The location of an object $x$ depends on how we choose our coordinate system. If we move the zero point, $x$ also changes. However, since we have translational invariance, we can always do such shifts without changing anything.
Now, in quantum theories, there is usually a lot of emphasis on quantities that are gauge independent. For example, the phase of a wave function in quantum mechanics can be changed using global $U(1)$ transformations and is therefore gauge dependent. So completely analogous to how we can shift the position of an object using translations, we can here shift here the phase of the wave function.
How are these two situations different? Since both, the location and the phase of the wave function, depend on how we choose our coordinate systems, they both shouldn't be measurable?!
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