Special Relativity damtp.cam.ac.uk（狭义相对论damtp.cam.ac.uk）.pdfVIP

Chapter 6 Special Relativity 6.1 Basic concepts 6.1.1 Comparison with Newtonian dynamics Three basic assumptions of Newtonian dynamics are: 1. There is a special class of reference frames, called inertial frames: an inertial frame is one in which Newton’s first law holds. 2. Any two inertial frames are related by a Galilean transformation. 2 Time is absolute. 3. Newton’s second law (with Galilean invariant forces, including the universal law of gravitation) holds in any inertial frame. This is sometimes called the principle of Galilean relativity. The corresponding assumptions from Special Relativity are: 1. Same as the Newtonian assumption. 2. Any two inertial frames are related by a Lorentz transformation1 . 2 The speed of light is absolute. 3. Newton’s second law, with momentum suitably defined, (with Lorentz invariant forces, in- 2 cluding the Lorentz force ) holds all inertial frames. This is sometimes called the principle of special relativity.3 6.1.2 Consequences for Special Relativity Some consequent differences between Newtonian Dynamics and Special Relativity are as follows. • Newtonian absolute time is replaced by absolute speed of light: in Special Relativity, the speed of light in vacuo is c (about 3 × 108 metres per second) for all observers. • In Special Relativity, the notion of simultaneity is frame-dependent. This is a simple conse- quence of the fact that time is no longer absolute: each observer has his or own time and so observers will not agree on which events are simultaneous. • In Special Relativity, lengths are contracted and time is dilated4 in frames moving relative to the observer. This does not follow obviously from the assumptions of the previous section; it will be derived onc