# [time 201] Effects of Lorentz and Euclidian Metrics (Wick rotation)

Stephen P. King (stephenk1@home.com)
Fri, 09 Apr 1999 20:30:16 -0400

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.

In article <7d97so\$ur6\$2@pravda.ucr.edu>, baez@galaxy.ucr.edu (john
baez) wrote:
>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

I think that the Wick rotation can only be viewed as a mathematical
trick
used to perform calculations with complicated theories, because the
change
between Euclidean and Minkowski metric alters the physics in GR (General
Relativity):

It is known that under the influence of gravitation, GR bends the
timespace in such a manner that clocks (in general) cannot be
syncronized
by Lorentz tranformations, due to the fact that in the curved Lorentz
space there is no unique path to make the time conversions along.
However,
with a Euclidian metric, there is always such a unique path, the
shortest
one, and it would be possible to develop a universal time for the
Universe.

So assuming the Wick rotation imposes some conditions on the GR
curvature,
and limitations on the effects of gravitation, it seems me.

Hans Aberg

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