If two solids touch (and slide against each other for some distance), is it possible for there to not be a scratch on at least one of them?
More broadly I am interested in: what causes a scratch, and what is a scratch, but I am not seeking answers to those at this time.
Thank you very much
Incidentally I have had decent performance with PTFE, tungsten disulphide and similar as far as solid lubricants. On tools, hard ceramic coatings are used to improve wear resistance.
Note, even materials like polished steel have a certain degree of surface roughness, which will affect scratch resistance. According to Wikipedia, there is a von Mises yield criterion
for when a ductile material begins to yield; to avoid this, you need to keep the stress on it below a critical value.
I think the answer to your question, no, if two solids slide against each other, there will be degradation that is detectable somehow. To phrase it another way, bearings wear out eventually. I’ve seen work with scanning tunneling microscopes and atomic force microscopes detecting very slight degradation after very minimal sliding contacts.
You might also look up galling, which is a kind of frictional damage. It’s especially common without lubrication when both the solids are made of the same substance.
Thank you both very much
This is helpful to know
This agrees with my intuition that there should be some threshold value 
Those microscopes sound very cool!
If I’m ever in a situation where surface condition/preservation matters, I will be sure to consider how much degradation is occurring in relation to how much degradation is permittable
I’m have no significant knowledge in material sciences, but it seems to me that so long as there is friction between the two surfaces, there must be some sort of shear forces on the molecules of both of the surfaces, which will be sufficient to cause some of those molecules to break away from the surface, causing at least some degradation.
Hulk scratch!
Somewhat tangent to the topic: The Rolamite is an nearly frictionless bearing that operates ideally with no sliding contact between surfaces. As no materials are perfectly smooth, or able to operate without some slippage there is some residual friction that would be revealed as scratches under close examination.
It was my understanding that there is a very thin film of lubricant between two parts of a bearing, or between the bearing and the thing it’s bearing. No touching.
Only true for lubricated bearings. Low friction plastics like PTFE and HDPE can be used for lubrication free bearings. The Rolamite device I linked to above doesn’t require lubrication because the surfaces don’t slide against each other just as the wheels of a car don’t require lubrication between the tire and the road.
The rolamite does, however, require a strip of something flexible, and flexing any real-world material will involve losses.
Think about a related situation: polishing a surface so that it’s smooth. Wear is unavoidable, but perhaps scratching is avoidable. That is, we could have surfaces sliding past each other with the wear making them smoother rather than rougher.
Why avoid this? Isn’t a ductile material the scenario where there can be no scratching? A solid waxy material isn’t going to scratch.
Although I guess this doesn’t fit the “no degradation” supplementary stipulation in the OP.
Even the use of these instruments to measure surface degradation causes some degree of degradation. Operating techniques like “tapping mode” are intended to minimize their effect on soft surfaces like plastics and living cells, but if you can sense the surface, the surface can sense you.
It will smear and, if one surface or the other has inhomogeneities in hardness, stiffness, or surface height, those inhomogeneities will deform the mating surface.
I wonder if there are ductile/waxy materials that can be considered solid, but under friction their smooth surface moves but reforms a perfectly smooth surface. There would be “smearing” or perhaps even a thin layer of melting, molecules would be rearranged, but afterwards no detectable change in the smoothness of the surface.
But I guess a material like this cannot be polished, so it wouldn’t ever be perfectly smooth.
When you sharpen cutting tools, e.g. for woodworking, you work through progressively finer grits. The common wisdom is that you can move on to the next grit when the scratches you are creating have erased the coarser scratches you started with. When I get to the finest grits like a 10000x water stone or a diamond plate, I can’t see the scratches anymore, even with an optical magnifier, but I’ve seen scanning electron micrographs of sharpened and honed surfaces and there are still scratches. They’re just below the optical detection limit.
I think it depends on what you mean by “smooth” and on what scale you’re interested. I’d think there would be applications for soft, “smooth” bearing surfaces like you suggest, but tribology isn’t my field.
There are. Babbitt bearings are made from soft metals, softer than the steel shafts that run through them. Friction generated heat will cause the bearing surface to conform to the shape of the shaft even as the bearing and shaft materials expand in use. Shafts are polished mirror smooth where they are in contact with the bearing material which will be smoothed and polished to conform. However, there is still sliding contact between the materials which will never be perfectly smooth.
Not so much a typical bearing but grease seals are often used for inboard boat motor shafts to emerge from the hull underwater. They aren’t bearing much weight, but supply a continuously smooth water repellent contact surface.
Silver is incorporated into precision bearings, it has some natural lubrication characteristics other metals lack.
I was thinking of two similar surfaces of similar roughness. There may be friction between them, and, especially under load, even wear, but if some molecule moves around perhaps you would not necessarily call that a “scratch” even if there was some plastic deformation.
That also brings to mind: if you keep the two surfaces far apart, as in a magnetic bearing, they are not going to scratch each other.
There is a regime called “superlubricity”
where the coefficient of friction becomes really small, but I do not know how well that scales up to large surfaces and/or heavy loads. There is a graphic on page 490 of this already really old article
https://doi.org/10.1038/s41586-018-0704-z
featuring, progressively, nanotube-based frictionless rotational actuators, wear-free nanoscale read/write contacts in hard-disk drives, MEMS, low-friction ball bearings, and efficient mobile low-friction connectors.