Abstract
The principle of relativity states that there is no way to test if one is truly at rest or in uniform motion—even by measuring the speed of light. From this principle alone, Einstein arrived at two highly counter-intuitive conclusions. First, two events that are judged to occur simultaneously according to one set of inertial observers will not be judged to occur simultaneously according to a second set of inertial observers who are in motion relative to the first set. Stated differently, inertial observers who are in relative motion will measure different time intervals between two observed events—a phenomenon called relativistic time dilation. Second, a body which is judged to be a certain length according to one set of inertial observers will be judged to be a different length according to a second set of inertial observers who are in motion relative to the first. This phenomenon is called relativistic length contraction. In the following reading selection, Einstein introduces the Lorentz transformations, a set of mathematical relations which connect the space and time coordinates of events recorded by different observers.
General laws of nature are co-variant with respect to Lorentz transformations.
—Albert Einstein
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
See Chap. 20 of the present volume, which contains the Scholium after Newton’s Definitions in Book I of his Principia.
- 2.
Fizeau found \(W = w+v(1-\frac{1}{n^2})\) where \(n=\frac{c}{w}\) is the index of refraction of the liquid. On the other hand, owing to the smallness of \(\frac{vw}{c^2}\) as compared with 1, we can replace (31.21) in the first place by \(W=(w+v)(1-\frac{vw}{c^2})\), or to the same order of approximation by \(w+v(1-\frac{1}{n^2})\), which agrees with Fizeau’s result.
- 3.
For problems with only one relevant space dimension, \((\Updelta y)^2\) and \((\Updelta z)^2\) may be omitted from Eq (31.22).
- 4.
A Speed of Light Module (Model IF SLA) is available from Industrial Fiber Optics in Tempe, AZ. It consists of an apparatus which transmits 500,000 pulses per second from a red LED and two fiber optic cables. A dual-channel oscilloscope with 20-MHz bandwidth is required to measure the time interval between transmitted and received pulses.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2015 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Kuehn, K. (2015). Lorentz Transformations. In: A Student's Guide Through the Great Physics Texts. Undergraduate Lecture Notes in Physics. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-1366-4_31
Download citation
DOI: https://doi.org/10.1007/978-1-4939-1366-4_31
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4939-1365-7
Online ISBN: 978-1-4939-1366-4
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)