Waves & Whirlpools: on Energy, Structure, Matter, & Antimatter (Part II)

In our last post, we introduced the pond—the surface of a body of water serving as an intriguing analogy for spacetime—with waves as a transient expression of energy, much like photons or gravitational waves, and eddies representing charged particles like protons and electrons. We found that two whirlpools spinning the same direction will repel one another, much like two particles of the same charge—but what about ones spinning opposite directions?
Every known type of matter has a corresponding antimatter counterpart, equal in mass but opposite in charge: the negatively charged electron has the positron, while the proton has the anti-proton (which is composed of anti-quarks). We can convert light into matter in the laboratory: E=mc2 tells you how much electromagnetic energy you need to create a particle of mass m—but in reality you need twice that amount: no matter comes into existence without its corresponding antiparticle. The fact that we’ve never seen this rule broken in nature is behind one of the biggest mysteries in all of modern physics: if we’re all made of matter, where’s the antimatter that ought to have come into existence along with us?

A simplified chart visualizes the proton and electron’s relationships to their antimatter counterparts. Charge is indicated with color; protons and positrons are red, while electrons and anti-protons are blue. Mass is indicated by size.

That’s a mystery for another day, though. The important thing here is that this reaction can work both ways: matter and antimatter can be created from pure energy like photons, but when a particle meets its antiparticle, they annihilate one another and turn back into photons.

With that out of the way, let’s get back to the pond.

If an eddy’s angular momentum is analogous to a particle’s charge, it makes sense that oppositely charged particles, like a positron and an electron, would correspond to eddies of equal size spinning opposite directions. So what happens when you put two counter-spinning whirlpools near one another? Just like with the co-rotating eddies from before, it doesn’t matter how they’re positioned relative to one another; there’s only one possible relative orientation if they’re spinning opposite directions. In this case, though, the “gears” fit together nicely. At their point of closest approach, the flow lines of our counter-spinning whirlpools—our positron/electron pair—point the same direction. This creates an attraction between the two, just like we see in a real positron/electron pair!

Two gears with arrows around them to indicate that they are turning opposite directions, and to demonstrate that their teeth are moving the same direction at their point of closest approach.

But what happens when they meet? Remember, it’s the structure, the angular momentum of the whirlpools that gives them form and lets them keep energy localized in one spot. When one whirlpool meets another that’s spinning the opposite way, the structure of one undoes the structure of the other. Their angular momenta cancel out, and the vortices disappear.

The energy they contained can’t just disappear, though. It has to go somewhere, and as the water rushes in to fill those dimples and return the surface to equilibrium, the depressions spread out, radiating away as waves—just like the annihilation that matter and antimatter undergo when they meet, turning them into photons.

Mirror, Mirror: the Method of Image Charges
So how exact is this analogy? The similarity of charge to vorticity in a fluid is striking, but asserting that charge is a kind of vorticity is the kind of claim that sparks heated debate among physicists. Regardless, there’s another bit of physics that suggests a deep similarity between the two. It’s something we encounter in some context every day here on Earth, and you’re likely to learn to use in any advanced electrostatics course. It’s what’s known as the Method of Image Charges.

In a conductive object, electric charges can move around with relative ease. Imagine we have a large, perfectly conductive sheet, and we bring a small positively charged sphere up next to it, let’s say an inch away. The positive charge in our sphere attracts the electrons in the conductor, and they congregate near it. This congregation of electrons in the conductive sheet creates an electric field of its own, which we call an induced electric field, since it wouldn’t be there without our positively charged sphere.

The interesting thing is that the strength of this induced electric field is exactly the same as it would be if there were another sphere, opposite in charge but otherwise identical, on the other side of the conductive sheet—an inch away. The electrons in the conductor effectively create a negative mirror image of our positively charged sphere. It works the same way with a negatively charged sphere, only instead of attracting positive charges, the negatively charged sphere repels enough electrons that the protons in the conductor, remaining in place, create the positive mirror image.

A positive electric charge, sitting above a perfectly conductive surface, creates a negative mirror image. The induced electric field isn’t real—there’s no field inside a conductor—but its effects on the positive charge’s electric field are.
Image Credit: Geek3, via Wikimedia Commons (CC BY 3.0)

It’s no coincidence, then, that really reflective surfaces are pretty much always electrically conductive: the method of image charges is surprisingly similar to how a mirror works. When an electromagnetic wave strikes the silvered surface of a mirror, charges in the mirror ride that wave, moving around in response to it. That motion generates another electromagnetic wave, this one headed in the opposite direction—which we see as the reflected photon.

The point I’m driving at here, though, is that if you held an electron up to a mirror, you’d see that its reflection is a positron, the particle’s antimatter counterpart—same apparent mass, opposite charge. In a mirror, anything defined relative to the observer, like left and right, or clockwise and counterclockwise, is reversed. Is it a coincidence that charge is also reversed in a mirror, or does this point to a deeper insight on the true nature of electric charge?

We’ll dive deeper into that next time, but I hope the takeaway so far is clear: matter, every quark and electron on Earth, is just energy given form—a structured excitation of a three-dimensional surface. We are not marbles sitting on a sheet, we are eddies in the water—matter isn’t something embedded in spacetime; it is spacetime…with just a little bit of a twist.

—Stephen Skolnick

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