In the article “Reality and information: Is information a physical entity?” we analyze what we mean by reality, for which the models established by physics are taken as a reference since they have reached a level of formal definition not attained so far in other areas of knowledge.
One of the conclusions of this analysis is that physical models are axiomatic mathematical structures that describe an emerging reality layer without the need of connection with the underlying reality. This means that models describe reality at a given functional level. This makes reality closely linked to observation, which justifies our view of reality determined by our perception capabilities.
Consequently, reality can be structured into irreducible functional layers, and only when one looks at the edges or boundaries of the models describing the functionality of each emergent layer are there signs of another more complex underlying reality.
In this sense, physics aims to reveal the ultimate foundation of reality and has materialized in the development of quantum physics and in particular in the standard model of particles, although the questions raised by these suggest a more complex reality. However, the structure of layers could have no end and according to Gödel’s incompleteness theorem be an undecidable problem, that is, an unsolvable problem.
All this is very abstract, but with an example, we can understand it better. Thus, let us suppose the system of human color perception, based on three types of photoreceptors tuned in the bands of red, green or blue. Due to Heisenberg’s uncertainty principle, the response of these photoreceptors also responds to stimuli of near frequencies (in the future we could discuss it in detail), as shown in the figure. As a consequence, the photoreceptors do not directly measure the frequency of color stimuli, but instead translate their frequency into three parameters (L, M, S) corresponding to the excitation level of each type of photoreceptors.
This makes possible the synthesis of color by three components, red, green and blue in the case of additive synthesis, and yellow, cyan and magenta for subtractive synthesis. In this way, if the synthesized image is analyzed by means of spectroscopy the perception of the image in relation to color would have very little to do with the original. In the case of birds, the rainbow must have, hypothetically, 9 colors, since they are equipped with a fourth type of photoreceptor sensitive to ultraviolet.
One of the consequences of this measurement system, designed by natural evolution, is that the rainbow is composed of seven colors, determined by the three summits and the four valleys produced by the superposition of the photoreceptor response. In addition, the system creates the perception of additional virtual colors, such as magenta and white. In the case of magenta, this is the result of the simultaneous stimulation of the bands above the blue and below the red. In the case of white is the result of simultaneous stimulation of the red, green and blue bands.
From the physical point of view, this color structure does not exist, since the physical parameter that characterizes a photon is its frequency (or its wavelength λ= 1 / f). Therefore, it can be concluded that color perception is an emergent structure of a more complex structure, determined by an axiomatic observational system. But for the moment, the analysis of the term “axiomatic” will be left for later!
This is an example of how reality emerges from more complex underlying structures, so we can say that reality and observation are inseparable terms. And make no mistake! Although the example refers to the perception of color by humans, this is materialized in a mathematical model of information processing.
Now the question is: How far can we look into this layered structure? In the above case, physics shows by means of electromagnetism that the spectrum is continuous and includes radio waves, microwaves, heat, infrared, visible light, ultraviolet, etc. But electromagnetism is nothing more than an emergent model of a more complex underlying reality, as quantum physics shows us. So that, electromagnetic waves are a manifestation of a flow of quantum particles: photons.
And here appears a much more complex reality in which a photon seems to follow simultaneously multiple paths or to have multiple frequencies simultaneously, even infinite, until it is observed, being determined its position, energy, trajectory, etc., with a precision established by the Heisenberg’s uncertainty principle. And all this described by an abstract mathematical model contrasted by observation….
The search for the ultimate reasons behind things has led physics to deepen, with remarkable success, in the natural processes hidden to our systems of perception. For this purpose, there have been designed experiments and developed detectors that expand our capacity for perception and that have resulted in models such as the standard particle model.
The point is that, despite having increased our capacity for perception and as a result of our knowledge, it seems that we are again in the same situation. The result is that we have new, much more complex, underlying abstract reality models described in mathematical language. This is a clear sign that we can not find an elementary entity that can explain the foundation of reality since these models presuppose the existence of complex entities. Thus, everything seems to indicate that we enter an endless loop, in which from a greater perception of reality we define a new abstract model that in turn opens a new horizon of reality and therefore the need to go deeper into it.
As we can see, we are referring to abstract models to describe reality. For this reason, the second part of the article is dedicated to this. But we will discuss this later!