I will admit it, Ant-Man was never one of my favorite Marvel superheroes. I'm a big fan of Marvel, but Ant-Man just never seemed that cool. However, now that the Ant-Man movie is coming out, I'm interested. Yes, I'm fickle.

Let's take a look at Ant-Man and physics.

Ant-Man's Powers

There is often a problem with superhero movies. The problem is that the movies don't always match the comic book. The best example is the original Spider-Man (from 2002) in which Spider-Man shoots webs right out of his wrist. Of course in the comic book, Spider-Man has webs because Peter Parker created web-shooters that are based on chemistry.

So, what about Ant-Man? In the comics, Ant-Man can both get small (like an Ant) and he can get very large. According to the official Marvel page on Ant-Man, he can only get small. Suppose we say that Ant-Man has the following powers.

He can get small, as small as an ant or maybe even smaller (although Marvel site says "half an inch"—which really isn't ant-sized). Of course in the comic books, he can also get big—but they don't mention that doesn't seem to be a power in the movie.

He has the ability to communicate and/or control insects—like ants.

Here is the interesting one—when he is small, he still has the strength of his normal sized self.

That's really all it says about Ant-Man's powers on the official Marvel site.

Problems With Size

It doesn't take a deep understanding of physics to see that shrinking a human down to ant size has some problems. Let's consider what happens when he shrinks.

Mass and Density. Let's say that Scott Lang (the human in Ant-Man) is 1.8 meters tall with a mass of 86 kg (as stated on the Marvel Wiki page). What will happen to his mass when he shrinks? Well, there are couple of options. He could keep his same mass (he has a normal human strength) or he could keep his same density and have a lower mass in ant-size.

Let's first look at the case of constant density. If the density of a human is around 1,000 kg/m3 (humans have about the same density as water), then I can calculate the small Ant-Man mass if I know his volume. To approximate his new volume, I will say that Ant-Man has the shape of a cylinder.

If the smaller Ant-Man looks just like the bigger Ant-Man, then the radius and length of the "human-cylinder" must change by the same factor (which I label "a"). Now I can compare the volume of big and small Ant-Man.

This says that if Ant-Man shrinks to half his height (a = 0.5) then the volume would decrease by 0.53 = 0.125. Half the size is one eighth the volume. Ok, now suppose Ant-Man shrinks to half an inch (1.27 cm)? This would be a length scale change of 0.0127/1.8 = 0.007056. Using this value, I can find that the half inch Ant-Man would have a volume that is just 3.51 x 10-7 times that of big Ant-Man. Assuming a constant density, this means that tiny Ant-Man would have a tiny mass of 3 x 10-5 kg or 30 mg.

But this tiny mass is a big deal. Why? Because if he started with a mass of 86 kg and ended with a mass of 30 mg, where did the other 85.9999 kg go? Did it just disappear? Maybe it was converted to energy with the mass-energy equivalence of E = mc2 where c = 3 x 108 m/s. If that's the case, this mass change would produce 7 x 1018 Joules. That's enough energy to power all the stuff in USA for 7 months (based on my previous energy usage estimate). Of course that energy couldn't just go anywhere. Ant-Man would need to store it and use it when he wants to return to his normal mass. I wonder what kind of battery he could use.

Ok, but what if Ant-Man shrinks and keeps a constant mass? Since his mass remains constant but his volume decreases, his density would increase. If I do a similar thing as above, I find that the small Ant-Man would have a density that is 2.8 million times the density of a normal human. That's just crazy. This is way higher than the density of things you see around you. Also with normal mass and tiny Ant-Man feet, the pressure he would exert on things while standing would be just crazy. It would be like me trying to stand on loosely packed foam peanuts—I would just sink right through.

Other Tiny Problems. Ok, some other things to think about when he shrinks. Why is he still as strong as a normal sized human? How would he breathe if the oxygen molecules stay the same size but his tiny lungs are tiny? How would he talk to normal sized humans? His vocal chords would be too small to make the right frequency sounds.

There are lots of problems with being super small.

How Could Ant-Man Get Small?

The above problems are the things I think about at night. I think I have a solution. How can Ant-Man get small and not have mass problems? My answer: he doesn't actually get small. Ok, I know this is a crazy idea—but I'm trying to make this work.

Instead of getting small, Ant-Man pushes himself into extra dimensions. Let me give an example for a one dimensional object (that I will draw as a circle). This one dimensional circle is in normal space as shown on this one dimensional x-axis. Notice the two tick-marks on the x-axis.

Remember, this is just a 1-D human sized Ant-Man. Now when he "shrinks" he pushes out into another dimension. As a result, the normal x-axis gets pulled together like this.

Ant-Man is still the same size. However, the x-axis bends and pulls together making it look like he is smaller. Because the x-axis is stretched into another dimension, the two tick-marks on the axis are closer together. Everyone sees Ant-Man as smaller. He can also move around as though he is small. Finally, you could imagine this in 2-D fairly easily. Imagine a horizontal stretchy fabric to represent the two normal dimensions. When Ant-Man "shrinks", he pushes down on the fabric (in the third dimension). However, instead of making a big depression in the fabric, the fabric pulls back to sort of close up. The result is a smaller hole in the fabric making Ant-Man seem smaller.

The same thing could work in three dimensions—but that's difficult to imagine (since it's difficult to visualize 4 dimensions). This also solves some of the super-power problems.

What happens to his mass when he shrinks? Nothing. He is the same mass because he didn't shrink.

Human strength when small? Check. Again, he's not actually small.

Can he breathe when tiny? Yes, if I assume air can flow into this extra dimension, Ant-Man can breathe it there.

Technically, Ant-Man could "shrink" other things by pushing them into the 4th dimension.

Ok, so this what I came up with. It's not perfect, but I still like it.

Preemptive Comments

I've been told that if I don't add preemptive comments more often, I might lose my claim that I invented this blog accessory (really, this should be noted on my Wikipedia page). So here are some questions along with my answers. Really, it just saves everyone time.