SUPERFICIALLY considered, art and science appear to stand at opposite poles. One confines itself largely to spiritual and emotional values; the other deals directly with the concrete, precise and measurable. Yet it is not uncommon to find individuals with strong interest and even talent in both art and science. Judging by the correspondence that reaches this department of SCIENTIFIC AMERICAN, many artists turn to science for their avocation.

Douglass Crockwell, a professional painter and an amateur physicist, is a case in point. Crockwell's paintings have decorated the covers of leading U. S. magazines for the past quarter-century, and his scientific speculations have attracted the interest of physicists.

"The artist," writes Crockwell, "can no more escape the temptation to look for order in his sense-data than the physicist can ignore the esthetic qualities inherent in both his materials and his equations. The physicist and the artist strive toward a common goal. The concept of space, for example, is the special creation of the physicist. The portrayal of its nature is the problem of the artist.

"My active interest in physics grew naturally out of abstract painting. For 18 years I have been producing abstract animated films for little-theater audiences, and for 15 of those years I have been trying to develop an acceptable visualization in a motion picture of matter and energy as conceived in modern atomic physics. The motion picture is still just a dream. But I have had 15 years of fun trying to paint an object capable of behaving simultaneously as though it were a microscopic particle and a macroscopic wave.

"Experimental evidence indicates at least 20 different subparticles below the atom with as many different associated fields. Esthetically and intuitively, how ever, it is felt that there should be but one general particle with one general associated field, and that from these, all individual particles and fields should be derivable as special cases. Unfortunately the mathematicians, whose quantum scaffolding so well encloses the atom, do not have another Fraunhofer ladder to bridge the mysterious gaps between the various particles. Their dedicated floundering has brought the charge from many educated but nonscientific persons that the physics of our day has become absurd, a view shared by at least a few of the scientifically educated. Louis de Broglie, for example, feels that physics is in urgent need of a more down-to-earth structure for its fundamental particles. Physics, he says in his The Revolution in Physics, 'has found itself very much hindered by the exclusive use of the statistical psi wave to describe the particles. It prohibits the use of any structural image for these particles. It is permissible to believe that a change in viewpoint embodying a return to spatio-temporal images will help this situation.'

"In attempting to account for conflicting sense-data derived by experiment, our formal logicians have withdrawn ever farther into the realm of abstraction until, in adopting Heisenberg's principle of uncertainty, they have even placed a restriction on what it is possible for man to know. Herbert Dingle, professor of history and the philosophy of science at University College in London, sees the current dilemma as a product of confusion between sense-data and postulates. He calls attention to the sharp philosophical distinction between the green glow on the face of an oscilloscope as reported to the brain by the eye and the concept of the electron that was invented by man's imagination to account for the glow. The electron, he points out, is not necessarily an independently existing physical object. Certain sweeps of a pointer across a dial can be accounted for if a something exists in the form of a wave. Certain sweeps of other pointers across other dials can be accounted for if a something exists in the form of a particle. The dilemma arises, says Dingle, when we insist that both 'somethings' must be the same thing and then compound our befuddlement by attempting to confer upon these incompatible postulates the independent physical reality reserved by nature for our sense experiences. It strikes me as fortunate that the electron is not necessarily an independently existing 'thing,' but merely an invention of reason. We may discard it with impunity-as we discarded phlogiston and the luminiferous ether- without impoverishing nature in the least. The question is, what is to take the electron's place? With fingers crossed, I offer the following generalized particle-field.

"It seems reasonable, as a first thought, to accept each particle-field relationship as an inseparable something, which is perceived sometimes in one fashion and sometimes in another. We might also think of the particle portion of the effect as that which is received along the course of particle-field motion and the field portion of the effect as that which is experienced radial to the course or potential course [see illustration above left]. We know that some relationship of this sort exists, whether or not it is exactly as stated. Variation of one effect is accompanied by a reciprocal variation in the other effect. In other words, the more the particle-field manifests itself as a particle, the less it manifests itself as a field, and vice versa. Further, the intervention of another particle-field produces a potential state of variation.

"We also know that charged particles in motion exhibit a 'sense' or quality of right-or left-handedness which characterizes their charges. The field of a 'negative' particle seems to match the field of another negative particle when the two are in like parallel motion. This is also a property of positive particles. Fields of unlike charge seem to match when the particles move in opposite directions. From this we can infer a kind of tangential motion in space around the course of a particle-a motion which differs between particles of unlike charge. But we have learned to reject the idea of flow around the moving particle. Is another type of circular motion possible and, if so, would it not make an interesting starting point for our model?

"In consideration of these observed tangential field qualities, I should like to suggest a three-dimensional field in which every point describes a continuing motion of circular translation. Some of the fields are to be in left translation and others in right translation. Translation, strictly defined, is a form of motion in which all points of the moving body have the same velocity and direction at any instant. Strict circular translation can be demonstrated in two dimensions by placing a sheet of paper on a smooth desk top and rotating it by hand without losing parallelism between the edge of the paper and the edge of the desk top [drawing at right]. All points in my particle-field concept will have a similar circular motion but, since the response of the field is not instantaneous, the phase of rotation will vary from the center outward [drawing below]. In the latter illustration the circular translation has been sketched as arrow-tipped rectangles in order to indicate more clearly the lag in rotation of various areas as the field is explored along a radial path from the center. It is important to remember that the field does not rotate as a unit. The areas of the field vary only in the diameter and the phase of translation. As the field is explored from the center outward, the phase of rotation lags progressively. Hence its structure can be considered as a series of concentric phase shells, each 360 degrees out of step with adjoining neighbors.

"The field and particle are one, and at all points the action is similar. The diameter of translation is greatest when the particle is at relative rest. An increase of particle-field velocity is accompanied by an increased rate of rotation but a smaller radius of rotation In other words, with increased velocity, a specific point in the field rotates faster and describes a tighter circle. Outer regions of the field are characterized by similar translation but of lesser amplitude, and the lag in phase progresses radially with the velocity of light. As previously noted, shells of like phase, but each lagging 360 degrees, exist concentrically throughout the field. The greater the relative particle velocity, the more rapid the circular translation, the less the radius of translation and the closer the spacing of like-phase shells. The term 'frequency' may be applied to the density of the shell structure, and the shells may be thought of as standing wave fronts-but not as electromagnetic waves.

"The greater the phase frequency of the field, the greater will be the apparent mass or velocity of the particle. Momental mass is a property shared by bodies in relative motion, and appears in the field as a frequency shared by the two bodies. A single particle in a free space could have no velocity, momental mass or phase frequency. Absolute assignment of the portions of the shared frequency is impossible. Actually no difference appears between rest mass and momental mass in the observed field structure. When observed as a proton, the particle-field has a relative rest frequency 1,835 times that of a particle-field in opposite rotation which is observed as an electron [drawings above right]. These two particle-field states are in effect stable. The charged meson states, however, are unstable, and may represent distortions of the basic electron and proton states.

"Neutral particles are all believed to be multiplets of charged particles in rotative association, as shown in the drawing at the right. In atomic groups this is generally true. In the neutron and neutral mesons this is less certain, but may be indicated by the decay products. Within the neutron (and mesons) the basic proton and electron particle-fields (of which they are composed) are probably subjected to field distortions so extreme as to render them temporarily unrecognizable.

"Particle-field distortions occur when environmental restrictions prevent a complete reciprocation of particle and field effects. Thus we may have, if external motion is restricted, an abnormal phase frequency which might be interpreted as displacement current, electric field potential or excess mass. If internal tension reduces the phase frequency to less than it should be according to external velocity, then mass defect is observed (or a meson).

"Just why all protons should have one translation and most electrons another is not understood, although some system of priority exclusion may operate. Just why there should be two stable mass levels is also not understood, but these are problems shared by all theory.

"Particle motion always takes place along the axis of circular translation as the particle-field passes through other environmental fields. The fields appear to exert a combing action on one another. (One particle in a free space could conceivably have any external motion.) Particle-fields of opposite circular translation (that is, of unlike sense conjunction) tend to move apart. Particle-fields of like sense conjunction tend to move in parallel paths. A proton and an electron follow parallel paths when moving in opposite directions or rotating about one another, and two electrons do so when moving in the same direction. There is a tendency for the spacing to remain constant. Acceleration of both particle-fields causes them to move together. Deceleration of both causes separation.

"Passage of one particle-field through another of like translation results in a matching adjustment between the fields. This adjustment is oscillatory, and, if the contact is short, most of the frequency (phase-shell spacing) shifts from one field to the other. If the contact is extended, the fields may nearly match and share the total frequency and external motion. Under the Pauli exclusion principle, however, their field states could not be identical. This could be a picture of energy partition or transfer through induction. With trivial differences, it could also be a picture of energy transfer through classical particle contact. In a closed system the total frequency of the particle-fields is constant and shared mutually.

The fields of a proton and an electron revolving about one another on their respective sides of the axis at the center of mass would have, in effect, the same direction of circular translation or sense. The much greater radius of the electron would contribute just enough velocity, and hence momental mass, to establish a stable, rotating system. In the absence of external influence, the field mesh would, therefore, remain constant and the pair would continue in stable rotation indefinitely. An approaching external field or changing portion of field would cause a change of frequency, first in one and then in both particle-fields. A remeshing would be required to maintain the stability. The nearer the particle-field centers approach one another, the greater the b:, environmental change necessary to alter a'~ the meshing. A limiting or normal state is implied.

"At each remeshing of the fields, areas of intensification and interference shift throughout the two fields. These areas are most prominent along a common radial line. They move outward at the velocity of light. With oscillatory adjustment of the particle spacing, these areas change periodically, and may be thought of as electromagnetic waves or photons.

"In a more complex atom than hydrogen, the protons and electrons might be again visualized moving in a single -orbital plane. Fields would all be oriented to this plane. Thus all fields would mesh in the same sense or direction of circular translation. Certain particle-field distortions would occur because of the complex adjustments needed. In the complex atom, the orbit of neutron doublets would be located in the common plane of the atom, probably nearer the axis than the protons. The whole complex phase- frequency mesh would revolve as a unit with the relative motion of negative and positive particle-fields compensating for individual differences of sense translation. Energy transfer can take place on between shells of like phase or between harmonics arising through interference between these shell states. Obedience of energy-state transition to the laws of quantum mechanics is implied. Binding energy would appear as a mass defect caused by particle-field distortion.

"This atom would seem to have the simple geometry necessary for building molecular lattices. In addition, it has the attractive feature of demanding no mysterious and unknown pair of field forces-or to keep electrons from collapsing upon the nucleus and one to prevent the explosion of protons in the nucleus.

"Here, then, is a proposed model which appears capable of accounting for at least some of the conflicting sense-data reported during the past half century by experimental physicists. The approach is certainly nonprofessional and nonmathematical-perhaps noncerebral also. It is hoped that the results are not too contradictory as far as known experimental evidence is concerned. Perhaps this attempt, even though it is an amateur one, will encourage others to try. In defense of models generally I submit a line from the great James Clerk Maxwell's preface to his theory of electromagnetic radiation: 'In several parts of this treatise, an attempt has been made to explain electromagnetic phenomena by means of mechanical action....' "

IS there any justification for low-grade optical workmanship? In last month's issue James L. Russell of Cleveland, who has taught hundreds of amateurs to make their own telescopes, described one justification-expediency. He had observed that many beginners bogged down and quit before finishing their first mirror, in the mistaken belief that a less than perfect mirror would fail to function. He was able to increase the percentage who finished by deliberately for perfection, since even a poor mirror will perform well enough to please its owner for at least a season until his observing skill has become sophisticated. I described Russell's practical methods of teaching the art and promised to explain in terms of physical optics why even a poor mirror will work, to give a revised criterion for good mirrors and to show why an experienced observer needs one. What follows is not an over-all letting-down in standards but the provision of several widely differing standards for different observers' needs.

It has been said many times that in any reflector the famous Rayleigh criterion calls for precision of the surface to one eighth of a wavelength, or one 400,000th of an inch. So often has the term "good, honest, eighth-wave optics" been used in speech and writing that many have supposed it an inexorable standard. Actually the tolerance is relaxed at the outset to one 200,000th of an inch by the fact that in use of the mirror the eyepiece may be adjusted to an average focus. This is explained by F. B. Wright and by J. R. Haviland in the Amateur Telescope Making books. Alan E. Gee now explains it graphically [drawings left]. He writes: "In the first diagram, the curve being hyperboloidal, the observer automatically focuses the eyepiece at the best focus, b, where the circle of confusion is smallest, ignoring a. In the second the curve is spherical (undercorrected mirror) and he again selects b instead of a. For regular undercorrection or overcorrection this ability to focus results in a reduction of the effect of the spherical aberration by a factor of four. For the effect of zones no such statement can be made. The observer will still work at best apparent focus; however, where this will be, and how good it will be, depend upon such factors as the relative area or areas of the zones producing the errant rays, their intercept on the optical axis, and their angular subtense. Based on the Rayleigh limit, Wright's tolerances in Book One are all too stiff by a factor of two. A six-inch mirror is about at the Rayleigh limit if left spherical at f/8. I suspect more of these f/8 mirrors are worsened by attempted parabolization than are improved."

In this fundamental matter, governing all amateur telescope makers' exertions, Wright now assents with Gee and others who have challenged his standard as too exacting, saying, "I based my limits on smooth curves of surface viewed from the position of best average focus, then made the limits twice as strict as this calls for to take care of imperfect measurements or imperfect focusing, and from just plain conservatism."

Other reasons why poor mirrors work well enough to please uncritical users are: (1) A novice observer is likely to look most often at the moon, because it is such a spectacle, and, as Horace H. Selby has pointed out in Book Three, with a low-powered eyepiece almost any telescope will give a good impression of the moon, because the iris of the eye contracts so strongly under the high illumination that the aberrations have little effect on the sharpness of the image. (2) On many nights the turbulence of the earth's atmosphere tends to reduce the observational difference between a fine mirror and a poor one.

These reasons may seem to provide an alibi for sellers of poor telescopes As a matter of fact, the complaint against such merchants is not that their instruments are too poor for use by the average beginner but mainly that their claims of precision sometimes are too strong.

Having dealt with the soft side of the Rayleigh limit at least as generously as the facts of physical optics permit, let us now climb over the fence into the rarefied realm of the perfectionists. True as it is that few observers are expert enough and few nights of seeing good enough to exploit the superiorities of a fine mirror, for many amateurs much of the enjoyment of the hobby consists in the pride of achieving a precision within one millionth of an inch. The amateur telescope makers' chief contribution to science has been in producing precision optical instruments.

Furthermore, precision is not to be belittled even when it comes to ordinary use of the telescope. The one kind of observing for which it is profitable to approach and surpass the Rayleigh limit is the close observation of fine detail on the moon and planets. And this is just what most interests the average amateur. The detail is made visible by contrasts between adjacent areas. Without the contrasts there is no detail, and all is flat. These contrasts are heightened in proportion to the quality of the telescope. This can be proved by physical optics but observing demonstrates it dramatically. Here J. R. Haviland's statement in Book Two that perfection beyond the Rayleigh limit will not noticeably improve the image is inadequate. It has been shown that, for the faintest perceptible contrasts, the efficiency of a mirror rises from 62 per cent when corrected to the Rayleigh limit, to 92 per cent when the correction is carried to one fourth of that limit. The optical designer James G. Baker says in a private communication: "At very low contrast levels, such as obtain on the planetary disk, a mirror made as poorly as the Rayleigh limit will not perform well and a much better mirror should be the goal. Recent research has refined the rule-of-thumb tolerances expressed by Conrady in favor of more exact rules. French observations in the laboratory indicate that there is no real lower limit to the accuracy requirements for the observation of maximum contrast of faint details. For example, if the contrast level is as low as 1.01 to 1, it may be necessary to have the optical system perfect to within one fiftieth of a wavelength. Any amateur sincerely interested in a high quality mirror is likely to continue, as at present, seeking the best curve he can obtain."

Related observations and experiments have been made by André Couder and Jean Texereau. Couder is astronomer at the Observatory of Paris and co-author with André Danjon of the basic work Lurrettes et Télescopes. Texereau began as an amateur in 1933 with Amateur Telescope Making and is now a professional optician, one of his most recent pieces of work being a 24-inch Cassegrainian for Meudon Observatory, another a 20-inch Cassegrainian with its secondary supported on a plane-parallel glass plate instead of an obstructing spider. He is the author of La Construction du télescope d'amateur and leader of the amateur telescope-making group of the Astronomical Society of France. The upper photograph on the preceding page is a Foucault focogram from an eight-inch f/6 mirror he figured.

Couder and Texereau have studied the harmful effects of extremely small mirror defects, using a powerful optical lever-a phase-contrast photographic method of testing devised by the French astronomer Bernard Lyot. The Lyot test clearly discloses defects only one 500 millionth of an inch deep-one half angstrom!

The photograph above left is a Lyot picture of an ordinary five-inch mirror polished on a pitch lap painted with wax. The crosswise strip is the image of the photometric wedge used in the Lyot test. This test employs the basic Foucault setup, plus a phase plate and camera, but unfortunately requires that the mirror be made of optical glass because of the striae in plate glass and Pyrex. The prominent streaks are striae within the glass and must be ignored. Remaining are myriads of tiny defects about one 100-millionth of an inch deep. Not one of the little bumps (together called micromamelonnage) would be even faintly visible with the visual Foucault test, and this glass would have a featureless polish if directly examined with a 40-power microscope at the reflection from a concentrated light beam. Nevertheless these defects diffract enough light to lower a mirror's efficiency when used in observing faint contrasts on the moon or planets.

The two photographs at the right compare a focogram with a picture of the Lyot type, which we might call a "Lyot-gram." The upper picture is a focogram four times magnified, near the edge of a typically lumpy surface polished with HCF. It shows a mottled surface. Below it is a Lyot-gram of the same area; it reveals the depth of the micromamelonnage to be about eight 100-millionths of an inch.

The phase-contrast method has also proved that polish on paper with rouge, on waxed pitch with rouge and on pitch with cerium oxide or with Barnesite gives smoother surfaces than polish on HCF. The smoothness is in the order named. None of these gives nearly as smooth a surface as pure unwaxed pitch with rouge, especially when the final "wet" is almost completely dried up.

Our investigation of the easy and difficult sides of the Rayleigh limit has shown that there is no cut-and-dried standard of quality for a telescope mirror. Instead there must be a separate standard for each observer. A rather poor mirror will give pleasing images of stars and nebulae and of the moon and planets when viewed as a whole. But those who wish to resolve close double stars or observe details on the moon and planets, as well as those who take pride in their workmanship, will not aim at anything less than perfection.

Bibliography

THE SCIENTIFIC ADVENTURE: ESSAYS IN THE HISTORY AND PHILOSOPHY OF SCIENCE. Herbert Dingle. Philosophical Library, 1958.

AMATEUR TELESCOPE MAKING. Edited by Albert G. Ingalls. Scientific American, Inc., 1952.

AMATEUR TELESCOPE MAKING-ADVANCED. Edited by Albert G. Ingalls. Scientific American, Inc., 1952.

AMATEUR TELESCOPE MAKING-BOOK -THREE. Edited by Albert G. Ingalls. Scientific American, Inc., 1953.

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