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Taking $E={m}{c^2}$, we have mass and energy but no space and time. What is the best way of understanding the ways that space and time are passive and therefore unaccountable as mass and energy?

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In special relativity, mass / energy has no influence on spacetime.

However, in general relativity, the curvature of spacetime is directly related to energy, or equivalently, mass. The Einstein field equation $$R_{\mu \nu} - {1 \over 2}g_{\mu \nu}\,R + g_{\mu \nu} \Lambda = {8 \pi G \over c^4} T_{\mu \nu}$$ includes the stress-energy tensor, which describes the density and flux of energy and momentum in spacetime.

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E=m*c**2 is not the defining equation of relativity. The theory is called special relativity and the equation is a derived part of the results of the theory. It is the result of Lorenz transformations on moving systems, which do take care of space and time in addition to energy.

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