Skip to main content Accessibility help
×
Hostname: page-component-76fb5796d-vfjqv Total loading time: 0 Render date: 2024-04-28T20:09:27.395Z Has data issue: false hasContentIssue false

7 - Relativity and Least Action

Published online by Cambridge University Press:  26 March 2018

Alberto Rojo
Affiliation:
Oakland University, Michigan
Anthony Bloch
Affiliation:
University of Michigan, Ann Arbor
Get access

Summary

In 1905, Albert Einstein published a series of papers that constitute an unprecedented display of creativity. The paper Einstein (1905) published in June of this annus mirabilis deals with the theory of relativity, a work that eventually brought Einstein rock-star fame. The first sentence of the essay makes an aesthetic observation: “It is known that Maxwell's electrodynamics, as usually understood at the present time, when applied to moving bodies, leads to asymmetries which do not appear to be inherent in the phenomena” (italics added). Einstein discusses the meaning of this asymmetry with an example from the theory of electromagnetism. He observes that a magnet in motion relative to a wire loop produces an electrical current in the wire. According to Maxwell's theory, different equations apply when the magnet moves and the wire is stationary and vice versa. In one case, the magnet is moving with respect to the ether (a universal static substance that acts as the medium for transmission of light) and in the other, the magnet is at rest with respect to the ether. This asymmetry was unacceptable to Einstein. If the current is the same in both cases, then one is looking at the same phenomenon from different perspectives, or from different reference frames, thus making the idea of an ether superfluous. McCullagh's prediction (see the quotation on page 110) of an unexpected, simple and beautiful ether is perhaps fulfilled; non-existence is the ultimate simplicity. The new theory is based on two simple postulates:

  • The laws of physics take the same form for “all reference frames for which the equations of mechanics hold good” (inertial frames).

  • Light always propagates in empty space with a velocity c which is independent of the state of motion of the emitting body.

  • From this starting point, as simple as it is audacious, Einstein leads us through a path of impeccable logic that culminates in the notion that time, represented by the ticking of a wristwatch, is not an absolute phenomenon.

    It is remarkable that the equations that Einstein derives existed before his work. In 1895, the Dutch physicist Hendrik A. Lorentz, in order to explain some experiments by Michelson and Morley wrote a set of equations (identical to Einstein's) in which time appeared as a mathematical variable that depended on velocity and position.

    Type
    Chapter
    Information
    The Principle of Least Action
    History and Physics
    , pp. 162 - 188
    Publisher: Cambridge University Press
    Print publication year: 2018

    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
    ×