100 Best Books for an Education

A Revision and Update of Will Durant's 100 Best Books for an Education

Note 5



The Universe and Everything in it!




Our Picture of the Universe


People largely mythologized much of the universe until the time of the ancient Greeks. The famous Ptolemaic model prevailed for the most part from the second until the sixteenth century; it asserted that there were several crystal spheres rotating around the Earth, with every one of the planets, the Sun, and the Moon occupying one of these spheres and the stars inhabiting the outermost sphere. However, Nicholas Copernicus, a Polish canon, developed a simpler model. To try to confirm Copernicus, Galileo directed the earliest astronomical telescope heavenward in 1609. He determined that the Milky Way was not simply a whitish band through the sky but that it contained an enormous number of stars, far more than the few thousand observable with the naked eye. His examinations also refuted the idea of crystal spheres. This resulted in a recognition of the enormous complexity of the universe.

    Currently, the Big Bang* is the accepted theory of the origin of the universe. Support for it includes the detection of cosmic background radiation (CBR), which appears to arise equally from all directions. The CBR has qualities one would anticipate if the universe developed from an infinitely tiny compact region exploding.

* Since it proposes the universe originated somewhat like an explosion that caused all parts to fly quickly away in every direction.


Space, Time, and Motion


The Big Bang created space and time, but motion through space is contingent on three laws that Sir Isaac Newton codified:

    1) A body at rest tends to stay at rest; a body in motion moves at the same velocity in a straight line unless acted upon by a force. Galileo discovered this “law of inertia.” It infers that a body will move in a curved line only as long as a force is acting on it. When the force ceases, the body will move in a straight line.

    2) Mathematically, this law takes the form:


F = ma


and states that a continuous force will result in acceleration.*

    3) For every action there is an equal and opposite reaction. This is the basis for the jet engine and its cousin the rocket.

    From his second law of motion, Newton mathematically derived his law of gravity:


F = GmM/r2


where F is the force of gravity, G signifies the universal gravitational constant (6.674 x 10-11 newton m2/kg2), m and M are two masses, and r is the distance between them. This law infers that bodies falling close to the surface of the Earth will fall with identical rates of acceleration (disregarding the drag produced by air) at 9.8 m/sec2, and physicists typically label it g.

    Einstein’s general theory of relativity established laws of gravity more precise than Newton’s. As Stephen Hawking writes:


very accurate observations of the planet Mercury revealed a small difference between its motion and the predictions of Newton’s theory of gravity. Einstein’s general theory of relativity predicted a slightly different motion from Newton’s theory. The fact that Einstein’s predictions matched what was seen, while Newton’s did not, was one of the crucial confirmations of the new theory. However, we still use Newton’s theory for all practical purposes because the difference between its predictions and those of general relativity is very small in the situations that we normally deal with. (Newton’s theory also has the great advantage that it is much simpler to work with than Einstein’s!)

    Einstein’s theory [was] based on the idea that the laws of science should be the same for all observers, no matter how they are moving. It explains the force of gravity in terms of the curvature of a four-dimensional space-time. . . . In general relativity, bodies always follow straight lines in four-dimensional space-time, but they nevertheless appear to us to move along curved paths in our three-dimensional space. . . .

    Light rays too must follow geodesics in space-time. Again, the fact that space is curved means that light no longer appears to travel in straight lines in space. So general relativity predicts that light should be bent by gravitational fields. . . . It was not until 1919 that a British expedition, observing an eclipse from West Africa, showed that light was indeed deflected by the sun, just as predicted by the theory. . . . Another prediction of general relativity is that time should appear to slow near a massive body.


* Albert Einstein modified this in his special theory of relativity.


The Expanding Universe


Astronomers dedicated considerable efforts to advance the cosmological consequences of the general theory of relativity. Space, for instance, is curved, but physicists argue about whether it is a positively curved (such as a sphere) or negatively curved (such as a saddle). Einstein himself found that his theory envisaged the universe as either enlarging as if it were exploding, or imploding. He undertook to amend this by introducing a term in his equations to counter the prediction.* However in the 1920s, astronomer Edwin Hubble found that the universe really is expanding. General Relativity posits that the universe has a finite history, and leads to other predictions particularly when coupled with the laws of quantum mechanics.


The Three Basic Laws of Quantum Mechanics


When one studies effects on tiny masses and at tiny distances, it is essential to distinguish that things behave counterintuitively from their actions in the macro-world. For instance, the energy of an electromagnetic (EM) wave is contingent on an infinitesimal number known as Planck’s constant (6.62606957 x 10-34 joules per hertz), and it transmits in discrete “packets” based on Planck’s constant times the frequency. Max Planck termed these energy packets quanta i.e. the amount by which energy transfers in stages (instead of continuously), and their study is called quantum physics. The equation:


E = hν


where E is the energy, h is Planck’s constant, and ν the frequency of the light wave quantifies the energy of each “photon” or particle of light.

    Physicists later discovered that at times quanta behave like particles and other times like waves. Because of this, Werner Heisenberg formulated his Uncertainty Principle, which asserts that it is impossible to simultaneously specify with absolute precision the position and momentum of a quantum particle.

    The Pauli Exclusion Principle states that two particles of matter cannot share an identical quantum state. Bosons, particles of force, do not observe this rule.


Elementary Particles and the Forces of Nature


Ancient Greek philosophers originated the idea that matter was comprised of small indivisible particles called “atoms.” In 1803, John Dalton placed this hypothesis on a scientific basis, and it became the foundation of modern chemistry. Experiments by J.J. Thomson in 1897 were the first to show that atoms are divisible after all; that year he discovered the electron: a low-mass particle found orbiting atoms.

    The discovery of the particles that compose atoms totally transformed physics. Physicists subsequently created the Standard Model (SM) of elementary particles. In the SM, matter particles are called fermions, from Enrico Fermi who initially worked out the mathematics of their interactions in 1926. Each obeys the Pauli Exclusion Principle, which necessitates that they occupy an exact space. Matter is composed of leptons and quarks. The lepton family includes the electron one of whose traits is charge, an interaction with electric or magnetic fields. The charge of a single electron is -1. The muon is a high-energy counterpart to the electron but with a mass over 206 times it, and the tauon is the high-energy counterpart to the muon but with a mass almost 17 times that of the muon. Neutrinos, amongst the most commonplace particles in the universe, interact with normal matter so feebly that they are very hard to detect. Predicted in 1930 and first observed in 1955, neutrinos have a very tiny mass of less than 10-5 that of the electron. Different neutrinos couple with electrons, muons, and tauons. Each atom comprises a cloud of electrons about a center of positive charge designated the nucleus, which contains protons that were first discovered in 1911. They possess a charge that is identical to the electron but +1. Each proton is 1,837 times as massive as an electron. Next to it in the nucleus, the neutron is really like a neutral proton only slightly more massive (1,842 times the electron) and was discovered in 1932. They are stable when in a nucleus, but decay into other particles when outside it. In 1950, physicists discovered particles they termed “strange.” They are much heavier than the proton and neutron and eventually acquired the name hyperons. They also classified smaller then recently discovered particles as mesons. Starting in 1964, Murray Gell-Mann and others decided that a method explaining the characteristics of protons, neutrons, hyperons, and mesons is to consider the heavy particles as composed of combinations of even lighter ones. They named these tinier particles quarks, and there are six of them in all. Two quarks known as up and down make up protons and neutrons. Physicists later categorized “strange” particles as products of the strange quark. Similar to strange hyperons, the J/psi particle is a massive particle that emerges at high energies; a separate quark, the charm quark—the partner to the strange quark—produces it. Finally, there is a bottom quark that pairs with the top quark (which is the most massive, about as hefty as an atom of gold) and the final one to be discovered in 1995. All of this describes about 5% of the universe—ordinary matter; about 27% of matter is termed “dark matter,” and guesses abound as to its nature.

* This was his famous “cosmological constant”; he later called it his “greatest blunder,” but in 1998 scientists resurrected it to explain the mysterious “Dark Energy” that was causing the increasing acceleration of the universe.

Which is really just the speed of light divided by the wavelength.


When Paul A.M. Dirac* completed his mathematical formula of the theory of the electron in 1930, he noticed that one solution to his equations predicted a particle that was a mirror image of the electron except with a positive charge instead of a negative one—two years later scientists found the positron. Dirac’s equations predicted mirror images for all subatomic particles. In fact, it is feasible to create antiatoms by combining subatomic antiparticles. Scientists achieved just this in 1995 with the creation of some atoms of anti-hydrogen produced by causing a positron to orbit an anti-proton.

    Subatomic particles also create the forces that act on matter. The SM includes three of the four fundamental forces of nature: the strong and weak nuclear force and the EM force. Physicists collectively call the particles that produce these forces bosons after Satyendra Nath Bose who initially worked out the mathematics of their interactions; Einstein finalized these equations. The thus far discovered bosons are: gluons, pions, photons, W and Z particles, and the Higgs. According to the SM, the graviton is the only boson yet to be discovered. Eight distinct bosons called gluons create a force that binds quarks, and produces the “color” force. The color force is likewise the foundation of the strong force that binds the nucleus. Because of it, the study of quarks and gluons receives the name quantum chromodynamics (QCD). Predicted in 1935 and discovered in 1947, a pion transmits the strong force that binds protons and neutrons in the nucleus of atoms together, but since each pion emerges and vanishes virtually instantaneously physicists do not consider them components of the nucleus. The “photon” as a concept originated with Albert Einstein when he recognized that light (i.e. EM waves) acts occasionally as a particle—the photon therefore is the quantum of light and transmits the EM force. W and Z bosons mediate the weak nuclear force involved in radioactivity. At high energies the weak force unites with the EM, hence the W and Z are to a certain extent analogs to the photon and yet could not be more dissimilar, as the photon has a 0 rest mass and both W particles and the single Z particle are extremely heavy. Physicists found the Higgs in 2012 at CERN. They think it bestows mass to all other particles. Finally, the graviton generates the gravitational force through its exchange with other particles, but thus far, it remains theoretical. However, in 2000 the Laser Interferometer Gravitational Wave Observatory (LIGO) commenced operations pursuing the discovery of gravity waves i.e. the wave variety of the graviton. About 68% of the universe consists of “dark energy,” and a Theory of Everything (TOE) must account for this, as the SM does not.   

    Finally, Heisenberg in 1925 and Erwin Schrödinger in 1926 advanced two distinctive systems of the fundamental theory of subatomic particles called quantum mechanics. While the two appear very dissimilar, they produce the same results.


Interstellar Objects


In between subatomic particles and super massive black holes, we find interstellar objects. Nebulae are clouds of gas and dust visible in telescopes. Gaseous nebulae radiate light, often by the same means that a fluorescent bulb does: energy from stars ionizes the gas, which then fluoresces. Some dust nebulae also glimmer, usually reflecting the light of neighboring stars. Other dust nebulae are opaque blocking out part of the sky. Sir William Herschel investigated a category of nebulae that appeared to be giant spheres. He correctly determined that these planetary nebulae were balls of gas created when a star exploded.

    Collapsing clouds of gas and dust are thought to form brown dwarfs, bodies too small to be stars but too big to be planets. They radiate dimly because of the energy emitted by gravitational contraction. A brown dwarf must be between thirteen and eighty times the mass of Jupiter. The first one to be definitely identified orbits the star Gliese 229. Subsequently, astronomers have detected several more including some not orbiting other stars.

    Orbiting a star with the right amount of matter fairly describes a planet; our Earth is an atypical example. Its mass is 5.972 x1021 tonnes, it is the third planet from the Sun, and the only one in the solar system identified as harboring life. From space, it looks like a bright, blue-and-white sphere—blue since water covers some 70 percent of the surface and white because clouds shroud about half. The Earth’s atmosphere is 77% nitrogen, 21% oxygen, 1% water (on average), 0.92% argon, 0.04% carbon dioxide (and getting higher!) 0.002% neon, 0.0005% helium and 0.0002% methane. The Moon, the Earth’s only natural satellite, is 3,476 km in diameter. It is the most luminous body in the nighttime sky, repeatedly shifts its form as seen from Earth, and orbits every 29.5 days at an average distance of 385,000 km. Temperatures there can reach 134°C on the bright side and plummet to -170°C on the dark side.


Stellar Evolution, Black Holes, and Why They’re not so Black!


Stars are bodies of gas large enough to fuse hydrogen in their cores and produce helium. They radiate visible light as well as other EM radiation at different wavelengths. The hotter or bigger a star is the brighter. Dwarfs, or “main sequence,” stars are small—the most brilliant are blue dwarfs, the faintest red dwarfs; there are similarly white and brown dwarfs. Our Sun is a typical yellow dwarf. When a star has utilized the hydrogen in its core, different fusion reactions that begin with helium lead to carbon. These reactions are hotter than the fusion of hydrogen to helium. This extra energy triggers the hydrogen and helium layers beyond the core to enlarge. As a result, the star becomes a red giant because the outer layers are comparatively cool. When the Sun develops into a red giant in the distant future, it will enlarge nearly to the orbit of Earth, totally consuming Mercury and Venus, and searing Earth to a cinder. The next stage will lead to it becoming a White dwarf where the core has shrunk, because as a red giant it has depleted all its helium but is too tiny to start “burning” carbon, and the remaining atoms compress tightly together. This variety of star is enormously dense. Eventually becoming a black dwarf i.e. a white dwarf that has ceased radiating light.

    Nearly half the stars in the visible universe are really pairs of stars that orbit one another. Astronomers can occasionally see both stars, but more frequently they identify a star as part of a binary system because of the effect of the dimmer star’s gravitational attraction on its neighbor.

    Novae are stars that appear to emerge from nowhere and then disappear. The emergence of a new star in the sky amazed early peoples; but what actually happened was that a faint existing star abruptly brightened. Ancient Chinese astronomers named them guest stars. Prior to the telescope’s discovery, the faint stars were imperceptible so it appeared as if a “new” star sprung from nothing. Nowadays we understand that there are two distinctive types of “guest stars,” and we keep the name nova for one type and call the other supernova. Novae are dimmer than supernovae and may appear more than once. They arise when material from one star in a binary falls on the other triggering a flare up. Supernovae are explosions of huge stars, and are extremely dramatic when compared to the flaring up of a nova. One recounted by Chinese astronomers in 1054 was observable in the daytime. The vestige of this explosion is now the Crab Nebula.

    Some stars regularly change brightness and are termed variable stars (a nova varies its brightness but not at definite periods). The interlude differs with the reason for the change and the specific star. Certain variables are moieties of a binary system in which one star regularly eclipses the other. Others are called Mira variables and Cepheid variables, named for the first stars known of each type. Some Cepheids can be used to determine cosmic distances.

    After the violent explosion of certain supernovas and a resulting implosion of their cores, the result is a neutron star. The force maintaining electron separation is overwhelmed and they collide with protons causing the star to be composed solely of neutrons. Such stars may be as little as twenty kilometers in diameter but have masses between 1.39 and almost three times that of the Sun. All neutron stars spin quickly and radiate EM waves in a tight beam. Pulsars are neutron stars that radiate EM waves from their magnetic poles in a direction that reaches Earth where a radio telescope detects a fast on and off pulsing so regular that when first encountered astronomers believed them to be the creation of extraterrestrial beings. At its core, the Crab Nebula has a pulsar.

    A black hole is a body so dense for its mass that not even light can escape its crushing gravitational pull. As long ago as 1784, John Michell envisaged black holes; several later astronomers and physicists cited them to explain many odd astrophysical phenomena. Astronomers have detected black holes at the core of countless galaxies, including our own Milky Way, and scientists hypothesize that galaxies themselves form around super massive black holes. Astronomers have also found numerous smaller black holes believed to be the remains of supernova explosions. Quasars (Quasi-Stellar Objects) are remote sources of enormous energy named because they appear to have the dimensions and overall configurations of stars, but create far too much energy to be stars. There is evidence that black holes at the centers of far-off galaxies produce quasars. We cannot observe the stars in these galaxies because of the immense distances; therefore, we see only the quasar. Hawking discovered that due to the laws of quantum mechanics, a black hole must emit what has subsequently been called “hawking radiation.” Over great amounts of time, this radiation evaporates the black hole!

    Star clusters are stars that develop collectively; they are groupings of hundreds, thousands, or millions of stars. Open clusters, such as the Pleiades, encompass several hundred to a thousand stars amassed in an asymmetrical area perhaps tens of light-years across. There are approximately a thousand open clusters in the Milky Way. Globular clusters contain millions of stars, most very old, that have formed into an orb 100 to 200 light-years in diameter. There are around 150 known globular clusters in the Milky Way.

    Early in the 19th century, Herschel concluded that the Sun was a star in an immense lenticular star system, and that the Milky Way was the portion of the star system we perceive from our viewpoint within it. We now know that the Milky Way holds about 300 billion stars. Before 1924 telescopes lacked sufficient resolving power to confirm Herschel’s galactic hypothesis about certain nebulae. Now we know that these remote, grainy/cloudy patches in the sky are really millions of stars far outside the Milky Way which themselves have formed into other galaxies—precisely as Herschel predicted they would be. Observations with large telescopes have shown two principal types—spiral and elliptical—though certain galaxies are neither and are termed irregular.

    Galaxies also form clusters or groups associated in space. There may be only a few members to as many as thousands; around two dozen galaxies nearby form our Local Group which incorporates the Andromeda galaxy and the Large and Small Magellanic Clouds. The entire local group is moving through the universe together. The Local Group is a constituent of a supercluster of galaxies called the Local Supercluster, which comprises about 100 clusters.

* When Niels Bohr, says a famous story, was working with Dirac in the mid-1920s he lamented to Ernest Rutherford “Dirac never says anything.” Rutherford responded with a tale about a shopkeeper who appeased a disgruntled customer who had purchased a parrot that did not speak. “Please forgive me,” the shopkeeper said, “you wanted a parrot that talks, and I gave you the parrot that thinks.”


The Origin and Fate of the Universe


Countless outcomes in physics derive from several conservation laws, which all state that something cannot be created or destroyed. In a closed system, matter is conserved in all but nuclear reactions and other extreme conditions. Correspondingly, in a closed system, energy is conserved in all but nuclear reactions and other extreme conditions. By what mechanism does this take place? Energy comes in sundry forms: mechanical, chemical, electrical, heat, etc. As one kind is transformed into another (excluding nuclear reactions and other extreme circumstances), this principle guarantees that the total amount never varies, though it takes different forms.  

    Einstein discovered in his special theory of relativity that matter is merely congealed energy. He discovered the famous equation that relates mass and energy:


E = mc2


where E is the quantity of energy, m is mass, and c is the speed of light in a vacuum. One illustration of energy converting to mass appears in Einstein’s equation for how mass increases with velocity. If m0 is the rest mass, v the velocity of the body relative to an observer considered at rest, and c is the speed of light in a vacuum, then the mass, m, is provided by the equation


m = m0/√1-v2/c2


This explains one tenet of relativity that nothing can surpass the speed of light in a vacuum.* As it approaches this speed, so much of its energy converts to mass that it cannot maintain its acceleration. In both nuclear fission and nuclear fusion, matter converts into energy. Accordingly, matter and energy individually violate the conservation laws because each converts into the other. Therefore, the more general law is the law of conservation of mass-energy: the total amount of mass and energy must be conserved.

    Astronomers have long observed that galaxies are rotating as if they rest inside bigger, invisible structures. There are reasons to suppose that there is more matter in the universe than can be explained by the invisible matter encircling galaxies. Notions as to what this “missing mass” might be run the gamut from brown dwarfs to undiscovered subatomic particles. This missing mass plays a huge role in the ultimate fate of the universe. If there is enough, the universe would be “closed” and have positive curvature like the surface of a sphere.

    Conservation also applies to momentum, which is another way of restating Newton’s third law. This finds mathematical form in:


p = mv


where p is the momentum, m the mass, and v the velocity. A body traveling in a circle has a distinctive kind of momentum, angular momentum, which links mass, velocity, and acceleration (created by a force).

    Furthermore, conservation laws also apply to various properties connected with atoms and subatomic particles including charge, spin, isospin, and a category identified as CPT for charge conjugation, parity, and time. A partial violation of this last one may explain the abundance of matter vis-à-vis antimatter.


The Laws of Thermodynamics and the Arrow of Time


The first law of thermodynamics is identical to the law of conservation of energy. We must consider the transmission of heat as a form of energy to preserve the total amount of energy at a constant when examining a closed system. All bodies possess heat although there is not much at temperatures near absolute zero.

    The second law declares that heat in a closed system cannot move from a low temperature area to one of higher temperature in a self-sustaining process i.e. one that does not require energy from outside the system to maintain it. The second law has several inferences: 1) no perpetual motion machine is possible, 2) all energy in a closed system ultimately converts into heat that disseminates evenly throughout the system so that one can no longer acquire work from the system, and 3) the equations that depict the behavior of heat can also pertain to order and therefore to information. The term entropy signifies dispersed heat, disorder, or lack of information. A restatement of the second law is that in a closed system entropy continually increases. Because of this, physicists have discovered that time can only “flow” in one direction, and that effects cannot precede their causes.


Worm Holes and Time Travel


Is time travel possible? Hawking proffers this suggestion:


    In 1935, Einstein and Nathan Rosen wrote a paper in which they showed that general relativity allowed what they called “bridges,” but which are now known as wormholes. The Einstein-Rosen bridges didn’t last long enough for a spaceship to get through: the ship would run into a singularity as the wormhole pinched off. However, it has been suggested that it might be possible for an advanced civilization to keep a wormhole open. To do this, or to warp space-time in any other way so as to permit time travel, one can show that one needs a region of space-time with negative curvature, like the surface of a saddle. Ordinary matter, which has a positive energy density, gives space-time a positive curvature, like the surface of a sphere. So what one needs, in order to warp space-time in a way that will allow travel into the past, is matter with negative energy density.


* The central tenet of Einstein’s special theory of relativity states that all observers, no matter their own motion i.e. frame of reference, must measure the speed of light in a vacuum as invariant.


The Holy Grail of Physics


The SM is not a TOE. The particle of quantum gravity has yet to be discovered, though in theory it is known as the graviton, and the strong and electroweak forces are incompletely unified. Grand Unified Theories try to unify them. Along these lines, physicists dedicated considerable efforts to determining a workable relativistic quantum mechanics. Dirac expounded a relativistic electron theory in 1928, and in 1947 an acceptable quantized field theory, called quantum electrodynamics, developed unifying relativity and quantum theory vis-à-vis the interactions concerning electrons, positrons, and EM radiation. Beginning in the 1960s, the efforts of Hawking and others have been dedicated to a complete integration of quantum mechanics with relativity. A significant task for future physicists is to develop the TOE that would explain all of the fundamental particles, unify all the forces in nature, and provide an explanation of the ultimate fate of the universe.

    But alas . . . when we have nearly reached that exalted plateau some piece of data or a different theory will arise that tips the apple cart and makes us start all over again. . . .*

* Interested readers may find it immensely profitable to peruse Ahmed Farag Ali and Saurya Das’s theory that the universe is finite in extent but infinite in time and hence there never was a “big bang”! (Ahmed Farag Ali and Saurya Das, “Cosmology from quantum potential,” Physics Letters B, Volume 741:  276–279, 4 February 2015.)