No. You'd calculate the precision of the momentum measurement, realize that it entailed the position measurement had vanishingly small uncertainty, and decide to ignore quantum. Or better yet, you'd have a simple rule to apply (quantum mechanics, outside a very few specified exceptions, cannot productively be applied to macroscopic objects).
What, in the real world, approaches the speed of light?
The electrons in every iodine atom in every molecule of thyroxine in your body?
Even more relevantly, magnetism is in fact the relativistic effect of moving charges
Fair points all.
Let me rephrase:
What part of the Ford and Buick in the intersection approach the speed of light? (and has any effect at all on the outcome)
The electrons in every iodine atom in every molecule of thyroxine in your body?
Even more relevantly, magnetism is in fact the relativistic effect of moving charges.
More significantly, the insinuation in the original that relativity is unimportant (or worse, inapplicable) for subluminal objects ignores the profound implications of relativity to all levels of existence. The fact--just for example--that simultaneity does not exist in the Cartesian sense makes the prospect of constructing a self-consistent concept of "an instant of time" impossible. This places severe constraints on the spatial extent of intelligences, to take just one nontrivial consequence that seems quite far afield to someone who thinks the special theory obtains only near light speeds.
This is also a criticism of the first part of your own post: quantum mechanics is applicable to an enormous number of macroscopic phenomena. Metals, for example. Transistors. Superconductivity. Superfluidity. Phonons. The large structure of the universe. Fluctuations in the vacuum state that made creation of the universe ex nihilio possible. Bell's Theorem. And so on... and so on... The fact that quantum mechanics is "always applicable, but not always useful," is far too overstated in elementary physics texts. The truth is, we really don't know how far into the macroscopic world quantum mechanics "usefully" applies, not only because we haven't exhausted all the possibilities, but also because we really don't completely know how to carry this program out. If we did, things like quantum decoherence wouldn't be so philosophically difficult, and the process of associating Hermitean operators with physical quantities would not be so ad-hoc.