Category Archives: Perception of Reality

Reality as an irreducible layered structure

Note: This post is the first in a series in which macroscopic objects will be analyzed from a quantum and classical point of view, as well as the nature of the observation. Finally, all of them will be integrated into a single article.

Introduction

Quantum theory establishes the fundamentals of the behavior of particles and their interaction with each other. In general, these fundamentals apply to microscopic systems formed by a very limited number of particles. However, nothing indicates that the application of quantum theory cannot be applied to macroscopic objects, since the emerging properties of such objects must be based on the underlying quantum reality. Obviously, there is a practical limitation established by the increase in complexity, which grows exponentially as the number of elementary particles increases. 

The initial reference to this approach was made by Schrödinger [1], indicating that the quantum superposition of states did not represent any contradiction at the macroscopic level. To do this, he used what is known as Schrödinger’s cat paradox in which the cat could be in a superposition of states, one in which the cat was alive and another in which the cat was dead. Schrödinger’s original motivation was to raise a discussion about the EPR paradox [2], which revealed the incompleteness of quantum theory. This has finally been solved by Bell’s theorem [3] and its experimental verification by Aspect [4], making it clear that the entanglement of quantum particles is a reality on which quantum computation is based [5]. A summary of the aspects related to the realization of a quantum system that emulates Schrödinger cat has been made by Auletta [6], although these are restricted to non-macroscopic quantum systems.

But the question that remains is whether quantum theory can be used to describe macroscopic objects and whether the concept of quantum entanglement applies to these objects as well. Contrary to Schrödinger’s position, Wigner argued, through the friend paradox, that quantum mechanics could not have unlimited validity [7]. Recently, Frauchiger and Renner [8] have proposed a virtual experiment (Gedankenexperiment) that shows that quantum mechanics is not consistent when applied to complex objects. 

The Schrödinger cat paradigm will be used to analyze these results from two points of view, with no loss of generality, one as a quantum object and the other as a macroscopic object (in a next post). This will allow their consistency and functional relationship to be determined, leading to the establishment of an irreducible functional structure. As a consequence of this, it will also be necessary to analyze the nature of the observer within this functional structure (also in a later posts). 

Schrödinger’s cat as a quantum reality

In the Schrödinger cat experiment there are several entities [1], the radioactive particle, the radiation monitor, the poison flask and the cat. For simplicity, the experiment can be reduced to two quantum variables: the cat, which we will identify as CAT, and the system formed by the radioactive particle, the radiation monitor and the poison flask, which we will define as the poison system PS. 


Schrödinger Cat. (Source: Doug Hatfield https://commons.wikimedia.org/wiki/File:Schrodingers_cat.svg)

These quantum variables can be expressed as [9]: 

            |CAT⟩ = α1|DC⟩ + β1|LC⟩. Quantum state of the cat: dead cat |DC⟩, live cat |LC⟩.

            |PS⟩ = α2|PD⟩ + β2|PA⟩. Quantum state of the poison system: poison deactivated |PD⟩, poison activated |PA⟩.

The quantum state of the Schrödinger cat experiment SCE as a whole can be expressed as: 

               |SCE⟩ = |CAT⟩⊗|PS⟩= α1α2|DC⟩|PD⟩+α1β2|DC⟩|PA⟩+β1α2|LC⟩|PD⟩+β1β2|LC⟩|PA⟩.

Since for a classical observer the final result of the experiment requires that the states |DC⟩|PD⟩ and |LC⟩|PA⟩ are not compatible with observations,  the experiment must be prepared in such a way that the quantum states |CAT⟩ and |PS⟩ are entangled [10] [11], so that the wave function of the experiment must be: 

               |SCE⟩ = α|DC⟩|PA⟩ + β|LC⟩|PD⟩. 

As a consequence, the observation of the experiment [12] will result in a state:

            |SCE⟩ = |DC⟩|PA⟩, with probability α2, (poison activated, dead cat). 

or:

            |SCE⟩ =|LC⟩|PD⟩, with probability β2, (poison deactivated, live cat). 

Although from the formal point of view of quantum theory the approach of the experiment is correct, for a classical observer the experiment presents several objections. One of these is related to the fact that the experiment requires establishing “a priori” the requirement that the PS and CAT systems are entangled. Something contradictory, since from the point of view of the preparation of the quantum experiment there is no restriction, being able to exist results with quantum states |DC⟩|PD⟩, or |LC⟩|PA⟩, something totally impossible for a classical observer, assuming in any case that the poison is effective, that it is taken for granted in the experiment. Therefore, the SCE experiment is inconsistent, so it is necessary to analyze the root of the incongruence between the SCE quantum system and the result of the observation. 

Another objection, which may seem trivial, is that for the SCE experiment to collapse in one of its states the OBS observer must be entangled with the experiment, since the experiment must interact with it. Otherwise, the operation performed by the observer would have no consequence on the experiment. For this reason, this aspect will require more detailed analysis. 

Returning to the first objection, from the perspective of quantum theory it may seem possible to prepare the PS and CAT systems in an entangled superposition of states. However, it should be noted that both systems are composed of a huge number of non-entangled quantum subsystems Ssubject to continuous decoherence [13] [14]. It should be noted that the Si subsystems will internally have an entangled structure. Thus, the CAT and PS systems can be expressed as: 

            |CAT⟩ = |SC1⟩ ⊗ |SC2⟩ ⊗…⊗ |SCi⟩ ⊗…⊗ |SCk⟩,

            |PS⟩= |SP1⟩⊗|SP2⟩⊗…⊗|SPi⟩⊗…⊗|SPl⟩, 

in such a way that the observation of a certain subsystem causes its state to collapse, producing no influence on the rest of the subsystems, which will develop an independent quantum dynamics. This makes it unfeasible that the states |LC⟩ and |DC⟩ can be simultaneous and as a consequence the CAT system cannot be in a superposition of these states. An analogous reasoning can be made of the PS system, although it imay seem obvious that functionally it is much simpler. 

In short, from a theoretical point of view it is possible to have a quantum system equivalent to the SCE, for which all the subsystems must be fully entangled with each other, and in addition the system will require an “a priori” preparation of its state. However, the emerging reality differs radically from this scenario, so that the experiment seems to be unfeasible in practice. But the most striking fact is that, if the SCE experiment is generalized, the observable reality would be radically different from the observed reality. 

To better understand the consequences of the quantum state of the ECS system having to be prepared “a priori”, imagine that the supplier of the poison has changed its contents to a harmless liquid. As a result of this, the experiment will be able to kill the cat without cause. 

From these conclusions the question can be raised as to whether quantum theory can explain in a general and consistent way the observable reality at the macroscopic level. But perhaps the question is also whether the assumptions on which the SCE experiment has been conducted are correct. Thus, for example: Is it correct to use the concepts of live cat or dead cat in the domain of quantum physics? Which in turn raises other kinds of questions, such as: Is it generally correct to establish a strong link between observable reality and the underlying quantum reality? 

The conclusion that can be drawn from the contradictions of the SCE experiment is that the scenario of a complex quantum system cannot be treated in the same terms as a simple system. In terms of quantum computation these correspond, respectively, to systems made up of an enormous number and a limited number of qubits [5]. As a consequence of this, classical reality will be an irreducible fact, which based on quantum reality ends up being disconnected from it. This leads to defining reality in two independent and irreducible functional layers, a quantum reality layer and a classical reality layer. This would justify the criterion established by the Copenhagen interpretation [15] and its statistical nature as a means of functionally disconnecting both realities. Thus, quantum theory would be nothing more than a description of the information that can emerge from an underlying reality, but not a description of that reality. At this point, it is important to emphasize that statistical behavior is the means by which the functional correlation between processes can be reduced or eliminated [16] and that it would be the cause of irreducibility

References

[1] E. Schrödinger, «Die gegenwärtige Situation in der Quantenmechanik,» Naturwissenschaften, vol. 23, pp. 844-849, 1935.
[2] A. Einstein, B. Podolsky and N. Rose, “Can Quantum-Mechanical description of Physical Reality be Considered Complete?,” Physical Review, vol. 47, pp. 777-780, 1935.
[3] J. S. Bell, «On the Einstein Podolsky Rosen Paradox,» Physics,vol. 1, nº 3, pp. 195-290, 1964.
[4] A. Aspect, P. Grangier and G. Roger, “Experimental Tests of Realistic Local Theories via Bell’s Theorem,” Phys. Rev. Lett., vol. 47, pp. 460-463, 1981.
[5] M. A. Nielsen and I. L. Chuang, Quantum computation and Quantum Information, Cambridge University Press, 2011.
[6] G. Auletta, Foundations and Interpretation of Quantum Mechanics, World Scientific, 2001.
[7] E. P. Wigner, «Remarks on the mind–body question,» in Symmetries and Reflections, Indiana University Press, 1967, pp. 171-184.
[8] D. Frauchiger and R. Renner, “Quantum Theory Cannot Consistently Describe the Use of Itself,” Nature Commun., vol. 9, no. 3711, 2018.
[9] P. Dirac, The Principles of Quantum Mechanics, Oxford University Press, 1958.
[10] E. Schrödinger, «Discussion of Probability Relations between Separated Systems,» Mathematical Proceedings of the Cambridge Philosophical Society, vol. 31, nº 4, pp. 555-563, 1935.
[11] E. Schrödinger, «Probability Relations between Separated Systems,» Mathematical Proceedings of the Cambridge Philosophical Society, vol. 32, nº 3, pp. 446­-452, 1936.
[12] M. Born, «On the quantum mechanics of collision processes.,» Zeit. Phys.(D. H. Delphenich translation), vol. 37, pp. 863-867, 1926.
[13] H. D. Zeh, «On the Interpretation of Measurement in Quantum Theory,» Found. Phys., vol. 1, nº 1, pp. 69-76, 1970.
[14] W. H. Zurek, «Decoherence, einselection, and the quantum origins of the classical,» Rev. Mod. Phys., vol. 75, nº 3, pp. 715-775, 2003.
[15] W. Heisenberg, Physics and Philosophy. The revolution in Modern Science, Harper, 1958.
[16] E. W. Weisstein, «MathWorld,» [En línea]. Available http://mathworld.wolfram.com/Covariance.html.

Why the rainbow has 7 colors?

Published on OPENMIND August 8, 2018

Color as a physical concept

Visible light, heat, radio waves and other types of radiation all have the same physical nature and are constituted by a flow of particles called photons. The photon or “light quantum” was proposed by Einstein, for which he was awarded the Nobel Prize in 1921 and is one of the elementary particles of the standard model, belonging to the boson family. The fundamental characteristic of a photon is its capacity to transfer energy in quantized form, which is determined by its frequency, according to the expression E=h∙ν, where h is the Planck constant and ν the frequency of the photon.

Electromagnetic spectrum

Thus, we can find photons of very low frequencies located in the band of radio waves, to photons of very high energy called gamma rays, as shown in the following figure, forming a continuous frequency range that constitutes the electromagnetic spectrum. Since the photon can be modeled as a sinusoid traveling at the speed of light c, the length of a complete cycle is called the photon wavelength λ, so the photon can be characterized either by its frequency or its wavelength, since λ=c/ν. But it is common to use the term color as a synonym for frequency, since the color of light perceived by humans is a function of frequency. However, as we are going to see, this is not strictly physical but a consequence of the process of measuring and interpreting information, which makes color an emerging reality of another underlying reality, sustained by the physical reality of electromagnetic radiation.

Structure of an electromagnetic wave

But before addressing this issue, it should be considered that to detect photons efficiently it is necessary to have a detector called an antenna, whose size must be similar to the wavelength of the photons.

Color perception by humans

The human eye is sensitive to wavelengths ranging from deep red (700nm, nanometers=10-9 meters) to violet (400nm).  This requires receiving antennas of the order of hundreds of nanometres in size! But for nature this is not a big problem, as complex molecules can easily be this size. In fact, the human eye, for color vision, is endowed with three types of photoreceptor proteins, which produce a response as shown in the following figure.

Response of photoreceptor cells of the human retina

Each of these types configures a type of photoreceptor cell in the retina, which due to its morphology are called cones. The photoreceptor proteins are located in the cell membrane, so that when they absorb a photon they change shape, opening up channels in the cell membrane that generate a flow of ions. After a complex biochemical process, a flow of nerve impulses is produced that is preprocessed by several layers of neurons in the retina that finally reach the visual cortex through the optic nerve, where the information is finally processed.

But in this context, the point is that the retinal cells do not measure the wavelength of the photons of the stimulus. On the contrary, what they do is convert a stimulus of a certain wavelength into three parameters called L, M, S, which are the response of each of the types of photoreceptor cells to the stimulus. This has very interesting implications that need to be analyzed. In this way, we can explain aspects such as:

  • The reason why the rainbow has 7 colors.
  • The possibility of synthesizing the color by means of additive and subtractive mixing.
  • The existence of non-physical colors, such as white and magenta.
  • The existence of different ways of interpreting color according to the species.

To understand this, let us imagine that they provide us with the response of a measurement system that relates L, M, S to the wavelength and ask us to establish a correlation between them. The first thing we can see is that there are 7 different zones in the wavelength, 3 ridges and 4 valleys. 7 patterns! This explains why we perceive the rainbow composed of 7 colors, an emerging reality as a result of information processing that transcends physical reality.

But what answer will a bird give us if we ask it about the number of colors of the rainbow? Possibly, though unlikely, it will tell us nine! This is because the birds have a fourth type of photoreceptor positioned in the ultraviolet, so the perception system will establish 9 regions in the light perception band. And this leads us to ask: What will be the chromatic range perceived by our hypothetical bird, or by species that only have a single type of photoreceptor? The result is a simple case of combinatorial!

On the other hand, the existence of three types of photoreceptors in the human retina makes it possible to synthesize the chromatic range in a relatively precise way, by means of the additive combination of three colors, red, green and blue, as it is done in the video screens. In this way, it is possible to produce an L,M,S response at each point of the retina similar to that produced by a real stimulus, by means of the weighted application of a mixture of photons of red, green and blue wavelengths.

Similarly, it is possible to synthesize color by subtractive or pigmentary mixing of three colors, magenta, cyan and yellow, as in oil paint or printers. And this is where the virtuality of color is clearly shown, since there are no magenta photons, since this stimulus is a mixture of blue and red photons. The same happens with the white color, as there are no individual photons that produce this stimulus, since white is the perception of a mixture of photons distributed in the visible band, and in particular by the mixture of red, green and blue photons.

In short, the perception of color is a clear example of how reality emerges as a result of information processing. Thus, we can see how a given interpretation of the physical information of the visible electromagnetic spectrum produces an emerging reality, based a much more complex underlying reality.

In this sense, we could ask ourselves what an android with a precise wavelength measurement system would think of the images we synthesize in painting or on video screens. It would surely answer that they do not correspond to the original images, something that for us is practically imperceptible. And this connects with a subject, which may seem unrelated, as is the concept of beauty and aesthetics. The truth is that when we are not able to establish patterns or categories in the information we perceive it as noise or disorder.  Something unpleasant or unsightly!

Reality as emerging information

What is reality?

The idea that reality may be nothing more than a result of emerging information is not a novel idea at all. Plato, in what is known as the allegory of the cave, exposes how reality is perceived by a group of humans chained in a cave who from birth observe reality through the shadows projected on a wall.

Modern version of the allegory of the cave

It is interesting to note that when we refer to perception, anthropic vision plays an important role, which can create some confusion by associating perception with human consciousness. To clarify this point, let’s imagine an automaton of artificial vision. In the simplest case, it will be equipped with image sensors, processes for image processing and a database of patterns to be recognized. Therefore, the system is reduced to information encoded as a sequence of bits and to a set of processes, defined axiomatically, that convert information into knowledge.

Therefore, the acquisition of information always takes place by physical processes, which in the case of the automaton are materialized by means of an image sensor based on electronic technology and in the case of living beings by means of molecular photoreceptors. As algorithmic information theory shows us, this information has no meaning until it is processed, extracting patterns contained in it.

As a result, we can draw general conclusions about the process of perception. Thus, the information can be obtained and analyzed with different degrees of detail, giving rise to different layers of reality. This is what makes humans have a limited view of reality and sometimes a distorted one.

But in the case of physics, the scientific procedure aims to solve this problem by rigorously contrasting theory and experimentation. This leads to the definition of physical models such as the theory of electromagnetism or Newton’s theory of universal gravitation that condense the behavior of nature to a certain functional level, hiding a more complex underlying reality, which is why they are irreducible models of reality. Thus, Newton’s theory of gravitation models the gravitational behavior of massive bodies without giving a justification for it.

Today we know that the theory of general relativity gives an explanation to this behavior, through the deformation of space-time by the effect of mass, which in turn determines the movement of massive bodies. However, the model is again a description limited to a certain level of detail, proposing a space-time structure that may be static, expansive or recessive, but without giving justification for it. Neither does it establish a link with the quantum behavior of matter, which is one of the objectives of the unification theories. What we can say is that all these models are a description of reality at a certain functional level.

Universal Gravitation vs. Relativistic Mechanics

Reality as information processing

But the question is: What does this have to do with perception? As we have described, perception is the result of information processing, but this is a term generally reserved for human behavior, which entails a certain degree of subjectivity or virtuality. In short, perception is a mechanism to establish reality as the result of an interpretation process of information. For this reason, we handle concepts such as virtual reality, something that computers have boosted but that is nothing new and that we can experiment through daydreaming or simply by reading a book.

Leaving aside a controversial issue such as the concept of consciousness: What is the difference between the interaction of two atoms, two complex molecules or two individuals? Let’s look at the similarities first. In all these cases, the two entities exchange and process information, in each particular case making a decision to form a molecule, synthesize a new molecule or decide to go to the cinema. The difference is the information exchanged and the functionality of each entity. Can we make any other difference? Our anthropic vision tells us that we humans are superior beings, which makes a fundamental difference. But let’s think of biology: This is nothing more than a complex interaction between molecules, to which we owe our existence!

We could argue that in the case where human intelligence intervenes the situation is different. However, the structure of the three cases is the same, so the information transferred between the entities, which as far as we know have a quantum nature, is processed with a certain functionality. The difference that can be seen is that in the case of human intervention we say that functionality is intelligent. But we must consider that it is very easy to cheat with natural language, as it becomes clear when analyzing its nature.

In short, one could say that reality is the result of emerging information and its subsequent interpretation by means of processes, whose definition is always axiomatic, at least as far as knowledge reaches.

Perhaps, all this is very abstract so a simple example, which we find in advertising techniques, can give us a more intuitive idea. Let’s suppose an image whose pixels are actually images that appear when we zoom in, as shown in the figure.

Perception of a structure in functional layers

For an observer with a limited visual capacity, only a reality that shows a specific scene of a city will emerge. But for an observer with a much greater visual acuity, or who has an appropriate measuring instrument, he will observe a much more complex reality. This example shows that the process of observation of a mathematical object formed by a sequence of bits can be structured into irreducible functional layers, depending on the processes used to interpret the information. Since everything observable in our Universe seems to follow this pattern, we can ask ourselves the question: Is this functional structure the foundation of our Universe?

What do we mean by reality?

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!