Structure of the Universe

3. MICROCOSMOS: FROM LEUCIPPUS TO YUKAWA

With regard to the structure of the universe, the belief persists, that certain objects are fundamental and that others are derived, in the sense that the latter are composed of the former. In one version of this distinction, the fundamental objects are particles, or points of matter. Although the view of which objects qualify as fundamental particles has changed many times, the notion that the universe is ultimately made of such material points, moving through space, has endured in some form ever since the theory of atomism was first proposed by the Greeks Leucippus (5th century B.C.) and Democritus (c.460 - c.370 B.C.) in the 5th century B.C. (Whittaker, 1951 and 1953/1989).

An atom is the smallest unit of matter that is recognizable as a chemical element. Atoms of different elements may also combine into systems called molecules, which are the smallest units of chemical compounds (Figure 5). In all these processes, atoms may be considered as the ancient Greeks imagined them to be: The ultimate building blocks of matter. When stronger forces are applied to atoms, however, the atoms may break up into smaller parts. Thus atoms are actually composites and not units, and have a complex inner structure of their own.

Figure 5. The continuum of size and organizational level appears throughout the range of structural elements, from the fundamental particles to the highest-level systems of matter. Particles such as the quarks are known to be bound by strong forces. Protons and neutrons are bound within the atomic nucleus. The outer shell of atoms is bound to the nucleus by electromagnetic forces. A molecule may be thought of either as a structure build of atoms bound together by chemical forces or as a structure in which two or more nuclei are maintained in some definite geometrical configuration by attractive forces from a surrounding cloud of negative electrons. The evolution of the universe created a hierarchy of structural elements.

The first recorded speculations that matter consisted of atoms are found in the works of Leucippus and Democritus. The essence of their views is that all phenomena are to be understood in terms of the motions, through empty space, of a large number of tiny and indivisible bodies. The name "atom" comes from the Greek word "atomos", for "indivisible". According to Democritus, these bodies differ from one another in shape and size, and the observed variety of substances derives from these differences in the atoms composing them.

Greek atomic theory was not an attempt to account for specific details of physical phenomena. It was instead a philosophical response to the question of how change can occur in nature. Little effort was made to make atomic theory quantitative - that is, to develop it as a physical theory for the study of matter. Greek atomism, however, did introduce the valuable concept that the nature of everyday things was to be understood in terms of an invisible substructure of objects with unfamiliar properties. Democritus stated this especially clearly in one of the few sayings of his that has been preserved: "color exists by convention, sweet by convention, bitter by convention, in reality nothing exists but atoms and the void."

Although adopted and extended by such later ancient thinkers as Epicurus (341-270 B.C.) and Lucretius (c.95-55 B.C.), Greek atomic theory had strong competition from other views of the nature of matter. One such view was the four-element theory of Empedocles. These alternative views, championed by Aristotle among others, were also motivated more by a desire to answer philosophical questions than by a wish to explain scientific phenomena.

3.2 Atom

The atomic theory languished until the 18th and early 19th centuries, when physicists and chemists revived it to explain the properties of gases and some of the facts of chemistry. In these theories the fundamental particles, the atoms, remained indivisible points. The discovery in the late 19th and the 20th centuries that atoms were composite, rather than indivisible, set the stage for modern discoveries about fundamental particles (Pais, 1986; Whittaker, 1951 and 1953/1989).

When interest in science revived in Europe in the 16th and 17th centuries, enough was known about Greek atomism to form the basis for further thought. Among those who revived the atomic theory were Pierre Gassendi (1592-1655), Robert Boyle (1627-1691), and especially Isaac Newton. The latter part of Newton's book "Optics" is a series of detailed speculations on the atomic nature of matter and light, indicating how some of matter's properties are to be understood in terms of atoms.

In the 19th century, two independent lines of reasoning strengthened the belief in the atomic theory. Both approaches also began to reveal some quantitative properties of atoms. One approach, pioneered by John Dalton (1766-1844), involved chemical phenomena. The other, involving the behavior of gases, was carried out by physicists such as Rudolf Clausius (1822-1888) and James Clerk Maxwell (1831-1879).

Dalton's main step forward was his introduction of atomic weights. Dalton studied the elements then known and analyzed the data of their reactions with one another. He discovered the law of multiple proportions, which states that when several distinct reactions take place among the same elements, the quantities that enter the reactions are always in the proportions of simple integers - that is, 1 to 1, 2 to 1, 2 to 3, and so on. From this came the concept that such reacting quantities contain equal numbers of atoms and are therefore proportional to the masses of individual atoms. Dalton gave the lightest known element, hydrogen, an atomic weight of 1, and developed comparative atomic weights for the other known elements accordingly.

The study of gases in terms of atomic theory was begun by Daniel Bernoulli (1700-1782) in the 18th century. Bernoulli showed that the pressure exerted by a gas came about as the result of collisions of the atoms of the gas with the walls of its container. In 1811, Amedeo Avogadro (1776-1856) suggested that equal volumes of different gases, under the same conditions of pressure and temperature, contain equal numbers of atoms. Avogadro himself never estimated the magnitude of this value, although it is now known as the Avogadro number.

3.3 Electron

The history of particle physics has gone through four stages. In the first stage, Joseph J. Thomson (1856-1940) discovered (1897), by studying electricity passing through gases, that all atoms contain certain particles, called electrons, that carry a negative electric charge. Because atoms are electrically neutral, there must be balancing positive charges somewhere in the atom. Ernest Rutherford (1871-1937) proposed (1911), based on a series of experiments by Hans Geiger (1882-1945) and Ernest Marsden (1889-1970) that these positive charges are concentrated in a very small volume, called the atomic nucleus, at the center of the atom.

By the end of the 19th century almost all scientists had become convinced of the truth of the atomic theory. By that time, however, evidence was just beginning to accumulate that atoms are not in fact the indivisible particles suggested by their name. One source of such evidence came from studies using gas discharge tubes. In such tubes, a gas at low pressure is subjected to intense electrical forces. Under these conditions, various colored glows are observed to traverse the tube. One blue glow at one end of the tube, around the electrode known as the cathode, was observed for a wide variety of gases. The glow was shown by Joseph Thomson in 1897 to involve a stream of negatively charged particles with a charge-to-mass ratio, indicating the existence of a particle with a very small mass on the atomic scale. These particles were called electrons, and they were soon recognized to be a constituent of all atoms. That is, atoms are not indivisible but contain parts.

In the late 19th and the early 20th century it was also found that some kinds of atoms are not stable. Instead they transform spontaneously into other kinds of atoms. For example, uranium atoms slowly change into lighter thorium atoms, which themselves change into still lighter atoms, eventually ending up as stable atoms of lead. These transformations, first observed by Antoine Henri Becquerel (1852-1908), came to be known as radioactivity, because the atomic changes were accompanied by the emission of several types of radiation.

Atoms are ordinarily electrically neutral. Therefore the negative charge of the electrons in an atom must be balanced by a corresponding positive charge. Because the electrons have so little mass, the positive constituents of an atom must also carry most of the atom's mass. The obvious question arose as to how these varied parts are arranged within an atom. The question was answered in 1911 through the work of Ernest Rutherford and his collaborators. In their experiments they passed alpha particles - a type of radiation emitted in some radioactive decays - through thin gold foils. They observed that in some instances the alpha particles emerged in the opposite direction from their initial path. This suggested a collision with a heavy object within the atoms of the gold. Because electrons are not massive enough to produce such large deflections, the positive charges must be involved. Analyzing the data, Rutherford showed that the positive charge in an atom must be concentrated in a very small volume with a radius less than 10^-12 cm, or one ten-thousandth the size of the whole atom. This part of the atom was called the nucleus.

3.4 Atomic Nucleus and Photon

Rutherford proposed an atomic model in which the atom was held together by electrical attraction between the nucleus and the electrons. In this model the electrons traveled in relatively distant orbits around the nucleus. The model eventually proved successful in explaining most of the phenomena of chemistry and everyday physics. Subsequent studies of the atom divided into investigations of the electronic parts of the atom, which came to be known as atomic physics, and investigations of the nucleus itself, which came to be known as nuclear physics. This division was natural, because of the immense difference in size between the nucleus and the electron orbits and the much greater energy needed to producenuclear as compared to electronic changes.

The Rutherford model of the atom, however, had to face two immediate problems. One was to account for the fact that different atoms of the same element behaved in physically and chemically similar ways. According to the Rutherford model, electrons could move in any of the infinite number of orbits allowed by Newtonian physics. If that were so, different atoms of the same element could behave quite differently. This is actually a problem for any atomic model based on Newtonian physics, and it had already been recognized by Maxwell in 1870. The other problem was that, according to the principles of electromagnetism, electrons should continuously emit radiation as they orbit in an atom. This would cause the electrons to lose energy and to spiral into the nucleus.

An important step toward solving these problems was taken by Niels Bohr (1885-1962) in 1913. According to Bohr, the electrons in atoms cannot exist in arbitrary orbits. Instead they are found only in certain "states". The states in which they can exist are those in which the angular momentum of their orbits is an integer multiple of h / 2, where h is a quantity known as Planck's constant. This constant had been introduced by Max Planck (1858-1947) in his theory describing blackbody radiation.

According to the Bohr model of the atom, there is a so-called ground state for any atom. This ground state has the lowest energy allowed to the atom, and it is the same for all atoms containing the same number of electrons. An atom normally exists in this ground state, which determined the observed properties of a given element. Furthermore, according to Bohr, no radiation is emitted by an atom in its ground state. This is because energy must be conserved in the radiation process, and no available state of lower energy exists for the atom to balance any energy lost through radiation.

An atom can be removed from its ground state only when enough energy is given to it, by radiation or collisions, to raise an electron to an "excited" state. When the atom is excited, it will usually emit electromagnetic radiation rapidly and return to the ground state. The radiation is emitted in the form of individual packets or quanta, of light, called photons. Each photon has an energy equal to the difference between the energy of the excited states and the ground state of the atom. According to a formula developed by Planck and Einstein, this energy corresponds to a specific wavelength of the emitted light. Using this assumption about the allowed angular momenta for electrons, Bohr was able to calculate the precise wavelengths in the spectrum of the simplest atom, hydrogen.

In 1869, Dimitri I. Mendeléev (1834-1907) stated the rule that chemical elements arranged according to the value of their atomic weights exhibit a clear periodicity of properties. Eventually, Bohr was able to extend his atomic theory to describe, qualitatively, the chemical properties of all the elements. Each electron in an atom is assigned a set of four so-called quantum numbers. These numbers correspond to the properties of energy, total orbital angular momentum, projection of orbital angular momentum, and projection of spin angular momentum. It is also assumed - as had first been suggested by Wolfgang Pauli (1900-1958) in 1924 - that no two electrons in an atom can have the same values for all four quantum numbers. This came to be known as Pauli's exclusion principle. This principle influences the way in which the chemical properties of an element depend on its atomic number, that is the number of electrons in each atom of the element. A maximum number of electrons can occur for each energy level, and no more than that. For example, the lowest energy level of an atom - the one in which the electrons have zero orbital angular momentum - can contain up to two electrons. The one electron in a hydrogen atom exists at this energy level, as do the two electrons in a helium atom. For the next heavier atom, lithium, one of its three electrons must exist in a higher energy state, and as a result this electron can more easily be lost to another atom. Those electrons with approximately the same energy are said to form a "shell".

Although Bohr's model gives a qualitatively accurate description of atoms, it does not give quantitatively accurate results for atoms more complex than hydrogen. In order to describe such atoms, it is necessary to use quantum mechanics. This theory of atomic and subatomic phenomena was created by Erwin Schrödinger (1887-1961), Werner Heisenberg (1901-1976), Paul Dirac (1902-1984), and Pascual Jordan (1902-1980) in the 1920s. In quantum mechanics, the electron orbits are replaced by probability distributions that only indicate in which regions of space each electron is most likely to be found. An equation discovered by Schrödinger allows this distribution to be calculated for each atom. From the distribution, properties of the atom such as energy and angular momentum can be determined.

In the second stage, particle physics accommodated, through an analysis of isotopes of elements, that all atomic nuclei could be thought of as composed of two types of particles: the proton, which carries both mass and electric charge, and the neutron, which has about the same mass as a proton but is electrically neutral. This model was confirmed through the discovery (1932) of free neutrons by James Chadwick (1891-1974).

3.5 Neutron

Physicists by the late 1920s were convinced that they sufficiently understood the electronic structure of atoms. Attention therefore turned to the nucleus. It was already known that nuclei sometimes change into one another through radioactive decay. Rutherford had also shown, in 1919, that this could be accomplished artificially by bombarding nitrogen nuclei with high-energy alpha particles. In the process the nitrogen nucleus is converted into an oxygen nucleus, and a hydrogen nucleus, or proton, is ejected. It had further been discovered by Joseph J. Thomson, Francis W. Aston (1877-1945), and others that for a given element the nucleus sometimes occurs in several different forms that differ in mass. These chemically similar but physically distinct atoms were called isotopes. All of this provided evidence that atomic nuclei also had some kind of internal structure that could be explored through experiments and calculations.

Differences in the integer values of the electric charge and of the mass of many nuclei soon indicated that protons were not the only kind of particle to be found there. That is, the electric charge of a nucleus is always exactly an integer multiple of the charge of a proton, so knowledge of this electric charge always indicates how many protons a nucleus contains. The mass of a nucleus is also approximately - but not exactly - an integer multiple of the mass of a proton. For many atoms, however, these two integer values are not the same. For example, a helium nucleus has twice the charge but four times the mass of a proton. Clearly, nuclei contain something other than protons.

This problem was solved in 1932 with the discovery by James Chadwick of the neutron. This particle has no electric charge and is slightly more massive than a proton. Thus most nuclei are composed of both protons and neutrons, which collectively are known as nucleons. A helium nucleus contains two protons and two neutrons, which correctly give the total charge and mass of the nucleus. The isotopes of any given element contain equal numbers of protons but different numbers of neutrons. For example, an isotope of hydrogen, called deuterium, contains one proton and one neutron, and a heavier isotope, called tritium, contains one proton and two neutrons.

The problem then arose as to how atomic particles could be held together in such a small region as the nucleus. The force holding them had to be different from others then known to physicists. It was stronger than the electric forces that can break electrons away from nuclei. On the other hand, the nuclear forces between different nuclei that are far apart are very weak, much weaker than electric forces at such distances.

3.6 Fundamental Particles

The third stage of particle physics came with the recognition that protons, neutrons, and electrons - the constituents of ordinary matter - were but three of a vast number of similar particles, which differed only in a few properties, such as their mass, and in their stability against spontaneous decay. Experiments with particle accelerators indicated that these many subatomic particles could be readily produced from protons and neutrons, provided that enough energy was available to produce the additional mass of the new particles predicted by the rules of Einstein's relativity theory. These discoveries in the 1940s and 1950s indicated that the proton and neutron were not really fundamental particles and that they would have to be understood as part of a much larger family of similar objects.

By 1932 nuclei were known to be composed of protons and neutrons. It was then necessary to explain how nuclei were held together, and in 1935, the Japanese physicist Hideki Yukawa (1907-1981) predicted a smaller fundamental particle that was the carrier of a theorized strong interaction, one of the four fundamental interactions, or forces. This particle, called a -meson, was discovered in 1947. Since then a host of particles smaller than protons and neutrons have been discovered in the nucleus, all falling within two classes: Fermions, which obey the Pauli exclusion principle, and bosons, which carry the fundamental force. Modern nuclear physics centers on fundamental interactions between fermions and bosons. Protons and neutrons are composed of particles representing all four forces.

In the fourth stage, modern particle physics provided a successful explanation for the large number of particles. There are six different leptons: electron (e), muon (), tauon (), electron-neutrino (), muon-neutrino (), and tau-neutrino (). There are also six quarks denoted up (u), down (d), charm (c), strange (s), top (t), and bottom (b). For each of these particles there exists an anti-particle. Many of the models for particle interactions pair the leptons and quarks into families: (e - ), ( - ), ( - ), and (u-d), (c-s), (t-b). Experiments suggest that it is unlikely that there are more than these families. The interactions between these fundamental particles are mediated by gauge bosons (photon, intermediate bosons W^± and Z⁰, gluons).