If the source of sound is rushing toward you, the waves will not get to you any faster. However, in what is known as the Doppler effect, the waves will be compressed and the interval between them will be smaller. The decreased wavelength means a higher frequency, which results in a higher-pitched sound (or a lower one, when the siren passes by and starts moving away). A similar effect happens with light. If the source is moving toward you, the wavelength decreases (and frequency increases) so it is shifted to the blue end of the spectrum. Light from a source moving away will be red-shifted.
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Later, upon his father’s death, he became Max von Laue.
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The German phrase he used was “der glucklichste Gedanke,” which has usually been translated as “happiest” thought, but perhaps in this context is more properly translated as “luckiest” or “most fortunate.”
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Added to her 1903 physics prize, she thus became the first person to win Nobels in two different fields. The only other person to do so was Linus Pauling, who won for chemistry in 1954, and then won the 1962 Nobel Peace Prize for his fight against nuclear weapons testing.
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She was born Elsa Einstein, became Elsa Lowenthal during her brief marriage to a Berlin merchant, and was referred to as Elsa Einstein by Albert Einstein even before they married. For clarity, I refer to her as Elsa throughout.
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Although the school had been renamed, Einstein continued to call it the Polytechnic (“Polytechnikum”) and, for clarity, I will continue to use this name.
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See chapter 7. For purposes of this discussion, we are referring to a uniformly and rectilinearly accelerated reference frame and a static and homogeneous gravitational field.
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I am using the numbers in Einstein’s original calculations. Subsequent data caused it to be revised to about 0.85 second of arc. Also, as we shall see, he later revised his theory to predict twice the bending. An arc-second, or second of arc, is an angle of
1
?3,600 of a degree.
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Here’s how it works. If you are at some point in curved space and want to know the distance to a neighboring point—infinitesimally close—then things can be complicated if you have just the Pythagorean theorem and some general geometry to use. The distance to a nearby point to the north may need to be computed differently from the distance to one to the east or to one in the up direction. You need something comparable to a little scorecard at each point of space to tell you the distance to each of these points. In four-dimensional spacetime your scorecard will require ten numbers for you to be able to deal with all the questions pertaining to spacetime distances to nearby points. You need such a scorecard for every point in the spacetime. But once you have those scorecards, you can figure out the distance along any curve: just add up the distances along each infinitesimal bit using the scorecards as you pass them. These scorecards form the metric tensor, which is a field in spacetime. In other words, it is something defined at every point, but that can have differing values at every point. I am grateful to Professor John D. Norton for helping with this section.
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For clarity, I refer to the boy by both of his given names, Hans Albert, although his father invariably referred to him simply as Albert. At one point, Einstein wrote a letter to his son and signed it “Albert” instead of “Papa.” In his next letter, he awkwardly began, “The explanation for the curious signature on my last letter is that, in my absentmindedness, instead of signing my own name, I frequently sign for the person to whom the letter is addressed” (Einstein to Hans Albert Einstein, March 11 and 16, 1916).
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Einstein’s salary after tax was 13,000 marks. Inflation was beginning to set in, and the value of the German mark had fallen from 24 cents in 1914 to 19 cents in January 1918. One mark at the time would buy two dozen eggs or four loaves of bread. (A year later, the mark would be worth only 12 cents, and when hyperinflation began to rage in January 1920 only 2 cents.) Mari
’s stipend of 6,000 marks in January 1918 was thus worth about $1,140, or just under $15,000 in inflation- adjusted 2006 dollars. His proposal was to increase this by 50 percent.
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Chapter 14 describes Einstein’s revision of this view in a 1920 lecture in Leiden.
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See chapter 14 for Einstein’s decision to renounce the term when he discovered the universe was expanding.
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Described in chapter 14.
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The word Einstein used was
Although
generally means tribe, that translation can have some racial overtones. Some Einstein scholars have said that translations such as “kindred” or “clan” or “lineage” might be clearer.
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I have used the translation preferred by Abraham Pais. Einstein’s words in German were, “Raffiniert ist der Herr Gott, aber boshaft ist er nicht.”
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Governor Channing Cox had been thrust a version of the test earlier that week, and his first three responses were: Where does shellac come from? “From a can.” What is a monsoon? “A funny-sounding word.” Where do we get prunes? “Breakfast.”
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Robert Andrews Millikan would win the Nobel Prize the following year, 1923, for experimental work on the photoelectric effect he had done at the University of Chicago. By then he had become director of the physics lab at the California Institute of Technology, and in the early 1930s he would bring Einstein there as a visiting scientist.
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See page 119 for Newton’s thought experiment about whether water rotating in a bucket in empty space would be subject to inertial pressure and thus press against the sides of the bucket. See page 251 for Einstein’s 1916 view, which he was now revising, that an empty universe would have no inertia or fabric of spacetime.
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