system
Given the following post, respond as if you're commenting on Reddit:
human
Where do Newtonian physics stop and Einsteins' physics start? Why are they not unified?

Edit: Wow, this really blew up.  Thanks, m8s!
gpt
As a rule of thumb there are three relevant limits which tells you that Newtonian physics is no longer applicable.

1. If the ratio v/c (where v is the characteristic speed of your system and c is the speed of light) is no longer close to zero, you need special relativity.

2. If the ratio 2GM/c^(2)R (where M is the mass, G the gravitational constant and R the distance) is no longer close to zero, you need general relativity.

3. If the ratio h/pR (where p is the momentum, h the Planck constant and R the distance) is no longer close to zero, you need quantum mechanics.

Now what constitutes "no longer close to zero" depends on how accurate your measurement tools are. For example in the 19th century is was found that Mercury's precession was not correctly given by Newtonian mechanics. Using the mass of the Sun and distance from Mercury to the Sun gives a ratio of about 10^(-8) as being noticeable.

Edit: It's worth pointing out that from these more advanced theories, Newton's laws do "pop back out" when the appropriate limits are taken where we expect Newtonian physics to work. In that way, you can say that Newton isn't *wrong*, but more so incomplete.