I took into consideration Fizeau’s experiment and . . . the truth of the Maxwell-Lorentz equation in electrodynamics . . . [that] showed to us [in] the relations of the so-called invariance of the velocity of light that those equations should hold also in the moving frame of reference. This invariance of the velocity of light was, however, in conflict with the rule of addition of velocities we knew of well in mechanics. (p. 139; brackets added)
Given the two “considerations” mentioned in this paper, the invariance of the speed of light and the indistinguishability of moving inertial systems because the laws of inertial systems are equivalent, Einstein’s rejection of Newton’s conception of space and time as absolute frames of the universe follows with stunning simplicity. This is because the presuppositions of their calculations are just the converse of each other. Since in Newtonian mechanics the lengths of measuring rods and the rates of clocks are unaffected by their velocities, two systems in relative motion measuring the velocity of another object must find different dimensions. For example, an automobile that has a velocity of 50 miles per hour as measured by a person a rest on the earth will have a velocity of only 10 miles per hour if measured by a driver traveling at 40 miles per hour in the same direction. This is Galileo’s well-known “addition of velocities” principle mentioned by Einstein at the end of the previous quotation.
The anomaly is that though this is true of all other measurements, it is not true of light since anyone, regardless of their velocity, will find the velocity of light to be the same. This can be explained, according to Einstein, if the physical measuring instruments, the rods and clocks, are not as Newton assumed and is true of the relatively slight velocities on the earth, unaffected by their velocities. But for those approaching the velocity of light the measuring rods contract and the clocks slow down in ratio to their velocities thereby explaining the identical determination of the velocity of light irrespective of their different velocities. More explicitly, since v = d/t, if the measured distance is greater because of the retraction of the measuring rod and the duration longer because of the slowing of the clocks relative to their velocities, then v will increase proportionately to produce the invariant velocity of light. The formula for determining the degree of retraction and retardation is √(1- v2/c2).74
Another consequence is that as the system approaches the velocity of light mass increases tending to infinity, which is the reason no physical system can attain that velocity and thus light is a limiting velocity. In his second article on special theory, Einstein declared the equivalence of energy and mass as stated in his famous equation E = mc2 that superseded Newton’s famous equation F = ma at greater velocities, a further transition to a different conception of reality due to the limitations of Newtonian science. It also explains the sun’s tremendous source of energy and why its gravitation force is so much greater than any other solar body because its mass comprises 98 percent of the mass of the solar system.
While Lorentz’s and Einstein’s transformation equations correlate the spatial, temporal, and mass measurements from a system at rest to one in uniform motion, German mathematician Herman Minkowski in 1904 devised a formula √{(cT)2 – R2} that gave an identical value for the duration of two events measured by systems in relative uniform motion. As explained by G. J. Whitrow:
If, according to a particular observer, the difference in time between any two events is T, this associated spatial interval is cT. Then, if R is the space-distance between these two events, Minkowski showed that the difference of the squares of cT and R has the same value for all observers in uniform relative motion. The square root of this quantity is called the space-time interval between the two events. Hence although time and three-dimensional space depend on the observer, this new concept of space-time is the same for all observers.75
It is this formula, particularly, that gave rise to the conception of the universe as a four-dimensional continuum of events, three of space and one of time, a central feature of Einstein’s general theory of relativity.
However, according to this initial interpretation, because both systems are kinematic (devoid of forces) rather than dynamic due to their being inertial, the modifications attributed to the rods, clocks, and mass in the moving system by the one assumed to be at rest are reciprocal, either system being equal as the reference point. Thus in the special theory the effects are merely apparent rather than actual. Similar to the apparent reduction in size or motion of an object seen from a distance, this effect in the special theory is referred to as the “perspective of velocity.” It is also true that what has been described applies only to electromagnetic phenomena, not to mechanical or acoustical measurements.
In the latter cases the addition of velocities law holds so that the measurements of distant events, their duration, and whether they are simultaneous are relative to the system of reference. But since the velocity of light is constant it is independent of the motion of its source and of any moving detector. In contrast to velocity, the wavelength and frequency are affected, but in such a way that their product, which determines their velocity, remains constant. But since information about any distant event requires some causal transmission such as a light signal, no effect can appear before its cause, contrary to science fiction accounts.
As indicated, in contrast to the special theory of relativity, where the relativistic effects were considered apparent because they involve inertial systems devoid of forces, in the general theory where noninertial velocities are considered, the effects are actual. French physicist Paul Langevin’s voyage au boulet introduced in 1911, known in English as “the twins paradox,” offers a striking illustration. Leaving one twin on the earth with the other boarding a spaceship that accelerates to 1/20,000th less than the speed of light, the twin on the spaceship, owing to the enormous gravitational effect generated by its tremendous acceleration, will have aged two years, while the twin on the earth would have died during the two centuries that had elapsed on the earth.76 More recently these effects have been confirmed in precise experiments using clocks placed in jet aircrafts circling the earth indicating that the lifetimes of radioactive particles were extended by their greater velocities. Presently, the extreme velocities of the subatomic particles in physics have led to their being incorporated into relativistic quantum field theory.
Not satisfied with the restrictions imposed in the special theory by limiting the relative motions to inertial systems, in the general theory published in 1915 Einstein extended his investigations to nonuniform motions involving forces, but with the same intent of extending his explanations to new dimensions while also attaining greater uniformity and simplicity in the laws of nature. In these endeavors he did not utilize empirical experiments but ingenious thought experiments, such as comparing the effects of being in an elevator falling at the same rate as gravity (so that the free fall cancels the effect of gravity) to being suspended in a gravitational free region of outer space to demonstrate their inertial equivalences; or comparing the effect of being in a gravity free elevator in outer space with being pulled upward with the same accelerating force as an elevator on the earth to show their equivalence.
By these thought experiments he intended to demonstrate the equivalence of gravitational and accelerated motions by merely shifting one’s frame of reference, similar to mass and energy being equivalent. In another thought experiment he described falling from the roof of a house and releasing objects of different weights as he fell, concluding that since the falling objects were in the same gravitational field they would seem stationary relative to himself regardless of their weights. As he wrote in an unpublished paper in 1907:
The gravitational field has only a relative existence in a way similar to the electric field generated by magnetoelectric induction. Because for an observer falling freely from the roof of a house there exists—at least in his immediate surroundings—no gravitational field. Indeed, if the observer drops some bodies then these remain relative to him in a state of rest or of u
niform motion, independent of their particular chemical or physical nature (in this consideration the air resistance is . . . ignored).
The observer therefore has the right to interpret his state as “at rest.”77
In the same article he refers to this realization that the “gravitational field has only a relative existence” as “the happiest thought of my life. . . .”
As further vindication of this study showing how science has transformed our conceptions of reality, in 1931 he declared this to be true of Maxwell’s field theory:
Since Maxwell’s time, Physical Reality has been thought of as represented by continuous fields . . . not capable of any mechanical interpretation. This change in the conception of Reality is the most profound and the most fruitful that physics has experienced since the time of Newton.78 (italics added)
It was his dream that all the diverse explanations could finally be reduced to one set of laws in a unified field theory to which he dedicated his life—though it eluded him.
While the unification of the electromagnetic force with the strong and weak nuclear forces in the projected grand unified theory (GUT) has partially vindicated his dream, other unifications would prove elusive or unattainable, such as the reduction of gravity to electromagnetism and the elimination of the uncertainties in quantum mechanics. But his emphasis on simplicity, generality, and elegance in the formulation of theories has been enhanced by the recent discoveries of symmetries.
His correct predictions at the end of his 1918 article on the general theory of relativity of the precession of Mercury, the red shift due to the recession of stellar bodies, and especially photographs of the telescopic confirmation by British astronomer Arthur Eddington of the bending of light during a solar eclipse in 1919, and the more recent prediction of black holes from his theory support his claim to have created, at least partially, a new physical reality to replace Newtonian mechanics.
Chapter VII
CONSTRUCTION OF THE ATOM IN THE TWENTIETH CENTURY
Yet the full account of the revolutionary developments in the twentieth century still has not been related, such as the inquiries leading to a more precise conception of the interior structure of the atom. In England one of the first attempts was the “plum pudding” model of J. J. Thomson that consisted of a positively charged mushy sphere on which the negatively charged electrons were embedded, like plums in a pudding, so that their exterior negative charges balanced the positive charge of the mushy interior producing a neutrally charged atom. Among the obvious faults of this model was his attributing the mass of the atom not to the interior substance, but to the exterior electrons, which would prove to be the reverse of the actual structure.
Rutherford, who began his research under Thomson and later would succeed him as Director of the Cavendish Laboratory, having left Cambridge for Montreal, now accepted a position in Manchester, England, were he conducted his own more sophisticated experiments to investigate the interior of the atom. Working in an excellent laboratory and aided by two talented assistants—Hans Geiger, who would invent the Geiger counter for measuring radiation, and Ernest Marsden, who had emigrated from New Zealand to study with his famous compatriot—Rutherford, decided to use his discovered α particles with their positive charge, large mass, and great velocity to probe the interior of the atom.
Instructing his assistants to radiate α particles at thin gold foil and measure the percentage of deflections striking a scintillating screen set at various angles, they found that most of the particles passed directly through the thin foil with a few deflected at slight angles by the presumed existence of the interior atoms. He then suggested that Marsden alter the angle of the screen to see if any of the α particles would be deflected at a greater angle and was astonished when Marsden reported that a few had actually been deflected straight backward to the eyepiece, as if they had been repelled by some massive component within the interior of the gold foil. As an indication of his astonishment, Rutherford described his reaction as “quite the most incredible event that has ever happened to me in my life. It was almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you.”79
Undeterred by his astonishment, he began experiments to find a more precise explanation of the cause. Based on the measurements of the percentages of deflections at various angles, he devised a formula for measuring the angles of deflection, the velocity of the particles, and their charges. He also conceived of the nucleus as consisting of particles of a certain mass, along with a positive charge calculated by his formula indicating the atomic number of the element. Accordingly, he defined two of the properties of the nucleus, the atomic mass and the atomic number, that were independently confirmed by J. J. Thomson and H. G. J. Moseley based on X-ray emissions from the atom.
Apparently, from these X-ray emissions it was inferred that the atomic nucleus was surrounded by the negatively charged electrons, which are relatively massless, about 9 × 10-28 g, or 1,836 times less than that of the proton, but whose shells occupy most of the volume of the atom confirming an earlier conjecture by Jean-Baptiste Perrin in 1901 that the structure of the atom might resemble the solar system:
Each atom might consist . . . of one or more positive suns . . . and small negative planets. . . . If the atom is quite heavy, the corpuscle farthest from the centre . . . will be poorly held by the electrical attraction . . . . The slightest cause will detach it; the formation of cathode rays [electrons] will become so easy that [such] matter will appear spontaneously “radioactive. . . .”80
Indicative of how much progress was being made in explaining the structure of the atom Segrè states that the
new science of X-ray spectroscopy not only allows the study of deep electron shells and elementary chemical analysis on an unprecedented level of sensitivity and certainty: it also opens the way to the exploration of crystalline lattices and, more generally the architecture of solids and of molecules.81
It was decided that electrons in the outer shell cause the visible spectra, while the electrons in the inward shell are the source of the X-ray spectra. Apparently, it was Moseley’s and Thomson’s induced X-ray spectra that provided the evidence for the electron shells and Moseley who determined that the electron shells are related to the nuclear charge, thus providing independent evidence of the atomic number.
Becoming convinced that the experimental evidence supported his calculations, Rutherford presented his results first to the Manchester Literary and Philosophical Society in March 1911—the same society to which Dalton had submitted his atomic theory—and then sent a more detailed account in May to the Philosophical Magazine followed by another article entitled “The Structure of the Atom” in February 1914. Though he was unable to explain the exact causes of either atomic stability or radioactive instability, his conception of the composition of the nucleus and structure of the electron orbits was sufficient to enable physicists to formulate a clearer notational designation of the nuclear components and properties of the atom. For example, depicting the charge as plus or minus e and the number of the charged units as Z, then +Ze stood for the total charge of the nucleus with –Ze representing the total charge of the number of electrons in a particular atom.
Thus if there is an equal number of +Zes and –Zes, the charge of the atom is neutral, while ionization consists of the loss or gain of electrons and radioactive transmutations as a change in the nuclear number due to the emission of α, β, or γ rays. As Ne’eman and Kirsh state:
While emitting an alpha particle, the nucleus loses electric charge of +2e and a mass of about 4 amu. The process, which is also called alpha decay, or disintegration, lowers the atomic number Z by 2, and the mass number A by 4. The equation representing the alpha decay of uranium 238, for example, is: 92U238 → 90 Th234 + 2He4.82
Since the number of –Ze represents the number of electrons in the atom, which accounts for the chemical properties, it also indicates its place in Mendeleev’s Periodic Table. Since in ne
utral atoms the number of +Zes equals the number of –Zes, isotopes are atoms with identical chemical properties but different atomic weights. Yet while the chemical properties were attributed to the electrons, it still was not known what accounted for the nuclear numbers and weights. In 1919 Rutherford had discovered that when an a particle interacts with a hydrogen atom a hydrogen nuclear particle is ejected, but did this mean that atomic nuclei were all hydrogen nuclei?
After a number of experiments probing the nuclei of other atoms produced the ejection of the same entity, physicists decided they had discovered the first nuclear particle, naming it “proton,” after the Greek word protos meaning “first.” But they were still puzzled by the fact that the number of the nuclear particles of an atom did not match its mass or atomic weight. However, when James Chadwich, at the Cavendish Laboratory, probed the nuclei of lighter elements, such as beryllium, he discovered that a new particle was ejected that was quite massive but neutral in charge. Determining the mass of the particle to be nearly that of the proton and finding that it had a neutral charge, for obvious reasons he named it a “neutron” and received the Nobel Prize in 1935 for his discovery. Thus the discovery of subatomic particles was resolving many problems at a stroke, as Ne’eman and Kirsh affirm.
Three Scientific Revolutions: How They Transformed Our Conceptions of Reality Page 17
