In a recent sharpening article in FWW magazine the author stated that he regularly polishes down to 3 microns and at times down to 1 micron [.000039"].
In response to the article a reader infers this level of sharpening is ridiculous, I personally agree.
My logic is that a one micron edge will crumble in the case of highly tempered steel and at least deform in lower tempered steel cutting edges . the edges will continue to do so until they can sustain the localized bearing pressure due to use . In turn the local bearing pressure will depend on the force applied to the cutting edge, the hardness of the material being cut and lastly the bevel angle of the edge.
The only way these tolerances would work is if the material was infinitely strong we are nowhere near that level probably the closest thing we have to that is diamond.
The other assertion was the finely polished edges hold their edge longer. I am never quite sure about this .A finely ground edge will result in a even cutting edge which in turn will result in the whole cutting edge taking the load and thus reducing the overall edge stresses [and wear]. On the other hand edge ridges on the cutting edge due to a lesser degree of honing will break down due to higher local stresses until the stresses at the cutting edge are even out.
Polishing the back of the bevel may reduce frictional resistance of the tool when in use. If this is true microbevels make sense [a double bevel, the small secondary bevel close to the cutting edge ]. So instead of spending hours polishing the whole bevel, hone a fine microbevel and simply buff out remaining bevel with jewelers rouge .
-- mike hide