Reading Natural Philosophy: Essays in the History and Philosophy of Science and Mathematics

By David B. Malament | Go to book overview

10
A No-Go Theorem about Rotation
in Relativity Theory1

DAVID B. MALAMENT

Within the framework of general relativity, in some cases at least, it is a rather delicate and interesting question just what it means to say that a body is or is not “rotating.” Moreover, the reasons for this—at least the ones I have in mind—do not have much to do with traditional controversy over “absolute vs. relative” conceptions of motion. Rather they concern particular geometric complexities that arise when one allows for the possibility of spacetime curvature. The relevant distinction for my purposes is not that between attributions of “relative” and “absolute” rotation, but between attributions of rotation than can and cannot be analyzed in terms of a motion (in the limit) at a point. It is the latter—ones that make essential reference to extended regions of spacetime—that can be problematic.

The problem has two parts. First, one can easily think of different criteria for when a body is rotating. The criteria agree if the background spacetime structure is sufficiently simple, for example, in Minkowski spacetime (the regime of “special relativity”). But they do not do so in general. Second, none of the criteria fully answers to our classical intuitions. Each one exhibits some feature or other that violates those intuitions in a significant and interesting way.

My principle goal in what follows is to make the second claim precise in the form of a modest no-go theorem. To keep tilings simple, I'll limit attention to a special case. I'll consider (one-dimensional) rings centered about an axis of rotational symmetry, and consider what it could mean to say that the rings are not rotating around the axis. (It is convenient to work with the negative formulation.) The discussion will have several parts.

First, for purposes of motivation, I'll describe two standard criteria of nonrotation that seem particularly simple and natural. (1 could assemble a longer list of proposed criteria, but I am more interested in formulating a general negative claim that applies to all.)2 One involves considerations of

-267-

Notes for this page

Add a new note
If you are trying to select text to create highlights or citations, remember that you must now click or tap on the first word, and then click or tap on the last word.
One moment ...
Default project is now your active project.
Project items

Items saved from this book

This book has been saved
Highlights (0)
Some of your highlights are legacy items.

Highlights saved before July 30, 2012 will not be displayed on their respective source pages.

You can easily re-create the highlights by opening the book page or article, selecting the text, and clicking “Highlight.”

Citations (0)
Some of your citations are legacy items.

Any citation created before July 30, 2012 will labeled as a “Cited page.” New citations will be saved as cited passages, pages or articles.

We also added the ability to view new citations from your projects or the book or article where you created them.

Notes (0)
Bookmarks (0)

You have no saved items from this book

Project items include:
  • Saved book/article
  • Highlights
  • Quotes/citations
  • Notes
  • Bookmarks
Notes
Cite this page

Cited page

Style
Citations are available only to our active members.
Sign up now to cite pages or passages in MLA, APA and Chicago citation styles.

(Einhorn, 1992, p. 25)

(Einhorn 25)

1

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

Cited page

Bookmark this page
Reading Natural Philosophy: Essays in the History and Philosophy of Science and Mathematics
Table of contents

Table of contents

Settings

Settings

Typeface
Text size Smaller Larger Reset View mode
Search within

Search within this book

Look up

Look up a word

  • Dictionary
  • Thesaurus
Please submit a word or phrase above.
Print this page

Print this page

Why can't I print more than one page at a time?

Help
Full screen
/ 429

matching results for page

    Questia reader help

    How to highlight and cite specific passages

    1. Click or tap the first word you want to select.
    2. Click or tap the last word you want to select, and you’ll see everything in between get selected.
    3. You’ll then get a menu of options like creating a highlight or a citation from that passage of text.

    OK, got it!

    Cited passage

    Style
    Citations are available only to our active members.
    Sign up now to cite pages or passages in MLA, APA and Chicago citation styles.

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn, 1992, p. 25).

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences."1

    1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

    Cited passage

    Thanks for trying Questia!

    Please continue trying out our research tools, but please note, full functionality is available only to our active members.

    Your work will be lost once you leave this Web page.

    For full access in an ad-free environment, sign up now for a FREE, 1-day trial.

    Already a member? Log in now.