This
paper has generated a number of articles in the popular press: in New
Scientist, from Associated Press, the Swiss magazine
Facts, the Swedish daily Dagens Nyheter
and the Danish daily Information.
Max Tegmark's library: dimensions
Please click here to download the 400K postscript
version of the paper, including all the figures.
NOTE: If you can't read
ps-files, click instead to download
a PDF version of the paper. This can be viewed and printed
on any PC or Macintosh
using Acrobat Reader, downloadable for free from
Adobe.
Click
if you are interested in other research of mine.
On the dimensionality of spacetime
Author:
Max Tegmark
Abstract:
Some superstring theories have more than one effective low-energy limit,
corresponding to classical spacetimes with different dimensionalities.
We argue that all but the 3+1-dimensional one might correspond to ``dead
worlds'', devoid of observers, in which case all such ensemble theories
would actually predict that we should find ourselves inhabiting
a 3+1-dimensional spacetime. With more or less than one time-dimension,
the partial differential equations of nature would lack the hyperbolicity
property that enables observers to make predictions. In a space with more
than three dimensions, there can be no traditional atoms and perhaps no
stable structures. A space with less than three dimensions allows no gravitational
force and may be too simple and barren to contain observers.
Reference info:
Classical and Quantum Gravity, 14, L69-L75
Press coverage:
This paper has generated a number of articles in the
popular press. Here is an abridged version from the September 13 (1997)
issue of New Scientist:
My comment:
If you read the New Science article above, you noticed that it put the
following twist on my results: we're somehow lucky. In the original
paper, I suggest that we're not lucky at all. Rather, some superstring
theories and chaotic inflation models predict that spacetimes with many
different dimensionalities (up to 26, say) actually exist in exponentially
large regions that are for all practical purposes causally disconnected.
If you buy such a theory as well as my argument that all of the existing
spacetimes except the 3+1-dimensional one are uninhabitable, then you could
in principle have predicted that the spacetime you inhabit is 3+1-dimensional
even before you'd opened your eyes and checked. If you were an extremely
prodigal newborn baby, you could have paraphrased Descarte and said ``cogito,
ergo spacetime has 3+1 dimensions''. If you're a practical-minded string
theorist, then the message is simply that you needn't worry if the 3+1
compactification doesn't just ``drop out'' of your calculations - your
theory predicts that we'll observe 3+1 anyway.
This is from the December 18 1997 issue of
the Swiss magazine Facts (page 108), as part of their special feature about
the favorite Swiss topic: time.
This is from the September 21 1997 issue of
the Swedish daily paper Dagens Nyheter:
This is from the January 19 1998 issue of
the Danish daily paper Information:
This came from
Associated Press, and was
printed in a number of US daily newspapers:
My original paper, upon which these article were based, is at the top of this page
(click
here).
Return to my home page
This page was last modified September 8, 1999.
max@ias.edu