A screen's PPI is a fact about the panel. What your eye actually receives is PPD — pixels per degree of your field of view — and that depends just as much on how far away you sit. Sitting twice as far away halves the angular size of the screen and doubles the PPD, which is why a phone and a television can look equally sharp despite a six-fold difference in pixel density. Everything on this page follows from that one conversion, plus the angular limit of your own eye.
A 55-inch 16:9 screen is 47.9 inches wide. At 4K that is 80 PPI. Sit 8 feet away and you receive about 134 PPD — comfortably past the roughly 60 PPD that 20/20 vision can resolve. The same screen at 1080p delivers 67 PPD, also past the limit. That is the whole reason the 4K upgrade looked identical from the sofa: both were already finer than the eye could see. Walk in to 3.6 feet and 4K's pixels finally become individually invisible while 1080p's do not — which is the distance at which the upgrade actually pays.
PPI is a property of the screen alone. PPD is what your eye receives, because it also accounts for viewing distance. A phone at 460 PPI held at 12 inches and a 4K television at 80 PPI viewed from 8 feet deliver similar PPD — which is why both look equally sharp despite a six-fold difference in PPI.
Because at typical living-room distances both already exceed what your eye can resolve. A 55-inch screen from 8 feet gives about 67 PPD at 1080p — already past the roughly 60 PPD that normal vision distinguishes. The 4K version delivers 134 PPD, but that extra detail lands below your eye's resolving limit. Move closer or buy a bigger screen and the difference appears.
20/20 vision is defined as resolving detail subtending one minute of arc. A degree contains 60 arcminutes, so one pixel per arcminute is 60 pixels per degree. That is about 30 cycles per degree of alternating light and dark lines, which matches the measured contrast-sensitivity limit of the healthy eye.
Substantially. 20/10 vision resolves detail half the angular size, so it needs about 120 PPD before pixels disappear — twice the pixel density, or half the viewing distance, of someone with 20/20. About one person in a hundred tests at 20/10, and many people sit well below 20/20 without realising, which is why the same screen genuinely looks different to different viewers.
SMPTE recommends the screen fill at least 30° of your horizontal field of view for cinema content; THX recommends up to about 40° for a more immersive picture. Both are about immersion rather than resolution — you can satisfy them and still be too far to resolve every pixel, or sit inside them and see the pixel structure.