[inscrutablemike]

To put your point in other words, Newtonian mechanics isn't wrong. It's a system of measurement that is only useful at certain scales.

Imagine a yardstick that is only marked at full inches. You can use it to measure things in the scale of a couple of yards, a few feet, and many inches. You can't use it to measure anything smaller than an inch because it's not marked for that scale. You can't use it to measure anything more than a couple of yards because that's unwieldy. That doesn't mean that the yard stick is "wrong".

[gress]

This is a flawed analogy, because the yardstick is accurate at the scales for which it is practical, whereas Newtonian mechanics is inaccurate at all scales, just less so in its sweet spot.

[mikeash]

Newtonian mechanics is more accurate at yardstick scales than any real-world yardstick is.

[gress]

Of course. Nobody is arguing that Newtonian mechanics is not a phenomenal approximation at scales that are very useful for humans, but that doesn't make the analogy any less flawed.

[mikeash]

Then I don't understand what you mean. You said the yardstick is accurate at some scales whereas Newtonian mechanics is always inaccurate, which to me implies that the yardstick is more accurate at some scales.

[gress]

This is a fair point.

The yardstick analogy was set up by the parent to be 'because the yardstick doesn't have marks less than an inch'

Then yardstick is always an approximation that is useful within a particular domain, just as newtonian mechanics are always an approximation that is useful within a particular domain. So far we are in agreement.

Newtonian mechanics always produces an incorrect result, however when the error is small enough to be neglected, because our measurements are noisy or we have no requirement for greater precision, then we can say that they are accurate for our purposes. This is pretty much the definition of an approximation.

It also must be pointed out that in order to know whether our application falls within the domain of values for which Newtonian mechanics are accurate enough, we must also understand something about relativity and quantum mechanics.

Newtonian mechanics alone can't tell you anything about when it is grossly inaccurate, and when it gives you a value that is indistinguishable from experiment. You must understand its limits in order to use in in the general case. It is therefore not 'perfectly accurate', but merely a good approximation based on limited data.