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the sun. electromagnetic theory developed by the British physicist James Clerk Maxwell unequivocally predicted that an electron revolving around a nucleus will continuously radiate electromagnetic energy until it has lost |
all its energy, and eventually will fall into the nucleus. Thus, according to classical theory, an atom, as described by Rutherford, is unstable. This difficulty led the Danish physicist Niels |
Bohr, in 1913, to postulate that in an atom the classical theory does not hold, and that electrons move in fixed orbits. Every change in orbit by the electron corresponds |
to the absorption or emission of a quantum of radiation. The application of Bohr’s theory to atoms with more than one electron proved difficult. The mathematical equations for the next |
simplest atom, the helium atom, were solved during the 1910s and 1920s, but the results were not entirely in accordance with For more complex atoms, only approximate solutions of the |
equations are possible, and these are only partly concordant The French physicist Louis Victor de Broglie suggested in 1924 that because electromagnetic waves show particle characteristics, particles should, in some |
cases, also exhibit wave properties. This prediction was verified experimentally within a few years by the American physicists Clinton Joseph Davisson and Lester Halbert Germer and the British physicist George |
Paget Thomson. that a beam of electrons scattered by a crystal produces a diffraction pattern characteristic of a wave (see Diffraction). The wave concept of a particle led the Austrian |
physicist Erwin Schrödinger to develop a so-called wave equation to describe the wave properties of a particle and, more specifically, the wave behavior of the electron in the hydrogen atom. |
Although this differential equation was continuous and gave solutions for all points in space, the permissible solutions of the equation were restricted by certain conditions expressed by mathematical equations called |
eigenfunctions (German eigen, "own"). The Schrödinger wave equation thus had only certain discrete solutions; these solutions were mathematical expressions in which quantum numbers appeared as parameters. (Quantum numbers are integers |
developed in particle physics to give the magnitudes of certain characteristic quantities of particles or systems.) Schrödinger equation was solved for the hydrogen atom and gave conclusions in substantial agreement |
with earlier quantum theory. Moreover, it was solvable for the helium atom, which earlier theory had failed to explain adequately, and here also it was in agreement with experimental evidence. |
The solutions of the Schrödinger equation also indicated that no two electrons could have the same four quantum numbers—that is, be in the same energy state. rule, which had already |
been established empirically by Austro-American physicist and Nobel laureate Wolfgang Pauli in 1925, is called the exclusion principle. What is Matter In the 20th century, physicists discovered that matter behaved |
as both a wave and a particle. Austrian physicist and Nobel Prize winner Erwin Schrödinger discussed this apparent paradox in a lecture in Geneva, Switzerland, in 1952. A condensed and |
translated version of his lecture appeared in Scientific American the following What Is Matter? The wave-particle dualism afflicting modern physics is best resolved in favor of waves, believes the author, |
but there is no clear picture of matter on which physicists can agree Fifty years ago science seemed on the road to a clear-cut answer to the ancient question which |
is the title of this article. It looked as if matter would be reduced at last to its ultimate building blocks—to certain submicroscopic but nevertheless tangible and measurable particles. But |
it proved to be less simple than that. Today a physicist no longer can distinguish significantly between matter and something else. We no longer contrast matter with forces or fields |
of force as different entities; we know now that these concepts must be merged. It is true that we speak of "empty" space (i.e., space free of matter), but space |
is never really empty, because even in the remotest voids of the universe there is always starlight—and that is matter. Besides, space is filled with gravitational fields, and according to |
Einstein gravity and inertia cannot very well be separated. Thus the subject of this article is in fact the total picture of space-time reality as envisaged by physics. We have |
to admit that our conception of material reality today is more wavering and uncertain than it has been for a long time. We know a great many interesting details, learn |
new ones every week. But to construct a clear, easily comprehensible picture on which all physicists would agree—that is simply impossible. Physics stands at a grave crisis of ideas. In |
the face of this crisis, many maintain that no objective picture of reality is possible. However, the optimists among us (of whom I consider myself one) look upon this view |
as a philosophical extravagance born of despair. We hope that the present fluctuations of thinking are only indications of an upheaval of old beliefs which in the end will lead |
to something better than the mess of formulas which today surrounds our subject. Since the picture of matter that I am supposed to draw does not yet exist, since only |
fragments of it are visible, some parts of this narrative may be inconsistent with others. Like Cervantes’ tale of Sancho Panza, who loses his donkey in one chapter but a |
few chapters later, thanks to the forgetfulness of the author, is riding the dear little animal again, our story has contradictions. We must start with the well-established concept that matter |
is composed of corpuscles or atoms, whose existence has been quite "tangibly" demonstrated by many beautiful experiments, and with Max Planck’s discovery that energy also comes in indivisible units, called |
quanta, which are supposed to be transferred abruptly from one carrier to another. But then Sancho Panza’s donkey will return. For I shall have to ask you to believe neither |
in corpuscles as permanent individuals nor in the suddenness of the transfer of an energy quantum. Discreteness is present, but not in the traditional sense of discrete single particles, let |
alone in the sense of abrupt processes. Discreteness arises merely as a structure from the laws governing the phenomena. These laws are by no means fully understood; a probably correct |
analogue from the physics of palpable bodies is the way various partial tones of a bell derive from its shape and from the laws of elasticity to which, of themselves, |
nothing discontinuous adheres. The idea that matter is made up of ultimate particles was advanced as early as the fifth century B.C. by Leucippus and Democritus, who called these particles |
atoms. The corpuscular theory of matter was lifted to physical reality in the theory of gases developed during the 19th century by James Clerk Maxwell and Ludwig Boltzmann. The concept |
of atoms and molecules in violent motion, colliding and rebounding again and again, led to full comprehension of all the properties of gases: their elastic and thermal properties, their viscosity, |
heat conductivity and diffusion. At the same time it led to a firm foundation of the mechanical theory of heat, namely, that heat is the motion of these ultimate particles, |
which becomes increasingly violent with rising temperature. Within one tremendously fertile decade at the turn of the century came the discoveries of X-rays, of electrons, of the emission of streams |
of particles and other forms of energy from the atomic nucleus by radioactive decay, of the electric charges on the various particles. The masses of these particles, and of the |
atoms themselves, were later measured very precisely, and from this was discovered the mass defect of the atomic nucleus as a whole. mass of a nucleus is less than the |
sum of the masses of its component particles; the lost mass becomes the binding energy holding the nucleus firmly together. This is called the packing effect. The nuclear forces of |
course are not electrical forces—those are repellent—but are much stronger and act only within very short distances, about 10-13 centimeter. Here I am already caught in a contradiction. Didn’t I |
say at the beginning that we no longer assume the existence of force fields apart from matter? I could easily talk myself out of it by saying: Well, the force |
field of a particle is simply considered a part of it. But that is not the fact. The established view today is rather that everything is at the same time |
both particle and field. Everything has the continuous structure with which we are familiar in fields, as well as the discrete structure with which we are equally familiar in particles. |
This concept is supported by innumerable experimental facts and is accepted in general, though opinions differ on details, as we shall see. In the particular case of the field of |
nuclear forces, the particle structure is more or less known. Most likely the continuous force field is represented by the so-called pi mesons. On the other hand, the protons and |
neutrons, which we think of as discrete particles, indisputably also have a continuous wave structure, as is shown by the interference patterns they form when diffracted by a crystal. The |
difficulty of combining these two so very different character traits in one mental picture is the main stumbling-block that causes our conception of matter to be so uncertain. Neither the |
particle concept nor the wave concept is hypothetical. The tracks in a photographic emulsion or in a Wilson cloud chamber leave no doubt of the behavior of particles as discrete |
units. The artificial production of nuclear particles is being attempted right now with terrific expenditure, defrayed in the main by the various state ministries of defense. It is true that |
one cannot kill anybody with one such racing particle, or else we should all be dead by now. But their study promises, indirectly, a hastened realization of the plan for |
the annihilation of mankind which is so close to all our You can easily observe particles yourself by looking at a luminous numeral of your wrist watch in the dark |
with a magnifying glass. The luminosity surges and undulates, just as a lake sometimes twinkles in the sun. The light consists of sparklets, each produced by a so-called alpha particle |
(helium nucleus) expelled by a radioactive atom which in this process is transformed into a different atom. A specific device for detecting and recording single particles is the Geiger-Müller counter. |
In this short résumé I cannot possibly exhaust the many ways in which we can observe single particles. Now to the continuous field or wave character of matter. Wave structure |
is studied mainly by means of diffraction and interference—phenomena which occur when wave trains cross each other. For the analysis and measurement of light waves the principal device is the |
ruled grating, which consists of a great many fine, parallel, equidistant lines, closely engraved on a specular metallic Light impinging from one direction is scattered by them and collected in |
different directions depending on its wavelength. But even the finest ruled gratings we can produce are too coarse to scatter the very much shorter waves associated with matter. The fine |
lattices of crystals, however, which Max von Laue first used as gratings to analyze the very short X-rays, will do the same for "matter waves." Directed at the surface of |
a crystal, high-velocity streams of particles manifest their wave nature. With crystal gratings physicists have diffracted and measured the wavelengths of electrons, neutrons and protons. What does Planck’s quantum theory |
have to do with all this? Planck told us in 1900 that he could comprehend the radiation from red-hot iron, or from an incandescent star such as the sun, only |
if this radiation was produced in discrete portions and transferred in such discrete quantities from one carrier to another (e.g., from atom to This was extremely startling, because up to |
that time energy had been a highly abstract concept. Five years later Einstein told us that energy has mass and mass is energy; in other words, that they are one |
and the same. Now the scales begin to fall from our eyes: our dear old atoms, corpuscles, particles are Planck’s energy quanta. The carriers of those quanta are themselves quanta. |
One gets dizzy. Something quite fundamental must lie at the bottom of this, but it is not surprising that the secret is not yet understood. After all, the scales did |
not fall suddenly. It took 20 or 30 years. And perhaps they still have not fallen completely. The next step was not quite so far reaching, but important enough. By |
an ingenious and appropriate generalization of Planck’s hypothesis Niels Bohr taught us to understand the line spectra of atoms and molecules and how atoms were composed of heavy, positively charged |
nuclei with light, negatively charged electrons revolving Each small system—atom or molecule—can harbor only definite discrete energy quantities, corresponding to its nature or its constitution. In transition from a higher |
to a lower "energy level" it emits the excess energy as a radiation quantum of definite wavelength, inversely proportional to the quantum given off. This means that a quantum of |
given magnitude manifests itself in a periodic process of definite frequency which is directly proportional to the quantum; the frequency equals the energy quantum divided by the famous Planck’s constant, |
h. According to Einstein a particle has the energy mc2, m being the mass of the particle and c the velocity of light. In 1925 Louis de Broglie drew the |
inference, which rather suggests itself, that a particle might have associated with it a wave process of frequency mc2 divided by h. The particle for which he postulated such a |
wave was the electron. Within two years the "electron waves" required by his theory were demonstrated by the famous electron diffraction experiment of C. J. Davisson and L. H. Germer. |
This was the starting point for the cognition that everything — anything at all — is simultaneously particle and wave field. Thus de Broglie’s dissertation initiated our uncertainty about the |
nature of matter. Both the particle picture and the wave picture have truth value, and we cannot give up either one or the other. But we do not know how |
to That the two pictures are connected is known in full generality with great precision and down to amazing details. But concerning the unification to a single, concrete, palpable picture |
opinions are so strongly divided that a great many deem it altogether impossible. I shall briefly sketch the connection. But do not expect that a uniform, concrete picture will emerge |
before you; and do not blame the lack of success either on my ineptness in exposition or your own denseness—nobody has yet succeeded. One distinguishes two things in a wave. |
First of all, a wave has a front, and a succession of wave fronts forms a system of surfaces like the layers of an onion. You are familiar with the |
two-dimensional analogue of the beautiful wave circles that form on the smooth surface of a pond when a stone is thrown in. The second characteristic of a wave, less intuitive, |
is the path along which it travels—a system of imagined lines perpendicular to the wave fronts. These lines are known as the wave "normals" or "rays." We can make the |
provisional assertion that these rays correspond to the trajectories of particles. Indeed, if you cut a small piece out of a wave, approximately 10 or 20 wavelengths along the direction |
of propagation and about as much across, such a "wave packet" would actually move along a ray with exactly the same velocity and change of velocity as we might expect |
from a particle of this particular kind at this particular place, taking into account any force fields acting on the particle. Here I falter. For what I must say now, |
though correct, almost contradicts this provisional assertion. Although the behavior of the wave packet gives us a more or less intuitive picture of a particle, which can be worked out |
in detail (e.g., the momentum of a particle increases as the wavelength decreases; the two are inversely proportional), yet for many reasons we cannot take this intuitive picture quite seriously. |
For one thing, it is, after all, somewhat vague, the more so the greater the wavelength. For another, quite often we are dealing not with a small packet but with |
an extended wave. For still another, we must also deal with the important special case of very small "packelets" which form a kind of "standing wave" which can have no |
wave fronts or wave normals. One interpretation of wave phenomena which is extensively supported by experiments is this: At each position of a uniformly propagating wave train there is a |
twofold structural connection of interactions, which may be distinguished as "longitudinal" and "transversal." The transversal structure is that of the wave fronts and manifests itself in diffraction and interference experiments; |
the longitudinal structure is that of the wave normals and manifests itself in the observation of single particles. However, these concepts of longitudinal and transversal structures are not sharply defined |
and absolute, since the concepts of wave front and wave normal are not, The interpretation breaks down completely in the special case of the standing waves mentioned above. Here the |
whole wave phenomenon is reduced to a small region of the dimensions of a single or very few wavelengths. You can produce standing water waves of a similar nature in |
a small basin if you dabble with your finger rather uniformly in its center, or else just give it a little push so that the water surface undulates. In this |
situation we are not dealing with uniform wave propagation; what catches the interest are the normal frequencies of these standing waves. The water waves in the basin are an analogue |
of a wave phenomenon associated with electrons, which occurs in a region just about the size of the atom. The normal frequencies of the wave group washing around the atomic |
nucleus are universally found to be exactly equal to Bohr’s atomic "energy levels" divided by Planck’s constant h. Thus the ingenious yet somewhat artificial assumptions of Bohr’s model of the |
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