THE PROBLEM OF MATTER

(Continued)

  1. HISTORY (Continued).

    1. Bretrand Russell.
      The English philosopher, Bertrand Russell (1872-1970), was intially influenced by the Absolute Idealist, F. H. Bradley (1846-1924), but he quickly made his way to a Realist position. And along with G. E. Moore (1873-1958), he led an anti-Idealist forces in England. His rejection of Idealism stemmed from his study of mathematics and logic. He rejected the ultimacy of the subject-predicate form of expressions (propositions) in logic, not on the grounds of its inconsistency, but on the grounds of its narrowness. Russell in his Critical Exposition of the Philosophy of Leibniz (1900) found the key to Leibniz' metaphysics in the subject-predicate form of expression and sought to find a more adequate basis of philosophy in relations. Russell saw that the Idealist reduced a relation between two things to attributes of those things. The Idealist used this "doctrine of internal relations" as the basis of their Idealistic metaphysics. According to this doctrine, any relational fact - for example, that x is above y - is really a fact about the nature of the terms involved. This doctrine in effect refuses to take relations as ultimate. It follows from this doctrine that whenever any two things are related, each "enters into the nature of the other." When x is above y, then being above x is part of the nature of y and x is below y is part of the nature of y. Since everything is related to everything else in one way or another, it follows from this view of relations that everything enters into the nature of any given thing. Hence, this is another way of saying that there is no "other thing" relative to a given thing. In other words, the only thing that exist is one all-comprehensive entity. Russel came to believe that any philosophy that denies ultimate reality to relations must be mistaken. In addition, he came to think that mathematics would be impossible if this view of relations is held. Thus Russell came to hold and argue for a "doctrine of external relations", according to which relations have a reality over and in addition to the terms that they relate and do not enter into the definition of the terms that they relate. This led him to a kind of philosophical atomism, called "Logical Atomism". Since the traditional Aristotelian formal logic is based on the subject-predicate form of expressions or propositions that implies the doctrine of internal relations, with A. N. Whitehead (1861-1947) he developed a new system of logic, now called symbolic logic, capable of providing the premise for mathematics, which they published as Principia Mathematica in 1910 (Vol. 1), 1912 (Vol. 2), 1913 (Vol. 3), and a new edition in 1925-1927.

      Following the lead of William James, Russell developed the doctrine of neutral monism in his The Analysis of Mind (1921). According to this doctrine, the world is neither mental nor material, but composed of some neutral stuff which, organized according to the laws of physics are physical objects, matter, and when organized according to the laws of psychology are minds. James held that Mind and Matter are merely two different ways in which reality is organized. James held that the stuff which gets organized is "pure experience". This position gave him a number of advantages. He could avoid the mind-body dualism; he could explain how an object in one's person world could become an object in another's; and how "our minds could meet in a world of objects which they share in common." Russell abandoned this "pure experience" as the basic constitutent of the world. In his The Analysis of Mind (1921) Russell set out to construct the conscious mind out of sensation and images and gives a behavioristic analysis of desire, belief, and emotions. The results are admittedly equivocal. As to physical objects, Russell held that if they were not defined in terms of sense experience, we would have no way of knowing anything about them, but also we would not be able to understand them. Our knowledge about them is based on our knowledge by acquaintance of them. In his The Analysis of Matter (1927), Russell sets forth his view that the ultimate constitutents of the world are events. He does not continue to call his view "neutral monism", even though Chapter XXXVII is titled "PHYSICS AND NEUTRAL MONISM". He distinguishes between "mental events" and "physical events" that are "compresent". He asks, "Can a mental event be compresent with physical events?" He continues, "If yes, then a mental event has a position in the space-time order; if no, then it has no such position. This, therefore, is the crucial question." His analysis of mental events seems to reduce them to physical events, though he tries carefully not to identify mental events with physical events. His psychological analysis of mental events is behavioristic which treats mental events as causal processes of percepts in the brain. Russell says,

      "When I maintain that a percept and physical event can be compresent, I am not maintaining that a percept can have to a piece of matter the sort of relation which another piece of matter would have. The relation of compresence is between a percept and a physical event, and physical events are not to be confounded with pieces of matter. A piece of matter is a logical structure composed of events; the causal laws of events concerned, and the abstract logical properties of their spatio-temporal relations, are more or less known, but their intrinsic character is not known." [1]

    2. A. N. Whitehead.
      For the British philosopher, Alfred North Whitehead (1861-1947 A.D.), the world is a process in which there is a interrelated scheme of actual events, like a table, a rainbow, the life of a man, the explosion of a star, no one of which can be understood apart from its relation to other events. There are actual and possible events. Over and above the actual events there is a vast realm of possible events, of all things that could be. Any real event is a actualized possibility. The realm of the possible is in contact with the realm of actual, so that the possible enters into the actual. This raises the question: Why does the world actualize this particular set of possible events? Why this world rather than another? Whitehead believes that it is necessary to postulate such metaphysical factor to explain why this particular universe. He therefore postulates an agent which causes to emerge from the timeless realm of the possible this particlar cosmos. This agent is God, whom Whitehead calls "the Principle Of Concretion." God's function is to impose a limit upon the limitless number of possible events. Thus God determins an actual course of events which, "metaphysically speaking, might have been otherwise." Now it may be asked: Why is it that God makes concrete or actual this set of possibilities which is our world? What reason can be offered for God's having selected this world to actualize rather than another? Whitehead answers that there is no reason. The universe is ultimately irrational. "God is the ultimate limitation, and His existence is the ultimate irrationality. For no reaon can be given for just that limitation which stands in His nature to impose. God is not concrete, but He is the ground of concrete actuality."

      According to Whitehead, events occur, and objects relate to each other, in a four-dimensional space-time manifold, which he called the extensive continuum. The geometric properties of this field are defined by the method of extensive abstraction. Points, lines, planes, and other geometric elements, are ideal limits of converging classes of the appropriate kinds. For example, squares and circles converge to a point, while rectangles converge to line segments. These ways of approximation toward an ideal limit (compare the concept of the limit in differential calculus) involve time as well as space. Indeed, the character of space is dependent upon the character of time, and the ways of approximation of geometrical elements are fixed by the intersection of alternate time-systems. The ultimate elements of the space-time manifold are event-particles. An event-particle is an instantaneous point-flash, a point-event, or a point of instantaneous space, as much an instant of time as a point of space. Geometrical elements can thus be described as the loci of the complete set of event-particles covered by appropriately intersecting moments of different time-systems.

      Whitehead's theory of relativity differs from that of Einstein by being grounded in philosophical realism rather than operationalism. They differ also with respect to the importance of events. Where Einstein derived events from the intersecting of particles of matter, Whitehead derived matter from events as one of their contingent characteristics. Finally, where Einstein sought a unified field theory, Whitehead stressed the atomicity of nature as well as its continuity. In a unified field theory Whitehead thought that no knowledge would be impossible for finite minds with only partial perception of the world.

    3. Albert Einstein.
      The theoretical physicist Albert Einstein (1879-1955) was born in Ulm, Switzerland, studied at Zurick's Federal Institute of Technology and worked as an Official in the Bern Patent Office (1902-1909). He received his Doctorate from the University of Zurick in 1905 and was a Professor in Zurick, Prague, and from 1913-1933 in the University of Berlin. He was also Director of Physical Theory in the Kaiser Wilhelm Institute. In 1921 he received the Nobel Prize for his scientific work. When he was deprived of his office and German citizenship in 1933 by the Nazi, he came to the United States, accepting a position at the Institute of Advanced Studies, Princeton, New Jersey, where he spent the rest of his life. Einstein was influenced philosophically by Spinoza, Hume, and Ernst Mach (1836-1916).

      In his Special Theory of Relativity (1905), Einstein abandoned the Classical assumption of an absolute space and time. This change brought a new unity to the field of physics, and led to many fruitful results. This new view holds that time, space and velocity is relative to the inertial system; simultaneity can be established only within a given inertial system and will not be the same for observers in motion relative to a given system. Einstein developed transformation equations relating time, space and velocities as measured by two separate and moving systems of reference. In these equations the speed of light is a constant but the mass of body increases and time slows down as the speed of body increases approaching the speed of light. Einstein was impelled by these new transformation equations to apply the transformation equations to kinetic energy and radiant energy. In a second paper in 1905, titled, "Does the Inertia of a Body Depend Upon Its Energy Content?" [2] Einstein proposed the following problem. Suppose a body emits acertain amount of radiant energy L, and that we compare the total energy before and after the emission of the light energy, both from a frame of reference stationary with respect to the source and from a frame of reference that is moving with a velocity relative to the source. Einstein concluded.

      "If a body gives off the energy L in the form of radiation, the mass diminishes by L/c2. The fact that the energy withdrawn from the body becomes energy of radiation evidently makes no difference, so that we are led to the more general conclusion that

      The mass of a body is a measure of its energy-content; if the energy changes by L, the mass changes in the same sense by L/9 × 1020, the energy being measured in ergs, and the mass in grammes.

      It is not impossible that with bodies whose energy-content is variable to a high degree (e.g. with radium salts) the theory may be successfully put to the test.

      If the theory corresponds to the facts, radiation conveys inertia between the emitting and absorbing bodies." [3]

      In other words, there is a form of energy associated with mass m of a particle, which is called the total energy E of a particle with a rest mass m0 and moving with the speed v; this is defined it to be
      E = mc2 = m0c2/ √(1 - v2/c2) = γm0c2.
      where γ = 1/√(1 - v2/c2).
      This definition of the total energy of a particle results in the conservation of energy for a isolated system; but it does not include potential energy. Notice that the total energy of the particle is not zero when the particle is at rest. Setting v = 0 in this equation results in
      E0 = m0c2,
      where E0 is the energy of the particle when it is at rest, and it is called the rest-mass energy of the particle.
      Thus, since
      E = γm0c2, then
      E = γE0.
      Now the right hand side of this equation can be simplified by using the binomial theorm and neglecting terms with v4/c4 and the higher terms. For small velocities compared with velocity of light, the expression
      γ = 1/√(1 - v2/c2) = (1 - v2/c2)
      may be expanded by the binomial theorem:
      (x + y)n = xn + nxn-1y + [n(n-1)/(1·2)]xn-2y2 + ...,
      to the series
      (1 - v2/c2) = 1 + ½(v2/c2) + 3/8(v4/c4) + ...
      with continuously higher powers of v/c.
      Since v/c is a small fraction, the term with v4/c4 and the higher terms may be neglected, and the expression above for total energy
      E = γm0c2 becomes then
      E = m0c2[1 + ½(v2/c2)] = m0c2 + ½m0v2.
      This was interpreted by Einstein to mean that the energy associated with any particle is composed of two types: its permanent "rest energy" m0c2 and its classical kinetic energy ½m0v2. The last term on the right side of this equation has the same form as the classical kinetic energy K = ½mv2. But the first term on the right side m0c2 is probably the best known and the most dramatic consequence of the Special Theory of Relativity. It is called the "rest energy" E0 of the particle and it identifies the mass of the particle with energy. The rest energy is by definition the energy of the particle at rest, when v = 0 and K = 0. The total energy E of the particle moving with a speed v << c is the sum of its rest energy and its kinetic energy:
      E = E0 + K.

      Einstein constantly in his paper refers to inertia rather than mass. Thus, there culminates a long development starting with Newton's definition of mass as "quantity of matter," which carried with it the intuitive (and Aristotlian) sense of substance. Inertia, in modern physics, can hardly be identified as an innate property of a body. It is defined in terms of reaction with other bodies. In modern physics it is measured by the effect that one body has upon some other bodies external to it. And now Einstein's formulation advances this concept. Light energy possesses inertia just as much as do "ponderable" bodies, which are attracted to other "ponderable, massive bodies." It therefore possesses "mass." Furthermore, just as "energy" possesses mass, we can think of mass in terms of its energy equivalence, and the two terms, mass and energy, become different ways of describing the same quantity in the universe. And it did not take long for this perdiction of Einstein to be fully confirmed; today, the equivalence of mass and energy and the equation of their transformation E = mc2 has become one of great generalities of modern physics. This equation means that every particle of matter contains a vast amount of energy, which has been demonstrated by many experiments and by the nuclear bomb which has been inaccurately called the "atomic bomb".

      The fullest form of the total energy E = mc2 can be derived from
      E = γE0, or
      E = E0/ √(1 - v2/c2).
      Squaring both sides, we get
      E2 = E02/ (1 - v2/c2),
      and multiplying both sides by (1 - v2/c2) we get
      E2(1 - v2/c2) = E02,
      and removing the parenthesis on the left side we get
      E2 - E2(v2/c2) = E02,
      and since E = mc2, substituting it into the second term on the left side, we get
      E2 - (mc2)2 (v2/c2) = E02,
      and squaring (mc2)2 in the second term on the left, we get
      E2 - (m2c4) (v2/c2) = E02,
      and simplifying the second term on the left side, we get
      E2 - (m2c2v2) = E02,
      and rearranging the factors in the second term on the left side and moving it the right side, we get
      E2 = (m2v2c2) + E02,
      and replacing m2v2 with (mv)2, we get
      E2 = (mv)2c2 + E02,
      and substituting p for mv, we get
      E2 = p2c2 + E02 or
      (mc2)2 = (mv)2c2 + (m0c2)2.
      This equation is called mass-energy equivalence, where
      E = mc2 is the total energy of the particle,
      p = mv is the momentum of the particle, and
      E0 = m0c2 is the rest energy of the particle,
      where m0 is the rest mass of the particle.

      Also from the equation E = γE0, we can derive the mass increase relation. Substituting
      mc2 for E and
      m0c2 for E0, we get
      mc2 = γm0c2.
      Dividing both sides of this equation by c2, we get
      m = γm0, or
      m = m0/ √(1 - v2/c2)
      which is the mass increase relation.
      According to this relation, where m0 is the mass of the body at rest with respect to the observer and m is the mass of the body moving at the speed v relative to the observer, as the velocity v of the particle approaches the speed of light c, the mass increases. It is obvious that this as a definition of mass is negligibly different from the classical concept of mass except at very high velocities, since the ratio v2/c2 is ordinarily such a small fraction; the mass m of moving body is only significantly larger when the speed of the body v approaches the speed of light c. And as v approaches c, the ratio v2/c2 becomes almost one; and γ = √(1 - v2/c2) becomes close to zero. And since it is in the denominator of this formula for relativistic inertia (mass) and momentum (mv), these quantities become very large so that the resistance to acceleration becomes very large also. If the speed v were to be equal to the speed of light c, then its inertia (mass) and momentum (mv) would become infinite. But this is not possible, since it would take an infinite amount of energy to reach the speed of light. But the mass m of a body is still relative to the speed v of the body and its rest-mass m0 has a rest-energy
      E0 = m0c2,
      where E0 is the rest energy of the body and
      m0 is the rest mass of the body and
      c is the speed of light.

      The fact that it is impossible to accelerate an object to a speed above the speed of light means that Newton's laws of motion must in some way be modified. Since Newton's laws work well for almost all normal applications, the modified laws should differ from them only for speeds near the speed of light. As an object's speed approaches the speed of light, it becomes harder and harder to accelerate it. The same force results in a smaller and smaller change in the speed as the object's speed approaches the speed of light. That is, in other words, an object's resistance to acceleration, its inertia, increases. Einstein found that Newton's Second Law ("Force equals the time rate of change of momentum") could be saved only if the meaning of momentum were modified. And since momentum p is defined as mv, mass times velocity, the relativistic version of momentum must be:
      p = mv = m0v/ √(1 - v2/c2) = γm0v,
      where γ = 1/√(1 - v2/c2).
      And for the classical definition of momentum as mass times velocity to hold, then the definition of mass must be modified as follows:
      m = m0/ √(1 - v2/c2) = γm0,
      where m0 is the mass of the body at rest with respect to the observer and m is the mass of the body moving at the speed v relative to the observer. It is obvious that this definition of mass is negligibly different from the classical concept except at very high velocities, since the ratio v2/c2 is ordinarily such a small fraction; the mass of moving body is only significantly larger when the speed of the body v approaches the speed of light c.

      In his General Theory of 1916, Einstein generalized the results of the Special Theory from inertial systems to non-inertial systems having gravitational fields. This was necessary in order to account for the equivalence between gravitational and inertial mass. In this theory, gravitation is reduced to or is the effect of space-time curvature, and depends upon the masses distributed through the universe. Thus the concept of gravitational force as an action-at-distance force was explained. The confirmation of the General Theory is not as strong as that for the Special Theory; but the bending of light rays as they pass through a strong gravitational field has been observed. And the theory has predicted the expanding universe and that the universe is finite but unbounded.

      Einstein attempted to construct a unified field theory that would express all forms of matter and energy in single formula. The theory ran counter to the probabilistic features of the Quantum Theory; it was not successful. Einstein unsuccessful attempt was motivated in part by a preference for a predicatable, deterministic universe. This preference was partly motivated by his acceptance of his teacher Minkowski's conception of world lines in the view of space-time as a four-dimensional continuum in which future events are already determined. Einstein believed that God does not play dice with the universe, and he cited with approval the philosophy of Spinoza whose God expresses Himself in the orderly harmony of all beings.

    4. Modern Theories of Light.
      The ancient philosophers, and later Isaac Newton (1642-1727) and the majority of 18th century scientists, had adopted an atomic or corpusclar theory of light; but in the 17th century the Dutch physicist Christian Huygens (1629-1695) proposed a totally different conception of light. In his view light was an undulation propagated in a continuous medium, the aether, the latter being supposed to penetrated every material object and to fill all regions of space which appears void to us. The discovery in 1800 of the phenomena of interference and diffraction made by Thomas Young (1773-1829) and confirmed by Augustin Fresnel (1788-1827) and, later, of the development of the mathematical theory of waves by Fresnel and its verification by experiment in 1801, brought about, in the first half of the 19th century, a complete abandonment of the discontinuous or corpuscular view of light and the general adoption of the Wave Theory of Light. But now in the first half of the 20th century, Max Planck's explanation of the Law of Black Body Radiation (1900) and Einstein's explanation of the photo-electric effect (1905), the discontinuous view of light has returned in the Quantum Theory of Radiation. This theory assumed the existence of light-corpuscles, or photons. Unlike the corpuscles of matter, the energy of these photons are defined by the frequency of the radiation and not by their mass. But like the particles of matter they preserve their individuality in moving through space. This hypothesis was confirmed by experiment, particularly by X-ray scattering discoveried in 1923 by the American physicist H. A. Compton.

      But since the continuity interpretation of light has been confirmed by interference and diffraction experiments, the present theory of light is dualistic, holding that light has both a continuous and discontinuous aspect. Thus light has a dual nature; it shows wave properties in some situations and particle properties in other. That is, when a light ray exchanges energy with matter, the exchange can be explained on the assumption that a photon is absorbed (or emitted) by matter; on the other hand, if we wish to explain the propagation of light through space, then we can fall back on the assumption that light is waves. A further elaboration of this theory of propagation is that light is a cloud of photons whose density is proportional to the intensity of this wave.

      "In this way, therefore, a sort of synthesis of these two ancient rival theories are reached, so that we are enabled to explain interference phenomena as well as the photo-electric effect...." [4]

    5. The Photoelectric Effect.
      In 1905, the young Albert Einstein, working in the patent office at Berne, Switzerland, wrote three short scientific papers, any one of which would have assured him with lasting fame. One of these announced his special theory of relativity, another was on the Brownian motion, and the third was on the photoelectric effect, which applied Planck's quantum hypothesis more broadly than Planck had thought necessary.

      The photoelectric effect was discovered incidently by Heinrich Hertz in 1887 during the course of his experimental research that at the time furnished the most convincing proof of Maxwell's classical electromagnetic theory. Hertz noticed that electric sparks would jump more readily across the air gap between the metal spheres of the spark gap in the receiving circuit, if they were polished. He soon found that the sparks were influence by the light coming from the sparks in the spark gap of the transmitting circuit. Upon further investigation, he concluded that ultraviolet radiation was responsible for the phenomena and that the effect was greatest when the light fell on the negative terminal (cathode) of the spark gap. Being concerned with other problems, Hertz abandoned further study of the effect. Many others carried on a more detailed investigation of the phenomena. Wilhelm Hallwach showed that this emmission consisted of negative electricity and in 1899 J.J. Thomson published a paper in the Philosophical Magazine in which he showed that the negative electricity ejected by the ultraviolet light have the same e/m ratio as cathode rays. P. Lennard also obtained the same result. These electrons were called photoelectrons.

      The photoelectric effect consists in the fact that light upon striking certain metals cause electrons to be given off, transforming the radiant energy absorbed by the metal into kinetic energy of emitted electrons. According classical physics, it would be expected that as the intensity (thus energy) of light increases, the kinetic energy of the electrons emitted will increase. This would imply that, as the intensity of the beam increases, the velocity of the electrons emitted would increase. The classical view requires that the kinetic energy Ke of the electron is equal to
      Ek = ½mev2,
      where me is the mass of the electron, and v its velocity. But experimentally this is not what happens. Instead, the maximum velocity given to the electron is constant, regardless of the intensity of the light, but varies in direct proportion to the frequency.

      Einstein explained this in the following way. Electrons are embedded in the atoms of the metal and are held there by attractive forces. When light is shined on the surface of the metal of sufficient energy, the energy is used in two ways:
      (1) to overcome the attractive forces holding the electron to the metal atoms, and,
      (2) if there is any energy left over, it imparts that energy to the electron as kinetic energy.
      Therefore, for those electrons near the surface of the metal, less energy is required to overcome the "binding force," and there is more kinetic energy available. The "surface" electrons therefore acquire the maximum kinetic energy. Einstein expressed this relation by the following formula:
      hf = W + ½mev2,
      where W is the work required to free the electrons from the metal and is equal hf0 where h is Planck's constant and f0 is the threshhold frequency below which light will not free the electron. That is,
      W = hf0, where h = 6.625 × 10-34 joule-sec. Then
      hf = hf0 + Ek.
      Thus there is a linear relation between the frequency and the maximum kinetic energy of the electrons emitted. Note that there is nothing in the equation relating to the intensity of the light causing electron emission. But although the velocity of the elctrons does not depend in any way on the intensity of light, the number of electrons emitted does so depend. From this, Einstein, following Planck, concluded that the light is made up of quanta of energy or, as Einstein called them, photons. The energy of a single photon is given by hf. However, the more intense of the light, the greater the number of electrons emitted. The photoelectric emission of a single electron depends upon the absorption of a single photon. If the number of photons is increased, the number of emitted electrons is increased, but no change occurs in the maximum kinetic energy and hence the velocity of electrons. The Planck's constant h is the same for all metals. The threshold energy W, which is required to release electrons, does vary from metal to metal, being so large in the case of some metals, for example, platinum, that no photoelectric effect occurs.

      Now on the basis of the classical wave theory of light, all these phenomena are impossible to be explained. According that theory the energy of a wave of given frequency is dependent on its amplitude. If light consists of waves, the kinetic energy given to the electrons depends upon the amphlitude of the light waves. This explanation fails to hold true for the photoelectric effect.

      Einstein introduced modification of this classical theory of electromagnetic waves to account for photoelectric effect. Planck had modified the classical theory by quantizing the atomic oscillators. But Einstein further modified the theory by quantizing the waves or radiation. Light consists of quanta of energy, called photons. This theory of Einstein's that light consists of photons, seemed to be a return to Newton's corpuscular theory. But light is not material particles but is now regarded as composed of bundles of energy, called photons, each photon having a certain amount of energy depending on its frequency or color. In addition, it can be shown that each photon has certain momentum, equal to hf/c, and that as the photons strike a substance and are reflected, the change of momentum causes a small but measurable pressure. But according to the older wave theory light also had momentum and causes pressure.
      Is light, waves or particles?
      Since the wave theory cannot explain the photoelectric effect and similar quantum phenomena, and since the particle theory cannot explain many phenomena of interference and diffraction, both theories are needed to explain all these phenomena; they complement each other. Just as light waves have properties like particles, so light particles have properties like waves.

    6. Quantum Theory of Matter.
      This quantum theory of light had a profound influence on the Theory of Matter, when it was realized that the motion of material particles on a very small scale did not move according to the laws of classical Mechanics. As the result of the experiments of the British physicist Lord Ernest Rutherford (1871-1937) in 1911, the Danish physicist Niels Bohr (1885-1962) in 1913 developed the theory that atoms consists of electrons and protons. The atoms of an elementary substance was shown by Rutherford's alpha scattering experiments to consists of a central nucleus with electrons revolving around the nucleus. The nucleus has a positive charge equal to a whole number Z times the charge of the proton, and with Z negatively charged electrons revolving around the nucleus, where Z is called the atomic number of the element. So the entire atom is electrically neutral, since the charge on the proton is equal to the charge on the electron but with opposite sign. Almost the entire mass of the atom is concentrated in the nucleus, the protons being more massive than the electrons. The mass of the proton is about 1840 times that of the mass of the electron. The hydrogen atom is the simplest of the atoms, and consists of nucleus of a single proton around which a single electron revolved. The atoms of one element are differentiated from that of another element by the number Z of protons in their nucleus. The electrons revolve about the nucleus in a kind of miniature solar system, with the nucleus as the sun and the electrons as the planets. Niels Bohr (1885-1962) developed in 1913 an explanation how the electrons revolved about the nucleus by borrowing from the quantum theory previously developed by Max Planck. By quantizing the angular momentum of the electrons as they revolved about the nucleus, Bohr was able to restrict the electrons to certain orbits about the nucleus. This allowed him to quantized the radiation emitted or absorbed by the atom. Thus he was able explain the spectrum of an elementary substance which are composed of atoms.

    7. Atomic Structure of Matter.
      1. Alpha Scattering Experiment.
      2. Atomic Spectra.
      3. Planck's Quantum Hypothesis.
      4. Photoelectric Effect.
      5. Bohr Model of the Atom.
      6. Applications of Bohr Model.
      7. Multi-Electron Systems.
      8. Quantum Numbers.
      9. Pauli Exclusion Principle.
      10. Explanation of the Periodic Table.
      11. X-Ray Spectra of Heavy Atoms.

    8. Louis De Broglie.
      In September, 1923, Louis De Broglie (1892-1987) presented two papers that became his doctoral dissertation in which he proposed that
      "in the theory of matter, as in the theory of radiation, it was essential to consider corpuscles and waves simultaneously, if it were desired to reach a single theory, permitting of the simultaneous interpretation of the properties of Light and of those of Matter. It then becomes clear at once that, in order to predict the motion of particles, it was necessary to construct a new Mechanics -- a Wave Mechanics, as it is called today -- a theory closely related to that dealing with wave phenomena, and one in which the motion of a corpuscle is inferred from the motion in space of a wave. In this way there will be, for example, light corpuscles, photons; but their motion will be connected with that of Fresnel's wave, and will provide an explanation of the light phenomena of interference and diffraction. Meanwhile it will no longer be possible to consider the material particles, electrons and protons, in isolation; it will, on the contrary, have to be assumed in each case that they are accompanied by a wave which is bound up with their own motion." [5]
      De Broglie was even able to predict the wavelength of the associated wave belonging to an electron having a given velocity.

    9. Quantum Mechanics.
      One of De Broglie's thesis examiners knew Einstein and passed the thesis to him, who in turned recommended it to another colleague, Erwin Schrodinger (1887-1961). Few people paid attention to the thesis, but Schrodinger changed all that. He developed De Broglie's ideas mathematically and published in March, 1926, a single equation, now called Schrodinger's Equation, purporting to explain all aspects of the behavior of electrons in terms of De Broglie's matter waves. Thus was born a new branch of physics, called Quantum Mechanics.

      The dynamical variables used in classical mechanics, such as position and momentum, do not have definite values in Quantum Mechanics. Instead they are described by a quantity called a "wave function" into which is encoded probabilistic information about position, momenta, energies, etc. Thus in quantum mechanics the motion of particles is not deterministic, as in classical mechanics, but probabilistic. The wave function for a particular system is found by solving the Schrodinger's equation.

      In the case of a single point particle, the wave function may be thought of as an oscilating field spread throughout physical space. At each point in this space it has an amplitude and a wavelength. The square of the amplitude is proportional to the probability of finding the particle at that position; the wavelength, for a constant amplitude wave function, is related to the momentum of the particle. The particle will therefore have a definite position if the wave function is tightly bunched about a particular point in space; and it will have definite momentum if the wavelength and amplitude of the wave function are uniform throughout all of space. Typical wave functions for a system will not be of either of these types and there will be a certain amount of indefiniteness, or uncertainty, in both position and momentum. In particular, because of the mutually exclusive types of wave functions required for definite position and definite momentum, position and momentum cannot be definite simultaneously. This is known as the Heisenberg's Uncertainty Principle, and is an elementary consequence of the wavelike nature of particles. In a "coherent" state, which is a compromise between definite position and definite momentum, there is uncertainty in both position and momentum. This means that the laws of physics are no longer deterministic and phenomena that they describe are no longer subject to a rigorous determinism; they only obey the laws of probability. Heisenberg's Principle of Uncertainity gave an exact formulation to this fact.

      Introduction.

      1. Dual Nature of Light.
      2. Compton Effect.
      3. Dual Nature of Atomic Particles.
      4. Bohr Atom.
      5. Diffraction of Particles.
      6. Schrodingers Equation.
        1. Particle in a Box.
        2. Particle in a Potential Well.
      7. Interpretation of Wave Functions.
      8. Probabilistic Wave Function.
      9. Double Slit Diffraction.
      10. Heisenberg's Uncertainty Principle.
        1. Uncertainty of position and momentum.
        2. Uncertainty of time and energy.
      11. Principle of Complementarity.
      12. Einstein's Criticism of the Quantum Theory.
      13. Paul Dirac.
      14. Antimatter.
      15. Relativistic Quantum Mechanics.
      16. Electron Spin.
      17. Quantum Field Theory.

    10. Interpretation of Wave Functions.
      But exactly what is the significance of these particle wave functions? Should we think of an electron as a localized ball of stuff, or as some extended wave? And if it is a wave, what is waving? After all, there is no such thing as an aether light wave; a light wave is a handy paraphrase for time and space varying electric and magnetic fields. Are they matter waves? And what, then, is a matter wave?

      Schrodinger himself offered one of the first interpretations: The electron, he argued, is not a particle; it is a matter wave as the ocean wave is a water wave. According to this interpretation, the particle idea is wrong or only an approximation. All quantum objects, not just electrons, are little waves -- and all nature is a great wave phenomenon. The matter-wave interpretation was rejected by the Gottingen group led by the German physicist Max Born (1882-1970). They knew that one could count individual particles with a Geiger counter or could see their tracks in a Wilson cloud chamber. The corpuscular nature of the electron -- the fact that it behaved like a true particle -- was not a convention. But what, then, were the waves?

      It was Max Born himself who answered that perplexing and crucial question. His interpretation mark the end of determinism in physics and the birth of the God-who-plays-dice physics. It occurred in June, 1926, three months after Schrodinger's paper, and it profoundly disturbed the physics community. Born interpreted the de Broglie/Schrodinger wavefunction as specifying the probability of finding an electron at some point in space. What Born said was that the square of the wave amplitude at any point in space gives the probability of finding an electron there. For example, in the region of space where the wave amplitude is large, the probability of finding an electron there is also large. Similarly, where the wave function is small, the probability of finding the electron is also small. The electron is always a true particle and its Schrodinger's wave function only specifies the probability for finding it at some point in space. Born held that the waves are not material, as Schrodinger wrongly supposed; they were waves of probability, similar to actuarial statistic, giving the probable location of individual electrons. The description of the motion of quantum particles is inherently statistical; it is impossible to track them precisely. The best that a physicist can do is to establish the probable motion of a particle.

  2. SUMMARY.
    As can be seen from the above historical analysis, there is no unanimous agreement as to the nature of matter and answer to the question "What is matter?".
    In Classical Physics, matter is usually defined as anything that occupies space and has mass. Since density by definition involves both mass and volume (the space occupied by the mass), density is the fundamental property of matter.
    The mass-density ρ of matter is defined as the ratio of its mass to its volume. That is,
    ρ = m/V,
    where m = mass of the matter and V = its volume.
    Since the mass and volume of matter depends upon the sample, these cannot be used separately to identify the kind of matter that it is. However, the ratio of the mass to the volume for a given substance is the same for every sample of that substance, provided they are measured under identical conditions. Mass-density is thus the defining numerical physical property of matter.

    In Classical Physics, mass is usually defined in terms of Newton's Second Law of Motion:
    F = ma;
    that is, the mass m of a body is the ratio of the force F applied to the body to the acceleration a that this force produces:
    m = F/a.
    This mass m is usually called inertial mass to distinguish it from the gravitational mass that produces the gravitational attraction between two bodies, according to Newton's Law of Universal Gravitation:
    F = Gm1m2/r2,
    where G is the universal gravitational constant and m1 and m2 are the masses of the two bodies that are separated by the distance r between them, and F is the force of gravitational attraction between the two bodies.
    The weight of a body on the earth is the force of gravitational attraction between the body and the earth. If inertial mass is assumed to be equivalent to gravitational mass, then the weight of a body is related to inertial mass by Newton's Second Law of Motion:
    w = mg,
    where w is the weight of the body and is the force of gravity exerted on a body by the earth, and g is the acceleration due to this force of gravity.

    To the problem, "Is matter real?",
    Idealism says, "No"; the real is the rational (the universal and the necessary) and the rational is the real, and
    Materialism and the older Naturalism says, "Yes"; matter is the only real.
    Classical physics has answered, "Yes"; but
    twentieth century physics has answered, "No";
    matter is energy; or, more accurately, mass is related to energy:
    E = mc2.
    Einstein in his Special Theory of Relativity, was impelled by his new transformation equations relating time, space and velocities as measured by two separated and moving systems of reference, to apply the transformation equations to kinetic energy and radiant energy. In a second paper in 1905, titled, "Does the Inertia of a Body Depend Upon Its Energy Content?" Einstein showed that the mass of a body is a measure of its energy content. In other words, there is a form of energy associated with mass of a particle and this total energy E of a particle of mass m0 with the speed v is defined to be
    E = mc2 = m0c2/ √(1 - v2/c2) = γm0c2,
    where γ = 1/√(1 - v2/c2).
    This definition of the total energy of a particle results in the conservation of energy for a isolated system; but it does not include potential energy. Notice that the total energy of the particle is not zero when the particle is at rest.
    Setting v = 0 results in E0 = m0c2,
    where E0 is the energy of the particle when it is at rest, and it is called the rest-mass energy of the particle. Thus, since
    E = γm0c2, then
    E = γE0.
    This means that every particle of matter contains a vast amount of energy, which has been demonstrated by many experiments and by the nuclear bomb which has been inaccurately called the "atomic bomb".

    This identification of mass and energy as given in the form of the famous equation E = mc2 governs the transformation of mass into energy and vice versa. Through the application of this equation, many previously unexplained physical phenomena of the universe, such as the apparently inexhaustible source of heat of the sun and the stars, transmutation of radioactive elements, and other nuclear processes, were understood. And its application led to the development of atomic, or more accurately, nuclear energy. It does not tell us how to convert mass into energy, but identifies the amount of energy that is equivalent to the mass of the particle.

    The fullest form of E = mc2 can be derived from
    E = γE0. We get the following equation.
    E2 = p2c2 + E02 or
    (mc2)2 = (mv)2c2 + (m0c2)2.
    This equation is called mass-energy equivalence, where
    E = mc2 is the total energy of the particle,
    p = mv is the momentum of the particle, and
    E0 = m0c2 is the rest energy of the particle,
    where m0 is the rest mass of the particle.

    From this mass-energy equivalence relation, the mass-increase relation can be derived, as follows. Removing the parentheses on both sides, we get
    m2c4 = m2v2c2 + m02c4.
    Dividing both sides by c4. we get
    m2 = m2v2/c2 + m02.
    Solving for m, by moving the m2v2/c2 term to the left side,
    m2 - m2v2/c2 = m02,
    and factoring out m2 on the left side,
    m2 (1 - v2/c2) = m02,
    and dividing both sides by (1 - v2/c2),
    m2 = m02/ (1 - v2/c2),
    and taking the square root of both sides, we get
    m = m0/√(1 - v2/c2).
    According to this relationship, where m0 is the mass of the body at rest with respect to the observer and m is the mass of the body moving at the speed v relative to the observer, as the velocity v of the particle approaches the speed of light c, the mass increases. It is obvious that this as a definition of mass is negligibly different from the classical concept of mass except at very high velocities, since the ratio v2/c2 is ordinarily such a small fraction; the mass m of moving body is only significantly larger when the speed of the body v approaches the speed of light c. And as v approaches c, the ratio v2/c2 becomes almost one; and √(1 - v2/c2) becomes close to zero. And since it is in the denominator of this formula for relativistic inertia (mass) and momentum (mv), these quantities become very large so that the resistance to acceleration becomes very large also. If the speed v were to be equal to the speed of light c, then its inertia (mass) and momentum (mv) would become infinite. But this is not possible, since it would take an infinite amount of energy to reach the speed of light. But the mass m of a body is still relative to the speed v of the body and its rest-mass m0 has a rest-energy
    E0 = m0c2,
    where E0 is the rest energy of the body and
    m0 is the rest mass of the body and
    c is the speed of light.

    The entire Special Theory of Relativity is derived directly from two assumptions.

    1. The laws of physics are the same in all inertial systems. No preferred inertial systems exists. (The Principle of Relativity)
    2. The speed of light in free space has the same value c in all inertial systems. (The Principle of the Constancy of the Speed of Light)
    From these assumptions not only has scientists been able to explain all existing experimental results but to predict new effects which were confirmed by later experiments. No experimental objections to the Special Theory of Relativity has yet been found. Einstein explains that these postulates seem paradoxical only if we believe in an absolute definition of time intervals and lengths. He carefully examined how one measures times and lengths, and concluded that his postulates were not logically irreconcilable; but, if they are true, one must abandon the idea of absolute time and absolute space. They have been replaced by the constancy of the speed of light.

  3. CONCLUSION.
    Historically, to the question, "Is matter real?", some Christian philosophies have answered, "Yes", and some others have answered, "No", depending upon the influence of Greek Philosophy: Platonic, Neoplatonic, or Aristotelian philosophies.
    The Bible implies that matter is real, but it is not ultimate reality.
    "In the beginning God created the heavens and the earth." (Gen. 1:1).
    God created matter ("the earth") and it has a created reality.
    But in the next verse in Gensis 1, it says,
    "And the earth was without form, and void;
    and darkness was upon the face of the deep.
    And the spirit of God moved upon the face of the waters."
    (Gen. 1:2 KJV)
    And here in the Hebrew Bible, the subject of light comes up in the story of creation.
    "3 And God said, 'Let there be light'; and there was light.
    4 And God saw that the was good,
    and God separated the light from the darkness.
    5 God called the light Day, and the darkness he called Night.
    And there was evening and there was morning, one day."
    (Gen. 1:3-5)
    In the Christian New Testament in the Gospel of John, it says about the eternal Word of God,
    "3 All things were made through him,
    and without him was not anything made that was made.
    4 In him was life, and the life was the light of man.
    5 The light shines in darkness,
    and the darkness does not overcome it.
    6 There was a man sent from God, whose name was John.
    7 He came for testimony, to bear witness to the light,
    that all men might believe.
    He was not that light,
    but came to bear witness to the light.
    9 The true light that enlightens ever man
    was coming into the world." (John 1:3-9)
    Later in that gospel, Jesus says,
    "I am the light of the world,
    he who follows me will not walk in darkness,
    but will have the light of life." (John 8:12)
    And the Apostle John writes in his first epistle,
    "5 This is the message we have heard from him
    and proclaim to you,
    that God is light, and in him is not darkness at all.
    6 If we say we have fellowship with him
    while we walk in darkness,
    we lie and do not do the truth;
    7 but if we walk in the light, as he is in the light,
    we have fellowship with one another,
    and the blood of Jesus his Son cleanses us from all sin."
    (I John 1:5-7)
    Obviously from these passages of Scripture, the concept of light plays an important part in Christian teaching. But nowhere in the Scriptures is the nature of physical light discussed. But the ancient Greek philosophers did discuss and argued about the nature of physical light. They were the first to raise the question about the nature of light, and to formulate and dispute among themselves the proposed answers. But none of their speculations associated light with matter as has been done in the twentieth century Special Theory of Relativity.

ENDNOTES

[1] Bertrand Russell, The Analysis of Matter
(New York: Dover Publications, Inc., 1954,
reprinted by special arrangement with the author and Allen and Unwin.), pp. 383-384.

[2] Albert Einstein, "Does the Inertia of a Body Depend Upon Its Energy Content?"
The Principle of Relativity,
(New York: Dover Publications, Inc., 1952), pp. 69-71.

[3] Ibid., p. 71.

[4] Louis De Broglie, Matter and Light: The New Physics
(New York: W. W. Norton & Company, Inc., 1939.
Reprinted by Dover Publications, Inc.), p. 28.

[5] Ibid., pp. 46-47.