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You have object A of hardness 4 and glass B of hardness 6. Is this information alone enough to determine that, under any circumstances object A will never be able to scratch glass B?

For a more practical example, does this mean that it doesn't matter how hard you press, how fine the point of the object is, how long you keep scratching on B's surface, etc. a cat claw for example will never leave a scratch on a hardness 5 phone glass? Or is it just like un-noticeable/negligible?

This doesn't seem to make sense on an atomic scale, since both A and B should be losing loose atoms from their interaction.

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Welcome.

You're referring to the Mohs hardness scale, a qualitative scale to quickly determine, in the field, whether something scratches (carves a mark into) something else. It states nothing about the opposite direction. Of course, given enough pressure or kinetic energy the scraper can experience deformation as well, but that's not the meaning of the exercise.

One can pretty well scratch Gypsum with the finger nail and feldspar with a steel nail. You don't hammer things and do not scratch over and again or with more force than necessary. It's more like, for instance, cutting wood with a pocket knife. No molecules are counted and no microscopic traces investigated, it is just a superficial visual inspection for use in the field. Laboratory work comes later.

https://geology.com/minerals/mohs-hardness-scale.shtml

https://en.wikipedia.org/wiki/Mohs_scale_of_mineral_hardness

https://www.nps.gov/articles/mohs-hardness-scale.htm

Edit: To make some sciency disport out of this, here's a work that deals with the force of a large cat's claws and muscles against the bones of its prey.

Even though the claw, being made of keratin (same as horn, hoove, nail, ...), only has a Mohs hardness of 2.5, it can do considerable damage to a bone of hardness 5. That's because of the kinetic energy induced by the sweep of a paw and the chain of muscles at whose end it sits.

The field test based on Mohs hardness is not affected by the application of kinetic energy.

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  • $\begingroup$ Tungsten carbide will scratch glass but it depends partly on geometry and pressure $\endgroup$
    – blacksmith37
    Apr 18, 2020 at 20:15
  • $\begingroup$ Yep, it's Mohs 9, glass (quartz) is 7 (at most). $\endgroup$
    – user20217
    Apr 18, 2020 at 20:39
  • $\begingroup$ Ooops, I was thinking glass was harder. $\endgroup$
    – blacksmith37
    Apr 19, 2020 at 1:08
  • $\begingroup$ Ok but what I mean is, some people say that because a phone screen is x hardness, it won't get scratched by for example your keys or your cat. But even if the keys or the cat have a lower hardness than the phone screen, they can still leave a mark under certain circumstances, right? $\endgroup$
    – user361323
    Apr 20, 2020 at 17:14
  • $\begingroup$ A domesticated cat can't do harm to a phone by scratch or bite, a large cat will simply crush it. Key against phone is not geoscience. It should have gotten around to keep them in separate pockets ... $\endgroup$
    – user20217
    Apr 20, 2020 at 20:58

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