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atom, as well as of the older quantum theory in general, are superseded by the far more natural idea of de Broglie’s wave phenomenon.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 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.