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

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On the dimensionality of spacetime


Max Tegmark


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).
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This page was last modified September 8, 1999.