If I have a zero-width, infinitely-strong sword. Do I need to be worried about radiation when I cut things? [closed]

Question

Would the blade cutting through the atoms in the target material create unstable isotopes and would that be a concern for the wielder?

Answer 1

I'm going to answer this question, but I ask that you please pay attention, because part of what I'm going to explain is why you've asked a poor question.

You don't explain how scientifically-based you want the answer to be? Here's the problem:

You have a non-scientific weapon because no tangible object can be zero-width. You could theoretically have a one-atom-width device, call the atom unobtainium such that it won't react with any other element, but it's still not zero-width.

But let's run with zero-width. If you have a zero-width blade, does it have charge or not? Nothing has no charge. There are protons and electrons all over the place. OK, let's assume it has no charge whatsoever, meaning (theoretically) that atoms won't move based on the charge of the material used to make the weapon. Theoretically (I'm going to say that a lot), this leaves us with what we think is the perfect cutting edge and everything is sitting in space waiting to be cut. Schrödinger's cat is alive and well. Maybe.

Under those conditions you theoretically could get fission. Except that mere human strength or, more accurately, the force of human strength is paltry, insignificant, even irrelevant, compared to the strength of the weakest nuclear bond. In other words, if that edge hit an atom dead-on, the atom would just be pushed aside.

And that's assuming that the atoms are there to be pushed aside. Atoms move. At the size of space necessary to believe you could be dealing with fission they move a lot. It may look like your enemy is sitting still, but really he's a fuzzy blob of agitated atoms in desperate need of a Teddy Bear.

But, let's assume that's not an issue, either. What's our next problem? At the atomic level, there's a whomping lot of empty space in, around, and between atoms. I could be dead wrong about this (and one of our chemistry experts could and should correct me!), but methinks that your blade wouldn't cut anything at all. At zero width, it would simply pass through, for example, your enemy (who's standing before you with a more traditional sword, considered a blunt-force weapon compared to your sword, but he's gonna beat the living crap out of you with it).

But, let's ignore that, too and assume you can have a zero-width weapon, that human strength can divide atoms, that enough atoms will sit still for you to strike them, etc., etc., etc.

Before we move on, what have I taught you?

• Every time I said "theoretically" or "assuming" (or any variation of those two words) you should have thought to yourself, "darn, I forgot to add an important piece of information."

• The further you are away from "reality" the less "reality" can be a limiting condition to your answer.

• When you ask a question, it really helps if you list the limitations, conditions, and restrictions (in fact, you're required to list them. It's a reason to close your question if you don't). In your case, explaining exactly the nature of a single "hit" or swing of the weapon is expected to encounter would help. For example, the number of atoms that could result in fission due to a swing in mid-air is much, much, much less than you would encounter if you cut a rock in half — and neither of them are much of a problem compared to cutting a 10# ball of Plutonium-239 (which doesn't exist in nature, if I recall), which would result in a mushroom cloud. Maybe. Stupid cat. Assuming you actually hit and separated enough atoms to create a chain reaction.

• Finally, it really helps if you do a bit of research, first. There are plenty of online explanations for what fission is and what it takes to get it. Your having read a couple of them would have resulted in a much better question.

Yeah, yeah, yeah... but would there be any radiation?

In reality? I doubt it. All the atoms would just move aside because a human arm can't generate enough force to split an atom or start the reaction that could. Frankly, I don't even think you could cut off your opponent's arm. I think this blade would simply pass through anything you swung it at leaving everything unchanged in its path. If you think about it, ghastly amounts of "zero width" radiation pass through the human body every day... and we're not dropping limbs or anything.

And if you assume (there's one of those words again) that some atoms were split. You're not swinging for anything that has enough density to result in any kind of critical mass. In other words, even if you did get some radiation. You'd likely have a higher chance for getting cancer from sunbathing.

But in your world?

In your world that sword splits every atom in its path. Due to low material densities we're not leaving a trail of burning death and apocalyptic microwaves—but it's enough that if you don't mix a bit'o lead into the metal used to make your character's armor, then over time it will kill your character. The swordmaster's hands are closest to the blade, so they'll need the most protection.

So say we all....

And why do I like this explanation? Because a good story has balance between overwhelming strength and overwhelming weakness. Superman has krypton. Shazam! is a teenager. Batman has Robin. You get my drift. You need a weakness or your godlike weapon isn't actually any fun. What's the weakness?

If the wearer doesn't posses and use the right kind of armor... they're dead. It's very Michael Moorcock. I like it!

Answer 2

If your blade is really zero width, then it is not a blade in the usual sense of the word, it's actually a shield. It 'cuts' things by isolating the atoms on one side from the atoms on the other, so that they are no longer attracted by their chemical bonds and simply fall apart under gravity or angular momentum.

We can actually estimate how much force it will require to swing a sword like this. If an armoured human weighs approximately 125kg and has an average atomic weight (including the armour) of 25 amu, then they contain approximately $3\times10^{27}$ atoms. Atomic bond lengths are on the order of 200pm, so if the human is approximately 2m (ie $10^{10}$ molecular spacings) tall, then any cut is going to need to sever around $3\times10^{17}$ atomic bonds. With an average bond dissociation energy of say 5eV per bond, your cut needs to add around 0.25J to the target in order to 'reconfigure' it (best term for dismembering I've seen in a while!) from one bound-together piece to two separate pieces. To deliver that work over the 0.5m thickness of the torso unfortunately (for the target) requires a swinging force of just 0.5N, which is going to make for a scarily easy-to-swing weapon.

The atomic radius is five orders of magnitude smaller, so the same cut might expect to intersect $3\times10^{12}$ atomic nuclei. Almost 99% of the mass of the human body is made up of six elements: oxygen, carbon, hydrogen, nitrogen, calcium, and phosphorus, and all of these are lighter than iron and so cutting those nuclei requires an input of energy, not a release from nuclear fission. The exact energy will vary a lot depending on exactly how the atoms are divided, but for just one example, splitting ${}^{16}\mathrm{O}$ into two ${}^{8}\mathrm{Be}$ requires an input of $10^{-12}$J; so we're looking at around another $\mathrm{1J}$ to deal with any atomic slicing.

So one swing through a human torso might cause $3\times10^{12}$ atomic slicing events, the vast majority of which will produce elements lighter than Oxygen. Some highly-unscientific clicking around in the bottom quadrant of this table suggests that most of the products (if they're not stable) will decay by neutron or proton emission (which has a very sharp falloff and is very unlikely to reach even the bearer's hands), beta emission with an energy around $100 \mathrm{keV}$ (stopped by 1mm of water), and gamma radiation with energies up to (in the worst case) $1 \mathrm{MeV}$ (blocked by 1cm of various interesting metals). So only the gamma radiation is really concerning, as that's not a realistic amount of armour to wear.

Say the soldier makes one of these cuts every second, at a range of 1m. She's effectively standing 1m away from a gamma source like ${}^{60}\mathrm{Co}$ with an activity of $\mathrm{1 TBq}$. That's an exposure of $\mathrm{270 mSv/hr}$, which has various moderate negative effects, probably equivalent to a year's smoking cigarettes.

So TLDR, yes it causes some radiation exposure, but no, not something that's going to be immediately noticeable. Bearers of these weapons are unlikely to have long healthy retirements, but then you knew that anyway...

Answer 3

The sword you describe is an impossibility, of course. You know this. So the existing laws of physics wont be enough to answer your question. You will need to extend the laws of physics to incorporate your blade.

This means you need to define how the blade works. What does it actually mean for this blade to cut? Having zero thickness, it isn't going to move two atoms apart at all. That's how we usually cut: we push some atoms to the left, some to the right, and break the bonds between them. This won't do any pushing.

So how do you make it cut without cutting? This is where you have to invent the physics. One candidate might be that it blocks forces from passing through the blade. That way, when the blade is between two pieces of an atom, there are no forces holding them together. This sounds like it might "cut" something!

Now you have to ask about how it does it. What happens while it is cutting? Can it create infinite energy? Consider a very large blade. I hold it under a heavy object, blocking the effects of gravitational forces on the object, tap it so that it floats upward (sans gravity). Then when it's high up, I attach a rope to it, move the blade, and let it fall down, generating power by pulling on a generator with the rope. This is like the "gravity battery" installations, except it generates infinite energy! It does so because this idea of simply stopping the forces naively allows us to create geometries that defy the conservation of energy.

What if you don't like the idea of your blade tech being able to offer infinite energy for free? Well, we have to adjust the physics. Now here the physics community can help. The fundamental forces operate with "fields," which are continuous. Anything that manipulates the fields must do so smoothly. So our blade can't suddenly decrease the fields as it cuts. It has to "push them out of the way." The fields need to be distorted as the blade approaches so that, by the time the blade gets there, all of the field lines have already been shoved out of the way.

This, conveniently gives us our answers. Such field distortions are actually exactly the sort of thing the atoms in a real knife make. And more importantly, you can prove that they must be 3 dimensional. Just like a 1-dimensional singularity in a black hole defines a 3-d event horizon around it, your 2-d blade projects some 3-d shape within which it does these field manipulations.

And now we can start looking at the impacts of that. We haven't said how wide it is. It has to have finite width (to avoid the infinite energy paradoxes), but it can have any finite width you please. In order to stand a chance of cutting a nucleus, it would need to be no thicker than $10^{-15} \text m$, the width between protons in a nucleus.

Of course, the nulcii are moving. Try chopping a cotton ball in half with a knife midair, and you'll see the problem. In order to cut a cotton ball, you need to rely on the inertia of the cotton ball. If you don't move fast enough, the cotton ball simply moves out of they way, pushed by the knife. Likewise, you depend on the nuclii of the atom to have enough inertia to keep the ball in place.

How fast do you have to cut? Well this is interesting because we start to get numbers. The strong force is 137 times stronger than electrostatic forces at this distance. So we can ask what sorts of abuse this atom faces electrostatically, and at least 137 times that is needed to cut it apart.

And our first sign that this wont happen is that we can look at ionizing radiation. Ionizing radiation is powerful enough to knock an electron from its orbit. The mere fact that we are interested in whether it ionizes or not suggests just how far these energy levels are from splitting an atom. Ionization is way easier.

How about jumping right to nuclear fission itself? It turns out that we can talk about the energies required, the fission-input energy. Neutrons used to split U-238 need about 1MeV to even stand a chance of splitting it. We'll use this as a bound - everything else is going to take even higher energies.

I did some calculations, and 1MeV can only really be achieved at relativistic speeds. In nuclear reactors, this is accomplished by the raw speed of the neutrons. So you would need to swing your blade at relativistic speeds in order not to simply push the atom aside. Yes, this is the "fast-neutron reactor" speed. There are slower thermal-neutron reactors, but they operate on the fact that neutrons have no charge, so can "sneak" into the nucleus. To cope with our blade stopping forces, we had to have an electrostatic effect, thus the atom moves out of the way rapidly.

Now this was for just one particular blade physics. You are welcome to come up with others. You might make one which only stops strong forces, not electrostatic ones, making your blade act more like a neutron. But then we need to ask how it "cuts" in the first place!

Answer 4

Cutting process

We cut things in many ways.

Chip forming. The excess material is gradually removed from workpiece in smaller chips by Milling, Drilling, Turning.

Shearing. This process uses a moving blade to push against the fixed workpiece like Punching, Stamping.

Abrasive Material Removal. The excess material is gradually removed from workpiece through erosion by Grinding or Lapping.

In all these processes, intermolecular forces are overcome. Molecules in different parts or chips remain intact.

Cutting Atoms

Your sword is made of molecules. It cannot enter atoms.

Even if you think of a hypothetical thin blade, you cannot cut atoms by any of the above three ways because you need to overcome the Strong Nuclear Force which may not be possible.

Suppose it really cuts the atoms

Fission Process

Nuclear fission is a reaction in which the nucleus of an atom splits into two or more smaller nuclei. The fission process often produces gamma photons, and releases a very large amount of energy even by the energetic standards of radioactive decay.

So if your sword is able to split the nucleus, you will get a fission process.