There are examples of symmetry in everyday life. Consider the symmetric artful designs in a palace, in a temple, or in a garden as in Fig. 4.1. The garden looks the same if you substitute one column for another, or if you interchange any two tiles of the same color on the floor. Under such transformations nothing seems to have changed even though we know that we have made some changes. Such transformations are examples of symmetries of the garden in this picture.
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Actually, symmetry considerations alone are insufficient to uniquely arrive at general relativity. An additional condition, that the equations should not involve more than two derivatives, is also needed to exclude other more complicated equations. The potential higher derivative modifications of general relativity actually occur as higher energy corrections that come from a more fundamental approach, such as string theory.
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Bars, I., Terning, J. (2010). Symmetry and Perspective. In: Nekoogar, F. (eds) Extra Dimensions in Space and Time. Multiversal Journeys. Springer, New York, NY. https://doi.org/10.1007/978-0-387-77638-5_4
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