Translating symmetry, CPT symmetry, and chirality into terms of relation physics seemed like an interesting addition to our thought experiment, but proved to be extremely challenging. Due to the large number of factors that must be simultaneously considered, this is a notoriously difficult subject for a macroscopic brain, virtually ‘impossible’ to grasp. Moreover, it was only in 2012 that proof of the violation of time symmetry was provided. This was done using B mesons, also not necessarily the easiest topic.

CPT-symmetry
Charge, in terms of relation behavior, results from the interaction between a system and its environment. Time, in a coherent perspective, is nothing more than the most probable direction of development. Improbable developments also occur but are neutralized in the broader context of the universe. But what about parity? Parity provides information about the spatial structure of a particle and whether, when mirrored in orientation relative to its environment, it remains identical or is experienced as different to that environment. Stated differently: will the mirrored image exhibit different behavior when interacting with the environment?

What are symmetries exactly? Sometimes it helps to just start writing and formulate very precisely. Step 1: How do we distill the question to its core? CPT symmetry means that physical laws remain the same if (and only if) all charges are replaced by their opposites, all spatial dimensions are mirrored, and time is reversed. So, it involves the mirroring of spatial dimensions and time. Come again…..? Do these concepts even apply at the quantum level?

Mirroring and symmetries are macroscopic concepts. They are of no use when dealing with probability distributions that can redistribute not only linearly but also angularly at the same time. We lack the macroscopic imagination to wrap our heads around this. Remember the Feynman diagrams? They show that spatial dimensions are interchangeable with time during interactions.

In the above interactions, photons perform magic with space and time (degrees of freedom).

With a complete mirroring of all factors, we essentially turn the universe inside out, resulting in the universe of antimatter. We have the ability to somewhat comprehend this. But there are also intermediate forms that make it much more complex. Therefore, let’s proceed very precisely and use the term ‘degrees of freedom’ instead of dimensions, space, or time. See also the animation of the sine wave in chapter 1.

In this context, we might also think about how gluons, together with quarks, allow various spatial dimensions (degrees of freedom) to mutually change, forming protons and neutrons with the spatial structure of an ‘impossible’ Penrose triangle. Refer to the figure of the triangle in section 6.17 about strong force and QCD. Gluons have the ability to manipulate spatial dimensions.

But the most spectacular role in exchanging degrees of freedom is reserved for the W and Z bosons. They represent the weak force and serve as an intermediate step in transitions from one type of fermion to another. Take β¯decay, a form of radioactive decay. In this process, a neutron changes into a proton (due to a change from a down quark to an up quark), and an electron and antineutrino are formed as byproducts. A W¯ boson is the intermediate step in this process. The W boson manipulates spatial dimensions and time (specifically the antineutrino) simultaneously in one action. When elementary ‘particles’ (sets) first form a W boson and then break down into new particles, the W boson must be responsible for the deformation of space and time, or more precisely, the switching of degrees of freedom. The W boson does something similar to photons and gluons (the other bosons), but even more complex.

Conservation of information
When charge (C), parity (P), and time (T) are emergent – and thus not foundational – phenomena, they won’t help us discover fundamental laws. It might be more useful to consider the conservation of information. When C, P, or T symmetry is violated, it appears that information disappears, but, in fact, it has shifted to degrees of freedom outside the symmetry. Combining various degrees of freedom is necessary to arrive at a conclusive result. When considering all degrees of freedom together, the sum adds up correctly. Take a look at the animation in chapter 1 for additional insights.

Contemplating the switch of information to other degrees of freedom – something unimaginable in macroscopic images – it might be helpful to think of that information temporarily existing in a superposition until a collapse occurs. This is analogous to the many virtual states simultaneously present, the path integrals described by Feynman. In chapter 2, we referred to this crossover of information to other degrees of freedom as angular redistribution of information.

The universe determines the direction
It is said (see, for example, on YouTube ‘Why the Weak Nuclear Force Ruins Everything’ by Sci Show) that the weak force (W and Z bosons) distinguishes between matter and antimatter. But perhaps we should see it the other way around, and the coherent universe directs the processes. It’s not the weak force that should be central, but rather the coherence. Information does not accumulate. That’s why developments should follow the same direction.

Let’s take β¯decay again as an example. Here, a down quark first transforms into a W boson. In this process, all degrees of freedom are neutralized. The W boson knows no time (it is a boson), and spatial degrees of freedom are also in the mix. All information is in superposition. Subsequently, the whole collapses into an up quark, electron, and right-handed antineutrino. One could say that the angular momentum of the universe has determined the direction. A universe of antimatter would push the process in the opposite direction.

Source: wikipedia

The central superposition of information, as discussed in chapter 2, might be envisioned as a probability wave/sine wave (is there a better word? Don’t hesitate to enrich us!) that returns to itself. Imagine these waves collectively forming a rhythm in the universe. This can only happen when the waves have the same direction and are in phase with all the other central superpositions that angularly distribute information in the universe. In this way, the central superposition of information could be visualized as a spherical (or point-like??) probability distribution. Unfortunately, we don’t have macroscopic examples or images to illustrate this phenomenon.

Parity and chirality
The section on quantum spin describes that spin is not an intrinsic property of a set but the result of coherence between the set and the environment in a universe that allows changes to be channeled in one specific direction. This leads macroscopically to a spin direction, either spin up or spin down, depending on the initial orientation with the environment. Think of nuts and bolts with the same thread direction but moving in opposite directions. The collapse of entanglement with the environment, the interaction, has determined the direction. Quantum spin is not an objective property. Only an observer engaging in interaction knows or experiences the spin direction. Both are entangled with their environment. The orientation is tested against the environment.

The same applies to the concept of chirality. Left- or right-handedness is subjective. Without an observer, chirality has no meaning. It is conceivable that an observer, during interaction – the shifting of information – with an object/structure, experiences a difference in orientation towards one direction or the other. However, chirality is a macroscopic concept and has no fundamental meaning.

Intermezzo: the Wu experiment (1956)
Because there were indications of P-symmetry violation in the weak interaction, the Chinese-American physicist Chien-Shiung Wu designed an experiment. She was an expert in beta decay and wanted to test parity conservation in the laboratory: Does the weak interaction distinguish between left and right?

Wu opted for observations before and after mirroring quantum spin because the direction of the spin vector does not change upon mirroring (it is an invariant). In which direction are the decay products emitted in beta decay relative to the spin direction? And what happens after spin is reversed?

Wu used the radioactive isotope cobalt-60, ⁶⁰Co. This is unstable and rapidly decays into nickel-60, ⁶⁰Ni, releasing an electron and an antineutrino. It is an example of β¯-decay that proceeds via the weak interaction. Although the formed ⁶⁰Ni is stable, it is in an excited state and immediately decays to its ground state, emitting two photons. An additional advantage of this is that measuring the direction of the photons can be used as an extra control. What direction do they follow? To orient the spin of all atomic nuclei as accurately as possible, Wu created a strong magnetic field. The material was also stabilized by cooling it to a temperature just above absolute zero (0.003 K).

Wu now recorded the direction of the emitted electrons and photons. For parity conservation, it would be necessary for them to be emitted in equal quantities in all directions. After all, that is the only outcome that remains the same when mirroring left and right, just like the invariant spin direction.

Source: Wikipedia

What turned out to be the case? The electrons escaped in one preferred direction. With this, she proved the violation of parity for the weak interaction.

The Ozma Problem
The outcome of Wu’s experiment means that it is possible to define left and right on a macroscopic level without referring to the human body. This solves The Ozma Problem.

However, from a relation perspective, it is not a specific characteristic of the weak interaction that distinguishes between left and right. It is, in a general sense, the preferred direction of the universe that does so. Information is redistributed via angular exchange, regardless of degrees of freedom or symmetries, based on probability. And because everything is interconnected, there is a dominant direction.

The concept of symmetry does not apply at the quantum level
Charge, parity, time, and chirality are macroscopic concepts that are not applicable at the quantum level. Relation sets have the ability to undergo angular changes, switching information to other degrees of freedom. Unfortunately, we have no macroscopic images for this. How do we visualize something physical that is connected (and remains connected) to the environment and can still interchange left/right, front/back, and up/down? And even reverse time to become antimatter? Your mind boggles when you try to imagine that. However, relation sets can do that. Through information in superposition within a probability cycle, in a coherent universe that, with a collective angular momentum (all cycles are in phase with each other), jumps to the most probable option each time.