Presymmetry of Classical Relativistic Fields

The physical act of accelerating observation instruments has an obvious counterpart in Newtonian physics: It is the transformation induced by $(\overrightarrow{\mathrm{x}}, t)\to (\overrightarrow{\mathrm{x}}+\frac{1}{2}\overrightarrow{\mathrm{a}}{t}^2, t)$. In special relativity, a theoretical counterpart for physical acceleration has been introduced only for a small subset of measurement procedures, such as clocks and yardsticks, but not for such instruments as accelerometers. We propose a general theoretical counterpart for physical accelerations in Minkowski space. In the algebra $\mathcal{O}$ of observation procedures, it induces automorphisms, not of $\mathcal{O}$ but of a point subalgebra ${\mathcal{O}}_x\subset \mathcal{O}$ that is associated to a single point $x$. From the postulates of presymmetry, we deduce a generalized version of Newton's second law; an acceleration-invariant subset ${\bigcup }_{\mathrm{}\left(x\right|\mathrm{}{x}_0=0)}{\mathcal{O}}_{\mathrm{xc}}$ of instant observation procedures provides complete predictive power. The main technical contribution of the paper is the introduction of a topological algebra $\mathcal{O}$ in which local subsets associated to a single point are proper (although unbounded) subalgebras, whose automorphisms are discussed.