3 ms·

Declaring our theoretical understanding of fluid dynamics flawed because Navier-Stokes requires the continuum assumption strikes me as being similar to declarin

Declaring our theoretical understanding of fluid dynamics flawed because Navier-Stokes requires the continuum assumption strikes me as being similar to declaring General Relativity flawed because it fails to include quantum theory. Navier-Stokes and General Relativty are incomplete, yes, but they are remarkably accurate and useful over the range for which their governing assumptions hold—we have complementary theories that operate over ranges for which the governing assumptions for NS and GR no longer apply. Aesthetically, it would be lovely to have a master equation that works from the molecular scale up to the bulk scale. Practically, that master equation would likely reduce into the familiar forms that are presently used.

vanderZwan 11y ago
> similar to declaring General Relativity flawed because it fails to include quantum theory. Or similarly declaring classical mechanics flawed for not being accurate around light speed (just trying to give another, possibly more relatable analogy - although your GR/quantum theory is more appropriate because it also deals with macro/micro scale). There's a reason we still teach Newton's laws in high school, aside from being easier to grasp: it's accurate enough for basically any practical situation. If you're is not dealing with light speed (so.. particle accelerators and not much else), synchronised time measurements over long distances[0] or space stuff, you are not going to need it. And even in the space case: when they taught us special relativity in our first year of physics, our professor was quick to point out that classical mechanics was accurate enough to calculate the trajectories of the Apollo missions. Physics, or at least applied physics, is all about finding the sweet spot between good enough approximation vs ease of calculation, and knowing where you're "wrong" in case you need more accuracy. [0] Because of the earth's rotation - handwave handwave something with inertial frames.

vanderZwan 11y ago

> similar to declaring General Relativity flawed because it fails to include quantum theory. Or similarly declaring classical mechanics flawed for not being accurate around light speed (just trying to give another, possibly more relatable analogy - although your GR/quantum theory is more appropriate because it also deals with macro/micro scale). There's a reason we still teach Newton's laws in high school, aside from being easier to grasp: it's accurate enough for basically any practical situation. If you're is not dealing with light speed (so.. particle accelerators and not much else), synchronised time measurements over long distances[0] or space stuff, you are not going to need it. And even in the space case: when they taught us special relativity in our first year of physics, our professor was quick to point out that classical mechanics was accurate enough to calculate the trajectories of the Apollo missions. Physics, or at least applied physics, is all about finding the sweet spot between good enough approximation vs ease of calculation, and knowing where you're "wrong" in case you need more accuracy. [0] Because of the earth's rotation - handwave handwave something with inertial frames.