But there is an accepted standard for human visual acuity, which is the basis of the "retina display" claim.There's no "Retina Display Consortium" comprised of independent reviewers or engineers who have collectively determined an industry standard measurement for declaring a display as "Retina".

Visual acuity - Wikipedia
...which is that a human eye with 20/20 (or 6/6 in metric) can separate details separated by an angular distance of 1 arc minute. That equates to 1.75mm at 6 metres (20 feet - the basis of "20/20" aka "6/6" vision) or 1/300" at 12" (the basis of the "retina display" claim for the iPhone 4 - see also the use of 300dpi as the 'standard' for acceptable print quality although, to be fair, Apple also had their fingers in that pie with the original LaserWriter).
...and it's an angle so it depends on both the PPI and typical distance from the screen, which is why it can be ~300 ppi for a phone at 12", ~220 ppi for a laptop - typically viewed from a bit further away - and ~160ppi for 27" display viewed at 22".
So, yes, there is a simple and objective bit of math you can do to work out whether the angular size of a pixel on a particular display is less that 1 arc minute at a given viewing distance:
angle (radians) = 1/(ppi*viewing distance)
multiply by (180*60)/Pi to get angle in arc minutes
...less than 1 means it is "retina".
Whether that literally translates to "can't see the pixels" is a bit more slippery. What it really says is that beyond that limit you couldn't visually separate (say) two lines 1 pixel apart (that one is easy to try at home) - and the human brain can do all sorts of visual processing tricks up to and including just plain making stuff up. Then there's the issue of how well different people's eyes focus at different distances, let alone how it interacts with your varifocal glasses... But it's a pretty good rule of thumb that, at less than 1 arc minute per pixel, you're going to see rapidly diminishing returns from cramming in more pixels.
Of course, it's also worth remembering that the Apple displays have better colour gamut, contrast and brightness than a lot of cheaper 4k displays - including that bonded glass/optical coating c.f. the cheaper matte anti-glare coating that even the LG 5k display doesn't match - which will all affect your perception of the quality. Expensive display is nicer - shock horror - and apparently, if you stand far enough away, you can't see the difference between $1600 and $700...