  In this paper, we discuss some subtle concepts, such as coordinate,
measurement, simultaneity, Lorentz-FitzGerald contraction, singularity in
fundamental physics. The explanations of these concepts in textbooks are
usually incomplete and lead to puzzles. Some long-standing paradoxes such as
the Ehrenfest one are caused by misinterpretation of these concepts. The
analysis shows these concepts all have simple and naive meanings, and can be
well understood using suitable logical procedure. The discussion may shed light
on some famous paradoxes, and provide some new insights into the structure and
features of a promising unified field theory.
