Skip to main content Accessibility help
×
Hostname: page-component-76dd75c94c-7vt9j Total loading time: 0 Render date: 2024-04-30T09:03:06.315Z Has data issue: false hasContentIssue false

3 - Space-time splitting

Published online by Cambridge University Press:  03 May 2011

Fernando de Felice
Affiliation:
Università degli Studi di Padova, Italy
Donato Bini
Affiliation:
Consiglio Nazionale delle Ricerche (CNR), Rome
Get access

Summary

The concept of space-time brings into a unified scenario quantities which, in the pre-relativistic era, carried distinct notions like time and space, energy and momentum, mechanical power and force, electric and magnetic fields, and so on. In everyday experience, however, our intuition is still compatible with the perception of a three-dimensional space and a one-dimensional time; hence a physical measurement requires a local recovery of the pre-relativistic type of separation between space and time, yet consistent with the principle of relativity. To this end we need a specific algorithm which allows us to perform the required splitting, identifying a “space” and a “time” relative to any given observer. This is accomplished locally by means of a congruence of time-like world lines with a future-pointing unit tangent vector field u, which may be interpreted as the 4-velocity of a family of observers. These world lines are naturally parameterized by the proper time τu defined on each of them from some initial value. The splitting of the tangent space at each point of the congruence into a local time direction spanned by vectors parallel to u, and a local rest space spanned by vectors orthogonal to u (hereafter LRSu), allows one to decompose all space-time tensors and tensor equations into spatial and temporal components. (Choquet-Bruhat, Dillard-Bleick and DeWitt-Morette 1977).

Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×