Chapter 16: Gravitation and the creation of dynamic particles

Synopsis

Quantum field theory relies on the energy of the vacuum caused by fluctuations to give particulate reality to the continuous fields imagined to exist in a Hilbert space defined on Minkowski space. In this book we have made Hilbert space primordial and kinematic, driven in the initial instance by a dynamic initial singularity. All the subsequent particles created from the singularity have the same structure: each dynamic particle has an associated kinematic Hilbert space which controls its interaction with other particles, the phenomenon we call measurement. All the actual processing and communication in the Universe is performed in this Hilbert space. Kinematic quantum mechanics selects stationary states which derive energy from gravitational potential and become dynamic particles.

Table of contents



16.1: Dinosaurs, birds and Newton's General Scholium

16.2: The quantum evolutionary origin of stable states


6.3: The simple relationship between gravitation and quantum theory

16.4: The modern problem with gravitation

16.5: Entropy and the cycle of explanation


16.1: Dinosaurs, birds and gravitation

It is a wet and grey day and I am sitting in the garden watching the birds defy gravity. They are protected and propelled by feathers that date back to the age of dinosaurs. Like guided missiles, they swoop over the fence, feather their wings and land precisely on the clothes line.

Gravitation has played a role in every feature of this landscape, from the anatomy and physiology of the birds to the shape of the trees, fences and houses, my posture on my chair and even the thermonuclear reactions that bring us the light from the Sun.

Its principal power lies in the fact that its negative potential energy is the source of the positive dynamic energy from which the visible Universe is made. This means that in a subtle sense, gravitation plays the role of the God in Newton's General Scholium, establishing the dynamics of the universe.

He wrote:

This most beautiful System of the Sun, Planets, and Comets, could only proceed from the counsel and dominion of an intelligent and powerful being. . .. Isaac Newton (1713): The General Scholium to the Principia Mathematica

Newton's Scholium paints a traditional picture of God. Here my story is quite different but our stories agree at one point. Gravitation is in effect the substantial presence of divinity that brings possibility into reality.

Gravitational potential is understood here to be like money held by the Universe at call to enable the realization of dynamic systems with positive energy. On this analogy the unit of value is the quantum of action. The conservation of energy is a consequence of the zero sum bifurcation of action into positive and negative energy which is closely related to the bifurcation of action into energy.time and momentum.distance arising from the creation of spacetime

I began this project with the work of Aristotle, written 2600 years ago. Aquinas synthesized science and theology in the Middle Ages when Aristotle was still the epitome of science. Galileo liberated science from Aristotle in the seventeenth century. Sixty years ago I discovered Aquinas and set out to repeat his achievement, to harmonize modern physics and traditional theology. Our modern understanding of gravitation and quantum theory have made this task more complex but much more exciting. I have reinterpreted Aristotle’s form and matter into kinematic and dynamic motion and related them to the variation and selection driving evolution .

Einstein's path to gravitation is described Chapter 15: Potential + kinetic = zero energy universe. We now turn to a more detailed description of the relationship between gravitation and quantum mechanics which was established at the beginning of creation and replaces, in my mind, the old quantum field theory which is incompatible with theology. Quantum field theory - Wikipedia

16.2: The quantum evolutionary origin of stable states

We have assumed that the initial singularity is pure action, identical to the Thomistic God of the Roman Catholic Church. In chapter 11: The axioms of Hilbert space we imagined each basis state as a pure tone. Superposed at random these states add up to a normalized vector which would sound like noise. This kinematic “noise vector” provides the random variation necessary to fuel the creativity of evolution. This formal entity is analogous to the vacuum in quantum field theory.

The role of quantum mechanics, described in Chapter 14: Evolution and intelligence, is to detect the subtle superpositions of vectors in Hilbert space that correspond to stable states or standing waves. The mathematical mechanism for this activity is the mapping of Hilbert space onto itself by self-adjoint or hermitian operators. From the mathematical point of view, success in this operation requires the solution of the eigenvalue problem which can be set up as an eigenvalue equation.

Much of the work in quantum physics involves specifying and solving this equation. This requires creative work because the eigenvalues available from physical experiments are quite insufficient to determine the problem. The problem, once defined can be solved, in realistically complex cases, only by recursive numerical methods.

We suspect that nature solves this problem using a technique analogous to evolution by natural selection. The kinematic eigenvectors produced by quantum selection serve as the foundation for the net step in creation, the addition of energy from gravitation. This step is analogous to the idea in field theory that discrete particles are energized by fluctuations in the vacuum. The alternative described here we might call the Hilbert vacuum. It is formal and kinematic, driven by the omnipotence of the singularity, so that it does not cause the cosmological constant problem (See Chapter 26: An alternative to quantum field theory?).

16.3: The simple relationship between gravitation and quantum theory

Chapter 14 describes how quantum mechanics discovers of standing waves among superpositions of the vectors arising in the Hilbert space described in Chapter 11: The axioms of Hilbert space.

The negative potential in the gravitational field is equivalent to the positive energy of the particles. This is equivalent to the Universe measuring itself as described in Chapter 20: Measurement— the interface between Hilbert and Minkowski spaces. In this way we maintain the zero-energy status of the Universe while creating the dynamic particles within it. The energy of these particles corresponds to the frequency of the eigenvalues selected by quantum theory.

We assume that this kinematic Hilbert space is in perpetual motion driven by the energy of the particles with which it is associated, beginning with the omnipotent initial singularity. Because the interior of the initial singularity is not extended in space and time we assume that all these basis vectors of the Hilbert space are superposed. We assume from the cybernetic principle of requisite variety that the initial symmetry has limited control over its behaviour so the creation of a Hilbert space within itself is a sequence of random events.

The next step we imagine in the creation of the Universe is the creation of Minkowski space to be described in the next Chapter, 17 The interactions of a random set of particles may undergo another round of selection in Minkowski space. The result of this process is the stable set of elementary particles and their unstable analogues that have been identified experimentally. These particles comprise the standard model. The stage is set for the particles of the standard model to begin binding into more complex structures, atoms, molecules, the Universe and ourselves.

16.4 The modern problem with gravitation

The apparent success of quantum field theory in the explanation of the three interactions, electromagnetic, weak and strong suggests that it should be possible to develop a quantum theory of gravitation. The success with the first three fields depended on the invention of renormalization to control the unphysical appearance of mathematical infinities in the theory. Kerson Huang (2013): A Critical History of Renormalization

Infinities first entered physics when Lorentz began thinking about the electron. He conceived the electron as a particle existing in spacetime whose self mass diverged linearly to infinity as its radius tended to zero, the first of many unrealitic ultraviolet catastrophes that have plagued mathematical physics, possibly due to inappropriate application of mathematical formalism. We may imagine that black holes are a recent and realistic version of this problem.

Renormalization saved the quantum field theories by plausibly eliminating the infinities and by providing explanations for confinement and asymptotic freedom in quantum chromodynamics. Feynman thought it was a bit dodgy, but was pleased that it worked. Unfortunately it does not work for gravitation.

Because gravitation is unrenormalizable within standard quantum field theory, the search for quantization has led to an enormous amount of relatively unsuccessful physical and mathematical speculation about the fundamental structure of the Universe.

Here we are confronted by the interface of the formalist world of mathematical perfection, where computations made with real numbers yield results of unlimited precision, and the noisy world of physical reality where precision is limited by noise and uncertainty. In this situation error is controlled by quantization. Shannon's theory makes it possible to move gigabytes of information over noisy connections without error (see Chapter 19: Quantization—the mathematical theory of communication).

Conversely, we should not expect to find quantization where error is impossible, Since gravitation couples universally to energy alone, we can imagine that gravitation involves unconstrained and therefore intrinsically error free and non-quantized interaction: codeless communication. It seems to work perfectly as a continuous theory. Quantization is unnecessary. This may be why gravitation is capable of creating real ultraviolet catastrophes.

16.5: Entropy and the cycle of explanation

Science has been through a long line of paradigm changes since ancient Greeks like Thales and Aristotle turned from myth and poetry to empirical science. We are somewhere in the most recent phase of this process.

We assume that the initial singularity is just a single state, a single particle. Boltzmann's entropy equation S = k log W where W is a count of the independent states of a system shows that when W = 1, S is zero. In its present state the entropy of the Universe is huge no matter how we count it. Its mass is at least 10⁵³ kilograms. If we apply the equations E = mc² and f = E/h we find that the universe operates at about 10¹⁰⁰ actions per second. Universe - Wikipedia

We might expect the complexity of a true and sufficient explanation to be equivalent to the complexity of the system to be explained. The initial structureless singularity, like the traditional divinity, simply exists and there is nothing more to be said about it.

An important idea in this book is the relationship between dynamics and kinetic entities, drivers and driven: in epistemology between reality and ideas; in classical physics between time and space; in quantum physics between complex and real numbers; and in theology between matter and spirit.

Kinematics models motion, as in the cinema, where we know that what we see on the screen is not real. The sequential images created by cameras, animators and computers deceive us. Dynamics, on the other hand, deals with the real causes of action. On a large scale, the classical mathematical formalism of the differentiable manifold provides a precise model of observed reality. It is based on the special theory of relativity, which is classical and kinematic. It tells us how the world works, but does not explain why. The explanation lies in the behaviour of the particles formed by the collaboration of kinematic quantum mechanics and dynamic gravitation, our living god.

Mathematics, as practised by users of mathematics, is kinematic. The symbols do not move themselves. This is the essence of formalism. When we read Turing's proof we must imagine his machine and manipulate its components in our minds. The result is a deterministic logical process, a proof. Turing then shows that there are conclusions his machine cannot reach. There is no way to manipulate the machine to overcome this limitation as long as it remains deterministic.

Philosophers may ask whether mathematics exists independently of mathematicians or whether we make it ourselves. Hilbert's formalist program suggests that we make it, a kinematic product of our dynamic minds. The assumption that the Universe begins with no structure at all implies that the evolutionary process that creates the Universe also creates the mathematics embodied in it, and following Hilbert we share in this power. Cosmogenesis is cognitive. The formalist program of mathematics may nevertheless enable us to imagine entities like infinity, geometric continuity and particles of zero size that are inconsistent with reality.

Mathematical stories that are interesting and logically consistent are admitted to the mathematical canon. Organizations like the Clay Mathematics Institute are aware that physical speculation is a rich source of mathematical ideas so they promote cross fertilization by offering real big money hoping to energize work in this domain. Carlson, Jaffe & Wiles(2006): The Millennium Prize Problems

Copyright:

You may copy this material freely provided only that you quote fairly and provide a link (or reference) to your source.

Notes and references

Further reading

Books

Carlson (2006), James, and Arthur Jaffe & Andrew Wiles, The Millennium Prize Problems, Clay Mathematics Institute and American Mathematical Society 2006 1: The Birch and Swinnerton-Dyer Conjecture: Andrew Wiles 2: The Hodge Conjecture: Pierre Deligne 3: The Existence and Smoothness of the Navier-Stokes Equation: Charles L Fefferman 4: The Poincare Conjecture: John Milnor 5: The P versus NP Problem: Stephen Cook 6: The Riemann Hypothesis: Enrico Bombieri 7: Quantum Yang-Mills Theory: Arthur Jaffe and Edward Whitten  Amazon   back

Links

Isaac Newton (1713), The General Scholium to the Principia Mathematica, 'Published for the first time as an appendix to the 2nd (1713) edition of the Principia, the General Scholium reappeared in the 3rd (1726) edition with some amendments and additions. As well as countering the natural philosophy of Leibniz and the Cartesians, the General Scholium contains an excursion into natural theology and theology proper. In this short text, Newton articulates the design argument (which he fervently believed was furthered by the contents of his Principia), but also includes an oblique argument for a unitarian conception of God and an implicit attack on the doctrine of the Trinity, which Newton saw as a post-biblical corruption. The English translation here is that of Andrew Motte (1729). Italics and orthography as in original.' back

Kerson Huang (2013), A Critical History of Renormalization, ' The history of renormalization is reviewed with a critical eye,starting with Lorentz's theory of radiation damping, through perturbative QED with Dyson, Gell‐Mann & Low, and others, to Wilson's formulation and Polchinski's functional equation, and applications to "triviality", and dark energy in cosmology. Dedication: Renormalization, that astounding mathematical trick that enabled one to tame divergences in Feynman diagrams, led to the triumph of quantum electrodynamics. Ken Wilson made it physics, by uncovering its deep connection with scale transformations. The idea that scale determines the perception of world seems obvious. When one examines an oil painting, for example, what one sees depends on the resolution of the instrument one uses for the examination. At resolutions of the naked eye, one sees art, perhaps, but upon greater and greater magnifications, one sees pigments, then molecules and atoms, and so forth. What is non‐trivial is to formulate this mathematically, as a physical theory, and this is what Ken Wilson had achieved.' back

Quantum field theory - Wikipedia, Quantum field theory - Wikipedia, the free encyclopedia, ' Quantum field theory treats particles as excited states (also called quantum levels) of their underlying quantum fields, which are more fundamental than the particles. The equation of motion of the particle is determined by minimization of the action computed for the Lagrangian, a function of fields associated with the particle. Interactions between particles are described by interaction terms in the Lagrangian involving their corresponding quantum fields. Each interaction can be visually represented by a Feynman diagram according to perturbation theory in quantum mechanics.' back

Universe - Wikipedia, Universe - Wikipedia, the free encyclopedia, 'The Universe is all of spacetime and everything that exists therein, including all planets, stars, galaxies, the contents of intergalactic space, the smallest subatomic particles, and all matter and energy. Similar terms include the cosmos, the world, reality, and nature. The observable universe is about 46 billion light years in radius. back