Edited sentence: , but become completely arbitrary, so that for example one can define an entirely new timelike coordinate according to some arbitrary rule such as , and Einstein's equations will still be valid., the change introduced by the transformation may be different at every point in space.A qualitative difference between gauge symmetries and other symmetries of physics is that gauge transformations need not be global, like the  example; they may be local, i.After this gauge transformation , where V is the potential, the laws of physics governing electricity and magnetism (Maxwell's equations) would remain valid.But only differences in potential are physically measurable, which is the reason that a voltmeter must have two probes, and can only report the voltage difference between them.For example, an electric field can be described in terms of an electric potential (voltage) that is defined at every point in space, and in practical work it is conventional to take the Earth as a physical reference that defines the zero level of the potential, or ground.For example, in Einstein's theory of general relativity, coordinates like x, y, z, and t are not only "relative" in the global sense of translations like , rotations, etc.For example, one symmetry of the laws of physics, which is not a gauge symmetry, is time translation symmetry, in which one offsets the times on all clocks by some consistent amount, say one hour, ; this does not result in any violation of the laws of physics, because the laws do not change over time.Gauge symmetries act in a similar way on fields.Gauge symmetry, like other symmetries in physics, is a statement that any physical system can be changed in certain ways without violating the laws of physics.Modern physics describes the universe in terms of fields such as the electric, magnetic, and gravitational fields, and a general feature of such fields is a symmetry known as gauge symmetry.Theories incorporating such a symmetry are called gauge theories, and although gauge symmetry is found in classical theories such as general relativity and electromagnetism, it achieves its full importance in the context of quantum mechanical field theories.Thus, one could choose to define all voltage differences relative to some other standard, rather than the Earth, resulting in the addition of a constant offset