Big or small, stout or thin, all people, no matter who or where they are have approximately the same density (the ratio of mass to volume) of about one gram per cubic centimeter. This is the density of water, and since we are all mostly water, it is ours as well. A few years ago, thousands of physicists working in a massive international collaboration, discovered the mechanism that gives all matter its mass. Just over fifty years earlier, one single scientist working alone uncovered the secret of size.
On July 4th, 2012, physicists working at the Large Hadron Collider at CERN in Geneva, Switzerland announced the discovery of the Higgs Boson. This fundamental particle, long predicted to exist, is an excitation of the Higgs field that permeates all of reality. Verification of the existence of the Higgs field answered a fundamental question of science – why do different particles, such as electrons or protons, have different masses. The omnipresent Higgs field can be thought of as a fluid through which all particles must move. If the fluid is thick or dilute, then it is either harder or easier to move, and the particle will have either a heavy or light mass. The viscosity of this 'fluid' depends on the strength of the particle's interaction with the Higgs field,. With verification of the Higgs mechanism, physicists understand why atoms have the mass that they do.
Insight into why atoms have the size that they do was provided in Marvel comics' Tales to Astonish no. 27 (cover date Nov. 1961). In the story "The Man in the Ant Hill," Dr. Henry Pym makes one of the most significant scientific breakthroughs of the century – and then promptly pours his discovery down the drain. Pym had synthesized an elixir that can shrink any matter, including himself when he pours his concoction on his skin. Reducing his size to that of an insect, he has a harrowing adventure inside an anthill, and upon his escape and restoration to his original size, he disposes of the formula, concerned that it poses too great a danger. This amazing potion was essentially a delivery system for a new fundamental particle that controlled an object's size that is termed the Pym Particle!
If we knew how to change the strength of the coupling between matter and the Higgs field (we don't), we would be able to change the mass of any object, making it heavier or lighter at will. In analogy with the Higgs Particle, the Pym Particle is presumably a consequence of a Pym Field that is all around us. Henry Pym apparently not only discovered the existence of the Pym Field, through its corresponding Pym Particle, but also how to vary the coupling between atoms and this surrounding field, thereby making them larger or smaller on demand.
Now, scientists actually do know why atoms have the size that they do, which turns out to be bad news for those hoping for real world Fantastic Voyages. Nearly a century ago, quantum mechanics, the branch of physics that concerns the properties of atoms and how they interact with light, enabled physicists to calculate the average radius of an atom. An atom consists of a heavy nucleus of positively charged protons and electrically neutral neutrons, surrounded by much lighter, negatively charged electrons. The protons in the nucleus attract the electrons, much like the massive sun pulls the planets in the solar system.
At first physicists thought the analogy was nearly exact, with the electrons exhibiting elliptical orbits around the nucleus, but the work of Werner Heisenberg and Erwin Schrödinger in the mid-1920s found that one could not in any meaningful way ascribe particular trajectories to the electrons. Rather, the best one can calculate is the probability that a measurement will find the electron at a given distance from the nucleus. Nevertheless, knowing this probability enables the determination of the average distance of the electron from the nucleus, which can be used as a proxy for the atom's radius. A relatively simple calculation finds that the average radius for a given atom is determined by various fundamental constants such as the mass and charge of the electron, the dielectric permittivity (which governs the strength of an electric field), Planck's constant (that determines the scale of quantum effects) and a factor of 4π. All of these constants have one thing in common – they are constant and not open to change. All atoms, except for the very lightest ones, are roughly the same size – with a diameter of about 1/3 of a nanometer (ten billionths of an inch).
And this is why it is so hard to make yourself smaller or larger. You can't just remove or add atoms, for, after all, where would they go or come from; where do you store them; and how do you make sure they all wind up back where they are supposed to when you wish to return to your original size? In the comics it is suggested that Pym particles access the Kosmos dimension (who knew?) where the excess matter comes and goes, but we are trying to be serious here. Nor can you just squeeze the atoms closer together. The atoms in your body are already in direct physical contact, and the repulsion between electrons in neighboring atoms keeps them from getting any closer without exerting pressures typically found at the center of the Earth. In order to change your size, you need to do something impossible, namely take a collection of constants that determines the size of the atoms in your body, and make them non-constant, subject to change. And this is where Henry Pym's (alas, fictional) genius comes in.
What the Pym field presumably does is change the magnitude of these constants. For example, if Planck's constant, which is already a pretty small number, becomes ten times smaller, then the resulting average radius of all atoms affected would be reduced one hundred times. A six-foot tall person would shrink down to a height of ¾ of an inch, nearly small enough to ride on a carpenter ant. Of course, the radius (which is half the diameter) of an atom is only one length, and the three-dimensional volume of the atom varies as the cube of the radius, becoming one million times smaller.
However, this ant-sized person would risk falling right through the floor. The Pym field has changed the size of the atoms in a person, but not how many atoms they have nor their mass. The person would weigh the same as at their original height, but only now all of this mass would be compressed into a very tiny volume. The pressure underneath their feet would be ten thousand times greater than at their normal size, and if they were to actually sit on an ant when miniaturized, it would instantly be squished.
So, what gives? Apparently when Henry Pym shrinks so that his volume is reduced by a factor of a million, his mass also is reduced by the same factor of a million, so the ratio of mass to volume, that is, the density, remains unchanged. He has the same density while insect-sized as when he is full size – one gram per cubic centimeter. Thus he is able to ride ants without harm. However, both the comic book and movie versions of Ant-Man stress that there is no reduction in strength when our hero is insect sized.
The force of a punch is determined by the cross-sectional area of your biceps, not their length. At ant-sized, this force is smaller, but the cross-sectional area of your fist is reduced by the same amount, so the pressure packed into a punch in unchanged. But is there a way to amplify this force, so that when he throws his weight into a punch, it is his full-sized weight and not his tiny ant-scale weight?
One way this might be accomplished is through a cross-interaction between the Higgs field (controlling the atoms' mass) and the Pym field (affecting its size). When Ant-Man needs to ride atop a flying ant, there is a strong connection between the Pym and Higgs particles, so that reduction of one causes a reduction in the other, and his density remains unchanged. When Ant-Man needs to knock out a security guard or toss a toy train, the coupling between Higgs and Pym fields is broken. Then he momentarily is small yet with his full-grown weight. Being struck with a punch of a 160-pound adult, across a tiny surface area of a shrunken fist, would exert quite a pressure. As to how Ant-Man is able to couple and decouple these two fundamental fields at will – well, superheroes must have their secrets, but I'm willing to bet that it involves the Kosmos dimension and the quantum realm in some way.
Speaking of secrets, in addition to being able to shrink, Ant-Man is also able to communicate with ants. Ants exchange information with each other through the emission of chemical trails excreted from their bodies, which are detected by other ants' mouths. How Ant-Man accomplishes this… perhaps there are some questions into which science should not look too closely.