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The relationship between the foundations of mathematics and physics is atopic of of much interest. This paper continues this exploration by examinationof the effect of space and time dependent number scaling on theoreticaldescriptions of some physical and geometric quantities. Fiber bundles provide agood framework to introduce a space and time or space time dependent numberscaling field. The effect of the scaling field on a few nonlocal physical andgeometric quantities is described. The effect on gauge theories is to introducea new complex scalar field into the derivatives appearing in Lagrangians. U(1)invariance of Lagrangian terms does not affect the real part of the scalingfield. For this field, any mass is possible. The scaling field is also shown toaffect quantum wave packets and path lengths, and geodesic equations even onflat space. Scalar fields described so far in physics, are possible candidatesfor the scaling field. The lack of direct evidence for the field in physicsrestricts the scaling field in that the gradient of the field must be close tozero in a local region of cosmological space and time. There are norestrictions outside the region. It is also seen that the scaling field doesnot affect comparisons of computation or measurements outputs with one another.However it does affect the assignment of numerical values to the outputs ofcomputations or measurements. These are needed because theory predictions arein terms of numerical values.

Space and time dependent scaling of numbers in mathematical structures: Effects on physical and geometric quantities