text
stringlengths
59
1.12k
atom, as well as of the older quantum theory in general, are superseded by the far more natural idea of de Broglie’s wave phenomenon. phenomenon forms the "body" proper of
the atom. It takes the place of the individual pointlike electrons which in Bohr’s model are supposed to swarm around the nucleus. Such pointlike single particles are completely out of
the question within the atom, and if one still thinks of the nucleus itself in this way one does so quite consciously for reasons of expediency. What seems to me
particularly important about the discovery that "energy levels" are virtually nothing but the frequencies of normal modes of vibration is that now one can do without the assumption of sudden
transitions, or quantum jumps, since two or more normal modes may very well be excited simultaneously. The discreteness of the normal frequencies fully suffices—so I believe—to support the considerations from
which Planck started and many similar and just as important ones—I mean, in short, to support all of quantum The theory of quantum jumps is becoming more and more unacceptable,
at least to me personally, as the years go on. Its abandonment has, however, far-reaching consequences. It means that one must give up entirely the idea of the exchange of
energy in well-defined quanta and replace it with the concept of resonance between vibrational frequencies. Yet we have seen that because of the identity of mass and energy, we must
consider the particles themselves as Planck’s energy quanta. This is at first frightening. For the substituted theory implies that we can no longer consider the individual particle as a well-defined
permanent entity. That it is, in fact, no such thing can be reasoned in other ways. For one thing, there is Werner Heisenberg’s famous uncertainty principle, according to which a
particle cannot simultaneously have a well-defined position and a sharply defined velocity. This uncertainty implies that we cannot be sure that the same particle could ever be observed twice. Another
conclusive reason for not attributing identifiable sameness to individual particles is that we must obliterate their individualities whenever we consider two or more interacting particles of the same kind, e.g.,
the two electrons of a helium atom. Two situations which are distinguished only by the interchange of the two electrons must be counted as one and the same; if they
are counted as two equal situations, nonsense obtains. This circumstance holds for any kind of particle in arbitrary numbers without exception. Most theoreticians will probably accept the foregoing reasoning and
admit that the individual particle is not a well-defined permanent entity of detectable identity or sameness. Nevertheless this inadmissible concept of the individual particle continues to play a large role
in their ideas and discussions. Even deeper rooted is the belief in "quantum jumps," which is now surrounded with a highly abstruse terminology whose common-sense meaning is often difficult For
instance, an important word in the standing vocabulary of quantum theory is "probability," referring to transition from one level to another. But, after all, one can speak of the probability
of an event only assuming that, occasionally, it actually occurs. If it does occur, the transition must indeed be sudden, since intermediate stages are disclaimed. Moreover, if it takes time,
it might conceivably be interrupted halfway by an unforeseen disturbance. This possibility leaves one completely at sea. The wave v. corpuscle dilemma is supposed to be resolved by asserting that
the wave field merely serves for the computation of the probability of finding a particle of given properties at a given position if one looks for it there. But once
one deprives the waves of reality and assigns them only a kind of informative role, it becomes very difficult to understand the phenomena of interference and diffraction on the basis
of the combined action of discrete single particles. It certainly seems easier to explain particle tracks in terms of waves than to explain the wave phenomenon in terms of corpuscles.
"Real existence" is, to be sure, an expression which has been virtually chased to death by many philosophical hounds. Its simple, naive meaning has almost become lost to us. Therefore
I want to recall something else. I spoke of a corpuscle’s not being an individual. Properly speaking, one never observes the same particle a second time—very much as Heraclitus says
of the river. You cannot mark an electron, you cannot paint it red. Indeed, you must not even think of it as marked; if you do, your "counting" will be
false and you will get wrong results at every step—for the structure of line spectra, in thermodynamics and elsewhere. A wave, on the other hand, can easily be imprinted with
an individual structure by which it can be recognized beyond doubt. Think of the beacon fires that guide ships at sea. The light shines according to a definite code; for
example: three seconds light, five seconds dark, one second light, another pause of five seconds, and again light for three seconds—the skipper knows that is San Sebastian. Or you talk
by wireless telephone with a friend across the Atlantic; as soon as he says, "Hello there, Edward Meier speaking," you know that his voice has imprinted on the radio wave
a structure which can be distinguished from any other. But one does not have to go that far. If your wife calls, "Francis!" from the garden, it is exactly the
same thing, except that the structure is printed on sound waves and the trip is shorter (though it takes somewhat longer than the journey of radio waves across the Atlantic).
All our verbal communication is based on imprinted individual wave structures. And, according to the same principle, what a wealth of details is transmitted to us in rapid succession by
the movie or the television picture! This characteristic, the individuality of the wave phenomenon, has already been found to a remarkable extent in the very much finer waves of particles.
One example must suffice. A limited volume of gas, say helium, can be thought of either as a collection of many helium atoms or as a superposition of elementary wave
trains of matter waves. Both views lead to the same theoretical results as to the behavior of the gas upon heating, compression, and so on. when you attempt to apply
certain somewhat involved enumerations to the gas, you must carry them out in different ways according to the mental picture with which you approach it. If you treat the gas
as consisting of particles, then no individuality must be ascribed to them, as I said. If, however, you concentrate on the matter wave trains instead of on the particles, every
one of the wave trains has a well-defined structure which is different from that of any other. It is true that there are many pairs of waves which are so
similar to each other that they could change roles without any noticeable effect on the gas. But if you should count the very many similar states formed in this way
as merely a single one, the result would be quite wrong. In spite of everything we cannot completely banish the concepts of quantum jump and individual corpuscle from the vocabulary
of physics. We still require them to describe many details of the structure of matter. How can one ever determine the weight of a carbon nucleus and of a hydrogen
nucleus, each to the precision of several decimals, and detect that the former is somewhat lighter than the 12 hydrogen nuclei combined in it, without accepting for the time being
the view that these particles are something quite concrete and real? This view is so much more convenient than the roundabout consideration of wave trains that we cannot do without
it, just as the chemist does not discard his valence-bond formulas, although he fully realizes that they represent a drastic simplification of a rather involved wave-mechanical situation. If you finally
ask me: "Well, what are these corpuscles, really?" I ought to confess honestly that I am almost as little prepared to answer that as to tell where Sancho Panza’s second
donkey came from. At the most, it may be permissible to say that one can think of particles as more or less temporary entities within the wave field whose form
and general behavior are nevertheless so clearly and sharply determined by the laws of waves that many processes take place as if these temporary entities were substantial permanent beings. The
mass and the charge of particles, defined with such precision, must then be counted among the structural elements determined by the wave laws. The conservation of charge and mass in
the large must be considered as a statistical effect, based on the "law of large numbers." Simultaneously with the development of wave mechanics, Heisenberg evolved a different mathematical analysis known
as matrix mechanics. According to Heisenberg’s theory, which was developed in collaboration with the German physicists Max Born and Ernst Pascual Jordan, the formula was not a differential equation but
a matrix: an array consisting of an infinite number of rows, each row consisting of an infinite number of quantities. Matrix mechanics introduced infinite matrices to represent the position and
momentum of an electron inside an atom. Also, different matrices exist, one for each observable physical property associated with the motion of an electron, such as energy, position, momentum, and
angular momentum. These matrices, like Schrödinger’s differential equations, could be solved; in other words, they could be manipulated to produce predictions as to the frequencies of the lines in the
hydrogen spectrum and other observable quantities. Like wave mechanics, matrix mechanics was in agreement with the earlier quantum theory for processes in which the earlier quantum theory agreed with experiment;
it was also useful in explaining phenomena that earlier quantum theory could not explain. Schrödinger subsequently succeeded in showing that wave mechanics and matrix mechanics are different mathematical versions of
the same theory, now called quantum mechanics. Even for the simple hydrogen atom, which consists of two particles, both mathematical interpretations are extremely complex. The next simplest atom, helium, has
three particles, and even in the relatively simple mathematics of classical dynamics, the three-body problem (that of describing the mutual interactions of three separate bodies) is not The energy levels
can be calculated accurately, however, even if not exactly. In applying quantum-mechanics mathematics to relatively complex situations, a physicist can use one of a number of mathematical formulations. The choice
depends on the convenience of the formulation for obtaining suitable Although quantum mechanics describes the atom purely in terms of mathematical interpretations of observed phenomena, a rough verbal description can
be given of what the atom is now thought to be like. Surrounding the nucleus is a series of stationary waves; these waves have crests at certain points, each complete
standing wave representing an orbit. The absolute square of the amplitude of the wave at any point is a measure of the probability that an electron will be found at
that point at any given time. Thus, an electron can no longer be said to be at any precise point at any given time. The impossibility of pinpointing an electron
at any precise time was analyzed by Heisenberg, who in 1927 formulated the uncertainty principle. This principle states the impossibility of simultaneously specifying the precise position and momentum of any
particle. In other words, the more accurately a particle’s momentum is measured and known, the less accuracy there can be in the measurement and knowledge of its position. This principle
is also fundamental to the understanding of quantum mechanics as it is generally accepted today: The wave and particle character of electromagnetic radiation can be understood as two complementary properties
of radiation. Another way of expressing the uncertainty principle is that the wavelength of a quantum mechanical principle is inversely proportional to its momentum. As atoms are cooled they slow
down and their corresponding wavelength grows larger. At a low enough temperature this wavelength is predicted to exceed the spacing between particles, causing atoms to overlap, becoming indistinguishable, and melding
into a single quantum state. In 1995 a team of Colorado scientists, led by National Institutes of Standards and Technology physicist Eric Cornell and University of Colorado physicist Carl Weiman,
cooled rubidium atoms to a temperature so low that the particles entered this merged state, known as a Bose-Einstein condensate. The condensate essentially behaves like one atom even though it
is made up of thousands. - Physicists Condense Supercooled Atoms, Forming New State of Matter A team of Colorado physicists has cooled atoms of gas to a temperature so low
that the particles entered a merged state, known as a "Bose-Einstein condensate." This phenomenon was first predicted about 70 years ago by the theories of German-born American physicist Albert Einstein
and Indian physicist Satyendra Nath Bose. The condensed particles are considered a new state of matter, different from the common states of matter—gas, liquid, and solid—and from plasma, a high
temperature, ionized form of matter that is found in the sun and other stars. Physicists have great expectations for the application of this discovery. Because the condensate essentially behaves like
one atom even though it is made up of thousands, investigators should be able to measure interactions at the atomic and subatomic level that were previously extremely difficult, if not
impossible, to study The condensate was detected June 5 by a Colorado team led by National Institutes of Standards and Technology physicist Eric Cornell and University of Colorado physicist Carl
Wieman. Their discovery was reported in the journal Science on July 14. Cornell and Wieman formed their condensate from rubidium gas. Several groups of physicists, including the teams in Texas
and Colorado and a group at the Massachusetts Institute of Technology, have been working to form pure condensate in recent years. The goal of the investigations has been to create
a pure chunk of condensate out of atoms in an inert medium, such as a diffuse, nonreactive gas. The effort began when methods of cooling and trapping became refined enough
that it seemed possible to reach the required conditions of temperature and density. The Colorado team used two techniques: first laser cooling and then evaporative cooling. The laser technique used
laser light whose frequency was carefully tuned to interact with the rubidium atoms and gently reduce their speeds. A number of lasers were aimed at the gas to slow the
motion of the atoms in different directions. The Colorado physicists then switched to evaporative cooling. In this method, the gas is "trapped" by a magnetic field that dwindles to zero
at its center. Atoms that are moving wander out of the field, while the coldest atoms cluster at the center. Because a few very cold atoms could still escape at
the zero field point of the trap, the physicists perfected their system by adding a second slowly circling magnetic field so that the zero point moved, not giving the atoms
the chance to escape through it. Physicists will now begin to explore the properties of the condensate and see what other materials they can use to form it. One unusual
characteristic of the condensate is that it is composed of atoms that have lost their individual identities. This is analogous to laser light, which is composed of light particles, or
photons, that similarly have become indistinguishable and all behave in exactly the same manner. The laser has found a myriad of uses both in practical applications and in theoretical research,
and the Bose-Einstein condensate may turn out to be just as important. Some scientists speculate that if a condensate can be readily produced and sustained, it could be used to
miniaturize and speed up computer components to a scale and quickness not possible before. The prediction that a merged form of matter will emerge at extremely low temperatures is based
on a number of aspects of the quantum theory. This theory governs the interaction of particles on a subatomic scale. The basic principle of quantum theory is that particles can
only exist in certain discrete energy states. The exact "quantum state" of a particle takes into consideration such factors as the position of the particle and its "spin," which can
only have certain discrete values. A particle’s spin categorizes it as either a boson or a fermion. Those two groups of particles behave according to different sets of statistical rules.
Bosons have spins that are a constant number multiplied by an integer (e.g., 0, 1, 2, 3). Fermions have spins that are that same constant multiplied by an odd half-integer
(1/2, 3/2, 5/2, etc.). Examples of fermions are the protons and neutrons that make up an atom’s nucleus, and Composite particles, such as nuclei and atoms, are classified as bosons
or fermions based on the sum of the spins of their constituent particles. For instance, an isotope of helium called helium-4 turns out to be a bose particle. Helium-4 is
made up of six fermi particles: two electrons orbiting a nucleus made up of two protons and two neutrons. Adding up six odd half-integers will yield a whole integer, making
helium-4 a boson. The atoms of rubidium used in the Colorado experiment are bose particles as well. Only bose atoms may form a condensate, but they do so only at
a sufficiently low temperature and high density. At their lab in Colorado, Cornell and Wieman cooled a rubidium gas down to a temperature as close to absolute zero, the temperature
at which particles stop moving, as they could get. The slower the particles, the lower their momentum. In essence, the cooling brought the momentum of the gas particles closer and
closer to precisely zero, as the temperature decreased to within a few billionths of a degree Kelvin. (Kelvin degrees are on the scale of degrees Celsius, but zero Kelvin is
absolute zero, while zero Celsius is the freezing point of water.) As the temperature, and thus the momentum, of the gas particles dropped to an infinitesimal amount, the possible locations