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Einstein group
Albert Einstein, in searching for the transformation group for his unified field theory, wrote:
Every attempt to establish a unified field theory must start, in my opinion, from a group of transformations which is no less general than that of the continuous transformations of the four coordinates. For we should hardly be successful in looking for the subsequent enlargement of the group for a theory based on a narrower group.
==The Poincaré group==
The Poincaré group, the transformation group of special relativity, being orthogonal, the inverse of a transformation equals its transpose, introducing discrete reflections. This, in turn, violates Einstein's dictum for a group "no less general than that of the continuous transformations of the four coordinates." Specifically, any pair of Euler angles ''θ''''k'' and −''θ''''k'' are not independent, nor are any pair of boosts ''v''''k''/''c'' and −''v''''k''/''c''. Available parameters are thus reduced, from the 16 needed to express all transformations in a curved spacetime, per the general principle of relativity, ∂''x''''μ''′/∂''x''''ν'', to the 10 of the Poincaré group.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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