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The work is based on two premises: local availability of mathematics to anobserver at any space time location, and the observation that number systems,as structures satisfying axioms for the number type being considered, can bescaled by arbitrary, positive real numbers. Local availability leads to theassignment of mathematical universes, $V_{x},$ to each point, $x,$ of spacetime. $V_{x}$ contains all the mathematics that an observer, $O_{x},$ at $x,$can know. Each $V_{x}$ contains many types of mathematical systems. Theseinclude the different types of numbers (natural numbers, integers, rationals,and real and complex numbers), Hilbert spaces, algebras, and many other typesof systems. Space time dependent scaling of number systems is used to definerepresentations, in $V_{x}$, of real and complex number systems in $V_{y}$. Therepresentations are scaled by a factor $r_{y,x}$ relative to the systems in$V_{x}.$ For $y$ a neighbor point of $x,$ $r_{y,x}$ is the exponential of thescalar product of a gauge field, $\vec{A}(x),$ and the vector from $x$ to $y.$For $y$ distant from $x,$ $r_{y,x}$ is a path integral from $x$ to $y.$ Someconsequences of the two premises will be examined. Number scaling has no effecton general comparisons of numbers obtained as computations or as experimentaloutputs. The effect is limited to mathematical expressions that include spaceor space time integrals or derivatives. The effect of $\vec{A}$ on wave packetsand canonical momenta in quantum theory, and some properties of $\vec{A}$ ingauge theories, is described.

Effects on quantum physics of the local availability of mathematics and space time dependent scaling factors for number systems