This is the kind of answer I come to this site for.

I realized reading the question things would be bad, just not this bad... Would the situation be changed at all by not having the protons move that far? If you could move them, say 1 meter away, the attraction between the protons and the sword would be ginormus. They would collapse into each other, and an explosion would follow. A pretty bad one. But is there any chance at least the sun would survive? Is there any safe distance to move the protons?

@RadovanGarabik Note to self: as a rule of thumb, extracting protons from random objects is a bad idea. Beautiful answer. (+1)

Presumably you could carefully remove the protons from just a small part of the sword. By calibrating this, you could limit the damage.

This doesn't seem right to me - if you converted the 1 kg of matter into antimatter and it then fully annihilated with matter around it, that would release 2kg*c^2 = 1.8e17 J of energy, which is less than the yield of the Tsar Bomba, which didn't come anywhere near destroying the earth. How could just the electrons somehow release significantly more energy than actually turning them into antimatter?

@RobWatts If you converted the 1 kg of matter into antimatter, then you've converted the electrons too, so you won't have a gigantic electric charge anywhere. And if you only converted the protons to antimatter, then you'd have the energy from annihilation plus the gigantic electric charge.

We can make this less world-ending simply by combining the excess electron with the removed proton to form a hydrogen atom. I'd expect some heat to be involved so it's quite possible that hydrogen atom with another combines with some circulating oxygen to make water.

just remove conservation of charge

Probably the least of your concerns, but a 4kg sword is too heavy for an ordinary human to do much with. Even a sword weighing 2kg would be a massive thing, wielded in two hands.

Now I really want to read a timeline of events 'what-if'-style. I imagine the the immediate surroundings (and matter of the unlucky wielder) would rush in to the sword very, very quickly and perhaps result in new exotic forms of matter? (I assume the following collisions would be more than enough to fuse them together). I have the same doubts about the effect on the sun as Rob Watts and @Rekesoft here, it doesn't seem quite right.

One other thing to be concerned about is the fact that having that large a mass of extra protons or electrons (owned by these newly created ions) would create an enormous mutual repulsion between them, overwhelming any plausible chemical or physical bonds between the ions and causing whatever the sword was now made of to instantly explode very, very violently as the ions attempt to escape from each other.

I wonder if Randall Munroe reads this site. If not, someone should tell him, this is a never ending source of "what if" wonders.

@rekesoft Why do you expect the electric field to be short-lived? If, like Radovan answer implies, the protons simply vanish, then there is no positive 6.4MC charge around to balance the electrons' (the overall electric charge of the universe is probably zero). The electrons of the sword will repel each other violently and will eventually disperse, but Gauss' theorem ensures that from the point of view of the Sun, the electric field will have more than enough time to counteract the gravitational pull.

@Erik I just wanted to say that! I did a little googling to make sure and was confirmed, even the largest greatswords didn't weigh over 3 kg, a 4kg one would be good maybe as a wallhanger...

Well, it sounds more like it will attract all the solar wind towards it, rather than ripping the sun apart, since the sun will presumably reach an equilibrium of charge as soon as you start sucking protons off it, where the protons would prefer to stay on the negatively-charged sun. Earth, however, is still obliterated.

@Erik Depends on your sword. A typical two-hander is estimated as about 3 kilos while the parade version can have up to 4.5 kilos!

I checked the electric potential energy of a 4kg ball of iron with one proton removed from each atom. I got 5*10^24 J. It's a long way off from blowing up the earth (that takes 10^32 J), but it's equivalent to a small cargo ship full of antimatter. Antimatter has a higher base energy conversion, but electrostatic energy scales quadratically with both charge and closeness. Since this is a whole lot of charge in a very small space, the energy density outpaces antimatter.

The electric potential is not directly applicable. The strong&weak nuclear forces are what matter. Further, you've ignored the energy you put in to "pull out" that proton -- say an extremely energetic photon, e.g.

Question from a physics noob: how does nuclear transmutation work, then? Or more precisely, how does/could it work without destroying the Sun with an enormous electric discharge?

@user253751 Consider the fact that the Sun is a giant thermonuclear non-stop exploding fusion bomb, held together by gravity... and suddenly you yank protons to one side and electrons to the other one. I would not be surprised to see a supernova-like event (nova-like is certain).

From fanfiction.net/s/9584823/13/Depart-Azkaban:

It considers the mass, but it fails to consider the photons released by accelerating charge; I think those would be enough to incinerate the planets before the electrons got there, so I don't think this is right:

> In the next twenty minutes, Venus and then Mars were unmade. Each died in darkness, the sun's last rays having outpaced the avenging electrons.