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zankaon
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What is general covariance? See a very informative discussion at: https://www.physicsforums.com/showthread.php?t=197220&highlight=general+covariance"
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General covariance is a principle in physics that states that the laws of nature should appear the same to all observers, regardless of their frame of reference or coordinate system.
General covariance is important because it allows us to formulate physical theories that are consistent and applicable in all reference frames. This is crucial in understanding the fundamental laws of nature.
General covariance is a key principle in Einstein's theory of relativity. It is incorporated in the equations of general relativity, which describe how gravity works in the presence of matter and energy.
Special covariance is a principle that applies to special relativity, which describes the laws of physics in inertial reference frames. General covariance extends this principle to include non-inertial reference frames and the effects of gravity.
General covariance is a fundamental principle in physics, and as such, it cannot be tested or proven. However, it has been confirmed through numerous experiments and observations, and is widely accepted as a fundamental aspect of our understanding of the universe.