The Physics of Size, and the Movie “Ant-man and the Wasp”
It is a subject of curiosity of the size of various life forms, and the physics involved, which help us understand size and structure. Usually we just accept life forms as being what they are, before we figure out how they fit into evolution and their environment. Besides my usual warnings or apologies for not being an expert in most of what I discuss, I am being lazy and not even looking up the literature on this. Apologies to those who are experts.
I won’t be giving away the plot, but it is apparent from the ending of the last movie that traveling into the quantum realm would be a key.
While thinking about this, I remember one of my favorite movies and books was Gulliver’s Travels by Jonathan Swift in 1726. The Encyclopedia Brittanica considers him the foremost prose satirist in the English Language, and he should therefore be my hero. Since Gulliver did not have the technology to shrink, or increase his size, Swift had him travel to entire societies which had tiny people, or giants. In Ant-man, his compatriots in raids are ants and other insects. The heroine Hope becomes the Wasp.
Even changing size by a factor of two can be dangerous to a human’s body structure. Scott shrinks from say 5 feet or 60 inches (to make calculation simple) to maybe an inch, or a factor of 60. Yet his shape stays the same. Then he goes up to 50 feet (as discussed in the previews), or a factor of 10. The main point is that our legs act as supporting beams, and our weight pressure is distributed across the cross section and onto the feet. If you proportionately shrink or lengthen each dimension, the leg cross section grows like the square of the scale size. Yet the weight of a proportionately scaled person, if at the same density, increases proportionate to the volume, or the cube of the scale size.
Shrinking down a factor of 60 decreases the leg cross section by 1/3600, but the body mass by 1/216,000, or 1/60 the pressure per unit area of the leg. Hence, ant-man could get by with legs shrunk in width by the square root of 60, or 7.75. While ants have 6 legs, they and all insects have remarkably skinny legs, as also would Swift’s Lilliputians.
On the other hand, increasing our scale size by a factor of 10, our leg cross section grows by 100 in area, but our weight by 1000. So the pressure on each square inch of our leg bones would be increased by a factor of 10, leading to breaks. It is as if a 150 pound person were carrying 1,500 pounds. The total mass of muscles to move the leg would also increase by 1,000, but the cross section of tendons to do so would only increase by 100, so there would be a lot more sprains.
This leads to the undiscussed and unexplained question of what happens to all of your mass when you shrink. And where do you get the mass to re-expand? Where does the mass and E=mc^2 energy come from when you become a giant? If Ant-man didn’t lose the weight when he shrank, the weight would break his legs, make it impossible for him to move, and punch a hole in any weak floor.
Even the general accounts of scaling do not discuss how to scale into the “Quantum Realm”, which I will discuss. It’s not to criticize the imagination of Marvel’s character developers, but to illustrate the physics of various size scales to the movie’s audience.
The characters tossed around quantum physics words, but not in apparently meaningful sentences. So the audience should not think they are unsophisticated in quantum physics, because it was all gibberish. They used a few typical quantum words like “phase”, “probability”, “sub-atomic”, and “quantum entanglement”.
Shrinking atomically led to empty space, which is correct, but then became a lava lamp. That amount of matter would make space massive, instead of essentially massless, because it is empty. The energy density of dark energy is very spread out. Dark matter may be elementary particles, but they are not concentrated like ordinary matter is.
I could have said that they consulted a particle physicist if they showed quarks and gluons in nucleons. I could have said that they consulted a string theorist if they had shown strings. They did have a temporary tetrad crystal phase, but that became the meaningless lava lamp.
They mixed quantum mechanics with our minds. This was a very earlier phase by Schrodinger, until we learned that the mind functioned by macroscopic neurons firing. Even the chemical packets that activate synapses are macroscopic. Since quantum phenomena do have uncertainty attached to them, imagine driving to work where every one of thousands of different actions only had a certain probability of being chosen or performed correctly. You would never make it. So quantum mind links are not only unlikely, but would be catastrophic.
Like any good time machine, their quantum travel machine was electromagnetic, and had turning coils like an electric motor or generator. However, motors and generators don’t usually time travel, or quantum entangle. Like “Back to the Future” and “Star Trek”, they also race to a high speed to time or space transport. I at least go a reasonable speed to space transport. But their accelerations would crush you in an instant.
There is a connection between atomic size r and the mass of the electron m that for the first Bohr atom orbit of Hydrogen is simply r = alpha/ m, where alpha is the fine structure or square of the electron charge in appropriate units. It’s numerical value is small, about 1/137. If you are to shrink atoms and lighten their mass, m would have to get smaller. Paradoxically, that makes the radius r bigger. So shrinking below the atomic scale doesn’t seem feasible.
Computer memory bit sizes are approaching so few molecules that they will soon hit a limit where they cannot be counted upon for 100% accuracy. Then, we will have to advance to real quantum computing.
Funding high energy accelerators, like the Large Hadron Collider at CERN, Geneva, however, does examine fundamental interactions at scales thousands of times smaller than the size of the proton or neutron. They are also probing exciting ideas of new “supersymmetric particles”, or new dark matter interactions, and finding out what dark matter is. Their funding in billions of dollars actually comes down to less than a dollar a year for everyone on the planet. Their results are published in the Press and TV news, and specials, without the cost of a theater ticket. Stay tuned.
One quantum physicist in the film was named Bill Foster. I thought this was an odd coincidence. It turns out that Bill Foster is a standard Marvel character who is black, and who can also increase his size. The name was familiar to me, however, in that Bill Foster is one of the three physicists in Congress, representing the Fermilab district near Chicago. He also worked on the proton decay search with the UC Irvine Neutrino group. We really need more scientists in the Congress.
It was really an interesting and exciting film. Maybe it will encourage young people to learn more about quantum mechanics. I recently gave a lecture to OLLI about how the sun generates energy, and found that it all depends on quantum tunneling to produce the standard fusion of hydrogen into helium nuclei.