The philosophy of physics literature contains conflicting claims on the heuristic significance of general covariance. Some authors maintain that Einstein's general relativity distinguishes itself from other theories in that it must be generally covariant, for example, while others argue that general covariance is a physically vacuous and trivial requirement applicable to virtually any theory. Moreover, when general covariance is invested with heuristic significance, that significance as a rule is assigned to so-called “active” general covariance (or diffeomorphism equivalence), underwritten by the principle of background independence, rather than to general covriance as Einstein understood it (in the sense of coordinate transformations). While agreeing with the latter group of commentators that general covariance indeed carries heuristic significance, I argue that a background independent theory need not be generally covariant and that instead the Principle of Equivalence as Einstein understood it (i.e., not the infinitesimal version of the principle) provides the key to understanding the heuristic power of general covariance as a “mathematical sieve” for determining the gravitational field law. However, heuristic significance accrues to general covariance only indirectly, by its encompassing the relativity of frames underwritten by Einstein's principle of equivalence.

物理学文献的哲学包含对一般协方差的启发意义的矛盾主张。一些作者认为，爱因斯坦的广义相对论与其他理论有所不同，因为它必须例如，通常的协方差是协方差的，而其他人则认为，总体协方差是几乎适用于任何理论的物理上的虚无和琐碎的要求。此外，当一般协方差具有启发性意义时，通常将该重要性分配给所谓的“主动”一般协方差（或微分同等性），并由背景独立性原则承保，而不是爱因斯坦所理解的一般协方差（就坐标变换而言）。尽管同意后一组评论者的观点，即一般协方差确实具有启发性意义，但我认为背景独立理论不一定是协方差的，而是爱因斯坦理解的等效原理（即，而不是原理的无穷小形式）提供了理解广义协方差的启发力作为确定引力场定律的“数学筛”的关键。但是，启发式意义仅通过包含爱因斯坦等价原理所支持的框架的相对性而间接地产生于一般协方差。