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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


  1. This is really good material. Thanks so much for putting this up. This is where a lot of the best insights come from- merely recognizing the same principles underlie diverse phenomena. Please keep going with this stuff.

    I keep wondering if the similarity is merely between transverse motion and longitudinal motion, because the motion of an EM wave is always transverse to the divergence of the E field (the field lines), just like the water surface wave is transverse to the convergence (negative divergence) of the water in the whirlpool.

    Can't wait to hear what you have to say about the analog to vorticity in a charge. That part seems difficult to imagine. For a whirlpool to have any permanence, it has to have a space into which it drains, because otherwise, the pressures will quickly equalize and it will disperse (sort of like decay, because the angular momentum is still there, but the radius spreads out). But a charge is seemingly permanent. So to me, that implies some kind of space into which the field lines drain. I can't imagine the analog to that. Can't wait to hear what you have to say about it, though. Great post. Please continue.

  2. Vincent,
    In a superfluid, a vortex can persist indefinitely without dispersing or having anywhere to "drain" to. Regardless, we'll get into stabilized vortices in the next post!

  3. Thanks for the reply. I hadn’t thought of that. This stuff is pretty good. If you have a link to more material of yours, please let me see it.

  4. Another thing that strikes me is that your description of the charge in the mirror is a very simple, intuitive description of charge-parity symmetry. Feynman mentioned something similar in one of his books, where he said something like, “at first, it looked like parity symmetry was broken, but then it turned out, if you went to another galaxy, where everything was made of antimatter, it would still be symmetric...” Not only are the orientations flipped by the mirror, but the field lines are flipped, also, giving your symmetry back. I don’t quite know how to say it better, but that’s what it sounds like to me.

    Another thing that strikes me is that your whirlpools are very similar to Susskind’s “gravity corset” picture he often draws, in which an energy density pries apart the “lacing” Of entanglement of regions of space. Because it is a region where the surface area bulges due to energy, but also, because the bulge itself can be said to be the energy. Sorry if I’m taking over your comments section.

  5. Hi Positron (Stephen),
    I was waiting for you all to comment on the massive Falaco Solitons that exist in the southern part of the world oceans (southern part of the Indian, Southern, & Pacific Ocean). They are called "modons". These have been observed in satellite photos on a scale of thousands of kilometers and last in the ocean for periods of time exceeding six months. See this reference to a currently open paper: link: Paper's Title:"Rapid water transport by long-lasting modon eddy pairs in the southern midlatitude oceans - C Hughes - Geophysical Research Letters - Dec 2017"

    Or you can find this article in Newsweek:

    Personally the name Falacon Soliton works for me. They come in sizes from those found in a hot cup of tea all the way up to these monsters in the oceans and also on the Gas Giants. They are suitable candidates for matter-antimatter particles and they even occur in type II superfluids such as liquid helium or Bose-Einstein Condensates.

    Good Elf

  6. Come on, man, let's see part three.


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