Ok, I know there hasn't been a post here for over a year, but I looked the thread over and there are a few things here that could stand some clarifying.
First, Japanese weaponry. Through various means (smelting technique, composite (different types of iron and steel) construction, and surface hardening (actually edge hardening)), traditional Japanese swords had a very hard and somewhat brittle edge integrally connected to a much softer and more flexible back. The thick back provided strength and suppleness, the hard edge could be polished to be extremely sharp and to retain that sharp edge for a long time between sharpenings. This produced a weapon that was well-suited for the demands of combat between foes wearing various types of segmented or laminar armor. The super sharp edge was also very effective against unarmored foes.
However, the secret to the cutting ability of this weapon is the edge. To the naked eye, it appears to be as smoothly polished as the flat of the blade. However, under a microscope, tiny nicks, breaks, and chips in the last micrometer of the edge can be observed. These had the effect of providing a "micro-serrated" edge. As any afficiando of these weapons is aware, they cut soft materials much better with a draw cut than with a straight chop. The micro-serrations effectively turn the edge into a sort of molecular saw. Not bad for technology developed several hundred years ago.
Most other ultra-hard materials mentioned in this thread (especially diamond) have the disadvantage of being very brittle. As the gentleman who handled professional grade ceramic knives in the kitchen mentioned, these have very sharp edges and cut very well, but cannot be handled carelessly lest they shatter. This is typical of all ceramic materials due to their fracture stress properties. Although diamond is not strictly speaking, a ceramic, it's extreme hardness allows it to behave as one. The problem with brittle blades, of course, is that when struck against a hard object, they have a high likelihood of breaking. This is especially true for any blade used as a hand-to-hand weapon against similar weapons. As we see, both the European and Oriental swordsmiths weren't stupid!
One possibility seems to have been overlooked. There are several processes that can embed small pieces of diamond, of the scale of the "serrations" in the Japanese blades as described above, into softer materials. I should point out that the hardest steel imaginable is still much softer than diamond. With proper polishing, these bits of diamond would form a shape similar to the points of the teeth of a saw, with the softer metal between them wearing to form the voids between the saw teeth. I don't recall that anyone has every tried to create a practical cutting instrument using this technique. The technology is quite simple and available today, should anyone wish to try it.
Nanofiber technology is intriguing for the role of a cutting instrument, simply because a thinner edge is easier to push through a material than a thick one, and the maximum possible fineness of the edge is determined by materials properties. Nanofibers, which hold the potential for very high specific strengths, lend themselves to this. However, I feel some sort of serration must be introduced to the edge for the reasons pointed out above. It may be possible to eventually construct a blade composed mostly of nanofibers oriented in the long direction of the blade, but with a few "sawtooth" nanofibers or embedded diamond crystals "grown" in a direction perpendicular to the blade.
There was mention of nuclear weapons cutting through anything, or not being able to do so. Nuclear explosives have two properties of interest to us here. First, they release enormous amounts of heat. This heat load will cause any material known to man to vaporize, provided it remains in the vicinity of the explosion. They don't so much cut their way through objects as melt (or vaporize) their way through.
The second property is that a nuclear explosive detonated in a gaseous environment such as earth's atmosphere produces a shock wave in that gas, expanding outward at high speeds (initially, supersonic speeds) from the point of the explosion. When this shock wave encounters frangible items such as poorly-reinforced concrete buildings, those items are fractured and literally blown away by the high-speed winds accompanying the shock wave. So, a concrete wall that is too far away from the explosion to be vaporized or melted may still be smashed by the shock. Note that this shattering mechanism doesn't work in the vacuum of space. Again, the nuclear device doesn't so much "cut" something as "break" it.
There is a rather fascinating exception to this. During one of the US aboveground bomb tests back in the 1950's, two large (~4 ft. diameter) iron spheres, coated in graphite for thermal protection, were placed next to the test bomb on either side. After the detonation, they were found roughly 1/2 mile from ground zero in opposite directions, little the worse for wear. The explanation is that the high blast force generated by the bomb was enough to propell them away from the explosion faster than the massive heat release could melt through first the graphite coating and then the iron underneath. Being solid spheres, there was no internal structure to be crushed by the blast. Effictively, they behaved as giant elastic tennis balls...or baseballs, if you prefer that analogy. This test was part of the rationale for the Orion project, a concept for pulsed nuclear spacecraft propulsion that was conceived back in the 1960s but never built.
The point to all this discussion of nuclear explosives in a thread about cutting devices is that any sort of plasma device, that is, a "light saber" would "cut" by the same mechanism as a nuclear device: extreme heat. I suggest that any such device powerful enough to cut through say, a bank vault, would either emit so much thermal radiation that it gave the wielder third degree burns, or else the thermal energy would be so well contained within the "blade" of the device that it might to be difficult to detect the heat leakage if you placed your bare hand an inch or two away from the "blade". I suppose it depends on what sort of plasma and heat containment technology you postulate for such a thing.
