The impact of quantum theory on modern physics

DIE NATURWISSENSCHAFTEN 60. Jahrgang, 1973 Heft 10 Oktober

The Impact of Quantum Theory on Modern Physics

Victor F. Weisskopf

Massachusetts Insti tute of Technology

"" II est ~ peine ndeessaire de [aim remar- quer combien la thdorie des Quanta s'dearte de tout ce qu'on avait imagind jusqu" iei, ce serait, sans aucun doute, la plus grande revolution et la plus pro]onde que la philosophic naturelle sit subide depuis Newton."

Henri Poincard (1912)

In troduct ion

The discovery of the quantum of action by Max Planck at the turn of our century was the beginning of one of the most fruitful and also most revolutionary developments in science. Rarely have our views regarding the basis of the properties and behavior of mat ter been changed and expanded as profundly as in the three decades following Planck's discovery. The subsequent discoveries of the quantization of energy in atoms, the existence of photons, the particle- wave duality were in direct contradiction to the fundamental tenets of classical physics. I t became abun- dantly clear that the mechanics of systems of atomic size is based upon quite different laws than those which are observed to govern the behavior of macro- scopic objects. A new foundation of mechanics was to be found in order to describe and understand atomic phenomena. I t took a quarter of a century before this task was accomplished. In the third decade of this century the paradoxes of quantum theory were solved and a new rational description of the dynamical behavior of small systems was established in terms of the new quantum mechanics. I t was discovered by a unique effort of a small group of physicists in a momentous development which took place essentially in the years t924 to t928. The leading spirits were Niels Bohr, Werner Heisen- berg, Erwin Schroedinger, Max Born, Wotfgang Pauli, Louis DeBroglie, Paul Dirac, Pasqual Jordan and Hans Kramers. Never before have so few done so much in such a short time.

Successes o / Q u a n t u m Mechanics

Atomic Structure The first important success of quantum mechanics was the quanti tat ive explanation of the hydrogen spectrum. Bohr's original tentative quantization rules were put on a firm basis. The properties of hydrogen, i{s spectrum and transition probabilities, could be

derived from a relatively simple theory, the non- relativistic quantum mechanics of a single electron under the influence of the attractive field of the proton. The quantum states are represented by state functions which are expressed in terms of well-known mathe- matical functions, from which all properties of the hydrogen atom can be deduced. Some details - such as the fine structure of the terms - could only be explained by Dirac's relativistic wave equation to which we return later on. Another decisive success of quantum mechanics con- sisted in the quantitat ive explanation of the properties of the hel ium atom. This problem defied the earlier a t tempts of quantization by the Bohr-Sommerfeld rules, because it is not a periodic system. Quantum mechanics can deal with problems of several electrons. The relevant state functions cannot be expressed in closed form but they can be calculated to any desired approximation. The Pauli principle plays an essential role in the dynamics of the helium atom. In the ground state, for example, the two electrons occupy the same orbital, similar to the ground state of the hydrogen atom. The Pauli principle requires that the spins of the two electrons are opposed to each other. Parallel spins are possible only if the electrons are in different orbitals. Among the excited states, one finds two rather different series of quantum states in helium ; one containing the states of parallel spin, the other the states with antiparallel spin of the electrons (ortho- and para- helium). I t is surprising at first sight, that the states with parallel spin are so different from those with antiparallel spin. After all, the electrons don' t differ much when the spin is inverted. The magnetic forces caused by the magnetic moments are very small compared to the electric forces that determine the properties of the quantum states; the electric forces do not depend on the spin orientation. Quantum mechanics has completely cleared up this p rob lem. I t is a special example of how the Panli principle works in regard to electron spins. I t requires a different symmet ry of the state functions in the case of parallel and antiparallel spins. A change of relative spin direction then is connected with a considerable change of the state function; it must be antisymmetric for parallel spins and symmetric for antiparalM ones. This difference in symmetry causes a change of energy, much larger than the small magnetic spin interaction

NaturwissenschMten 60, 441--446 (t973) �9 by Springer-Verlag 1973 441

would cause. Thus the relative spin orientation of electrons acquires a special rigidity since its change affects the energy relations via the symmet ry of the state function. This effect has led to an explanation of ~erromagnetism, a phenomenon in which the electron spins in a metal are held parallel by these effects, which are much stronger than their magnetic interaction. Heisenberg was the first to find the qualitative interpretation of both riddles - helium spectrum and ferromagnetism - long before a quanti tat ive t reatment was carried ont. The Pauli principle also plays an essential role in the understanding of the structure of atoms with several electrons. The ground state of an atom is best described in terms of independent "orbitals" for each electron. These orbitals are filled with two electrons each, in the order of increasing energy until all electrons are placed (Bohr's "Aufbau-Pfinzip"). A qualitative discussion of the consequences of this simple principle leads directly to a convincing explanation of the periodic system o/ elements found by Mendeleyev in t870: The systematics of these orbitals reproduces almost automatically the famous periods and similarities among elements. Whenever certain numbers of electrons are assembled in their lowest orbitals, the configuration acquires a specially symmetric and well rounded shape which is referred to as a closed shell. These are the ends of Mendeleyev's periods, the chemically inert noble gases. One, two or three electrons added to such closed shells produce chemically similar atoms, such as the alkali metals, the alkaline earth metals, etc. I t remains a remarkable feat of visionary intuition that Niels Bohr was able to express correctly the main features and most of the details of this explanation in 1922 when neither quantum mechanics nor the Pauli principle were known. Today the structure, the dynamics and the spectra of all atoms are well understood. There is hardly any important question left that is not, or could not be solved with quantum mechanics by numerical method s .

Molecular Structure

Perhaps the most extensive success of quantum mechanics was the unification of chemistry and physics: the recognition of the nature of the chemical bond. When two atoms are brought nearer together from a distance large compared to their size, the total energy changes as function of the distance, because of the ensuing deformation of the electronic orbitals. A bond is formed if the energy decreases to a minimum value at the bonding distance; no bond is formed if the energy increases. The former happens in most cases - in particular, when the spin directions of the outer electrons are opposed so tha t a pair of them can form a common orbital. Then both of them are a t t racted by either nucleus, and a .binding results which is stronger than the unavoidable electric repulsion between the nuclei. The forming of a common orbital (homopolar bond) is not the only mechanism that leads to a lower total energy when atoms approach each other. Another simple mechanism (ionic bond) occurs when one of the atoms has a loosely bound electron and the other has a strong affinity for an additional electron. The atoms

then exchange an electron when brought together and the ensuing opposite ions at t ract each other and form a bond. There are many other mechanisms tha t lead to bond- ings between atoms. All cases can be described as the forming of a common quantum state of the combined electrons and nuclei under the influence of their mutual electric attractions and repulsions, a quantum state whose energy is lower than the sum of the energies of the separated atoms. Quantum mechanics explains the chemical bond in a fundamentally simple way: it is recognized as a purely electrostatic effect. There is an increased net electrostatic attraction between nuclei and electrons under bonding conditions. The quantum state of the combined system contains rearranged orbitals that give rise to this increase. The immense variety of chemical compounds are all manifestations of a simple fundamental force of nature: the electrostatic interaction of charged particles. This is one of the most significant insights that quantum mechanics has provided.

The Structure of Solids

~Knowing about the nature of the different bonds between atoms also led to an understanding of the structure of the crystalline structure of solids. The simplest examples are the ionic crystals. They are materials which consist of two types of atoms, each tending to become ions with opposite charges. The positive and negative ions are held together by electrostatic attraction in a regular lattice array. The equilibrium is reached when the electron cores of the ions touch each other. Then the Pauli principle sets up strong repulsive forces since it prevents the core electrons from occupying the same regions in space. In most other solid materiMs the bonding is based upon the fact that in close packing the outer electrons of the atoms are able to move from one atom to the next, thus experiencing the attraction of more than one nucleus. The net effect of the resulting electric attractions and repulsions is binding which keeps the material together. Quantum mechanics has provided a conceptual framework for the understanding of the properties of such solids. I t is based upon two quantum effects which are manifest if electrons move within a regular array of positive ions forming an ordered crystal lattice. The first is the fact that a wave is not scattered by a regular array of obstacles. Therefore an electron penetrates through the lattice almost as if it were in empty space. I t is scattered only by small

, irregularities of the lattice caused by thermal motion or impurities. The second is the fact that the quantum states of the electrons freely moving in the lattice, ~orm groups of states with kinetic energies from zero to a certain max imum value. These groups are apt ly called "bands" because of the energies of the states Within a group are distributed ah~ost continuously between the minimum and the max imum values. The materiM becomes a metallic conductor if the states of a band are partially filled. Then the electrons are easily made to move by an electric field such that they form a current; they perform transitions in small steps to the empty states at slightly higher velocity in the direction of the field. The material becomes an

442 Naturwissenschaften 60, 44t--446 (1973) �9 by Springer-Verlag t973

insulator if the bands are fully occupied. Then the Pauli principle does not allow any change of state and no net current can be produced. The concept of filled or partially filled electron "bands" helped to explain an enormous body of observations relating to the electric, magnetic and optical behavior of metals and insulators. I t not only explained the existence of semi-conductors, but it also led to the production of new types of semi-conductors and to the design of new artifacts such as the transistor. One of the latest successes of the quantum mechanics of metals has been the explanation of superconduc- tivity, that is the complete disappearance of any resistivity in some metals at low temperature in spite of the presence of lattice irregularities. I t was understood as an effect of the interactions between electrons caused by their common deforming effects upon the lattice. The formulation of those effects needed the invention of a new language for discussing the collective behavior of interacting electrons, a language which turned out to be equally useful for the understanding of other similar collective effects at low temperature, such as the superfluidity of liquid helium.

Nuclear Physics

So far we have been dealing with the application of quantum mechanics to atomic and molecular problems, that is to the motion of electrons in the electric field of atomic nuclei. The nuclei themselves are objects much smaller than the dimensions of atoms; their size is of the order of several t 0 -13 cm. As far as the dynamics of atoms and their aggregates is concerned, the nuclei act as heavy mass points endowed with a charge and sometimes with a magnetic or electric multipole moment. Any internal dynamic structure would have little influence on atomic physics because of a fundamental relation in quantum mechanics between energy and size of a system. The excitation energies of dynamical systems are of the order of magnitude of the kinetic energies K of their constituents. A lower limit of that energy can be inferred from the linear dimensions d of the system: K>~ h2/ (2rod2). Here m is the mass of the constituents. Insert- ing the mass of a nucleon and nuclear dimensions, we get K >~ t 0 5 eV, a value much higher than the excitation energies of atoms. Hence in atomic physics it is allowed to consider the nucleus as an inert object without any internal dynamics, as an elementary particle. In t932 Chadwick discovered the existence of the neutron. I t became evident that the nucleus is a system composed of protons and neutrons (nucleons), held together by a new force of nature, much stronger than electric forces. A closer s tudy of nuclear scattering and the properties of simple nuclei has revealed some of the properties of tile nuclear force. I t is a short- ranged force with a range of a few t0 -is cm acting between pairs of nucleons; it can be approximated by a potential which is at tractive over most of the range but turns repulsive at smaller distances. The quantitat ive details depend on the relative spin orientation and on the symmetry of the state function of the two nucleons. I t seems to be a complex phenomenon, rather like an indirect manifestation of a more funda-

mental effect at a yet unknown level, not dissimilar to the chemical forces as a manifestation of the electrostatic interaction of atomic constituents. Taking the nuclear force as an empirically determined potential energy, the dynamics of nuclei presents a typical quantum mechanical situation of particles under the influence of essentially at tractive forces. Indeed, tile development of the theory of nuclear structure turned out to be a repeat performance of quantum mechanics, with results that bear some similarities with atomic dynamics. There are two features, however, which limit the variety of nuclear phenomena compared to the atomic world: One is the short range of the force, which prevents the existence of stable excited states in the deuteron, the "hydrogen a tom" of nuclear physics; the deuteron has only one stable quantum state, the ground state. The second is the fact that there is a net positive charge to any assembly of protons and neutrons, which makes very large aggregates unstable: Hence, there is a limit to the number A of constituents (A , -~250) tha t will stick together for a reasonable t ime 1. The analogies between nuclear and atomic or molecular dynamics are numerous: The spectra of excited states show a certain similarity in their quantum numbers and in the radiative transition probabilities; there exists a similar "Aufbau" principle, which leads to a periodic system of nuclear properties, with a series of "closed-shell" nuclei in analogy to the noble gases. The number of constituents forming the closed shells is not the same because of the different nature of the forces: in particular, because of their peculiar depend- ence on the relative spin directions. We find rotational and vibrational nuclear spectra, in analogy to molecular systems. Some new phenomena were found in nuclear physics which have no analogy among atomic processes. The most significant are the phenomena of "weak interactions" which appear in form of radioactive decays.

T h e simplest manifestation is the decay of the neutron into a proton. The neutron has a slightly larger mass than the proton by 1.2 MeV. The corresponding energy and charge difference is emitted in that decay in form of a pair o/particles: an electron and an antineutrino : n - + p + e + 7. This is a very slow process compared to other nuclear reaction times; the half-life of the neutron is 12 minutes. There is an opposite process: p - + n + ~ + v , in which a positron ~ and a neutrino are emitted. However, this decay process can only occur within a nucleus, under conditions when the change of a proton to a neutron is energetically so favorable that it overcompensates the fact that the neutron is heavier than tile proton. The proton and the neutron should be considered here as two quantum states of the same particle, albeit with different charge. The two decay processes are transitions between those states with the emission of a so- called "lepton"-palr (electrons, neutrinos and their antiparticles are leptons). The concept of quantum state is widened to include states differing in electric charge.

t Only elements up to iron ( 54 consti tuents) are stable for an infinite time. If A > 250, the mean lifetime before fission will measure in years or less. W h e n A reaches the order of 10% grav i ty effects produce stability. Such enormous nuclei m a y be realized in the so-called neut ron stars.

Naturwissenschaf ten 60, 441--446 (t973) �9 by Springer-Verlag t973 443

One of the most surprising features of weak interaction processes is the lack o/ mirror symmetry. There is a fundamental difference observed between left and right. For example, the neutrinos are exclusively emitted with a left-handed spin relative to their propagation, the antineutrinos with a right-handed spin. No other natural process exhibits this asymmetry.

Further Devel@ments

Relativistic Quantum Mechanics

The applications of quantum mechanics to atoms, atomic aggregates and nuclei mostly deal with situat- ions in which the relative velocities of the particles are small compared to the velocity of light. Therefore, the effects of relativity can be neglected. Most of the successes of quantum mechanics are based on this fact; the neglecting of relativistic effects not only simplified the application of quantum mechanics, it also avoids some conceptual difficulties that are not yet overcome. These difficulties are connected with the finite speed of propagation of interactions between particles, for which there exist today only rather rudimentary ways of dealing. Nevertheless, a number of successful steps were taken to account for the effects of relativity in quantum mechanics. Further- more, the a t tempt to formulate quantum mechanics in accord with relativity opened up new insights into the basic properties of matter . I t led directly to the concept of antimatter and to the processes of its creation and annihilation. As early as t 927 Dirac conceived a relativistic quantum mechanics concerning a single charged particle moving in an electromagnetic field. This equation endows the particle with a spin and a magnetic moment of the correct sizes as observed with the electron. The spin and its magnetic properties appear as basic features of the wave equation. When this equation is applied to the motion of an electron in the field of a fixed point charge, the resulting state functions accurately describe the filie structure of the spectrum and other observed relativistic effects in the hydrogen atom. The difficulties of finite propagation speed of interactions do not yet appear in this problem because of the static nature of the field. There is one important feature of the Dirac equation whose significance was not immediately realized. I t contains solutions which seem to correspond to states with negative kinetic energy. Obviously such states are physically impossible. I t was soon recognized, however, tha t these states have physicM significance, but that they can and must be interpreted in a different way: they are states of positive kinetic energy representing an electron of opposite charge and magnetic moment, the positron. Thus the existence of antiparticles is implicitly contained in the Dirac equation. Furthermore, tha t equation Mso allows for the processes of creation and annihilation of particle- antiparticle pairs which, indeed, occur in nature. For example, a light quantum of sufficient energy m a y be absorbed by the electric field of a nucleus and an electron-positron pair is created in the process. In- versely an electron and a positron may transform themselves into light quanta upon collision. I t remains a remarkable test imony to the simplicity and depth

of Dirac's equation that the existence of the positron was predicted by the theory before it was observed in nature. The particle-antiparticie duality and the processes of creation or annihilation of these pairs do not only occur with electrons or with other particles with a spin of one half unit, as described by the Dirac equation. I t is a general consequence of relativistic quantum mechanics that any entity, whatever its spin, has two forms of realization, particle and antiparticle ~, which under suitable conditions are created together and annihilate each other. Part icle and antiparticle must have the same mass and spin, but must be opposite in charge and in any other quant i ty that is conserved in the processes of creation and annihilation.

Field Theory

Relativistic quantum mechanics faces the problem of a finite propagation speed of interactions. The forces responsible - the electromagnetic field, the nuclear force, the weak interactions - cannot be considered as simple attributes of the interacting particles, they have a dynamics of their own. The concepts of quantum mechanics have been applied to the dynamics of such fields and their coupling with other entities. The most successful of these "field theories" is the quantum mechanics of the electromagnetic interactions between charged particles, such as electrons and protons. I t is called "Quan tum electrodynamics". In a field theory the distinction between "particles" and "interacting field" is largely eliminated. The particles are the quanta of a field, namely the field of the particle waves; the quantization of the interacting field gives rise to "particles" namely the field quanta, such as photons for the electromagnetic field, and mesons for the nuclear field. I t is typical for a field theory, that the number of part icles and antiparticles is not fixed: Field quanta are emitted and absorbed, particles such as electrons or protons are created or annihilated together with their antiparticles. The number of entities is fixed only when the energy exchanges are small compared to the rest-mass energy; that is under non-relativistic conditions. Clearly the number of light quanta is never fixed since their rest-mass is zero. Unfortunately it is not yet possible at present to make use of field theories in a consistent way. Even quantum electrodynamics is still beset with certain intrinsic difficulties, connected with the electromagnetic self-energy of the charged particles. Some of these difficulties existed already in the classical theory of the electron; they are related to the unknown internM structure of the electron. An infinitely small charged particle (point charge) would lead to an infinitely large self-energy; the energy contained in the Coulomb field becomes infinite in the immediate neighborhood of the point. A finite particle creates fundamental difficulties for any relativistic theory. Even today, these problems have not yet been solved, but a modus vivendi ("Renormalization") has been found for the use of the theory for any practical pur- pose except the calculation of the self-energy and

2 The light quantum and some of the uncharged mesons have a special position; in these cases the particle and its antiparticle are identical.

444 Natnrwissenschaften 60, 44t--446 (t973) �9 by Springer-Verlag t973

related magnitudes, such as masses and effective charges. The methods for obtaining results from field theory inspire of the appearance of infinite masses and charges have been extremely successful in quantum electrodynamics. For example, it was possible to calculate some deviations from the Dirac value of the magnetic moment of the electron and the muon, that agreed surprisingly well with the measured values. Another example is the calculation of small shifts in the energies of tile quantum states of hydrogen and other atoms (Lamb shift) in excellent agreement with observation. I t must be emphasized, however, that these methods for the "practical" use of field theories are based upon the very small value of the "coupling constant", a number which characterizes the strength by which the field is coupled to its sources. In the electromagnetic case this constant is e2/hc (e is electron-charge, h is Planck's constant and c is light velocity) which has the small va lue t/137 and, furthermore, the coupling is of a very simple kind. The situation is not so good with other types of interaction. The nature of the nuclear force is not yet well understood; any a t tempt to formulate it in form of a field theory, however, leads to large coupling constants, and therefore precludes the application of renormalization difficulty. The corresponding coupling constant for the weak interactions is very small, but the form of the interaction does not seem to be simple enough for a renormalized field theory.

High-Energy Physics During the last two decades it became possible to accelerate particles to energies of many billion electron volts. These energies exceed the rest-mass energy of the proton and neutron. Many new and surprising phenomena were discovered when such particle beams were made to collide with matter. A rich world of unexpected particles, reactions and transformations appeared at the targets of the accelerators. What we face in this new realm of phenomena seems to be a proliferation of pair-creation and annihilation phenomena. I t abounds in particles and antiparticles of all kinds that are created and transformed into other ones. Furthermore, entities, such as the proton and the neutron, seem to appear ill many different quantum states; transitions between these quantum states are accompanied by the emission and absorp- tion of a new kind of particles or quanta, the so-called mesons. The mesons also appear in many different quantum states. There seems to be a strong interaction between mesons and nucleons in their various quantum states; the nuclear force is one of the manifestations of this interaction. Today we have no other means to describe all these observations but the language of quantum mechanics and field theory. We find ourselves in an exasperating situation: The phenomena are not unlike what one would expect to occur when strong interactions are active, but the conceptual difficulties have not per- mitted us to verify or to disprove the validity of quantum mechanical field theories in this realm of phenomena. I t is by no means sure yet whether quantum mechanics and field theory are an adequate formulation, or represent an abortive effort to formulate the unknown in a wrong language.

The weak interactions seem to play a large role in these processes. Many decays of particles into others, and some scattering phenomena, can be identified as manifestations of an interaction similar to the one which produces the emission of electron-neutrino pairs. A new heavy form of electron appears - the muon - when tile energy exchanges in weak or electromagnetic interactions are high enough to produce it. We do not know the significance of this partner to the ordinary electron, whose only distinction from the electron seems to be a 200 times higher mass. In high-energy processes, too, the weak interactions exhibit a lack of left-right symmetry, occurring in the opposite sense when particles and antiparticles change their role. Thus, nature seems to be symmetric with respect to left and right exchanges if at the same time there is a change from world to antiworld. Even this symmetry has recently been found to be slightly broken in some weak-interaction processes.

Epilogue

Quantum theory has caused a revolution in our view of the material world which pervades all fields of natural science. The language in which natural phenomena are interpreted has undergone a thorough change. Concepts such as quantum state, excitation energy, transition probability, wave function, orbital, reso- nance, light quantum, etc., have replaced the concepts of classical mechanics and electromagnetism. Quantum mechanics had its most extensive success in the interpretation of atomic and molecular phenomena where the energy exchanges are below the nuclear excitation threshold. Here a singular feat of unification was achieved: The structure and dynamics, the properties and behavior of atoms, molecules and their aggregates are understood to be based upon one simple and well-understood force: the electromagnetic interactions between electron and atomic nuclei. The new approach to atomic dynamics led to three importalit insights into the character of the atomic world. Firs t it led to a conception of typical dimensions in size and energy which dominate atomic phenomena. Their scale and measure is understood. The sizes of the electron waves confined by the electrostatic attraction of the nucleus necessarily are of the order of the Bohr radius - aB-~h2/me ~" - and their energies are of the order of the Rydberg unit - R = m e * / 2 h ~. Thus atomic dimensions are reduced to basic fundamental constants. Quantum mechanics also defines a typical length and energy for nuclear phenomena. The nature of the nuclear force is not yet understood, however, and therefore cannot be expressed in terms of fundamental constants. Taking into account the empirical knowledge of the strength and character of this force, one obtains a characteristic length of several 10 -13 cm and an energy of the order of t 06 eV as tile natural scales for nuclear phenomena. Second, quantum mechanics introduces a "morph ic" trait, which previously was absent in physics but not in nature. The atomic world abounds in characteristic shapes, typical properties, ever recurring qualities, from the identity of all atoms of a given kind to the faithful reproduction of living species. The morphic character

Naturwissenschaften 60, 441--446 (1973) �9 by Springer-Verlag 1973 445

has its root in the electron wave function. I t assumes special shapes and patterns, defined by the electric field which the electron faces within the atom. These pat terns are characteristic for each atomic and molecular species, and reflect the specific symmet ry of the situation. They are the fundamental shapes of which all things in our environment are made. They always appear, identical and unchanged, whenever the a tom finds itself under tile same conditions, independent of its previous history. I t is remarkable tha t we actually find in the world of atoms what Pythagoras and Kepler sought vainly to find in the motion of the planets. They believed tha t the Ear th and other planets move in special orbits, each unique to the planet and determined by some ult imate principle that is independent of the particular fate and the past history of our planetary system. There is no s u c h principle in the motion of planets, but there is one tha t dominates the motion of particles in atoms and nuclei. The third new insight of quantum mechanics concerns the nature of a quantum state. I t is a well-defined indivisible entity. The results of certain measurements, however, are expressible only in terms of probabili ty distributions. This lack of complete predictability is a consequence of the fact that the measurement inter- feres with the system and destroys the subtle indivi- duality of the quantum state. This situation often is described as a breakdown o/causality since a complete knowledge of the quantum state does not lead to exact predictions of the results of all measurements. Here is an important difference between tile classical and the quantum mechanical description. The former considers the state of a system such tha t every detailed feature is amenable to an exact measurement. Tile lat ter describes the system as being in a particular quantum state of which not every measurement is determined. The detailed structure of a system is contained in the total i ty of all its quantum states, reflecting the fact that the measurement of a feature that is not determined in a given quantum state would involve transitions into other states. The m o s t striking example of this situation is the radioactive decay of a nucleus in its ground state. The time of decay cannot be predicted exactly. Any a t tempt to pry into the internal dynamics of the nucleus in order to find out what causes an individual decay, would inevitably transfer the nucleus into m a n y of its excited states, and thus completely change its decay. The successes of quantum mechanics are ample proof that the ideas introduced by the quantum revolution

have vast ly improved our understanding of the behavior of matter . A language was created for a rational description of the atomic world, and much deeper insights were gained into the ways in which nature builds up tile entities of which all mat ter is composed. Our knowledge is far f rom complete; there are two different kinds of frontiers at which new knowledge and better understanding is sought: the "internal" and the "external" frontiers. The first kind includes the studies of the structure and behavior of complex atomic aggregates, which yet defy our understanding, inspire of the fact that the principles that govern atomic structures and interactions are well known. Examples of largely nonunderstood structures are amorphous substances, membranes, mat te r under highly ionized conditions (plasma physics), and com- plicated macromolecules which, under suitable conditions, give rise to the varied phenomena of life. There exist only rudimentary methods to deal with complex and highly organized forms of matter , where non-linear relations between relevant magnitudes are the rule, and new kinds of superstructures appear. The situation is quite different from the behavior of well separated atoms or simple atomic aggregates, where the quantum states are widely spaced in energy and therefore are relatively impervious to perturba- tions. New concepts and new ways of thinking and formulating will be necessary to get a bet ter understanding of the hierarchies of structures which are found in nature. The "external frontiers" of physics are those where phenomena are studied which are outside the world of atoms and their aggregates, that is outside the world which is explainable by electromagnetic interactions between charged particles. They are tile frontiers of nuclear physics, of high-energy physics and of astro- physics. In these fields the principles which govern the processes are largely unknown; we do not know the nature of the nuclear forces, of weak interactions, and we are deeply puzzled by the phenomena discovered at very high energies, tile various new particles and antiparticles. The astronomical discoveries also present us with new phenomena whose significance and origin are not fully recognized, such as quasars, pulsars and exploding galaxies. Some of these new discoveries may find their interpretation within the realm of quantum mechanical ideas, but some may indicate a new way of natural behavior which is beyond compre- hension with present concepts.

Received February 19, 1973

446 Naturwissenschaften 60, 441--446 (1973) �9 by Springer-Verlag 1973

Documents

The impact of quantum theory on modern physics