Quantum information
What is the most fundamental form of information? Which independent parameters, which degrees of freedom, constitute the beginning of everything? Our classical understanding of space comprises three dimensions, with time being regarded as the fourth dimension. Are these independent parameters? Is it possible that both space and time emerge from the same degrees of freedom? Try to envision space, time, and even dimensions as derivatives from quantum information. They might be emergent phenomena that only manifest on the macroscopic scale. Let’s explore how many degrees of freedom of information are needed to describe our world. Tip: Occasionally refer back to the animation from chapter 1 for a visual aid.

To save your precious time, we’ll bypass an endless series of attempts, and trial and error. We’ll start with six linear degrees of freedom and a central rotation with two directions. However, keep in mind that ‘left/right’ (x-axis), ‘up/down’ (y-axis), ‘front/back’ (z-axis), ‘past/future’ (t-axis), ‘linear’, and ‘rotation’ are macroscopic concepts. They are not suitable for quantum information. It’s better to think in terms of information that is interchangeable via superposition. Quite challenging, isn’t it?

Graphic representations as aids
We emphasize relations. A ‘particle’ (a macroscopic term) is formed by its relations.
A particle ís its relations

Lineair distribution       
How to draw such a particle? The lines in the figure represent the six relations; relations between neighbors. The six relations together constitute a ‘particle’. The figure is a diagram for linear degrees of freedom. They are flattened here in a two-dimensional drawing. Keep in mind that these particles do not form a regular grid.

It involves shapeless information. The quantum world is not a Matrix, it is not made up of ones and zeros or regular axes. They are probability distributions, quantum systems governed by ψ.

Reconsider: In the case of an isolated particle (assuming this were possible), the different degrees of freedom cannot be labeled as x-, y-, z-, or t-axes. Space and time only emerge through relations with other particles. Each particle exists in the space and time with which it is entangled
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Angular distribution
Superposition and angular distribution of relations might be representable as a flattened intersection of six directions. At the center lies the overlap, the superposition. With every change, information can be redistributed in one of the six directions. Angular redistribution of information alters the particle’s orientation in relation to its surroundings.

Qudits
When we talk about superposition of six linear degrees of freedom and a central rotation with two directions, we are referring to qudits: superposition of quantum information with a d-number of alternatives. Part 1 has already described that this is fundamentally different from a system with qubits, which involves the superposition of only two states, 0 and 1. In the latter case, Shannon entropy can be used. This is not possible with qudits. Something else is required, and we will return to that.

Note: a relation also describes a part of the neighbor
Keep in mind that a relation – an entanglement between two neighbors – says something about both neighbors. When we describe a particle, we are also describing parts of its neighbors.

Space, time, dimensions, they are interchangeable
The star Proxima Centauri is 4.22 light-years away from Earth. A light-year is the distance that a photon travels in vacuum in one year. A light-year is a unit of space and time combined! When we travel through space, we are also traveling through time. We exist within the space and time with which we are entangled.

Pixels. Change occurs in increments
Suppose information is unevenly distributed; then, the redistribution of information existing in superposition and entanglement – the probability distribution – must proceed in quantized steps of one probability cycle/wavelength of information. This is also one wavelength of quantum time. When we follow the no-hiding theorem – which we do – there cannot be, at no point, a bit more or a bit less information in the universe. Information, therefore, has to shift collectively as in a pixelated world. One increment is one change. In macroscopic terms, this involves a Planck time step, a Planck length step, or an orientation step (with the reduced Planck constant, ħ = h/2π). However, even here, we must let go of the notions of length, time, and orientation and instead think in terms of information. Pixels at the quantum level are not units of time, space, or orientation. At this level, it’s nothing more than formless information. It’s one cycle of a probability distribution. And yes, steps and cycles are, of course, equally macroscopic concepts because they imply space, time, and orientation. Can anyone come up with a better term for this? If so, please let us know.

Interlude: dimensions
Although the concept of dimensions is more fundamental than space and time, dimensions are also emergent. They result from coherence. From a macroscopic perspective and with the help of macroscopic terms, the emergent nature of dimensions can be described as follows: An isolated point or particle – assuming it were possible – has no dimensions. Two points that have a relation form a first dimension. Their relation creates a line. Three points that are interconnected and not on the same line constitute a two-dimensional plane. More than three interconnected points that do not lie in a single plane make up a three-dimensional space. Part 1 of our book has described that the same holds true for the concept of time. However, when it comes to a fusion of space and time, our macroscopic imagination falls short once again. Except when we think about light-years in space travel, perhaps. In that context, we can see that space and time are equivalent, and that we exist within the space and time with which we are entangled.

From a quantum perspective, we can view dimensions in terms of the superposition of six states, six directions. Upon collapse, a single state emerges from superposition, establishing a new relation for the observer. At the quantum level, dimensions are still primitive, formless, and malleable. When a vast amount of information coheres, the dimensions of space and time, as we know them on a macroscopic level, come into being.

What happens when shared information is redistributed?
As an illustration of the redistribution of information, let’s consider an electron falling from a higher to a lower energy state (shell) within an atom and emitting a photon in the process. In terms of relation physics, information that initially resided between the electron and the atomic nucleus will jump to a position outside the atom. Simply because, in the context of the universe’s coherence at that moment, it is the most probable option. This is how a photon is created. The event takes place within a single pixel. Simultaneously, countless other changes are occurring in the universe (each involving a linear and/or angular change). The total amount of information in the universe remains the same. In the next moment (the next event), the new photon will begin to share its information with all its neighbors. The information remains in superposition until the next collapse. The path integral formulation of quantum mechanics states that a photon takes all possible paths. This way, the photon’s information is in many places at once. In doing so, it contributes to the background information (see ‘neutral field’ in chapter 5).

Information propagates as waves throughout the universe. While the universe is indivisible because everything is interconnected, events/changes occur in increments. Is that time? Or space? It’s both. If we want to move away from the space and time with which we are entangled, we have to bridge both space and time. It’s just a matter of how we label it. Think of light-years in space travel. Or simply consider information jumps.

Angular redistribution has a dominant direction
One more thing: When everything is interconnected (1), changes occur both linearly and angularly (2), and the no-hiding theorem applies (3) during information redistribution, everything must, on average, change in the same direction. Exceptions involving changes in the opposite direction – the direction of improbability – do occur, but they are short-lived and on a small scale. This relates to the formation of antimatter, which, due to its high improbability, represents a significant potential energy (potential change). This will be discussed in more detail later.

In the view described above, the universe is not a three-dimensional static grid. In macroscopic terms, it would be natural to think in terms of a grid with ‘rotating’ elements. However, this implies isolated elements. Therefore, it’s better to think in terms of a superposition of linearly and angularly changing information following probability.