What is "gauge" in General Relativity? I am trying to concoct a dumbed-down explanation of the significance of gauge in physics (and especially in General Relativity (GR)) that my limited intellect can cope with. I need some serious correcting about how to unravel the differences between “gauge” in mathematics and in physics: To mathematicians (see for instance Terence Tao’s explanation) gauge seems to be associated with using coordinates to quantitatively describe and model a geometrical object. He writes: (e.g. to convert lengths into numbers associated with units). The utility of such conversion is that the tools of mathematical analysis may then be used, say to compare objects when coordinate systems vary with say Differential Geometry when the base space being treated is non-Euclidean. Or, in ordinary space, integration, Fourier analysis etc. To use coordinates one must choose items like: a scale, units, an origin, an orientation and maybechirality (direction of circulation, clockwise or anticlockwise). This is called fixing a gauge. If the same fixed gauge is chosen across the space spanned by the object or objects being described,the gauge is said to be global. If the choice varies from one location to another it is said to be local. Terence Tao writes: In physics (which is much younger than mathematics) quantitative mathematical models ofphysical objects and their behaviours depend on parameters --- quantities that vary from case to case. A model may be said to span a “parameter space”, where, I suppose, it forms a geometrical object complete with a numerical character that can be modeled and analysed mathematically. In situations where a parameter cannot be measured physically, as with the vector potential in the theory of electromagnetism, the arbitrarily fixed “gauge” of the parameter space is global (and explains electric charge conservation). Here the gauge-invariant parameter space is Euclidean so that differential geometry need not be invoked. A similar situation prevails when the parameter space is circular, modulo 2 pi, as with the phases of wave functions in quantum mechanics. The non-Euclidean geometry of the four-dimensional spacetime of General Relativity, on the other hand, is rendered dynamic by the presence of mass and energy, which means that differential geometry, or tensor analysis with coordinates, is used numerically to describe geometrical objects. (Marcus has pungently described this as: “... Coordinates are "gauge" meaning physically meaningless redundant trash”....) But in this case the gauge used to convert geometrical objects in spacetime into numeric objects, although invariant, is just the S.I.: confusingly even when "dynamic" means the “expansion” of the isotropic everywhere-and-everywhen FLRW model of cosmology. Its invariance across spacetime corresponds to the conservation of momentum and energy (at least on a local scale). Is this the sense in which GR is considered to be a gauge theory? Or is it only when GR is treated as a quantum field theory with excitations called gravitons that GR is classed as a gauge theory? Or why (without too much jargon, please) is GR classed as a gauge theory?