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Radioactive Decay Series

Lorentz transformation equations, anomalous result, Michelson-Morley experiment, beta factor, classical physics

In 1905, Einstein published the first of two important papers on the theory of relativity, in which he dismissed the problem of absolute motion by denying its existence. According to Einstein, no particular object in the universe is suitable as an absolute frame of reference that is at rest with respect to space. Any object (such as the center of the solar system) is a suitable frame of reference, and the motion of any object can be referred to that frame. Thus, it is equally correct to say that a train moves past the station, or that the station moves past the train. This example is not as unreasonable as it seems at first sight, for the station is also moving, due to the motion of the earth on its axis and its revolution around the sun. All motion is relative, according to Einstein. None of Einstein's basic assumptions was revolutionary; Newton had previously stated “absolute rest cannot be determined from the position of bodies in our regions.” Einstein stated the relative rate of motion between any observer and any ray of light is always the same, 300,000 km/sec (186,000 mi/sec), and thus two observers, moving relative to one another even at a speed of 160,000 km/sec (100,000 mi/sec), each measuring the velocity of the same ray of light, would both find it to be moving at 300,000 km/sec (186,000 mi/sec), and this apparently anomalous result was proved by the Michelson-Morley experiment. According to classical physics, one of the two observers was at rest, and the other made an error in measurement because of the Lorentz-FitzGerald contraction of his apparatus; according to Einstein, both observers had an equal right to consider themselves at rest, and neither had made any error in measurement. Each observer used a system of coordinates as the frame of reference for measurements, and these coordinates could be transformed one into the other by a mathematical manipulation. The equations for this transformation, known as the Lorentz transformation equations, were adopted by Einstein, but he gave them an entirely new interpretation. The speed of light is invariant in any such transformation.

According to the relativistic transformation, not only would lengths in the line of a moving object be altered but also time and mass. A clock in motion relative to an observer would seem to be slowed down, and any material object would seem to increase in mass, both by the beta factor. The electron, which had just been discovered, provided a means of testing the last assumption. Electrons emitted from radioactive substances have speeds close to the speed of light, so that the value of beta, for example, might be as large as 0.5, and the mass of the electron doubled. The mass of a rapidly moving electron could be easily determined by measuring the curvature produced in its path by a magnetic field; the heavier the electron, the greater its inertia and the less the curvature produced by a given strength of field (see Magnetism). Experimentation dramatically confirmed Einstein's prediction; the electron increased in mass by exactly the amount he predicted. Thus, the kinetic energy of the accelerated electron had been converted into mass in accordance with the formula E=mc2 (see Atom; Nuclear Energy). Einstein's theory was also verified by experiments on the velocity of light in moving water and on magnetic forces in moving substances.

The fundamental hypothesis on which Einstein's theory was based was the nonexistence of absolute rest in the universe. Einstein postulated that two observers moving relative to one another at a constant velocity would observe identically the phenomena of nature. One of these observers, however, might record two events on distant stars as having occurred simultaneously, while the other observer would find that one had occurred before the other; this disparity is not a real objection to the theory of relativity, because according to that theory simultaneity does not exist for distant events. In other words, it is not possible to specify uniquely the time when an event happens without reference to the place where it happens. Every particle or object in the universe is described by a so-called world line that describes its position in time and space. If two or more world lines intersect, an event or occurrence takes place; if the world line of a particle does not intersect any other world line, nothing has happened to it, and it is neither important nor meaningful to determine the location of the particle at any given instant. The “distance” or “interval” between any two events can be accurately described by means of a combination of space and time, but not by either of these separately. The space-time of four dimensions (three for space and one for time) in which all events in the universe occur is called the space-time continuum.

All of the above statements are consequences of special relativity, the name given to the theory developed by Einstein in 1905 as a result of his consideration of objects moving relative to one another with constant velocity.

Article key phrases:

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