33: Cognitive cosmogenesis: A systematic integration of physics and theology
Here and elsewhere we shall not obtain the best insights into things until we actually see them grow from the beginning (Aristotle quoted in Jaeger) Werner Jaeger (1997):Aristotle: Fundamentals of the history of his development
Research is to see what everybody has seen and think what nobody has thought Peter Osper (1957): Review: Albert Szent-Györgyi (1957): Bioenergetics
Physics is a point of view for understanding the totality of [humanity] and our Universe John J. Hopfield (2024_12_08): Nobel Lecture: Physics is a point of view
Contents:
1. Abstract: The evolutionary source of human value2. Introduction: The medieval foundation of Christian theology
3. The problem with quantum field theory: cart before horse?
4. A theological singularity: the God of Aquinas
5. The Trinity: God acquires structure by self awareness
6. The presence of mathematics in the physical world
7. The creation of Hilbert space
8 The contrasting roles of observation in classical and quantum mechanics
9. Quantum intelligence, linear operators and the eigenvalue equation
10. Naked gravitation bifurcates into potential and kinetic energy, giving substantial reality to the stable forms produced by quantum mechanics.
11. The interactions of bosons and fermions and determine the metric of Minkowski space.
12. From Minkowski space to general relativity.
13. Comparison to quantum field theory
14. A quantum mechanical description of a parliamentary democracy with a mixed economy.
1. Abstract: the evolutionary source of human value
Since Galileo Galilei introduced scientific method we have developed a comprehensive scientific story of our origin. We understand that he universe has evolved from a structureless initial singularity to its present state over 14 billion yeas. Many people see this story as an alternative to the multitude of oral and scriptural narratives that have arisen since our species appeared. These ancient human beliefs often serve as sources and justifications for the human values that establish just and durable societies and the roots of human spirituality.
Evolution has two phases. The first is random creativity, variation, an element of chaos. The second is selection, the introduction of order. The criterion in this phase is the ability to reproduce since variants that fail to reproduce are lost. We see the foundation of this phase of evolution in the intelligence of quantum mechanics which brings order out of chaos by solving the eigenvalue equation.
Our values are embedded in us by the reproductive phase which is facilitated by nurture, cooperation and the ancient admonishment propagated by Jesus of Nazareth; love god, the environment that supports you; love your neighbour, your fellows who support you. These principles, mutatis mutandis apply to survival in an evolutionary system at all levels from fundamental particles to nations and the planetary environment. Jonathan Sacks (2015): Not in God's Name: Confronting Religious Violence
The formalism of evolution is closely related to the P vs NP in the theory of computation. NP processes explore random processes; P processes execute deterministic processes like successful reproduction. Stephen Cook (2006): The P Versus NP Problem
2. Introduction: The medieval foundation of Christian theology
The first academic philosophy to enter Christianity was Neo-Platonism, associated with the Hebrew Bible through the Septuagint translation into Greek. This Old Testament became the foundation text of Christianity and the Christians developed their own New Testament in the next century. Christian theology entered a new epistemological phase when the work of Aristotle became available in the medieval universities. Septuagint - Wikipedia, John Willinsky (U of Chicago Press, 2018): The Intellectual Properties of Learning: A Prehistory from Saint Jerome to John Locke (Chapter 7)
The next step the evolution of theology proposed here, reverting to some degree to the Metaphysics of Aristotle, is to introduce theology into the realm of empirical science via the hypothesis that the universe revealed by physics plays all the roles traditionally attributed to the Christian God: creator, sustainer and judge.
The definitive Western conflict between traditional Christian theology and nascent Western science centred on Galileo Galilei (1564 - 1642) during a debate about the structure of the Solar System. The Church drew its position from narratives in the Bible. The Hebrew leader Joshua needed more time to defeat the indigenous inhabitants during their occupation of the Promised Land. He asked Yahweh for help:
It was then, when the LORD delivered up the Amorites to the Israelites, that Joshua prayed to the LORD, and said in the presence of Israel: Sun, stand still at Gibeon, Moon, in the valley of Aijalon! The sun stood still, the moon stayed, while the nation took vengeance on its foes. Joshua 10:12-13: Sun, stand still at Gibeon (USCCB)
Galileo, on the other hand, had seen the phases of Venus with his telescope. This showed, without doubt, that the Earth orbits the sun. He was convicted of heresy by the Roman Inquisition for expressing this view and forced to recant to save his life.
On the centenary of Einstein’s birth on 10 November 1979 the Roman Pope Saint John Paul II foreshadowed a modern study of this “Galileo Affair”. In 3 July 1981 the Papal Academy of Science established a Study Commission for this purpose. The Pope announced the conclusions of this study in an address to a Plenary Session of the Academy on 31 October 1992:
4. [. . .] One might perhaps be surprised that, at the end of the Academy’s study week on the subject of the emergence of complexity in the various sciences, I am returning to the Galileo case. Has not this case long been shelved and have not the errors committed been recognised?That is certainly true. However, the underlying problems of this case concern both the nature of science and the message of faith. It is therefore not to be excluded that one day we shall find ourselves in a similar situation, one which will require both sides to have an informed awareness of the field and of the limits of their own competencies. Saint John Paul II (1992_10_31): Address to the Plenary Session on ‘The Emergence of Complexity in Mathematics, Physics, Chemistry and Biology’.
Throughout his discussion of the Church’s treatment of Galileo the Pope sticks firmly to the ecclesiastical dichotomy between revelation and science.
He explains:
12. [. . .] There exist two realms of knowledge, one which has its source in Revelation and one which reason can discover by its own power. To the latter belong especially the experimental sciences and philosophy. The distinction between the two realms of knowledge ought not to be understood as opposition. The two realms are not altogether foreign to each other; they have points of contact. The methodologies proper to each make it possible to bring out different aspects of reality [. . .].14. Humanity has before it two modes of development. The first involves culture, scientific research and technology, that is to say whatever falls within the horizontal aspect of man and creation, which is growing at an impressive rate. [. . .] The second mode of development involves what is deepest in the human being, when, transcending the world and transcending himself, man turns to the One who is the Creator of all. It is only this vertical direction which can give full meaning to man’s being and action, because it situates him in relation to his origin and his end.
A fundamental argument against this bifurcation of knowledge and reality is that reality is one. There is one universe and one God, and they are identical. This argument has two elements.
The first, following the idea from Aristotle displayed at the beginning of this article, is to go back to the beginning and postulate an initial singularity which embraces both realms of knowledge, constrained only by local consistency. This is an analogue of the current big bang theory. Hawking & Ellis (1975): The Large Scale Structure of Space-Time
Rather than choosing something like a black hole, as suggested by Hawking and Ellis, we use the Christian model of God, developed by Aquinas from the work of Aristotle. Like Thomas’s God, our initial singularity is eternal, omnipotent and totally without structure. Aquinas, Summa, I, 3, 7: Is God altogether simple?
The second is to show that Darwin’s theory of evolution is an explanation of creation that takes care of all aspects of both humanity and the universe, from the beginning to any conceivable end. Because the initial singularity is omnipotent, it acts. Because it has no structure it acts at random, thus implementing the creative input to evolution, variation.
The selective limits on both divinity and creation are set by the the principle of non-contradiction, the logical foundation of the ontological test of survival.
This situation is illustrated by a standing problem in the science of computation known as P versus NP. P describes the power of a deterministic universal Turing machine. NP describes a potentially more powerful process that arrives at conclusions by random action. Nevertheless, its results can be tested by a P process. In evolution, a rabbit may be designed by an NP process, but the reliable reproduction of rabbits, and therefore their survival, must depend on P processes. Stephen Cook (2006): The P Versus NP Problem
With very few exceptions, if any, every living creature dies. Only those random events that are consistent with their environment and able to reproduce can survive. This principle of selection works in science as everywhere else. A consequence of this selection, with the status of a scientific principle, is that any self-contradictory hypothesis is ipso facto false, and that any appearance of an apparent contradiction will ultimately be, through further study, resolved.
At present our potential theory of everything, quantum field theory, cannot deal with gravitation. It also faces an intractable cosmological constant problem which renders doubtful the way it imagines the origin of energy.
Hobson, Efstathiou and Lasenby ask:
How can we calculate the energy density of the vacuum? [. . .] The simplest calculation involves summing the quantum mechanical zero point energies of all the fields known in Nature. This gives an answer about 120 orders of magnitude higher than the upper limits on Λ set by cosmological observations. This is probably the worst theoretical prediction in the history of physics! Hobson, Efstathiou & Lasenby (2006): General Relativity: An Introduction for Physicists, page 187.
The root of the problem appears to be the idea that the discrete finite nature of the quantum of action creates uncertainty which creates oscillations which are equivalent to energy according to the quantum mechanical relationship discovered by Planck, E =ℏω. The energy causing the cosmological constant problem appears to come from nowhere.
The energy studied by Planck is the radiation of a hot black body. It is is not a consequence of quantization. Clearly the hypothesis underlying the calculation quoted by Hobson is incorrect. The issue has also attracted attention from Weinberg. The existence of non-existence of zero point energy is a matter of measurement rather than theory. Steven Weinberg (2000): The Cosmological Constant Problems
Here I follow Feynman and others with the view that the total energy of the universe is zero, the sum of equal and opposite quantities of potential and observable energy. We are continually aware of negative gravitational potential in everyday life and we see that all the material structure of the universe is the product of the positive kinetic energy created opposite to potential energy. Richards Feynman (2002): Feynman Lectures on Gravitation, pp 9 - 10.
3. The trouble with quantum field theory: cart before horse?
Einstein’s general relativity is a field theory, but his first major discovery, the special theory of relativity, became a stumbling block for quantum field theory which has dogged it ever since. Steven Weinberg points out that quantum field theory is the way it is because (with certain qualifications) this is the only way to reconcile quantum mechanics with special relativity. Steven Weinberg (1995): The Quantum Theory of Fields Volume I: Foundations, page 49
The traditional approach to quantum field theory assumes that Einstein’s 4D Minkowski space-time is fundamental and builds quantum field theory on top of it. Hermann Minkowski (1908): Space and Time – lecture given at the 80th Meeting of the Natural Scientists in Cologne on September 21, 1908.
Since in quantum mechanics observables are represented by hermitian operators which act on the Hilbert space of state vectors, one expects the analogue in relativistic quantum mechanics of a classical observable field to be a set of hermitian operators defined for each point of space-time and having a well-defined transformation law under the appropriate group. Streater & Wightman (2000) PCT, Spin, Statistics and All That, page 96
The alternative proposed here is to make naked gravitation primordial and identify it with the model of God proposed by Aquinas. By naked gravitation I understand Einstein gravitation as it exists prior to its bifurcation into potential and kinetic energy, the quantum creation of elementary fermions and bosons and the appearance of Minkowski space.
On this point our physics differs radically from Aristotle and Aquinas who conceive matter and potential as passive. Aristotle used the axiom no potential can actualize itself to argue for the existence of the unmoved mover. Aquinas used Aristotle’s axiom in his first proof for the existence of God. Aquinas, Summa: I, 2, 3: Does God exist?
In modern physics potential is active. We become aware of gravitational potential as soon as we start learning to walk. Gravitational potential is one half of our awareness of divinity, holding us firmly on Earth. The other half, the rest of reality, is the kinetic energy which appears when zero-energy naked gravitation is split by quantum mechanics into negative potential and positive kinetic energy. It is this kinetic energy which turns quantum forms into the material structure which, like a brain, embodies the mind of god
4. A theological singularity: the God of Aquinas
Einstein first formulated general relativity for a universe of constant size. In the thirties astronomers discovered the “red shift” of light from distant galaxies which shows that the universe is expanding.
The field equation of relativity is non-linear and difficult to solve. Einstein’s first triumph was to approximate the motion of the perihelion of Mercury. In 1916 Karl Schwartzchild found a solution for the field surrounding a massive point source. In the 1970s Penrose, Hawking and Ellis predicted the existence of holes or singularities in the field of gravity which were subsequently observed by astronomers and named black holes. Roger Penrose (2020): Nobel lecture 2020: Black Holes, Cosmology and Space-Time Singularities
It is natural to assume that an expanding universe might have started from a point source now known as the initial singularity. Hawking and Ellis proposed that the emergence of the universe might be understood as a time reversed black hole.
A black hole does not seem to be a very satisfactory model for an initial singularity since we might imagine that it contains all the energy of the universe and is therefore enormously massive. We now know of black holes that are billions of times heavier than the Sun.
My Christian candidate for the source of the universe is the model of God developed by Aquinas from the Metaphysics of Aristotle. Aquinas defines God as actus purus, where actus is a Latin translation of Aristotle’s terms energeia and entelecheia. There I see a hint of the quantum of action. Here, I understand the quantum of action as a logical operator and Aristotle’s term energeia refers to the intellectual activity of the unmoved mover. At the structureless level of the initial singularity we may identify it with the traditional God. In the Latin Old Testament the creative action of God is represented by the verb fiat, let there be. Michael Bordt (2011): Why Aristotle's God is not the Unmoved Mover
§213 of the modern Catholic Catechism reads:
The revelation of the ineffable name "I AM WHO AM" contains then the truth that God alone IS. The Greek Septuagint translation of the Hebrew Scriptures, and following it the Church's Tradition, understood the divine name in this sense: God is the fullness of Being and of every perfection, without origin and without end. All creatures receive all that they are and have from him; but he alone is his very being, and he is of himself everything that he is. Catholic Catechism: §213 God alone IS
The God of Aquinas has three properties consistent with an initial singularity. Simplicity, eternity, and omnipotence. As noted above, I identify this god with naked gravitation. Aquinas, Summa, I, 10, 2: Is God eternal?, Aquinas, Summa I, 25, 3: Is God omnipotent?
The phrase fullness of being means that God represents all possible existence. We may think of the boundary of a divine universe in logical terms. If you try to get outside a universe that occupies the whole space of possibility you go into the forbidden region of impossibility. The traditional God cannot create a universe outside itself since all the logically consistent space is already taken.
We must rule out the other traditional attribute of divinity, omniscience. The ancients associated intellectual knowledge with immateriality, so insofar as they held that God is maximally immaterial, it followed for them that God is maximally intelligent.
In modern terms, the intelligence of God is ruled out by their simplicity since we hold as we see from experience, that all information, the subject of intelligence, requires material representation. Aquinas, Summa: I, 14, 1: Is there knowledge in God?, Rolf Landauer (1999): Information is a Physical Entity
Naked gravitation is a structureless, eternal, omnipotent, substantial topological space, an empty set, ∅, continuous, complete and convex. This topology is consistent with the axioms of probability theory and fixed point theory. Andrei Kolmogorov (1956): Foundations of the Theory of Probability, Brouwer fixed point theorem - Wikipedia
From a cybernetic point of view naked gravitation carries no information and so it is like an uncontrolled roulette wheel. When, given its omnipotence, it acts, it acts at random. This random activity is the source of the variation that makes evolution possible.
Because neither Divinity nor Nature can realize contradictions inconsistent structures resulting from random action are impossible. An inevitable consequence of life is death. Only those living entities that can reproduce themselves can endure for more than one lifetime. The selective phase of evolution is therefore extinction by failure to reproduce.
All the fundamental particles seem to be able to reproduce themselves. There is one composite particle, the proton, described by quantum chromodynamics, which appears to live forever. High energy experiments intended to break a proton into its constituent parts fail. Instead, when enough energy is available our attempts to destroy protons merely produce more protons. Proton decay - Wikipedia
5. The Trinity: The traditional God acquires structure by self awareness.
The God of the Hebrew Bible, Yahweh, is a jealous God, conscious of their own supremacy and quick to kill usurpers: I am the Lord Your God [. . .] You shall have no other Gods before me (Exodus 20:2-3).
Like most of the Gods of antiquity they were something of a ruthless warlord. They have motivated their imperial followers to whittle down the vast variety of ancient human cultures to a handful of major religions by conquest and occupation.
The next step in Yahweh’s theological evolution was the transformation from the unique God of the ancient Hebrews into the Christian Trinity, Father, Son and Spirit. Widespread acceptance in the Roman Empire of the claim by Jesus of Nazareth to be the Son of Yahweh established him as second person of the Trinity.
Traditionally the third person, the Spirit, plays an important role in the survival of the Church founded by Jesus. They made the spectacular appearance described in the Acts of the Apostles:
When Pentecost day came round, they had all met in one room when suddenly they heard what sounded like a powerful wind from heaven, the noise of which filled the whole house in which they were sitting; and something appeared to them that seemed like tongues of fire; these separated and came to rest on the head of each of them. They were all filled with the Holy Spirit, and began to speak foreign languages as the Spirit gave them the gift of speech. (Acts, 2: 1-4).
Despite some opposition from the pagan Roman establishment, Christianity spread rapidly through the Empire. The Emperor Constantine became Christian in 312 ce. At the Council of Nicea in 325 ce 300 bishops worked out a political settlement with the Roman state and enacted a broad conspectus of Christian doctrine in the Nicene Creed.
Further problems with the divine status of the Son and the Spirit led the Emperor Theodosius to convene the First Council of Constantinople in 381. This Council dealt further with the establishment of the Church and confirmed and augmented the Nicene Creed, which became settled doctrine. This Niceno-Constantinopolitan Creed is still recited by Christians. Mario Baghos: The Historical Context of the Nicene-Constantinopolitan Creed
Christianity became the established religion of the Empire and, with variations, it maintained this status in the imperial European powers that followed Rome.
The doctrine of the Trinity sets a difficult problem for theologians, many of whom had a Jewish and Neoplatonic background: how were they to reconcile the simultaneous unity and triplicity of their God?
Augustine of Hippo (354 – 430) provided a comprehensive resolution in his book De Trinitate, written between 400 and 428 ce. His book founded a theology of the Trinity which was further developed by Aquinas (1225 – 275) and Bernard Lonergan (1904 – 1984). Augustine (419, 1991)The Trinity
Augustine derives his treatment of the Trinity from three biblical texts. The first, in Genesis asserts that God created people in their own image (I, 27–28). This led Augustine to feel that there is some similarity between the divine and human minds. He found further support in the use of the term word (verbum, λογος) in the first chapter of John's Gospel. There the Word of God is understood to mean the person, Jesus.
From these data, Augustine concluded that the Son is conceived the mind of the Father by analogy with our human conception of words prior to speech. Augustine understood the Word of God in the mind of God as the Son of God. In a similar way the love of the Father for the Son is a real divinity, the Spirit. Aquinas and Lonergan have followed this same approach.
Here we follow Augustine and understand that universe reflecting on itself may duplicate itself. Mathematically, we might attribute the origin of structure in the initial singularity to the operation of Brouwer’s fixed point theorem which applies to the mapping of any continuous, convex and compact set onto itself.
Christian dogma confines the Trinity to three persons. Here I prefer a communication theoretical definition of person: an entity capable of sending and receiving messages. From this point of view every fundamental particle and every structure made from fundamental particles, like ourselves, is a person. The analogy of the Trinity may be extended to a countable infinity of autonomous individuals.
6. The presence of mathematics in the physical world
Landauer’s opinion that information is physical means that information is represented by physical entities like these letters, particles like photons, or any other persons. I have already noted that the modern idea of information means that the simplicity of the traditional God and its analogue, naked gravitation, deprive them of the ability to know and control.
We imagine that the first step in the creation of the world within an initial singularity is the creation of a Hilbert space following Brouwer’s fixed point theorem. We may refine this idea by contrasting two philosophical conceptions of mathematics, Platonism and Formalism. Øystein Linnebo (Stanford Encyclopedia of Philosophy): Platonism in the Philosophy of Mathematics, Richard Zach (Stanford Encyclopedia of Philosophy): Hilbert's Program
Platonism imagines that the forms of mathematics are real and substantive, like Plato’s forms. They are eternal, not created but discovered. This could be true in the current world but could not be true in the initial singularity because there is no structure present to discover.
The alternative is Hilbert's formalism, imagining mathematics in the current era as a creation of human minds, a symbolic game bounded only by consistency . Hilbert’s formalism depends on refinements to the logical expression of mathematical ideas published by Whitehead and Russell. Whitehead and Russell (1910): Principia Mathematica
We imagine that, starting from nothing, the universe must follow a formalist course, but given the idea that mathematics is information and information is physical, we must imagine this process to be ontological rather than epistemological. So the universe does not think up a mathematical model and the implement it, but rather it constructs systems and we later discover the mathematics embedded in these systems that have been validated by their consistency and survival in an evolving world. The requirement that ontological functioning requires that formalism be consistent is therefore embedded in the mathematics that may be extracted from nature and represented formally in print or some other medium. Hilbert's program - Wikipedia
This might explain the difficulties that arise in quantum field theory from mathematical assumptions that zero-sized particles and geometrical continua are real. Perhaps these particles and continua do not exist despite having led to the development of renormalization to recover epistemological consistency. Renormalization may work because the world is quantized, integral or digital.
7. The creation of Hilbert space
From the point of view of the mathematical theory of communication we can view the universe as a network of communication sources and quantum mechanics as the software that operates this network. The operation of a network in classical Minkowski space depends heavily in computers to encode, decode and route communications. The belief that quantum communication and computation are at least as powerful as their classical analogues suggests that postulating a quantum mechanical foundation to a classical network is feasible. We choose Hilbert space as the foundation of our universal source, since it is the space of quantum mechanics. John von Neumann (2014): Mathematical Foundations of Quantum Mechanics
John von Neumann defines the basic properties of Hilbert space in three axioms:
2. They can be multiplied by a number a to give af.
3. They have an inner product, written (a, f) which yields a complex number, a measure of distance between the elements which serves as a foundation for the geometry of Hilbert space.
Von Neuman points out that:
The noteworthy feature of the operations af, f ± g, (f, g) is that they are exactly the basic operations of the vector calculus: those which make possible the establishment of length and angle calculations in Euclidean geometry or the calculations with force and work in the mechanics of particles.
Hilbert space is formulated with complex numbers which are inherently periodic and describe vibrations, so helpful intuitive models of Hilbert space are sound, music and speech.
A source Ahas an alphabet or vocabulary of i letters or symbols ai each of which has a probability pi subject to the constraint that the sum of these probabilities in any particular language is 1. The quantum mechanics operating behind any of these languages honours the probabilistic constraint of communication theory by its property of unitarity. This property is a feature of the Schrödinger equation which is understood to govern the evolution of independent quantum systems.
So let us now go into the interior of naked gravitation and apply the formalist approach to creating the universe. At this point there is no energy in the universe but naked gravitation is actual and substantive, like Aristotle’s first mover. Unmoved mover - Wikipedia
The axioms of Brouwer’s theorem apply in naked gravitation. It is a structureless, eternal, omnipotent, dynamic topological space, an empty set, ∅, continuous, complete and convex and capable of mapping itself into itself like Augustine’s God.
The theorem establishes that a function f(x) mapping a continuous, convex compact set onto itself identifies a particular point x which is its own image, f(x) = x. If we imagine that the functions mapping the initial singularity onto itself are Turing computable there is a countably infinite set of them, potentially creating a countably infinite set of fixed points which we take to be a basis for Hilbert space.
We therefore have a countable infinity of possibilities to choose from plus all the possibilities created by superposing these possibilities, and so on. As in genetic evolution, and we may be confident that within this space of possibilities there will be some states that can reproduce themselves and therefore become fixtures in the world. We can assume that every formal structure in the world can be represented by vectors in a suitable Hilbert space.
8. The contrasting roles of observation in quantum and classical mechanics
Einstein radically revised classical physics with his theories of special and general relativity. His work struck deeper however, into the methodology of physics, summing it up in principles of covariance. The core idea is that the universe is the same, regardless of the state of any observer.
The transformation of the observed reality to what the observer actually sees must therefore be a function of the relationship between the observer and the observed system. When everything is moving inertially this is the Lorentz transformation. Accelerated classical motion is also covariant but the transformations are more complex, represented by Einstein’s field equation. In human terms classical general covariance is analogous to dictation. I dictate and you listen and you are not permitted to talk back to me.
The quantum world is much more natural. It involves conversation. Every communication is a meeting. There are always two actors and they are changed by the meeting. Because there are two basically uncorrelated actors the outcome of every quantum interaction has the random element we observe in quantum interactions in classical space.
A successful meeting occurs when people understand one another. In quantum mechanical terms this means sharing eigenvectors in the tensor product the Hilbert spaces embodied in each particle. Although both the state vectors in a quantum meeting may be the superposition of a large number of basis vectors, information is only transferred when the same state is shared by both observer and observed. Wojciech Hubert Zurek (2008): Quantum origin of quantum jumps: breaking of unitary symmetry induced by information transfer and the transition from quantum to classical
The metric in Hilbert space measures the distance between states. The Born rule shows that the probability of observing states that are close together is higher than the probability for states that are far apart. In quantum mechanics the distance between states is not a matter of spatial distance but of angle or phase which is more closely related to time.
9. Quantum intelligence, linear operators, the eigenvalue equation and the creation of particles
The beauty of the randomness of periodic events like waves is that they vary around zero so stationary points can be created by superposing equal and opposite directions from zero to get static systems that do not vary, nodes. The whole mechanism of quantum mechanics revolves around finding stationary nodes called eigenvectors and their corresponding eigenvalue in complex periodic systems like the electrons in an atom.
The eigenvalue equation selects stationary points out of the perpetual variation in Hilbert spaces created at random in uncontrolled singularities. These stationary points, like species in the evolution of life, are the selected structures that make the world.
This insight combined the work of Bohr and de Broglie to understand the orbits of atomic electrons in Minkowski space. In Minkowski space the quantum of action has the dimensions of angular momentum. Bohr found that the only permissible orbits for atomic electrons in Minkowski space are those whose angular momentum is an integral multiple of the quantum of action.
An analogous relationship holds in abstract Hilbert space where processes are logical and there are no variables corresponding to classical distance, time or angular momentum. Instead our insights must be logical, expressed in mathematical language.
In a vector space of n dimensions the operator A may be written as a square array of n × n rational or complex numbers. An eigenvector x is a one dimensional string of these numbers. A wave function is the set of coefficients of the basis states that constitute such a vector. The eigenvalue λ is a real rational number. The problem, for both nature and physicists, is to find an operator A, a set of n dimensional eigenvectors x and corresponding eigenvalues λ that have the relationship
Ax = λx
A λ and the corresponding x are called an eigenpair and the different x s are the spectrum of the operator A. Since λ is simply a number, the effect of the operator A is to change the length of the vector x in each case and its associated probability but not its direction.
Since in Hilbert space the information about a state is carried by direction, this result means that the observable feature of a particular state is the real number λ. These values appear to be defined in nature to a very high degree of precision. Since the λs observed in Minkowski space must be real numbers quantum mechanics gives special attention to self-adjoint or hermitian operators A which have a spectrum of real values on their diagonals. Hermitian matrix - Wikipedia
Although the mechanism of quantum mechanics is built on complex numbers, all the numerical inputs and outputs in Minkowski space are real numbers. One might feel that the essential content of quantum mechanics is the relationship between real and complex algebra which describes the relationship between motion and stillness. This old problem dates back at least to the contrasting opinions of the ancient Greeks Parmenides (reality is fixed) and Heraclitus (everything flows).
Physicists studying quantum mechanics are continually faced with the eigenvalue problem. The information that they start with is quite sparse with respect to the problem. All they have is experimental measurements of λs, for instance the frequencies of the photons emitted by an atom. From this data they have to work out plausible pairs of operators and eigenvectors to give the observed results.
The reason for calling this essay cognitive cosmology is that I feel that the ability of the universe to solve what quantum mechanics understands to be the eigenvalue problem suggests that it is intelligent. A solution to an eigenvalue problem seems to be equivalent to an intellectual insight. It is a puzzle rather than a calculation and in the general case we approach a solution by recursive trial and error.
Quantum evolution operates at the interface between the possible and the real, like biological evolution. We find random processes exploring spaces in which there is an occasional viable structure that it capable of reproducing.
One reason for holding that quantum mechanics is more powerful than Turing computation is the belief that quantum computation is a continuous error free analogue process not confined, like Turing machinery, to discrete binary logical processes. In a two dimensional Hilbert space we represent the qubit |𝜓⟩ with the equation |𝜓⟩ = a|0⟩ + b|1⟩ where a and b are assumed to be continuous complex numbers (mod 2𝜋) such that a2 + b2 = 1. This suggests that |𝜓⟩ has a continuous range of values.
These values may or may not exist. What we do know is that when we observe |𝜓⟩ all we ever see is either | 0⟩ or |1⟩. Nevertheless in the invisible abstract world of quantum evolution the existence of a continuous analogue process may contribute to the discovery of the fixed quantum states which may endowed with reality by the addition of energy.
A Turing computation is a long string of discrete logical operations. A quantum measurement, the equivalent of a quantum computation, is understood to be a single operation. It may not necessarily be fast however. The decay of a uranium nucleus can take billions of years.
This set up and solution of the eigenvalue problem is the act of quantum mechanical insight. In Aristotelian terms, we might say that linear operators are the agent intellect of the universe. In De Anima, Aristotle suggests that the human intellect must be separate from matter. This arises from his hylomorphic model of change where he argues that matter constrains form. This leads him to think that the universality of human intellect shows that it cannot be a material organ. Christopher Shields (Stanford Encyclopedia of Philosophy b): The Active Mind of De Anima III 5
Nature, it seems must also work by trial and error, finding stable eigenvectors amid the noise of Hilbert space. These vectors are in effect the genes of stable particles which will derive energy from gravitation to become real as described in the next section. As we have described the universe here, quantum mechanics in Hilbert space is the logical creation of the forms of potentially independent material particles. We may call this cognitive cosmogenesis.
We may simplify our study of elementary particles by exploiting the observed fact that all these particles are either bosons or fermions, so we can imagine a two dimensional Hilbert space, |𝛹⟩ = a|boson⟩ + b|fermion⟩ whose base states are |boson⟩ and |fermion⟩. It may be objected that laboratory work in quantum mechanics has revealed super-selection rules which forbid the superposition of charged and uncharged states. This is true in Minkowski space. Everything we observe is either a fermion or a boson. In the interests of simplicity we avoid this issue by assuming that abstract states corresponding the bosons and fermions can coexist in some Hilbert space.
We assume that these forms have evolved under the influence of the random development of Hilbert space in naked gravitation and the selection of stationary states by quantum mechanics. They have the selective advantage that they can reproduce themselves and that they open the way to the creation of Minkowski space and the further evolution of the universe.
As with biological evolution, selection for survival in a variable universe is specifically related to the ability to reproduce. In quantum mechanical terms this requires the existence of hermitian operators corresponding to members of the known spectrum of elementary particles. This spectrum appears to have been quite stable since very early in the life of the universe. As we can see in the enormous variety and detail of living creatures, there seems to be no practical limit to evolutionary creativity. We base this idea on studies of quantum computation and quantum communication described in books such as Nielsen and Chuang. The evolution of living physiology seems to explore the quantum mechanical limits of possibility. Nielsen & Chuang (2016): Quantum Computation and Quantum Information, William Bialek & Allan Schweitzer (1985): Quantum Noise and the Threshold of Hearing
10. Forms are made real by kinetic energy arising from the bifurcation of naked gravitation
In modern physics we identify matter and energy, and we understand the creation of kinetic and potential energy by the bifurcation of gravitation. This process is demonstrated by the cycle of a pendulum. Recognition of the reality of potential energy was a necessary step toward the formulation the principle of conservation of energy.
We guess than the formation of stable quantum forms in zero-energy naked gravitation induces gravitation to split into kinetic and potential energy. The kinetic energy embodies the quantum form to create a real particle, a fermion or a boson. The potential energy couples newly formed particles together, enabling them to interact with each other. Gravitational potential keeps grounded in Earth. Electrical potential takes care of most of chemistry. The weak and strong potentials control nuclear physics.
11. The interactions of bosons and fermions determine the metric of Minkowski space.
Since the discovery of the electron by J J Thompson in 1897 laboratory experiments have identified approximately 60 elementary particles. All of these particles fall into one of two families, bosons and fermions. We may imagine these families to be the basis states of a two dimensional Hilbert space near the origin the universe. Elementary particle - Wikipedia
Bosons carry information between fermions by transporting phase unchanged through spacetime. The majority of bosons are massless and travel at the speed of light on null geodesics. This made possible in Minkowski space by the negative element on the diagonal (1, 1, 1 -1) of the 4 x 4 matrix representation of the Minkowski metric. The 1, 1, 1 portion of the metric represents the Euclidean space necessary for the free motion of massive fermions obeying the exclusion principle.
The existence of the null geodesic suggests that we can introduce a third round of zero-sum bifurcation into the universe, The first was the introduction of Hilbert space in naked gravitation by analogy with Augustine’s theory of the Trinity. The second was the bifurcation of naked gravitation into potential and kinetic energy. The null geodesic now suggests that space and time are two facets of some underlying entity that quantum mechanics has presented to us in the form of fermions and bosons,
Given this structure, the non-relativistic version of the Schrödinger equation operates in Hilbert space and the promotion of the eigenstates of this equation into real fermions and bosons by energy contributed from the bifurcation of gravitation would seem to be the source rather than a consequence of the Minkowski metric. The interactions of real particles thus become subject to Lorentz transformations based on the speed of light as Einstein explained to us. Albert Einstein (1905): On the Electrodynamics of Moving Bodies
Ian Duck and E.C.G. Sudarshan (1998)It has long been surmised that the distinction between fermions and bosons is the consequence of a mathematical spin-statistics theorem which derives the difference between these two classes if particle from special relativity. Duck and Sudarshan discuss this idea at length motivated by Feynman’s apology in his Lectures on Physics that he does not know an elementary explanation of the difference. Their overall conclusion is that the connection between spin, statistics and relativity is not very clear. The way may stand open for the idea here that relativity and Minkowski space are consequences of nonrelativistic quantum theory. Ian Duck and E.C.G. Sudarshan (1998): Toward an understanding of the spin-statistics theorem
Here the positive kinetic energy and negative potential energy created from gravitation by quantum mechanics both contribute to the creation of elementary particles and to the stabilization of structures like atoms and molecules made from elementary particles.
12. From Minkowski space to general relativity
Minkowski space gives structure to the universe. At the end of his article on the field equation of gravitation Einstein notes that the postulate of general relativity cannot reveal to us anything new and different about the essence of the various processes in nature than what the special theory of relativity taught us already. Albert Einstein (1915): The Field Equations of Gravitation
13: Comparison with quantum field theory
From the point of view of the story told here we may be able to propose solutions to the problems arising in quantum field theory (QFT) described by Kuhlmann.
Ot radical solution is to found the Universe on the model of God devised by Aquinas, eternal, omnipotent and absolutely simple, without any structure to represent information and not, therefore, omniscient. We identify this divinity with a primordial form of universal gravitation, naked gravitation, within which a mathematical fixed point theorem induces a chaotic Hilbert space and quantum mechanics which selects stationary structures in this space, the forms of elementary particles.
The bifurcation of gravitation into potential and kinetic energy endows these forms with the energy to become real particles and the potential to bind to one another. These particles fall into two classes, fermions and bosons and their interactions establish the metric of Minkowski space, so defining the classical structure of the space in which we live, and forming the foundation for Einstein relativity which defines the structure of the universe. I call this picture cognitive cosmogenesis, CC , because it relies on the intelligence and information processing capacity of quantum theory,
As presented in this short article my story is vague, but suggests a simple picture of a universe beginning from an eternal, omnipotent structureless singularity. It is proposed for discussion as an alternative to quantum field theory which is beset by some philosophical problems. QFT is based on two centuries of data collection which is not in doubt. The problem lies in the interpretation of this data.
Kuhlmann writes:
He continues:
In contrast to many other physical theories there is no canonical definition of what QFT is. Instead one can formulate a number of totally different explications, all of which have their merits and limits. One reason for this diversity is the fact that QFT has grown successively in a very complex way. Another reason is that the interpretation of QFT is particularly obscure, so that even the spectrum of options is not clear.
(As an aside, focusing on the number of particles, or degrees of freedom respectively, explains why the famous renormalization group methods can be applied in QFT as well as in Statistical Physics. The reason is simply that both disciplines study systems with a large or an infinite number of degrees of freedom, either because one deals with fields, as does QFT, or because one studies the thermodynamic limit, a very useful artifice in Statistical Physics.)One gets a very different kind of access to what QFT is when focusing on its relation to QM and the special theory of relativity, SRT. Historically, QFT resulted from the successful reconciliation of QM and SRT. In order to understand the initial problem one has to realize that QM is not only in a potential conflict with SRT, more exactly: the locality postulate of SRT, because of the famous EPR correlations of entangled quantum systems. There is also a manifest contradiction between QM and SRT on the level of the dynamics. The Schrödinger equation, i.e., the fundamental law for the temporal evolution of the quantum mechanical state function, cannot possibly obey the relativistic requirement that all physical laws of nature be invariant under Lorentz transformations.
And he concludes:
In conclusion one has to recall that one reason why the ontological interpretation of QFT is so difficult is the fact that it is exceptionally unclear which parts of the formalism should be taken to represent anything physical in the first place. And it looks as if that problem will persist for quite some time.
The story here gives a radically different picture of the universe.
Here are a few points I see in favour of CC
1. It provides a general framework which does not appear to contradict any of the data. It is not mathematical but may provide some of the insight recommended by Feynman:
A physical understanding is completely unmathematical, imprecise, an inexact thing but absolutely necessary to a physicist. Feynman, Leighton and Sands FLP II_02: Chapter 2: Differential Calculus of Vector Fields
The idea is supported by Dirac’s feeling that mathematical success does not guarantee correctness:
The rules of renormalization give surprisingly, excessively good agreement with experiments. Most physicists say that these working rules are, therefore, correct. I feel that that is not an adequate reason. Just because the results happen to be in agreement with observation does not prove one's theory is correct. . . . I have spent many years searching for a Hamiltonian to bring into the theory and have not yet found it. I shall continue to work on it as long as he can, and other people I hope will follow along such lines. Peter Goddard (1998): Paul Dirac, The Man and His Work, page 28.
2. The proposal in CC to create particles through a process involving the quantum solution of the eigenvalue equation coupled with the provision of energy to realize particles from gravitation endows each particle with a hermitian operator which governs its interactions with other particles in a way analogous to the role of our mental states in our interactions with one another, which cover the spectrum from love to murder.
3. The provision of 2 above eliminates the need for field, since particles are equipped to resolve all one-to-one interactions. The infinity, continuity and lack of a clear ontological basis for fields creates most of the problems listed by Kuhlmann. Even before Gödel and Turing destroyed his formalist dream, Hilbert clearly rejected the relaity of infinity:
In summary, let us return to our main theme and draw some conclusions from all our thinking about the infinite. Our principal result is that the infinite is nowhere to be found in reality. It neither exists in nature nor provides a legitimate basis for rational thought — a remarkable harmony between being and thought. David Hilbert (1925): On the Infinite
4. The infinities that arose in the adaptation of quantum mechanics to relativity forcesd the development of renormalization, a procedure that Feynman compared to sweeping problems under the carpet. The approach taken here keeps quantum theory clear of relativity until after the introduction particles and Minkowski space. In the absence of spurious infinities, renormalization is unnecessary. Richard P. Feynman (1965): Nobel Lecture: The Development of the Space-Time View of Quantum Electrodynamics2
5. QFT cannot deal with gravitation because it cannot be renormalized and renormalizaztion is absolutely essential to QFT as long as it built on continuous Minkowski space.
6. QFT imagines the origin of energy as a consequence of quantum fluctuation. The quantum in CC is a certainty principle, a logical operator, rather than an uncertainty principle. Energy in the zero energy universe of this story arises from breaking the symmetry of primordial gravitation into potential and kinetuc energy.
I conclude by emphasizong two principles lie at the heart of my exposition and use them to construct a simple political model of the world based on quantum theory that holds at all scales.
The first I call the heuristic of simplicity. We are working at the base of the Universe right next to the initial singularity. Although theologians talk about the ineffable mysteries of God, if God is really absolutely simple there is nothing to be said about them except that they exist. As Aquinas puts it, the essence of God is their existence. The true story must begin quite simply.
As our picture of the universe becomes more complex, we are still subject to the information theoretical constraint that the entropy of the explanation should be equivalent to the entropy of the system described. This effects the courtroom injunction to tell the truth, the whole truth and nothjng but the truth. We expect the complexity of explanation to be equivalent to the complexity of the reality explained.
The second is the symmetry with respect to complexity built into quantum theory by unitarity. Communication theory shows that the sum of the probabilities of the phonemes in human speech or the symbols in human writing is 1, identical to the sum of the probabilities of the outcomes of a quantum observation. This probabilistic symmetry applies to all forms of communication, regardless of its complexity
This idea is implicit in quantum theory through the normalization of vectors independently of the dimension of the operative Hilbert space so the vector representing the universe comprising the superposition countable infinity of basis states representing (say) fundamental particles has length one and direction defined by the Universe.
Although the difference in scale between fundamental particles and an ideal democratic polity is immense, they are formally quite similar. Democratic politics, like quantum mechanics, fits in Hilbert space. Voting itself is linear, a form of superposition. Individuals and political parties are characterized by their directions in political space which may be modelled as vectors in a Hilbert space. Every person is represented by a basis vector and their sums in various combinations present us with a comprehensive picture of the political directions in an electorate. There seems to be fundamental harmony between democratic politics and the nature of the world.
