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Jul 8, 2017 at 6:34 comment added SRS 1. I get your point. Since the scale transformation property of $\textbf{F}$ is not known a priori, because the form of $\textbf{F}$ is not known, Eq.(2) does not prove that Newton's law is not scale invariant. 2. But if $\textbf{F}$ is a constant force then Eq.(2) does break the scale invariance. 3. Isn't that physically surprising? Surprising because there is no intrinsic time scale or length scale in the problem that can be constructed from the constant $F$ and $m$. Then why is the scale invariance broken with constant $\textbf{F}$ (physically)? @ACuriousMind
Jan 21, 2017 at 17:40 vote accept SRS
Jan 21, 2017 at 14:37 history answered ACuriousMind CC BY-SA 3.0