从场论中近似经验等价性得到的永久欠定：无质量和有质量标量引力、中微子、电磁、杨-米尔斯和引力理论
Permanent Underdetermination from Approximate Empirical Equivalence in Field Theory: Massless and Massive Scalar Gravity, Neutrino, Electromagnetic, Yang-Mills and Gravitational Theories
摘要：
经典场论和量子场论不仅为现存的经验等价性概念提供了现实的例子，而且还提供了新的经验等价性概念，既有模态的，也有偶发的。一个简单但现代的引力案例可以追溯到19世纪90年代，但显然完全忽略了最简单的相对论类比，结果是一个错误的主张已经扎根，即即使没有光的弯曲，狭义相对论也不可能容纳引力。中微子质量不为零的观点最近才被接受，这表明被广泛忽视的粒子质量不为零的可能性有时得到了证实。在电磁场的情况下，在经典和量子水平上，麦克斯韦理论和普罗卡的具有大量光子的电磁学的单参数族之间存在永久的欠确定性，普罗卡的电磁学在零光子质量的极限下近似麦克斯韦理论。虽然杨-米尔斯理论在经典上表现出类似的近似等价性，但量子化通常会打破这种等价性。一个可能的例外，包括统一的电弱理论，可能允许光子有质量项，但不允许杨-米尔斯矢量玻色子有质量项。即使在经典水平上，有质量和无质量（爱因斯坦）引力之间的不确定性也受到当代争议。
英文摘要：
Classical and quantum field theory provide not only realistic examples of extant notions of empirical equivalence, but also new notions of empirical equivalence, both modal and occurrent. A simple but modern gravitational case goes back to the 1890s, but there has been apparently total neglect of the simplest relativistic analog, with the result that an erroneous claim has taken root that Special Relativity could not have accommodated gravity even if there were no bending of light. The fairly recent acceptance of nonzero neutrino masses shows that widely neglected possibilities for nonzero particle masses have sometimes been vindicated. In the electromagnetic case, there is permanent underdetermination at the classical and quantum levels between Maxwell's theory and the one-parameter family of Proca's electromagnetisms with massive photons, which approximate Maxwell's theory in the limit of zero photon mass. While Yang-Mills theories display similar approximate equivalence classically, quantization typically breaks this equivalence. A possible exception, including unified electroweak theory, might permit a mass term for the photons but not the Yang-Mills vector bosons. Underdetermination between massive and massless (Einstein) gravity even at the classical level is subject to contemporary controversy.
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