Special Relativity

Abstract

Although the word “relativity” is synonymous with Albert Einstein, Galileo Galilei was actually the first scientist to formulate what we now call

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1.
According to current measurements, the speed of light is \(299792.458 \;{\text{km/s}}\) and it is convention to denote it by the letter \(c\).
2.
Otherwise the speed of light would vary depending on the observer’s speed relative to the ether.
3.
The derivation of this equation is presented at the end of the chapter.
4.
The derivation of length contraction can be found in most basic undergraduate physics textbooks.
5.
This limit is attained only by particles with a zero rest mass, like the photon.
6.
Physicists often use the Greek letter \(\Delta\) to denote the change in a given quantity. For example, in the text above, \(\Delta x\) means the change in the value of \(x\) from one end of the line segment to the other end.
7.
Recall for a right-angle triangle \(h^{2} = a^{2} + b^{2}\), where h is the length of the hypotenuse, and \(a\) and \(b\) are the lengths of the other two sides.
8.
In this problem we are only concerned with the special relativistic effect of time dilation, which makes the satellite clock run slower. But there is also a general relativistic effect which makes time run faster for the satellite, because it is in a weaker gravitational field than a clock on Earth (we will discuss this in Chap. 4). If we were to take into account both effects, then we would actually find that the satellite clock runs faster overall.

Authors

Delia Perlov
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Alex Vilenkin
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Perlov, D., Vilenkin, A. (2017). Special Relativity. In: Cosmology for the Curious. Springer, Cham. https://doi.org/10.1007/978-3-319-57040-2_3