First, the angular resolution of the human eye is approximately 0.02 degrees, or 0.00035 radians. That means your eye cannot distinguish any angle smaller than that or put another way, any angle that size or smaller will all look like the same angle.
If you are sitting 2 meters from the screen (approx 6ft) that means the smallest meaningful pixel size you can see is:
2m * 0.00035 = 0.0007 m = 0.7mm
If a pixel is smaller than 0.7mm on a side you can't tell the difference between a 0.7mm pixel and a smaller pixel, or, more accurately, your eye will smear together pixels smaller than 0.7mm on a side into a 0.7mm on a side blob.
A 55" 16:9 screen has the dimensions 47.94" wide by 26.96" high.
47.94" wide is 1217.7mm wide
Now for pixels...
1080p = 1920 x 1080
4k = 3840 x 2160
So 1080p pixel on such a screen is 1217.7mm/1920 = 0.63mm
And a 4k pixel will be half that -- 0.32mm
But as noted, the smallest pixel you can see under the stated conditions is 0.7mm which is more than either of those. The optics of the human eye and simple math mean that your eye will smear together and essentially average four 4k pixels into a 1080p pixel. So you won't get any extra resolution or clarity when sitting 6' away from a 55" 4K screen vs a 55" 1080p screen.
