Stephen Paul King (stephenk1@home.com)
Thu, 25 Mar 1999 18:39:43 GMT
On 24 Mar 1999 21:08:49 GMT, baez@galaxy.ucr.edu (john baez) wrote:
>In article <F8uMvJ.7K7@world.std.com>,
>Doug B Sweetser <sweetser@world.std.com> wrote:
>
>>Why hasn't the Euclidean realm won over Minkowski or the reverse?
>>Appearently nature likes both pictures, or we would have gotten a clear
>>winner by now. This sounds somewhat like the old wave/particle debate:
>>accepting both is the best way to move forward. Therefore the algebra
>>of nature must be such that switching between both forms is trivial.
>
>Fundamentally it *is* trivial: you just replace the time variable t by it.
>This goes by the fancy name of "Wick rotation". Then the Minkowski metric
>
>- dt^2 + dx^2 + dy^2 + dz^2
>
>becomes the Euclidean metric
>
>dt^2 + dx^2 + dy^2 + dz^2
>
>All quantum field theorists worth beans accept and use both the Euclidean
>and Minkowskian pictures when appropriate. However, there are often subtle
>reasons for preferring one over the other, and this is where things get
>tricky.
>
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