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What law of physics needs to change in order to create nuclear (proton-neutron "crystalline like mesh") plate armour ?

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You need a Neutron Star

This kind of thing only really happens in Nuclear pasta, which is formed at a very specific depth of a neutron star. Nuclear pasta is matter that has stopped existing in its normal atomic form due to gravitational forces shove atoms together enough that the nuclear attraction between protons / neutrons and the repulsion of protons from Coulomb forces pretty much cancel each other out.

This gets even better: nuclear pasta has a "lasagna" form, where it exists in sheets. Some "nuclear lasagna," if somehow harvested, would be in sheets, so you could form plate armor.

The Problems

  1. You need to harvest material from a neutron star, where gravity is really, really strong. Strong enough that whatever is going to that depth of the star, if made of modern materials, is going to stay there. I suppose you could try getting the star to eject some of its nuclear pasta, but you should see point #3.
  2. Your armor would be super heavy. Nuclear pasta has a density of the order of $10^{14} g/cm^3$. Of course, you could try to get away with much, much thinner armor because of it's high density. I have not done the math, but I suspect this plate armor may be prohibitively heavy.
  3. There is no guarantee that it will hold up if hit. Since this material relies on coulomb and nuclear forces being in balance, one jolt one way or another could cause the matter to condense or explode. In either case, you do not want to be wearing that armor when that happens.

For armor, you want a high strength to weight ratio, and for it to be light enough that the person (or whatever you're putting armor on) can still move. If you want something more realistic, try a carbon nanotube composite as your material of choice for armor.

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    $\begingroup$ Surely it would explode at the point of harvesting from the neutron star, as at that point the three forces in balance are gravity (in), nuclear (in) and coulomb (out)? Would removing the gravity (or moving the nuclear pasta away from it's stable state point) cause the 'jolt' mentioned in point 3? $\endgroup$ – Joe Bloggs Dec 18 '15 at 9:40
  • $\begingroup$ Very good answer by the way, I'm just interested in the properties of such a weird degenerate form of matter. $\endgroup$ – Joe Bloggs Dec 18 '15 at 9:40
  • $\begingroup$ @JoeBloggs It's hard to say. I suppose it depends on how it was harvest from the star, but I'm afraid I don't have any idea how you would. In any case, what qualifies as a jolt large enough to cause the matter to explode/implode is beyond my current knowledge. $\endgroup$ – PipperChip Dec 18 '15 at 13:35
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    $\begingroup$ The fact the nuclear pasta is a thing makes me happy. Also it makes me seriously reconsider my stance on Pastafarianism. $\endgroup$ – Sean Boddy Dec 20 '15 at 6:13
  • $\begingroup$ I thought nuclear pasta had to do with boiling noodles in the microwave. Great answer. $\endgroup$ – KorvinStarmast May 20 at 14:11
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I realize this is thread has been resurrected from a long slumber, but I'd like to address a few issues in the case that the accepted answer is later used as a reference for anyone with similar questions:

@PipperChip correctly points out that the only place to find super dense nuclear matter is within neutron stars. However, the physical explanation given is incorrect and this effects the final answer.

Neutron stars are super dense constructs resulting from gravitational forces having overcome a large mass star's ability to support itself against gravitational collapse through heat produced from nuclear reactions.

While neutron degeneracy is often cited as the force supporting the star against collapse into a black hole (probably in analogy to the electron degeneracy found in white dwarfs), it is actually mostly the result of the repulsive so called hard core of the nucleon-nucleon interaction which supports the neutron star from gravitational collapse. At these densities, the coulomb force plays a very small role in the overall equilibrium condition. In any case, at the densities found beyond the (iron-nickel) crust of neutron stars, neutrons dominate with most calculations placing the percentage at 60-90% neutrons depending on the density, and hence depth, within the star.

While a neutron star must be electrically neutral in a non-local sense, it certainly has large charge imbalance on a local scale which is responsible for large magnetic fields produced by these constructs.

Since the gravitational force is balanced out by the nucleon-nucleon interaction, with small contributions from quantum effects (degeneracy pressure) and the electromagnetic interaction; if the material were removed from the star it would explode apart in spectacular fashion. The density could not be sustained since there would be no forces keeping the nuclear matter held together.

Nuclear matter found in neutron stars is best characterized as a fluid, and is not locked into a crystalline lattice as described in the OP. The reason for this is that nuclear matter is only stable when held together in the presence of extremely attractive potentials like those found in neutron stars. In the absence of external, attractive potentials, nuclear potentials are only capable of fluid-like interactions forming small scale stable structures; hence the periodic table. Any attempt to increase the number of neutron or protons to nuclear matter beyond the elements of the periodic table results in an unstable form of matter in which either neutrons or protons are said to "drip" out, and nuclear decay to a stable element occurs.

To answer OP's question, the nuclear potential would need to be modified to allow for stable neutron-proton crystalline structures.

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