Prime Numbers: The Hidden Secrets Within Black Holes
Just as physics has its own basic particles, mathematics has its own fundamental elements — prime numbers. Prime numbers are unique because they cannot be divided into smaller natural numbers, they can only be divided by themselves and 1. And now, these extraordinary numbers are offering brand new ways to explore some of the most profound mysteries of physics.
Over the past year, scientists have discovered that equations using prime numbers can illustrate features of black holes. The connection between prime numbers and the laws of the universe may not be as far-fetched as it seems. So, could the laws of physics be expressed in terms of prime numbers? Let's explore.
The Prime Numbers and Black Holes Connection
Black holes possess the most intense gravitational force in the universe. At their core, we find singular points known as singularities. According to classical physics, the gravity at these points should be infinite, leading to a breakdown in our understanding of space and time. However, researchers in the 1960s discovered a peculiar form of chaos surrounding these singularities that remarkably resembles a similar chaos observed in prime numbers.
This connection is an exciting opportunity for physicists, despite many of them not being very familiar with this aspect of number theory.
The Riemann Hypothesis and Prime Numbers
The cornerstone of number theory's conjecture on primes is the Riemann hypothesis, proposed in 1859. This hypothesis includes a formula with two main components. The first provides an alarmingly accurate estimate for the number of prime numbers lesser than a given number. The second component, known as the zeta function, fine-tunes the original estimate. The hypothesis is so vital to number theory that whoever can prove it stands to win a $1-million prize from the Clay Mathematics Institute.
Prime Numbers and The Universe
In the late 1980s, scientists pondered if there could be a physical system whose energy levels might be based on prime numbers. To answer this, a hypothetical particle with energy levels determined by the logarithms of prime numbers was proposed. These particles were named "primons" and a collection of them was referred to as a "primon gas." The function that counts the possible states of this gas is precisely the Riemann zeta function.
For a long time, the existence of these particles was merely theoretical and many doubted their existence. However, a mathematical link inside black holes was waiting to be discovered. Several decades later, researchers found evidence of fractal chaos emerging from the fluctuations of the zeta function's zeros, an idea that was finally proven recently.
The general theory of relativity also shows that the same chaos arises near a singularity. Recently, the ideas of "primons" were brought to life when researchers discovered that a "conformal" symmetry emerges inside the chaos near a singularity. This symmetry, along with some mathematical manipulations, revealed a quantum system near the singularity whose spectrum is organized into prime numbers - a conformal primon gas cloud.
A few months later, the research team expanded their analysis to a five-dimensional universe instead of the usual four. They found that an extra dimension introduced a new feature: a "complex" prime number, known as a Gaussian prime, which includes an imaginary component. The authors named this system a "complex primon gas."
Although it is still unclear whether the presence of prime number randomness near a singularity has a deeper significance, it is intriguing that the connection extends to higher dimensional theories of gravity, including some candidates for a fully quantum mechanical theory of gravity.
Recently, a new framework involving the zeta zeros was proposed that expanded the zeta function to include not just integers but all real numbers, including irrationals. This opened up even more powerful zeta function techniques to understand quantum gravity. Stepping back and looking at the bigger picture often reveals better ways to tackle long-standing problems.
While this novel approach of using prime numbers to understand black holes in quantum gravity is promising, it is just one of many competing for acceptance. "The kinds of things we're trying to understand, black holes in quantum gravity, are surely governed by some beautiful structures," one researcher says. "And number theory seems to be a natural language."