Abstract
Motion of an observer makes him measure Doppler shifted or Lorentz transformed light coordinates. These Lorentz transformations relate the velocities of particles which different observers measure, and change by aberration the directions, from which incident light rays are perceived. Aberration is conformal: angles and relative sizes of small, neighbouring objects agree in aberrated pictures. Lorentz transformations determine how the energy and the momentum of a particle depend on its velocity. The conservation of energy and momentum restricts the decay of a particle and the scattering of two particles with observable consequences.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
The light pulse moves into the opposite of the direction \(\mathbf{ e}\) from which it is seen.
- 2.
As meter per second (1.3), an arc second is just a number, \(1^{\prime \prime }=2\pi /(360\cdot 60\cdot 60)\approx 4.848\cdot 10^{-6}\).
- 3.
The matrices \(\varLambda _a\) arise from repeated infinitesimal transformation \(\omega =\mathrm{ d} \varLambda _{a}/\mathrm{ d} a)_{|_{a=0}}\) where the series \(\varLambda _a= \exp a\omega = 1 + a\omega + a^2\omega ^2/2\) consists of three terms only.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2012 The Author(s)
About this chapter
Cite this chapter
Dragon, N. (2012). Transformations. In: The Geometry of Special Relativity - a Concise Course. SpringerBriefs in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28329-1_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-28329-1_3
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-28328-4
Online ISBN: 978-3-642-28329-1
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)