I’m confused by the fact that in the article they discuss imaginary mass, but don’t even consider imaginary energy. However, we’ve made observations that imply that energy can be a little negative for a very short time (negative energy virtual particles), but actual negative energy has never been directly observed. So the physical law that forces energy to be real is: “energy is always real”. Negative matter, often called “exotic matter” and not to be confused with anti-matter, does exactly the opposite of what ordinary matter does. There are plenty of people excited about negative energy (so explore around), but don’t expect any of it to pan out.