiction convention in Baltimore, heard one of the other speakers refer to a spaceship whose "engines were powered by timonium," and he noticed that all the audience laughed in a knowing way, he was quite put out.
Only later did he learn that this was a purely local reference. Timonium sounds like the name of an element, similar to titanium or plutonium, but it is actually a suburb of Baltimore. There was little chance that Asimov would know about it, and the other speaker relied on that fact.
Why, though, was Asimov so sure that timonium wasn't an element, perhaps a newly-discovered one between, say, titanium and chromium? Simply because there is already an element, vanadium, between titanium and chromium; and there cannot be any others. Titanium has atomic number 22, vanadium 23, chromium 24. If you say in a story that someone has found another element in there, is it much like saying that you have discovered a new whole number between eight and nine.
In fact, although the normal ordering of the elements corresponds to their atomic weights, their numbering is just the number of electrons that surround the nucleus. Hydrogen has one, helium has
two, lithium has three, beryllium has four, and so on. Nothing has, or can have, a fractional number of electrons.
Moreover, the electrons are not buzzing around the nucleus at random, they are structured into "electron shells," each of which holds a specific number of electrons. Chemical reactions involve electrons only in the outermost shells of an atom, and this decides all their chemical properties. The shells have been given names. Proceeding outward from the nucleus, we have K, L, M, N, O, P, and Q. Easy to remember, but of no physical significance.
The innermost shell can hold only two electrons. Hydrogen has one electron, so it has a place for one more, or alternatively we might think that it has one electron to spare. Hydrogen can take an electron from another atom, or it can share its single electron with something else. Helium, on the other hand, has two electrons. That makes a filled shell, and in consequence helium has no tendency to share electrons. Helium does not react appreciably with anything. If you write a story in which a race of aliens are helium-breathers, you'd better have a mighty unusual explanation.
Other elements with closed shells are neon (complete shell of two plus complete shell of eight), argon, (shell of two plus shell of eight plus shell of eight), krypton, xenon, and radon. You may recognize these as the "noble gases" or "inert gases." All resist combination with other elements. Radon, element number 86, decays radioactively, but fairly slowly, over a period of days. Radioactive decay, since it involves the nucleus of the atom, is by our definition a subject for physics rather than chemistry.
Atoms with one space left in a filled shell also combine very readily, particularly when that "hole" can be matched up with an extra electron in some other element which has one too many for a filled shell. Elements with one electron less than a filled shell include hydrogen, fluorine, chlorine, bromine, iodine, and astatine. These elements are all strongly reactive, and collectively they are known as "halogens." Halogen means "salt-producing," for the good reason that these elements, in combination, all produce various forms of salts. The last element in the halogen list, astatine, element number 85, is also unstable. In a few hours it decays radioactively. However, the properties of astatine—while it lasts—are very similar chemically to the properties of iodine.
Atoms with one electron too many for a filled shell include the elements lithium, sodium, potassium, rubidium, and cesium. Known collectively as the alkali metals, they combine readily with the halogens (and many other elements) and form stable compounds. Note that we can choose to regard hydrogen as a halogen, an alkali metal, or both.
The actual number of electrons in each shell is decided by quantum theory. However, long before quantum theory had been dreamed up and before anyone knew of electrons, the elements had been formed into groups in terms of their general chemical properties. This was done by Mendeleyev, who about 1870 had developed a "periodic table" of the elements. It is still in use today, suitably extended by elements discovered since Mendeleyev's time—discovered, in large part, because he had used the periodic table to predict that they ought to be there.
We repeat, for emphasis: the chemical properties of an element are completely decided by the number of electrons in its outer shell only. There is no scope for adding new elements "in the cracks" of the periodic table, and little scope for new chemical properties beyond those known today.
Can we find a way around that hindrance, and give the writer some room to maneuver?
We can. The so-called "natural" elements begin with hydrogen, atomic number 1, and end with uranium, atomic number 92. Uranium is itself radioactive, so over a long enough period (billions of years) it decays to form lighter elements. Heavier elements than uranium are not impossible to make, but they are unstable. In a short time—for elements with high enough atomic numbers, small fractions of a second—they decay and become some other, lighter element.
If we could just make stable elements heavier than uranium, or anything else known to our laboratories today, a whole new field of chemistry would open up. These new "transuranic elements" could have who-knows-what interesting properties.
Now, as heavier and heavier elements are created beyond uranium, their radioactive decay to other elements normally takes less and less time. It seems hopeless to look for new stable elements. However, there is one ray of hope. The neutrons and protons that make up the atomic nucleus form, like the electrons outside it, "shells." When the number of neutrons in a nucleus has certain values (known as "magic numbers"), the corresponding element is unusually stable. Similarly, extra stability is achieved when the number of protons in a nucleus has "magic" values. If a nucleus has the right number of protons (usually written Z) and the right number of neutrons (usually written N), it is known as "doubly magic," and is correspondingly doubly stable.
Magic numbers, computed from the shell theory of the nucleus (and generally agreeing with experiment), are 2, 8, 20, 28, 50, 82, 114, 126, and 184. The theoretical calculations provide the higher values, but these are not seen in naturally occurring elements which end at uranium with Z=92. In principle, doubly-magic numbers would occur with any pair of these magic numbers, such as Z=20 and N=8. In practice, in every heavy nucleus, the number of neutrons is greater than or equal to the number of protons. Also, a nucleus is unstable if N exceeds Z (known as the "neutron excess") by a large factor. Given these two rules, we might expect nuclei of extra stability for Z=2, N=2; Z=8, N=8; Z=20, N=20; Z=28, N=28; and so on.
What we find in practice is that Z=2, N=2 is helium, and the nucleus is highly stable. Z=2, N=8 is not stable at all, because the excess of neutrons over protons is too large. Z=8, N=8 is oxygen, and it is very stable. So is Z=20, N=20 (calcium, stable), and Z=82, N=126 (lead, also stable).
We now see a possibility that doubly-magic, extra-stable elements might exist with Z=114 or Z=126, and a suitably high neutron number, N, of 184. Experiments so far have not led to any such elements, but the existence of an "island of stability" somewhere between element 114 and element 126 is a suitable offshore location for science fictional use.
Even more interesting is the possibility that humans might someday discover a way to stabilize naturally radioactive materials against decay. We know of no way to do this at the moment, but we can argue that it might be possible, with an analogy provided by Nature. A free neutron, left to itself, will usually decay in a quarter of an hour to yield a proton and an electron. Bound within a nucleus, however, the same neutron acts as a stable particle. The helium nucleus, two protons and two neutrons, is one of the most stable structures known. Perhaps, by embedding a super-heavy nucleus from the island of stability within some larger structure, we can prevent its decay for an indefinitely long period. The super-heavy transuranic elements might then share a property of the quark, that while we understand their properties, we never actually observe them.
5.2 The limits of strength. The strength and flexibility of a material, anything from chalk to cheese, depend on the bonds between its atoms and molecules. Since interactions at the atomic level take place only between the electrons in the outer shell of atoms, the strength of those bonds is decided by them.
The density and mass of a material, on the other hand, is decided mainly by the atomic nucleus. For every electron in an atom there must be a proton in the nucleus, plus possible neutrons, and the neutron and proton each outweigh the electron by a factor of almost two thousand.
We thus have an odd contrast:
Strength: determined by outer electrons.
Weight: determined by nucleus.
Using these two facts, without any other information whatsoever, we can reach a conclusion. The strongest materials, for a given weight, are likely to be those which have the most outer electrons, relative to the total number of electrons, and the least number of neutrons (which are purely wasted weight) relative to the number of protons.
The elements with the most electrons in the outer shell relative to the total number of electrons are hydrogen and helium. As we know already, helium is a poor candida
te for any form of strong bond. Also, whereas the hydrogen nucleus has no neutrons, the helium nucleus has as many neutrons as protons. We conclude, on theoretical grounds, that the strongest possible material for its weight ought to be some form of hydrogen. Of course, hydrogen is a gas at everyday temperatures, but that should not deter us.
TABLE 5.1 (p. 122) shows the strength/weight ratio of different materials. It confirms our theoretical conclusion. Hydrogen, in solid form, ought to be the strongest "natural" material—once we have produced it.
We have added to the table "below the line" a couple of extra items with a decidedly science fictional flavor. Muonium is like hydrogen, but we have replaced the single electron in the hydrogen atom with a muon, 207 times as massive. The resulting atom will be 207 times smaller than hydrogen, and should have correspondingly higher bonding strength.
Muonium, considered as a building material, is not without its problems. The muon has a lifetime of only a millionth of a second. In addition, because the muon spends a good part of its time close to the proton of the muonium atom, there is a fair probability of spontaneous proton-proton fusion.
Borderlands of Science Page 11
