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Relativity

Relativity - Special Relativity and Maxwell Equations by...

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Special Relativity and Maxwell Equations by Bernd A. Berg Department of Physics Florida State University Tallahassee, FL 32306, USA. (Version March 11, 2011) Copyright c by the author.

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Chapter 1 An introduction to the theory of special relativity is given, which provides the space- time frame for classical electrodynamics. Historically [2] special relativity emerged out of electromagnetism. Nowadays, is deserves to be emphasized that special relativity restricts severely the possibilities for electromagnetic equations. 1.1 Special Relativity Let us deal with space and time in vacuum. The conventional time unit is the second [ s ] . (1.1) Here and in the following abbreviations for units are placed in brackets [ ]. For most of the 20th century the second was defined in terms of the rotation of the earth as 1 60 × 1 60 × 1 24 of the mean solar day. Nowadays most accurate time measurements rely on atomic clocks. They work by tuning an electric frequency into resonance with an atomic transition. The second has been defined, so that the frequency of the light between the two hyperfine levels of the ground state of the cesium 132 Cs atom is exactly 9,192,631,770 cycles per second. Special relativity is founded on two basic postulates: 1. Galilee invariance: The laws of nature are independent of any uniform, translational motion of the reference frame. This postulate gives rise to a triple infinite set of reference frames moving with constant velocities relative to one another. They are called inertial frames . For a freely moving body, i.e., a body which is not acted upon by an external force, inertial systems exist. The differential equations which describe physical laws take the same form in all inertial frames (form invariance). Galilee invariance was known long before Einstein. 2. The speed c of light in empty space is independent of the motion of its source. The second Postulate was introduced by Einstein 1905 [2]. It implies that c takes the same constant value in all inertial frames. Transformations between inertial frames are implied, which have far reaching physical consequences. 1
CHAPTER 1. 2 The distance unit 1 meter [ m ] = 100 centimeters [ cm ] (1.2) was originally defined by two scratches on a bar made of platinum–iridium alloy kept at the International Bureau of Weights and Measures in S` evres, France. As measurements of the speed of light became increasingly accurate, Postulate 2 has been exploited to define the distance unit. The meter is now defined [6] as the distance traveled by light in empty space during the time of 1/299,792,458 [ s ]. This makes the speed of light exactly c = 299 , 792 , 458 [ m/s ] . (1.3) 1.1.1 Natural Units The units for second (1.1) and meter (1.2) are not independent, as the speed of light is a universal constant. This allows to define natural units , which are frequently used in nuclear, particle and astro physics. They define c = 1 (1.4) as a dimensionless constant, so that 1 [ s ] = 299 , 792 , 458 [ m ] holds. The advantage of natural units is that factors of c disappear in calculations. The disadvantage is that for converting back to conventional units the appropriate factors have to be recovered by dimensional analysis. For instance, if time is given in seconds

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