Mildred Catherine Benton

“ The Kennedy-Thorndike experiment does not afford a confirmation of the Lorenz transformation for time, but shows that light behaves as an ideal clock. The statement that relativity has caused a fusion of time and space is not true; the conformability of light to Newtonian mechanics, established by the Michelson-Morley and Kennedy-Thorndike experiments, makes it possible to define corresponding units of space and time in terms of light. ”

“ Current interest in the possibilities of space flight and the prediction that atomic clocks in earth satellites may be utilized to check Einstein's theory have focused attention on the clock problem in relativity, or the so-called time-traveler paradox and its implication. General theory holds that a precise clock will run more slowly at extreme altitudes than an earthbound clock because of differences in gravitational fields. ”

“ Modern speculations concerning the nature of time and space are discussed, and it is pointed out that the space-time world of the relativity theory is merely an artificial image. The two different ideas of time of the relativity theory are solely consequences of physically unfounded transformations of the coordinates of the image, or of unjustified applications of the theory of invariants. ”

“ In view of the paucity of experimental tests for the general theory of relativity, it is desirable to consider the uses to which a satellite vehicle could be put. The advance of the perigee is calculated similarly to the perihelion advance of Mercury; it amounts to only 15 seconds of the arc per year. However, the effect on a satellite clock is large and could be measured. With respect to an earth clock it is calculated to be a "red shift" for low-altitude orbits, zero shift for an orbit of one-half the earth's radius, and a "violet shift" for higher altitudes, where it approaches 7 x 10-10. ”

“ From the laws of classical mechanics, there would follow that the limited human lifetime and the limited mass-ratio of the rocket would permit ranges of some tenths of light years, i.e., over a very limited space of our galaxy and to the very next fixed stars only. ”

“ Although these discontinuities occur at points of discontinuity of the metric tensor, examination of a case in which the gravitational field is turned on smoothly reveals that the effect is a real one within the framework of the general theory of relativity. By the principle of equivalence, it follows that even in a real gravitational field when that field changes in time velocity, dependent terms in the acceleration of a particle exist. These become impulsive for abruptly changing fields and can even cause acceleration in the direction "opposite" to the field. ”

“ Circumstantial evidence for the contraction of a moving rod is given by the Michelson-Morley and other experiments; there is no evidence for the definite retardation of clocks. There is in physics, no explicit definition of a clock. By consideration of a clock of hour-glass type it is shown that the ratio of time intervals recorded by stationary and moving clocks is different according as the interval is measured by the number, by the total weight or by the total volume of similar particles falling into a receptacle. ”

“ As a consequence of this general solution, it is shown that a moving body, on becoming free from strain, immediately undergoes the exact Lorentz contraction, without the intervention of any forces of unknown origin, the necessity of which has been postulated by some relativists. The author next proceeds to deal with the so-called clock paradox. He takes the case of the observer A at rest in an inertial system, his world-line being OA, perpendicular to OX, the x-axis. ”

“ According to the leading cosmological theories, intergalactic space is spherical, the radius of curvature varying with time. According to Eddington, there are only two ways to account for the large speeds of recession of the spiral nebulae, they are produced either by a scattering force, (called cosmical repulsion) , predicted by the general theory of relativity, or the receding velocities now observed have existed from the beginning. For completeness, he advances as a third possibility an oscillating model of the universe. ”

“ The bearing of the relativistic contraction of time on this problem has been questioned, since it leads to an apparent paradox, but the best opinion is that the contraction would occur and that the returning astronaut would, in fact, find that time has gone more rapidly on the earth than in his space ship. ”

“ This writer contends that "there is no doubt whatever that the accepted theory of relativity is a complete and self-consistent theory and it quite definitely implies that a space-traveler will return from his journey younger than his stay-at-home twin brother." ”

“ A space-space representation is developed for nonrelativistic wave mechanics as was done for classical mechanics, by adding to the system a rotating body to serve as a clock, and applying the time-independent forms of the equations of motion. ”

“ Each observer will use his own length and time scales to determine their relative movement. They will agree as to the speed at which they are approaching or receding from each other, but the time at which they record the happening of some outside occurrence will not necessarily be the same for both of them. ”

“ The theory is not basically concerned with a comparison between different observers but between different coordinate systems which are available to a single observer. (2) It is not basically concerned with a comparison between stationary and moving systems but between descriptions of a single system with respect to different arbitrarily chosen standards of rest. (3) The familiar expression, "time retardation," does not relate to a physical change experienced by a clock but to a comparison of times of an event by two clocks, at least one of which is not present at the event. ”

“ Freely moving bodies move according to the inertia law, clocks and measuring rods behave according to the laws of the special theory of relativity. The local inertial systems have a relative acceleration with respect to each other, and it is in general not possible for a finite region to make a transformation of the gravitational field. ”

“ The customary form of physical space as the direct product of space-time and isotopic spin-space can be replaced by a certain fusion of these two spaces into one space if one widens the group from the Lorentz group to the conformal space-time group which endows particles with an intrinsic finite size. ”

“ Implication is that, of two observers who part company, travel with a relative speed, and rejoin one another, one will record a shorter lapse of time than the other. Thus, a time advantage will exist for the traveler on an extended voyage. The question naturally arises, Will space travel lengthen life? Some experimenters vouch that it will. Others debunk such a theory.
Einstein first introduced the clock paradox in 1905, although Michelson touched upon the subject in a report of his experiments in 1882. ”

“ The space-time interval between neighboring events for an observer moving with a particle is expressed in terms of the coordinates of an observer at rest relative to the center of spherical symmetry of a gravitational field. ”

“ The corrections to be applied to the readings of clocks in motion in order to realize the readings of an ideal clock if it were set moving are almost as various as the constructions themselves. The transformation formula for t is a logical consequence of that for x; it is the necessary consequence if Newtonian mechanics is to hold good for uniformly moving systems despite the change in x. ”

“ The behavior of clocks during travel in the curved space-time of the general theory of relativity is discussed, and effects observable in journeys in the solar system or on earth satellites are examined. ”

“ The equations of motion in Birkoff's flat space-time theory of gravitation are solved to the first order of approximation for small velocities. A particle moving approximately in a circular orbit is found to have a small acceleration perpendicular to the plane of the orbit. ”

“ The familiar "traveling twin paradox" is discussed in a particularly simple manner, using special relativity only. The asymmetrical aging of the twins is predicted using only the relativistic definition of simultaneity and the relativistic time dilatation. ”

“ The Lorenz contraction and the clock paradox.
"The author continues the investigation, begun in a former paper, of a rod moving in an inertial field in such a manner as to remain either unstrained or without change of strain, and illustrates graphically some of the conclusions. He obtains a general solution of the case in which a body receives acceleration not with consequent strains, but by the application of an impulse, such as might be communicated to a train by a push from a locomotive, so that after the dissipation of the resulting strain waves, the motion becomes steady. ”

“ In order to make definite the concept of the physical continuum discussed at length in the paper, coordinates have to be introduced. Such a continuum can be constructed from a finite number of observations, provided that the distance between two adjacent points is represented by a definite quadratic differential form of the relative coordinates dx: in this case any infinitesimal rigid point system can move freely throughout the continuum. The only continuum throughout which any rigid point system can move freely is the Euclidean continuum. ”

“ From the laws of relativistic mechanics, however, follows for those very neat optic-velocities a considerable dilatation of proper time on board of the vehicle relative to the terrestrial time, so that life of the crew and action of the rocket-motor occur slower, than would correspond to terrestrial time scale. ”

“ From this follows that within the life span of the crew and with limited mass-ratios of the rocket, every thinkable distance in space, up to nebulae millions of light-years distant can be covered, so that, expressed in technical terms, and from the standpoint of the crew, the vehicle seems to be able to move with considerable super optic-velocity. ”

“ A general discussion of the meaning of motion is undertaken. A distinction is made between the kinematic description of motion, in which forces are distinct from the space-structure, and the dynamical, in which forces play no part, but alterations in space-structure control the motions of bodies.
221. Subotowicz, M.⁠SATELLITES FOR CHECKING EINSTEIN'S RELATIVITY THEORY. Missiles and Rockets 2:57-59, illus., Feb. 1957. According to time-lengthening theories in Einstein's general theory of relativity, a clock in an earth satellite would run more slowly than one at relative rest on earth. ”

“ The author convicts, by quotations, even such experts as Einstein and Eddington of confusing the minds of readers of their popular writings on relativity by the use of language naturally interpretable as ascribing physical reality to the supposed behavior of the purely conventional contracting measuring rods and compensating clocks assumed for the purpose of popular explanation. ”

“ A distinction is made between the "postulate of relativity" and the "postulate of constant light-velocity," the former being taken to imply that if two bodies separate and reunite, there is no observable phenomenon that will show in an absolute sense that one rather than the other has moved. The claim that the second postulate involved no asymmetry is reiterated.
51. Dingle, Herbert.⁠THE CLOCK PARADOX IN RELATIVITY. Nature 180:1275-1276, Dec. 7, 1957. The writer has repeatedly pointed out that symmetrical ageing is an inevitable requirement of the postulate of relativity. ”

“ For the benefit of those who may wish to investigate further, or for those who have only a cursory interest, annotations indicative of the contents of each item are included. Whenever abstracting publications are quoted, the source is stated. It is believed that the majority of items are available for consultation in the larger public, or research libraries. ”

“ The experimental discovery of the dependence of length on velocity affects the whole of physics, and its effect is to show that certain conceptions thought to be independent and necessary are actually different forms of others already adopted. These results in no way remove the dependence of laws of physics on experience.
55. Dingle, Herbert.⁠RELATIVITY AND SPACE TRAVEL. Nature 177:782-784, Apr. 28, 1956. Calls for a re-examination of assumptions. Refers to ideas expressed by Sir George Thomson in his book "The Foreseeable Future;" and by W. H. McCrea, P. S. Epstein, and Einstein. ”

“ From the philosophical standpoint the importance of these revised equations lies in the fact that they dissipate the logical impasse and the mysticism which have been long associated with this subject. Also of philosophical import is that with the abandonment of the "principle" of the constancy of the velocity of light, the geometries which have been based on it, with their fusion of space and time, must be denied their claim to be a true description of the physical world.
127. Jackson, J.⁠SHORT CLOCKS AND THE EARTH'S ROTATION. Roy. Astron. Soc. Mon. Not. ”