But I can't apply force to individual atoms of the cup. I can only apply force on a large number of the atoms of the cup at once.

So, it seems to be that even if, were I to apply the entire force to a single atom of the cup, the atom would be removed, that would not impact my ability to pick up a cup, because I cannot apply the entire force to a single atom of the cup, instead, each atom of the cup which I apply force to has a much smaller force that I put on it.

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What I am talking about is if I were to apply the total force I apply on the cup to a single atom of the cup.

If I took a thin thread strong enough to support the weight of the cup, and threaded it through the handle of the cup, I would be applying the same total force to the cup, and I would be applying it to a much smaller number of atoms, but I think the number of atoms the force would be applied across would still be very large.

Perhaps a needle would be a better example (it would be hard to balance, but that is only a practical matter)

But then it seems to me that if I were to apply the force needed to lift the cup, on an area the same as that at the end of a needle, it seems quite likely that the needle would scratch the cup (and, in doing so, displace some of the atoms of the cup).

Therefore, it seems that the amount of force needed to remove an atom from a cup, may be less than that needed to lift the cup (at least for relatively heavy, and not all too hard, cups).

And, as far as a radius of an atom is a meaningful concept (which is, mostly, I think), it seems the radius is generally at most around 260 pm, so, a square bound around it (which should be in a sense an overestimate) should have an area of .2704 square nanometers. When I look up the surface area of a needle, I find that its about 12.6 mm^2 (on the lower end of the estimates).

So then, the head of a pin would then be around the surface area of 4*10^13 atoms, and then, because of the space between the atoms in the cup which I might have neglected to consider, maybe drop off a few orders of magnitude (lets say, 4 orders of magnitude. I think that seems safe.)

So then, if you took all the force that is being applied to the cup by the needle, and instead applied it to a single atom, the amount of pressure being applied somewhere on the cup would then be around 10^9 times as much.

Generally I don't think it seems all that hard to scratch a cup with a needle, but perhaps applying force to a single atom would not be as effective as applying half the force each to two atoms, at removing them from the cup. So, another few orders of magnitude at most I'd guess.

So then, scratching the cup with a needle is not all that much harder than lifting it,

If the total force from the pin when scratching the cup were all on a single atom, the pressure would probably be at least 10^9 as much (to the degree that pressure makes sense in this context)

removing a single atom probably does not require 10^3 times the force to remove due to the fact that the other atoms nearby do not have a similar force applied to them, I don't think (? but maybe it does?).

So, with the pressure from putting the force on a single atom instead of using a pin being 10^9 times more, I think then the force on that single atom would be 10^9 times more than the average force on a given atom when it is spread over the pinhead surface, and because I think it probably doesn't need 10^3 times as much more force to remove an atom when the surrounding atoms are not experiencing similar forces, or, at least doesn't need 10^9 times as much, I think the force used to scratch a cup with a needle, if applied to a single atom on the surface of the cup, would probably remove that atom from the cup.

And because the force needed to scratch the cup does not seem much more than that needed to lift a heavy cup,

I think using the force that would be needed to life a heavy cup, would, if applied to a single atom on the surface of the cup, be enough to remove the atom from the cup.

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I think a more relevant measure for whether something is an object might be whether it takes more than a given amount of pressure to remove parts of it, instead of taking a given amount of force. (or force per mass, or force per mol. . But it seems like pressure might work well?)

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uh, I've been assuming that you are, like me, just trying to reason this out, as opposed to actually, unlike me, really knowing the physics behind how materials stay together. If that is not the case, oops, I have made an error.

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regarding "object" being a human convention: Sure, but seeing as the gypsum pillar seems to be something that people would classify as an object, it seems like it would make sense to revise whatever definition we choose for "object" to include such a pillar.

Although, when I think about it more, maybe such a pillar might be best not considered an object, so much as something that, each of a certain type of parts of it would be an object if the rest of it were not there?

I guess it is useful to be able to talk about whether something is an object even in microgravity, so I guess maybe it makes sense to choose some amount of pressure\whatever needed to pull something apart, rather than whether it can be picked up without falling apart.

hmmm... ok I'm thinking pressure might not be quite right either?

I'm kind of confused because http://sites.bio.indiana.edu/~hangarterlab/courses/b373/lect... seems to say that water has a higher tensile strength than gypsum, which doesn't seem to make sense to me.

I'm guessing maybe that is only in a particular situation?

hmm...