The Theory of Relativity: and Other Essays
Page 8
Now we consider this same process with respect to the system K, which moves with respect to K0 with the constant velocity v in the negative Z0 direction. With respect to K the description of the process is as follows:
The body B moves in the positive Z direction with velocity v. The two complexes of radiation now have directions with respect to K which make an angle α with the x axis. The law of aberration states that in the first approximation where c is the velocity of light. From the consideration with respect to K0 we know that the velocity v of B remains unchanged by the absorption of S and S′.
Now we apply the law of conservation of momentum with respect to the z direction to our system in the coordinate-frame K.
I. Before the absorption let M be the mass of B; Mv is then the expression of the momentum of B (according to classical mechanics). Each of the complexes has the energy and hence, by a well known conclusion of Maxwell's theory, it has the momentum . Rigorously speaking this is the momentum of S with respect to K0. However, when v is small with respect to c, the momentum with respect to K is the same except for a quantity of second order of magnitude ( compared to 1). The z-component of this momentum is sin α or with sufficient accuracy (except for quantities of higher order of magnitude) S and S′ together therefore have a momentum in the z direction. The total momentum of the system before absorption is therefore
II. After the absorption let M′ be the mass of B. We anticipate here the possibility that the mass increased with the absorption of the energy E (this is necessary so that the final result of our consideration be consistent). The momentum of the system after absorption is then
We now assume the law of the conservation of momentum and apply it with respect to the z direction. This gives the equation
or
This equation expresses the law of the equivalence of energy and mass. The energy increase E is connected with the mass increase . Since energy according to the usual definition leaves an additive constant free, we may so choose the latter that
E = Mc2
A Biography of Albert Einstein
Albert Einstein (1879–1955) is among modern history’s greatest and most influential minds. He authored more than 450 scholarly works during his lifetime, and his advancements in science—including the revolutionary Theory of Relativity and E=mc2, which described for the first time the relationship between an object’s mass and its energy—have earned him renown as “the father of modern physics.”
Born in Ulm, in southwest Germany, Einstein moved to Munich with his family as an infant. As a child, Einstein spoke so infrequently that his parents feared he had a learning disability. But despite difficulties with speech, he was consistently a top student and showed an early aptitude for mathematics and physics, which he later studied at the Swiss Federal Institute of Technology in Zurich after renouncing his German citizenship to avoid military service in 1896.
After graduation, Einstein married his college girlfriend, Mileva Marić, and they had three children. He attended the University of Zurich for his doctorate and worked at the patent office in Bern, a post he left in 1908 for a teaching position at the University of Bern, followed by a number of professorships throughout Europe that ultimately led him back to Germany in 1914. By this time, Einstein had already become recognized throughout the world for his groundbreaking papers on special relativity, the photoelectric effect, and the relationship between energy and matter. He won the Nobel Prize in Physics in 1921.
In 1933, Einstein escaped Nazi Germany and immigrated to the United States with his second wife, Elsa Löwenthal, whom he had married in 1919. He accepted a position at Princeton University in New Jersey, where he stayed for the remainder of his life. At Princeton, Einstein dedicated himself to finding a unified field theory and played a key role in America’s development of atomic weapons. He also campaigned for civil rights as a member of the NAACP and was an ardent supporter of Israel’s Labor Zionist Movement.
Still, Einstein maintained a special affinity for his homeland. His connection to all things German and, in particular, to the scientific community in Berlin was probably the reason that throughout his years in America he so strongly valued his relationships with other German-speaking immigrants. He maintained a deep friendship with the founder of Philosophical Library, Dr. Dagobert D. Runes, who, like Einstein, was a humanist, a civil rights pioneer, and an admirer of Baruch Spinoza. Consequently, many of Albert Einstein’s works were published by Philosophical Library.
At the time of Einstein’s death in 1955, he was universally recognized as one of history’s most brilliant and important scientists.
Einstein smoking a pipe on the porch of his home in Princeton, New Jersey, in 1938. He was a very ardent pipe smoker and treasured the ritual of selecting different tobaccos and preparing them to be smoked.
Einstein in 1938 with Thomas and Katia Mann, in Princeton, New Jersey.
Einstein with his friends poet Itzik Feffer and actor Solomon Mikhoels, in 1943.
Einstein in 1945 in the study of his Princeton home.
Einstein in his Princeton study on the day that he received his honorary degree from the Hebrew University of Jerusalem, in 1949.
Einstein receiving the honorary degree from Israel S. Wechsler while at his Princeton home in 1949.
A photograph of Einstein in in the 1950s.
A portrait of Einstein at the Yeshiva University inauguration dinner for the Albert Einstein College of Medicine, at Princeton Inn on March 15, 1953.
A draft of a poem and some of Einstein’s calculations in his own hand.
An envelope Einstein used as scribbling paper.
Acknowledgments
1. From The American People’s Encyclopedia, copyright by the Spencer Press, Inc., Chicago, 1949.
2. From Science Illustrated; New York, April, 1946.
3. From The Journal of the Franklin Institute, Vol. 221, No. 3; March. 1936.
4. From Science; Washington, D.C., May 24, 1940.
5. A broadcast recording for the Science Conference; London, September 28, 1941, and published in Advancement of Science; London, Vol. 2, no. 5.
6. From Relativity—A Richer Truth by Philipp Frank; published by the Beacon Press, Boston, 1950.
7. From Technion Journal; New York, 1946.
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