All sorts of oddities emerge from equations that we have developed to describe reality. What is surprising is that rather than being simply mathematical artifacts, they actually show up in our physical world.
Perhaps the first such bizarro (see DC Comics) entity was antimatter; matter with an opposite charge and spin. A mathematical solution to Paul Dirac’s relativistic version of Schrödinger’s equation (it makes my head hurt just looking at it), antimatter was discovered 4 years after Dirac predicted it.
One of last year’s surprises was the negative frequencies that are solutions to Maxwell’s equations and have been shown to reveal themselves in components of light.
And, earlier this month, German physicists announced the ability to create a temperature below absolute zero.
So when we were told in physics class to throw out those “negative” solutions to equations because they were in the imaginary domain, and therefore had no basis in reality…uh, not so fast.
What I find interesting about these discoveries is the implications for the bigger picture. If our reality were what most of us think it is – 3 dimensions of space, with matter and energy following the rules set forth by the “real” solutions to the equations of physics – one might say that reality trumps the math; that solutions to equations only make sense in the context of describing reality.
However, it appears to be the other way around – math trumps reality. Solutions to equations previously thought to be in the “imaginary domain” are now being shown to manifest in our reality.
This is one more category of evidence that underlying our apparent reality are data and rules. The data and rules don’t manifest from the reality; they create the reality.