I’ve always respected the “fiction” part of “science-fiction”. I believe that if you correctly put your premises and if you remain consistent, everything is OK.
Nevertheless, it should not be a problem to compare a fictive universe with a the real world, and this is precisely what I’m about to do here, once again.
In Ant-man, there is this special suit that allows a human to shrink to the size of an insect (hence the name « ant-man »), or even smaller. In the movie, they say that they achieve this by reducing the space between the atoms.
Scientifically, this is not absurd at all. We do this in a lab. Well… sort of. And not in every lab. But still.
For instance, in order to fuse two atoms of hydrogen, one has to make two hydrogen nuclei come close enough so that the short-range attraction of the strong-force overcomes the long-range repulsion of the electric-force. The point at which the repulsion becomes an attraction is called the Coulomb-barrier.
In a tokamak — a particle accelerator dedicated to nuclear fusion — this is achieved by heating hydrogen atoms to tremendous temperatures, at over hundreds of millions of degrees. Only at those temperatures are the particles moving fast enough so that, when they collide, they come close enough together to fuse.
Getting to such high temperatures is hard, so there is an other solution. We can create a smaller hydrogen atom !
For that, we create what is called “exotic atoms”, and in this case, muonic hydrogen.
In this type of hydrogen, the electron is replaced with a muon: a negative particle with the charge of an electron but a much greater mass (and also with a very short half-life).
Its greater mass allows the muon to orbit much closer to the nucleus, and the whole atom is much smaller than regular hydrogen. Having that, a H2 molecule can be smaller too and the two nuclei are closer together. Thus, the temperatures to reach in order to fuse them are much lower. This is called “cold fusion” (even if we still speak about thousands of degrees).
This is one example of making small atoms.
How-to turn Ant-Man into a black-hole ?
Applying the above to a human being, however, would not be possible. First of all, muons are not stable : they decay after a matter of milliseconds.
But if it were stable ? Would it be possible ?
Sadly… no : the guy would indeed turn into a black-hole.
In a solid, the space between atoms is already minimal (that’s why solids are not compressible, like gases). If one compresses a solid above a point (a very high point, like in dying stars), the atoms and matter collapses: electrons and protons fuse into neutrons.
In a neutron-star, all the empty space that usually surrounds an atom-nucleus is filled with neutrons and matter reach an enormous density. One cubic centimeter of a neutron-star would weigh as much as the Himalaya chain.
If ones goes even further in compressing matter, and if we have a very big neutron star, then even all those neutrons can't hold the pressure and the matter degenerates to an ultimate point: a singularity. In other words, all the mass is compressed to a single point in space and we get a black-hole.
Any amount of matter is enough to create a black-hole, as long as you compress it sufficiently.
Take the earth, for instance: if you compress it to a sphere with a radius of 0.9 cm, the size of a marble that is, it turns into a black-hole.
Each object has it’s own size under which it turns to a black-hole. That specific size is called it’s Schwartschild's Radius.
For a 80 kilo man, that size would be 1.18 × 10^-22 meter (a ten-thousandth of the size of a proton).
In the movie, it seems that Ant-Man, at one point, goes far bellow this point. He should turn into a black-hole at some point, but he doesn’t.
So, in Ant-man, this part is only “fiction”. I’ll pass on that.
How small can one get?
Another problem rises after that though: how small can he get?
Answer: not indefinitely small (but he could get indefinitely smaller, if he shrinks asymptotically).
Physics predicts a “smallest size” of all.
Nothing, no objects of measurable distances, could be smaller than that smallest size. This is Planck's length, and would be as small as 1,6 × 10^−35 meters.
The same goes for the smallest achievable duration, called Plank's time: 5,3 × 10^−44 second.
So if Ant-Man shrinks for ever, it will be asymptotically, but it won’t be smaller than 1,6 × 10^−35 meters.
Very interestingly, this seems to happen in the movie: at one point, he doesn’t shrink anymore, at least not as fast as before. Did they take the Planck-length into account? This would be great, even if I don’t really think so.
The problem of sound when you’re very small
At this point, there is another thing that’s not real in that movie: sound.
In the movie, Ant-man shrinks.
We see that it goes smaller than a cell, ok.
Then than an atom, great.
Than sub-atomic particles, well, still good.
And then… Then we do not really know what we see. In fact we do not know what’s below the level of quarks, inside protons and neutrons.
A bit like is the movie Interstellar which depicts the insides of a black-hole, everything is quite beautiful and fancy, but it has no scientific value: every thing is at best an educated representation, but nothing is really known there. But this is not what bugs me.
The real problem lies with the fact that Ant-Man hears his daughter crying when he shrinks.
If one gets smaller than an atom, sound would not be part of reality. Sound is propagated through the vibration of atoms, that finally hits our internal ear. If we are much smaller than an atom, no atom can hit our ears. Sound does not exist at that scale.
Same goes on with us being on Earth: the Earth rotates, but do we feel it? No, because we rotate with it. We can only know it because we see the rest of the sky and celestial bodies rotate.
For Ant-Man being inside an atom, if he vibrates with an atom, He should not notice it, hence he should not hear the voice of his daughter. A bit like we humans do not really feel the rotation of the earth or its revolution around the Sun.
This was, for me, the only real scientifically-noticeable problem in that movie.
Oh, and there is also that claim where Ant-Man keeps his momentum (his mass) when he shrinks, but how can he still ride an ant, if he still weights 80 kilos?