The Martial Unity

Chapter 4555: The Origin of Higher Dimensons

The atmosphere in the office calmed down as the professor embraced his role. He had had some administrative work to do, but he postponed that. It may as well have not existed, as far as he cared. The professor heaved a deep breath before beginning his first lecture with the Emperor of Water.

”Let me begin with the origin of String Theory,” the man began. ”Two decades ago, shortly after the Unfolding and after we made knowledge exchanges with the elves, I set out to investigate hadrons. Hadrons are any particles made up of quarks held together by the strong nuclear force. At the time, these were relatively new concepts to us. Most of our sciences before that were esoteric, and while we had a conceptualization of the atom and the nucleus and its components, we hadn’t discovered the existence of quarks and force-carrying particles such as the gluons.”

Rui nodded, remembering that era of rapid knowledge transactions between Panama and the rest of the world. The scientists of Panama, many of whom were led by his brother Julian, set out to investigate and master the knowledge of the true world.

”I was particularly interested in identifying the behavior of these so-called hadrons back then,” the man explained. ”I came up with many potential models that seemed to accurately describe the observed behavior of these particles. In particular, the Euler beta function that I was discussing today was one of them. However, in all attempts at modeling the behavior of hadrons in the nucleus. I continuously ran into one problem. And this particular problem is actually a very common problem in theoretical physics.”

Rui nodded knowingly. ”You ran into infinities in the numbers.”

”Just so,” the professor replied appreciatively. ”If your models of the behavior of particles lead to infinite magnitude for any variable or operator, usually because the denominator in these equations is zero, then you have a problem. Because infinite anything would break reality as we understand it. In this particular case, I continuously ran into infinities when trying to compute the gravitational field of hadrons and pions of steady-state nuclei, using the standard zero-dimensional point model of particles, only to end up with black holes inside every nucleus.”

He smiled. ”Obviously, that isn’t what we observe. Otherwise, the entire universe would be made up of countless quantum black holes. At the same time, two of my colleagues were also running into similar problems, having picked up the same topic to research. So we came together to find a solution. And that solution was...”

He drew a line in the air. ”...To get rid of the zero-dimensional point model of particles. I stopped treating particles like dots that had zero, or near-zero, volume. This was controversial at the time. People had subconsciously assumed particles were dots, and contradicting that was contradicting a theoretical norm that is centuries old at this point. My colleagues and I faced a lot of heat. But we pushed on.”

His smile grew proud. ”We came up with the string. A one-dimensional filament that possesses a frequency of vibration. We conceptualized all particles as merely strings vibrating at different frequencies. Since the distance of the geodesic between two strings is not zero the way it would be for infinitely small dots, the infinities were resolved. That is the origin of String Theory; it was a theory to try and describe the hadrons in the nucleus and predict their behavior.”

”But it’s no longer the accepted theory for nucleonic physics, is it?” Rui asked with a curious tone of voice. ”It was replaced by Quantum Chromodynamics.”

The professor smiled bittersweetly. ”Indeed. QCD describes the nucleus infinitely better than String Theory did, and it instantly dethroned String Theory as the universally accepted consensus on how the particles of a nucleus behave. This kind of gutting is usually the death of a scientific theory. And String Theory normally would have died then and there. However...”

His tone grew more confident. ”String Theory predicted a spin-two particle whose traits matched the exact traits of the hypothesized graviton. And my colleagues and I managed to repurpose it from chromodynamics to being a solution for the well-known friction between General Relativity and Quantum Field Theory.”

Rui stroked his chin, pondering aloud. ”I forget. What’s the consensus in the scientific community at the moment?”

”It has been resolved, in several ways,” the professor replied. ”Quantization of space and time allows for a smooth conversion of General Relativity into Quantum Gravity. There are also traditionalist graviton solutions. There are even solutions that ’relativize’ quantum field theory. String Theory also resolves the contradictions extremely well on paper.

”...Multiple solutions that seem to work,” Rui pondered. ”That seems to me almost like people finding different paths to the top of a mountain. Towards one ultimate destination that everything is moving to.”

”That analogy is captures what I think is going on as well,” the professor nodded appreciatively. ”The better a theory is able to mathematically resolve all of our empirical solutions, the more it resembles other solutions that also do the same. This indicates that we’re moving in the direction of some ultimate theory of reality that possesses the traits of all of our theories.”

That was a fascinating state of affairs, albeit tangential to what he was really interested in.

Higher dimensions. That was what he was here for.

”Why the higher dimensions in String Theory?” he asked with curiosity. ”It seems rather odd to propose entire layers of reality that have never ever been observed.”

The professor smiled wryly, biting back the urge to say ’look who’s talking.’ But Rui heard his thoughts nonetheless, smirking.

”We didn’t conceive of higher dimensions because we wanted a more exotic world,” the professor chuckled. ”If you’ve skimmed through the equations, then you must have observed that the probability distribution of quantum fields doesn’t add up to one when you operate with three spatial dimensions. That is impossible. The probability distribution of the wave function must always add up to a perfect ’1’ or one hundred percent probability.

”Fifty percent here or fifty percent there,” he gestured with his hands. ”Or thirty-thirty-forty. Or five twenties. Of course, it’s a distribution and thus not countable as such, but it should always integrate into a total of one hundred percent probability. And... without higher dimensions, it does not add up to one hundred percent. If you work only with three dimensions, you end up with negative probability.”

Rui’s eyes lit up as he understood what the rationale for higher dimensions was. Indeed, negative probabilities were utterly incoherent. He wasn’t sure he could create negative probabilities even with his Martialverse. In comparison, higher dimensions, if they resolved this probability summation problem, would indeed be plausible.

He finally understood the rationale for why people would propose higher dimensions without ever discovering even the faintest hint of their existence.