Skip to main content Accessibility help
×
Hostname: page-component-84b7d79bbc-fnpn6 Total loading time: 0 Render date: 2024-08-03T03:17:23.693Z Has data issue: false hasContentIssue false

10 - Minkowski Space

from Part III - Relativistic Cosmology

Published online by Cambridge University Press:  04 May 2017

Bernard J. T. Jones
Affiliation:
Rijksuniversiteit Groningen, The Netherlands
Get access

Summary

Inertial frames are fundamental to special relativity, so much so that Einstein was keen to carry them over into his later general theory of relativity, albeit on a merely local basis. This chapter is about inertial frames from the point of view of Minkowski space and Lorentz transformations. After a brief reminder as to what the Lorentz transformation is, we move on to Minkowski's way of thinking by introducing his 4-space, with its 4-vectors and defining metric. We also introduce the covariant and contravariant representation of vectors in these coordinate systems. Once equipped with this we recast Maxwell's equation in our Minkowski space framework, ending with two tensor quantities: the electromagnetic field tensor (also known as the Faraday tensor) and the energy momentum tensor.

Why Relativity?

Limitations of Newtonian Theory

Our Universe, on the largest scales, appears to be homogeneous and isotropic. On those vast scales it is the force of gravity that governs its behaviour. Until the beginning of the 20th century, gravitational phenomena such as the motion of bodies in the Solar System were described in terms of Isaac Newton's theory of gravitation, written down by Newton some 250 years earlier. The successes of Newton's theory were truly remarkable. Not only did it provide an explanation of the orbits of bodies about the Sun, but it also made dramatic predictions that were subsequently verified: the return of Halley's comet and the existence of the planet Neptune. What more could one ask of a theory?

Despite those successes, two problems were evident even during the 19th century. There was the famous problem of the precession of the perihelion of Mercury's orbit about the Sun and there was the problem that Newton's theory could not address the cosmology of the time: a homogeneous and static Universe. Seeliger (1895) modified Newtonian gravity at large distances and his resulting cosmological model was perhaps the best one could do at the time.

However, at the end of 1915, Einstein published the first definitive version of his general theory of relativity, which provided a new theory of gravitation and with that came new cosmological models that could be tested against observations and applied to cosmology.

Throughout the rest of the 20th century numerous tests of Einstein's theory have established its overall validity for describing gravitational phenomena.

Type
Chapter
Information
Precision Cosmology
The First Half Million Years
, pp. 237 - 267
Publisher: Cambridge University Press
Print publication year: 2017

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.

  • Minkowski Space
  • Bernard J. T. Jones, Rijksuniversiteit Groningen, The Netherlands
  • Book: Precision Cosmology
  • Online publication: 04 May 2017
  • Chapter DOI: https://doi.org/10.1017/CBO9781139027809.012
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.

  • Minkowski Space
  • Bernard J. T. Jones, Rijksuniversiteit Groningen, The Netherlands
  • Book: Precision Cosmology
  • Online publication: 04 May 2017
  • Chapter DOI: https://doi.org/10.1017/CBO9781139027809.012
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.

  • Minkowski Space
  • Bernard J. T. Jones, Rijksuniversiteit Groningen, The Netherlands
  • Book: Precision Cosmology
  • Online publication: 04 May 2017
  • Chapter DOI: https://doi.org/10.1017/CBO9781139027809.012
Available formats
×