One of the most perplexing mysteries in the realm of physics is the absence of antimatter.

The concept of antimatter was first introduced by Paul Dirac through his groundbreaking equation for electrons, which predicted the existence of a particle with an opposite charge to that of an electron. Initially, Dirac suggested that this positively charged particle could be a proton, but it was later identified as the positron, the electron's antimatter counterpart.

Dirac's equation is symmetrical regarding these particles, implying that there’s no inherent feature that makes matter more significant or dominant than antimatter. This raises an intriguing question: where is all the missing antimatter in the cosmos?

This dilemma is referred to as baryon asymmetry and remains one of the prominent unsolved problems in both particle physics and cosmology.

Some theories propose that the absence of antimatter arises from certain asymmetries within the universe. Others speculate that there might be a parallel universe composed entirely of antimatter, possibly lying just beyond our observable universe. It's even suggested that antimatter could be repelled by matter's gravitational forces, leading it to reside far away, where entire stars and planets of antimatter could exist.

I believe the reason for our inability to observe antimatter may be significantly simpler and more intuitive. To grasp this, one must understand the nature of antimatter and its relationship with matter.

Every particle has an antimatter equivalent. For some particles, like photons, the counterpart is the particle itself. For others, such as electrons, the positron, their counterpart, is typically observed in particle accelerators and cosmic rays, where high energy levels generate them from other particles.

Elementary particles, which are those that cannot be subdivided into smaller components, include electrons, positrons, and quarks of both matter and antimatter. These represent the most fundamental examples of fermions—particles that possess a spin that is a multiple of 1/2.

Fermions, as far as current knowledge goes, are never their own antimatter counterparts. However, physicist Majorana, who mysteriously disappeared, theorized the existence of such particles. The search for Majorana fermions has continued since then, and I will explain why shortly.

Each particle possesses a spin, a quantum version of angular momentum. Unlike tops, particles do not spin in a conventional sense. Instead, they have angular momentum quantified in discrete amounts of 0, 1, or 1/2. This spin is responsible for the magnetic fields associated with charged particles. When spins align in a solid material, phenomena like permanent magnets occur.

To illustrate, consider spin as a form of symmetry. A spin-1 particle, for example, demonstrates rotational symmetry of a complete revolution. My office chair, which has 360-degree symmetry, appears unchanged after one full rotation. Conversely, a spin-2 particle, such as the hypothetical graviton, exhibits 180-degree symmetry, akin to an oval table. A spin-4 particle would have 90-degree symmetry, similar to a square table, while a spin-0 particle resembles a featureless sphere, appearing identical from any angle.

Particles with spin-1/2 exhibit a unique 720-degree symmetry, requiring two rotations to appear the same. This can be demonstrated using a plate trick.

For a simple experiment, hold a plate flat in your hand. Without dropping it or altering your hand's orientation, rotate your hand 360 degrees using your elbow, wrist, and shoulder, keeping the plate in the same position. You'll find that your arm twists. Repeat the process but in the opposite direction, and you'll untwist your arm. This illustrates the concept of 720-degree symmetry.

Atoms primarily consist of fermions, with some mass and energy derived from binding forces that are not composed of tangible particles. When discussing the missing antimatter issue, we primarily refer to the absence of antimatter atoms that would correspond to the matter atoms we are familiar with.

In physics, the relationship between matter and antimatter is governed by a symmetry known as Charge-Parity-Time (CPT) symmetry. For any charged matter particle, like an electron, its antimatter counterpart possesses the opposite, positive charge, hence the term positron.

A parity transformation involves creating a mirror image of a particle across one or more spatial dimensions.

Massive fermions do not exhibit symmetry under parity transformations alone, a characteristic referred to as a lack of chiral symmetry. This means there exist left-handed and right-handed electrons. The reason for the lack of attention on this topic is that they behave identically under normal electromagnetic interactions, differing only in relation to the weak force, which governs radioactive decay.

The third symmetry pertains to time, indicating time reversal. This functions similarly to parity but relates to time, allowing particles to propagate from the future back to the past.

Reversing a particle's charge yields its antiparticle, and simultaneously reversing parity and time returns the original particle.

This is fascinating because if a positron is essentially an electron traveling backward in time, then it is physically indistinguishable from an electron.

High-energy particle collisions, such as those occurring in particle accelerators, generate particle-antiparticle pairs. Even a sufficiently powerful laser can create them seemingly from nothing.

Once an electron and positron are generated, they typically move apart slightly before being drawn back together by their mutual electromagnetic attraction. Upon collision, they emit photons, or light.

Visualizing this process on a spacetime diagram—where space is represented on the horizontal axis and time on the vertical axis—reveals a circular pattern. Since the positron can be viewed as an electron moving back in time, it appears as a single particle tracing a circular path in spacetime, creating a closed loop.

This observation is crucial for understanding the fate of all that missing antimatter.

During the Big Bang, one would anticipate the creation of equal amounts of matter and antimatter. The Standard Model of particle physics upholds this symmetry.

Several explanations emerge:

1. There could be asymmetries beyond our current understanding of the Standard Model.
2. Antimatter might exist somewhere in the cosmos.

Some speculative theories introduce asymmetries beyond the Standard Model, with one of the most notable involving heavy neutrinos—neutrinos with greater mass than those currently known. Heavy Majorana neutrinos are theorized to be their own antiparticles and possess mass. These would have decayed early in the Big Bang, creating a disparity between matter and antimatter. Additionally, heavy neutrinos are considered potential candidates for dark matter, and their discovery would be groundbreaking.

Some more imaginative proposals suggest that the Big Bang produced two universes, one advancing into the future and another retreating into the past, tying into the CPT symmetry between matter and antimatter.

My perspective is considerably simpler and does not require alterations to the Standard Model or the existence of other universes. Instead, it hinges on a well-known mathematical transformation utilized for over two millennia: stereographic projection.

I won’t delve into stereographic projection in detail, as I’ve previously written a comprehensive article on the subject. In essence, it is a method of projecting from an infinite flat plane to a finite sphere and vice versa. This can occur in one dimension, transforming a line into a circle, or in higher dimensions, which elude visualization, though the math is sound.

For my analysis, I will employ the 2D version of this concept.

Stereographic projection has three noteworthy properties that I intend to utilize:

1. Circles on the plane correspond to circles on the sphere.
2. Lines on the plane become circles on the sphere that intersect at the North Pole.
3. Each point on the plane uniquely maps to a point on the sphere, including infinity, which maps to the North Pole.

Consider the spacetime diagram discussed earlier; it can be mapped to a sphere. In this scenario, infinitely distant time and space converge at a single point on the sphere: the North Pole.

If I take the electron-positron pair creation and annihilation cycle from the spacetime diagram and project it onto the sphere, it will also form a circle on the sphere.

Conversely, if I visualize an electron traveling from the infinite past to the infinite future in any spatial direction on the spacetime diagram, it will also map to a circle on the sphere, intersecting at the North Pole.

In simpler terms, the apparent symmetry between matter and antimatter observed during particle pair creation and annihilation is still present on the sphere for matter alone, as long as the matter does not originate from a creation event at a finite distance in the past.

The absence of observable antiparticles arises because particles never traverse backward in time on the spacetime plane. The curvature radius of their "circle" is infinite.

Alternatively, one can derive this by initiating a pair creation/annihilation loop and extending the creation and annihilation events to the infinite past and future while sending the antimatter segment of the loop to infinite distance. In this scenario, antimatter effectively disappears.

It's crucial to remember that for finite creation and annihilation pairs, the particle and antiparticle are the same entity; we are merely observing them at different points in their circular trajectory through spacetime.

If these particles were indeed created during the Big Bang, it could pose a challenge since the Big Bang occurred a finite time ago. However, we are not asserting this definitively. All we acknowledge is that there was a hot, dense period approximately 13.8 billion years ago, and the nature of what transpired "before" remains ambiguous.

It's also important to consider that our spacetime plane is dynamic, expanding in both space and potentially time. Thus, the Big Bang may effectively represent an infinite temporal distance in the past (as suggested by concepts such as logarithmic time, which Isaac Asimov discussed).

To validate this idea, we would need to possess far more knowledge about the Big Bang and the emergence of matter, particularly fermions, from it. If this hypothesis holds true, we may never derive answers from particle accelerators regarding the matter-antimatter imbalance in the universe, as one would need to access the beginning (or the end) of time to discover the truth.