We present new results regarding the long-range scalar field that emerges from the classical Kaluza unification of general relativity and electromagnetism. The Kaluza framework reproduces known physics exactly when the scalar field goes to one, so we studied perturbations of the scalar field around unity, as is done for gravity in the Newtonian limit of general relativity. A suite of interesting phenomena unknown to the Kaluza literature is revealed: planetary masses are clothed in scalar field, which contributes 25% of the mass-energy of the clothed mass; the scalar potential around a planet is positive, compared with the negative gravitational potential; at laboratory scales, the scalar charge which couples to the scalar field is quadratic in electric charge; a new length scale of physics is encountered for the static scalar field around an electrically-charged mass, ; the scalar charge of elementary particles is proportional to the electric charge, making the scalar force indistinguishable from the atomic electric force. An unduly strong electrogravitic buoyancy force is predicted for electrically-charged objects in the planetary scalar field, and this calculation appears to be the first quantitative falsification of the Kaluza unification. Since the simplest classical field, a long-range scalar field, is expected in nature, and since the Kaluza scalar field is as weak as gravity, we suggest that if there is an error in this calculation, it is likely to be in the magnitude of the coupling to the scalar field, not in the existence or magnitude of the scalar field itself.

中文翻译：

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五维广义相对论中的远程标量力

我们提出了有关从广义相对论和电磁的经典Kaluza统一出现的远程标量场的新结果。Kaluza框架恰好在标量场变为1时重现了已知的物理学，因此我们研究了统一周围标量场的摄动，就像在广义相对论的牛顿极限中对重力所做的那样。揭示了卡卢扎文献中未知的一系列有趣现象：行星标量在标量场中穿衣，占标量场质量能量的25％。与负重力势相比，行星周围的标量势为正；在实验室规模上，耦合到标量场的标量电荷的电荷为二次方。; 基本粒子的标量电荷与电荷成正比，因此标量力与原子力无法区分。预测行星标量场中带电物体的过强的电引力浮力，这种计算似乎是Kaluza统一的第一个定量的伪造。由于自然界中会想到最简单的古典场，即远距离标量场，并且由于Kaluza标量场与重力一样弱，因此我们建议，如果此计算中存在误差，则其幅度可能会很大与标量场耦合的函数，而不是标量场本身的存在或大小。