# If something is infinitely thin can it cut through anything? [closed]

Not sure if I heard this somewhere or how I came up with this idea but would something infinitely thin object be able to cut through everything effortlessly? For example, if I had a knife with its blade being infinitely/only one atom thick would it be able to cut through any material without any effort needed at al?

Also, since it's related, would if, let's say, we had a pin with an infinitely small point could it go through everything as well?

• To "cut through" I assume you mean to actually separate material. It still requires energy (effort) to break bonds in a material. Oct 19, 2015 at 21:40
• "Infinitely thin" is A Whole Lot Smaller (TM) than an atom's width. OK, seriously: the problem is in defining the limit of pressure (force per unit area) as the area goes to zero. It's kinda hard to find that limit, which is what you're sort of asking about. Oct 19, 2015 at 22:33
• An atom's diameter is on the order of angstroms (1e-10 meters), so if by "infinitely thin" you mean "one atom thick" then this is answerable. Oct 20, 2015 at 10:28

Also, since it's related, would if, let's say, we had a pin with an infinitely small point could it go through everything as well?

The problem with making a pin or knife edge so small or thin is that there will be potentially be very large stresses at that small area. That means in order for the pin tip or knife edge not to disintegrate or completely deform at first contact it needs to be made of a very stiff and strong material AND needs to be backed up with additional very stiff and strong material behind it. There is also the concern about possible buckling: If you have a pin tip that is so small in size and which is mounted on a pin shaft that is similarly small in diameter, then it will be very susceptible to buckling as soon as it makes contact with the target and the force on the tip starts to build up. Same thing with a very thin knife edge. The bottom line is that the hypothetical atom-sized pins or knife edges you describe probably wouldn't hold up well against the stresses that they would encounter against most materials.

Not necessarily. The assumption is that as it is infinitely thin, i.e. 2 dimensional, it can be inserted into a medium and experience no force. But not all forces act in the direction of insertion. For example, if you insert a conducting loop into a magnetic field with the field normal to the surface of the loop it will experience a force that acts to slow it down.

• ??? whats' this got to do with the question at hand? Oct 19, 2015 at 22:34
• the assumption in the statement an infinitely thin thing can cut any object'' is that an infinitely thin object would feel no force, therefore can be inserted into any object (i.e cut any object). Im merely pointing out that this isnt always that case. On the microscopic level, weather or not you can cut something depends on how much resistance force (in terms of electrostatic repulsion etc) you experience when inserting your cutting object into the medium. I can cut a neutron star with a banana if I can put enough energy into the banana. Oct 20, 2015 at 17:13

Well, it depends. If it's infinitely thin, what is it made of? I have the feeling that it would just phase right through the thing you want to slice.

When one throws around the term "infinite" and "infinity" one should be aware that one is working in a mathematical framework isomorphic with the mathematics of classical mechanics and electrodynamics.

Our experiments have shown us that when dimensions become smaller than the Heisenberg Uncertainty Principle dimensions, classical models break down. So an infinitely thin plane belongs to the quantum mechanical regime, as atoms which you propose to make it up with belong to that regime.

At the atomic level the bonds that hold a crystal , as an example, together, have to be broken, i.e. the atoms from your knife should interact with the atoms on its path into the crystal , that would take energy so there would be the effort in the insertion of your knife. The thinness helps in a statistical way, as the interactions of a two atom thick knife would be approximately twice as many and therefore approximately twice the effort. (A crystal seperates more easily as its symmetries allow for transfer of energy along orientations that are minimally bound).