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In this specific setting, it would be a speculative sci-fi thing, but this matter in specific isn't central to the plot.

The idea is that the time that it takes for a person to recover from a prosthesis implant is reduced significantly because the cuts in the nerves and tissue are so thin, they don't damage these parts too much. Unlike today's methods of cutting... Human "stuff".

The thing is, even with this theoretical width of the cutting mechanism (with lasers or just a solid scalpel), do we have the technology today to do that? It could be useful if I knew how distant we are today from the technology so I could speculate how common such technology would be in this future.

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    $\begingroup$ If the cut is a cut then it is too wide. That is, if the distance between molecules becomes sufficiently large so that inter-molecular bonds are broken, the inter-mollecular bonds are broken. If the distance is smaller than that you don't have a "cut". (The point being that it is not the "damage" which kills you, it is that the nerves etc. are now in two pieces.) (Think of it like this: no matter how thin a cut in the walls of a blood vessel, if there is a cut so that the wall is in two pieces, blood will spill out and widen the cut.) $\endgroup$
    – AlexP
    Jun 7 at 12:57

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Most surgical blades are steel, but some do use diamond or obsidian blades. The advantage of the obsidian blade is that the sharper with the cutting edge being ~ 30 angstroms as compared with a razor blade being 300-600 angstroms. The main benefit being less trauma to the cells, and for plastic surgery this reduces scaring. The disadvantage is the blades are brittle and can break.

“Under the microscope, you could see the obsidian scalpel had divided individual cells in half, and next to it, the steel scalpel incision looked like it had been made by a chainsaw.”

The problem with a lot of lasers for surgery is that there is a heat affected zone that is larger than the spot size of the laser. This can be reduced by using an ultrafast laser where the energy is deposited and material is ablated before the surrounding area is heated up. You can have a small spot size of about a micron but need to scan the laser and only remove a tiny amount of material with each pulse.

Most of the time the spot sizes for corneal reshaping a few hundred microns, and for other surgeries may be much larger.

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This is difficult to answer, as we have rather little knowledge about the detail of pain reception. Probably the thickness that will damage a cell membrane.

There are multiple types of pain receptors, but the most numerous are free nerve endings. These look like nerve fibres that enter the skin and end, as opposed to other sensory nerve endings that have a particular structure that detects a particular thing, like temperature.

We think that these free nerve endings are activated by physical damage, so a cut that will disrupt their cell membrane will cause their activation and the sensation of pain. As we have no way of making such a thin cut without doing other damage we cannot really test this.

Micrograph of skin sensory nerve endings Section of human digital skin immunostained for the demonstration of neuron-specific enolase that labels axons in nerve fibers and sensory corpuscles as well as Merkel cells. FNE: free nerve ending (white arrows); MC: Meissner corpuscles (black arrows); Mc-NC: Merkel cell–neurite complex (red arrows). bv: blood vessels; e: epidermis. Source

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