Introducing the divinity of the Universe
to pave the way for scientifically credible theology
Chapter 15: Potential + kinetic = zero energy Universe
Synopsis
We call the source of the Universe naked gravitation, the structureless initial singularity predicted by Einstein’s general relativity and discovered by Hawking and Ellis. The singularity has zero energy. The first step in the creation of the Universe, described in Chapter 5: Eternity, time and Hilbert space, is the formation of Hilbert space in the singularity. This space is in perpetual kinematic motion driven by the power of the singularity. The second step is the construction, by quantum mechanics, of stationary points in this Hilbert space. The third step, the subject of this chapter, breaks the symmetry of the singularity into the positive and negative energy of gravitation. The positive energy transforms the kinematic stationary points discovered by quantum mechanics into real dynamical particles, children of the initial singularity. The negative energy deepens the gravitational potential well that stabilizes the Universe.
Table of contents
15.1: Evolutionary epistemology15.2: Dynamics: from Newton through electromagnetism to general relativity
15.3: General relativity, initial singularity and zero-energy Universe
15.4: We live in a potential well: the cosmic microwave background
15.5: Action: the quantum initial singularity
15.1: Evolutionary epistemology
If the Universe were to be planned in advance, a large volume of information would be needed to define this plan. This information could not be contained in a structureless initial singularity. An alternative approach is to test the idea that the world arose by evolution from an eternal quantum of action with unlimited fertility controlled only by local consistency.
Natural selection selects the individuals that successfully mature and reproduce to carry their genes into the next generation. Survival is dictated by the relationship between individuals and the environment in which they find themselves. These environments are created by prior events on timescales ranging from the formation of stars and planets to local events like floods, fires and famines or the sudden appearance of a predator.
The generation of science is very similar to the process of biological evolution. The scientific community is simultaneously collecting data and trying to explain what this data means. These two processes inject a variety of hypotheses into science which is then tested by comparing them to more data.
In the seventeenth century, Isaac Newton used the work of Galileo and many other astronomers to build the foundations of classical mechanics. Newton's unifying concept is force. He defined force in terms of mass, length and time by his second law, force = mass × acceleration, where acceleration is rate of change of velocity, and velocity is the ratio of distance travelled to time elapsed. Newton's Laws of motion - Wikipedia
15.2: Dynamics: from Newton to general relativity
Newton described the laws that govern the behaviour of slow moving massive bodies in classical space and time.
Einstein’s developed the special theory of relativity because he realized that Maxwell's equations show that the speed of light must constant and independent of the motion of its sources and observers. It is a local phenomenon. This requires space and space and time to be combined into a single entity, spacetime, Minkowski space. Minkowski space - Wikipedia
Einstein records two insights that led him from special to general relativity. The first, his "happiest thought", was that a person in free fall would not feel their own weight. They do not feel any force because they are moving inertially. On the other hand, their speed is increasing as they fall. From a Newtonian point of view they are accelerating, yet feeling no force.
The second insight, known as the principle of equivalence, identifies gravitation and acceleration. Imagine you are in a closed opaque box. When you feel a force pulling you toward one side of the box there is no way for you to tell whether this force is the result of gravitation, as if the box were sitting on Earth, or if there is some agent accelerating the box so that you feel a force indistinguishable from gravitation. Equivalence principle - Wikipedia
The following statement corresponds to the fundamental idea of the general principle of relativity: All Gaussian coordinate systems are essentially equivalent for the formulation of the general laws of nature. Albert Einstein (1916, 2005): Relativity: The Special and General Theory
Gaussian coordinates provide a topological connection between arithmetic and space which is based on order rather than distance. This is why Einstein's theory does not provide a measure of the size of the Universe. It applies even though the Universe is expanding.
Gauss’s insight was extended to spacetime by Bernard Riemann who created a differentiable manifold which could be studied using tensor calculus. Einstein’s friend Marcel Grossman explained this idea to Einstein and it became the key to his theory. Albert Einstein & Marcel Grossman (1913): Outline of a Generalized Theory of Relativity and of a Theory of Gravitation
After few more revisions, Einstein wrote, in his final paper:
By that, the general theory of relativity as a logical building is eventually finished. The relativity postulate in its general form that makes the space-time coordinates to physically meaningless parameters, is directed with stringent necessity to a very specific theory of gravitation that explains the perihelion motion of Mercury. However, the general relativity postulate offers nothing new about the essence of the other natural processes, which wasn't already taught by the special theory of relativity. Albert Einstein (1915): The Field Equations of Gravitation
Since that time solutions of Einstein's theory, the development of precision measurements of the cosmic microwave background, the use of redshifts to estimate distance, and the recent development of gravitational wave observatories have given us a very precise and complete picture of the overall structure of the Universe. Cosmic microwave background - Wikipedia
15.3 General relativity, initial singularity and zero-energy Universe
Both the classical initial singularity and the zero energy Universe and are possible consequences of Einstein's general theory of relativity. Hawking and Ellis argued for the initial singularity and proposed that the big bang may be explained in terms of a time reversed black hole. Hawking & Ellis (1975): The Large Scale Structure of Space-Time
One apparent difficulty with the classical big bang theory is that it seems to imply that all the energy of the Universe was initially contained in the structureless initial singularity. This is difficult to understand, since energy and momentum exist in spacetime which is a product rather than the source of the big bang.
An answer to this difficulty, proposed by Feynman and others, is that the total energy of the Universe is zero. Feynman writes:
Another spectacular coincidence relating the gravitational constant to the size of the Universe comes in considering the total energy. The total gravitational energy of all the particles in the Universe is something like GMM / R, where R = Tc and T is the Hubble time. . . . .. If now we compare this number to the total energy of the Universe Mc2, lo and behold, we get the amazing result that GM2 / R = Mc2 so that the total energy of the Universe is zero. Richard Feynman (2002): Feynman Lectures on Gravitation
The potential binding energy of the Universe, the depth of the potential well in which it exists, may be exactly equal and opposite to the kinetic energy contained in all its observable elements. We might call this the classical answer, consistent with relativity. Even if Feynman's brief derivation of the zero energy universe described above is faulty, Berman suggests that given certain metric solutions to Einstein general relativity, the Universe would have zero energy. Marcelo Samuel Berman (2009): On the Zero-energy Universe
15.4: We live in a potential well: the cosmic microwave background
If Hawking and Ellis are right, we live in something like a black hole, that is a very deep potential well. This makes sense. We can no more leave the Universe than we could escape from a black hole.
In modern physics potential wells are the foundation of structure. An atom is a potential well. The electrons are bound to the protons by the electromagnetic force acting between them, just as we are stuck to our planet Earth by its gravitational attraction for us. In a potential well particles have negative energy. Added positive energy is required to get them out. It takes a lot of energy to put an astronaut into orbit and spacecraft get very hot as they dissipate their energy on their way back.
In the first moments after the classical big bang, the temperature of the new Universe is considered to have been almost infinite. It then cooled as it expanded, formed an immense number of particles and distributed the available energy between them. Most of these particles were probably photons. After three or four hundred thousand years (14 billion years ago) the temperature had dropped to about three thousand degrees. Things were then calm enough for electrons and protons to bind together to form hydrogen atoms. This binding set the unbound photons free to travel through the expanding Universe.
Since that time these photons have been climbing out of the potential well in which they were formed, losing energy as they go. Their average energy, expressed as temperature, has fallen from thousands of degrees to about 2.7 degrees above absolute zero. They are no longer hard ultraviolet radiation but soft microwave radiation, the cosmic microwave background.
The microwave background has now been mapped in exquisite detail across the sky. This background radiation has a black body spectrum and is quite homogeneous, but precise measurements reveal some detailed structure which is at present our best source of information about the structure of the Universe when it was a toddler.
15.5: Positive and negative energy: Broken symmetry
More that 2000 years have elapsed since Aristotle coined two terms energeia (lively energy) and entelecheia (completeness) which were both translated into the medieval Latin actus and its English equivalents act or action. Cohen & Reeve (2020): Aristotle's Metaphysics
For Aristotle action is opposed to potential. An action is something that actually exists. A potential is something that might exist. Aristotle thought potential was passive. He proposed an axiom: no potential can actualize itself. He used this to prove the existence of the unmoved mover and Aquinas (mis)used it to prove the existence of his God.
Modern physics sees potential as also active, as we learn as soon as we try to walk. The gravitational potential is always pulling us down. Potentials act whenever they are not inhibited, as when we learn to walk without falling or (in the opposite case) you touch a live wire. and feel the shock.
The discovery of the conservation of energy required the realization that energy comes in two forms, potential and kinetic, negative and positive, which are equivalent and add up to zero. The roles of potential and kinetic energy were clarified during the long period, beginning in the 17th century, that it took to establish the principle of conservation of energy. Two significant steps were the recognition of the mechanical equivalent of heat by Mayer, Joule and others, and Einstein's derivation of the equivalence of mass and energy from special relativity. Conservation of energy - Wikipedia
From a quantum mechanical point of view, energy is proportional to frequency, inversely proportional to the time interval it takes an action to occur. Since the initial singularity must be eternal quantum mechanics implies that its energy is zero.
We imagine a principle of zero sum bifurcation: symmetries break into two elements that add up to zero. (See Chapter 28, Principle 2) This we assume to be the case with naked gravitation, which begins with zero energy and breaks into potential (negative) and kinetic (positive) which add up to zero. Positive and negative energy appear, but the total energy of the Universe remains zero. In chapter 16 we see that gravitation acts as a source of capital, going into debt to make kinematic quantum states real and profiting from their dynamic energy so created to shape the Universe.
The pendulum in an example of a simple harmonic oscillator. It gives new meaning to Aristotle's terms potential and actuality and demonstrates that potential and kinetic energy are exactly equivalent, laying a foundation for the principle of conservation of energy. While kinetic energy is obvious in motion, potential energy, which is the source of the restoring force in an oscillator like a pendulum, is subtler and often invisible, hidden in the structure of space. The potential energy stored by a pendulum in motion is hidden in gravitation.
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Notes and references
Further reading
Books
Einstein (1916, 2005), Albert, and Robert W Lawson (translator) Roger Penrose (Introduction), Robert Geroch (Commentary), David C Cassidy (Historical Essay), Relativity: The Special and General Theory, Pi Press 1916, 2005 Preface: 'The present book is intended, as far as possible, to give an exact insight into the theory of relativity to those readers who, from a general scientific and philosophical point of view, are interested in the theory, but who are not conversant with the mathematical apparatus of theoretical physics. ... The author has spared himself no pains in his endeavour to present the main ideas in the simplest and most intelligible form, and on the whole, in the sequence and connection in which they actually originated.' page 3
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Feynman (2002), Richard, Feynman Lectures on Gravitation, Westview Press 2002 ' The Feynman Lectures on Gravitation are based on notes prepared during a course on gravitational physics that Richard Feynman taught at Caltech during the 1962-63 academic year. For several years prior to these lectures, Feynman thought long and hard about the fundamental problems in gravitational physics, yet he published very little. These lectures represent a useful record of his viewpoints and some of his insights into gravity and its application to cosmology, superstars, wormholes, and gravitational waves at that particular time. The lectures also contain a number of fascinating digressions and asides on the foundations of physics and other issues. '
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Hawking (1975), Steven W, and G F R Ellis, The Large Scale Structure of Space-Time, Cambridge UP 1975 Preface: Einstein's General Theory of Relativity . . . leads to two remarkable predictions about the universe: first that the final fate of massive stars is to collapse behind an event horizon to form a 'black hole' which will contain a singularity; and secondly that there is a singularity in our past which constitutes, in some sense, a beginning to our universe. Our discussion is principally aimed at developing these two results.'
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Links
Albert Einstein (1915), The Field Equations of Gravitation, ' In two recently published papers I have shown how to obtain field equations of gravitation that comply with the postulate of general relativity, i.e., which in their general formulation are covariant under arbitrary substitutions of space-time variables. . . . With this, we have finally completed the general theory of relativity as a logical structure. The postulate of relativity in its most general formulation (which makes space-time coordinates into physically meaningless parameters) leads with compelling necessity to a very specific theory of gravitation that also explains the movement of the perihelion of Mercury. However, 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. The opinions I recently voiced here in this regard have been in error. Every physical theory that complies with the special theory of relativity can, by means of the absolute differential calculus, be integrated into the system of general relativity theory-without the latter providing any criteria about the admissibility of such physical theory.' back |
Albert Einstein & Marcel Grossman (1913), Outline of a Generalized Theory of Relativity and of a Theory of Gravitation, ' The theory expounded in what follows derives from the conviction that the proportionality between the inertial and the gravitational mass of bodies is an exactly valid law of nature that must already find expression in the very foundation of theoretical physics. I already sought to give expression to this conviction in several earlier papers by seeking to reduce the gravitational mass to the inertial mass; this endeavor led me to the hypothesis that, from a physical point of view, an (infinitesimally extended, homogeneous) gravitational field can be completely replaced by a state of acceleration of the reference system. This hypothesis can be expressed pictorially in the following way: An observer enclosed in a box can in no way decide whether the box is at rest in a static gravitational field, or whether it is in accelerated motion, maintained by forces acting on the box, in a space that is free of gravitational fields (equivalence hypothesis).' back |
Cohen & Reeve (2020) (Stanford Encyclopedia of Philosophy), Ariatotle's Metaphysics, ' The first major work in the history of philosophy to bear the title “Metaphysics” was the treatise by Aristotle that we have come to know by that name. But Aristotle himself did not use that title or even describe his field of study as ‘metaphysics’; the name was evidently coined by the first century C.E. editor who assembled the treatise we know as Aristotle’s Metaphysics out of various smaller selections of Aristotle’s works.' back |
Conservation of energy - Wikipedia, Conservation of energy - Wikipedia, the free encyclopedia, 'In physics, the law of conservation of energy states that the total energy of an isolated system cannot change—it is said to be conserved over time. Energy can be neither created nor destroyed, but can change form, for instance chemical energy can be converted to kinetic energy in the explosion of a stick of dynamite. back |
Cosmic microwave background - Wikipedia, Cosmic microwave background - Wikipedia, the free encyclopedia, 'The cosmic microwave background (CMB) is the thermal radiation left over from the time of recombination in Big Bang cosmology. . . . The CMB is a snapshot of the oldest light in our Universe, imprinted on the sky when the Universe was just 380,000 years old. It shows tiny temperature fluctuations that correspond to regions of slightly different densities, representing the seeds of all future structure: the stars and galaxies of today.' back |
Equivalence principle - Wikipedia, Equivalence principle - Wikipedia, the free encyclopedia, ' In the physics of general relativity, the equivalence principle is any of several related concepts dealing with the equivalence of gravitational and inertial mass, and to Albert Einstein's assertion that the gravitational "force" as experienced locally while standing on a massive body (such as the Earth) is actually the same as the pseudo-force experienced by an observer in a non-inertial (accelerated) frame of reference.' back |
Marcelo Samuel Berman (2009), On the Zero-energy Universe, ' We consider the energy of the Universe, from the pseudo-tensor point of view (Berman,1981). We find zero values, when the calculations are well-done.The doubts concerning this subject are clarified, with the novel idea that the justification for the calculation lies in the association of the equivalence principle, with the nature of co-motional observers, as demanded in Cosmology. In Section 4, we give a novel calculation for the zero-total energy result.' back |
Minkowski space - Wikipedia, Minkowski space - Wikipedia, the free encyclopedia, ' By 1908 Minkowski realized that the special theory of relativity, introduced by his former student Albert Einstein in 1905 and based on the previous work of Lorentz and Poincaré, could best be understood in a four-dimensional space, since known as the "Minkowski spacetime", in which time and space are not separated entities but intermingled in a four-dimensional space–time, and in which the Lorentz geometry of special relativity can be effectively represented using the invariant interval x2 + y2 + z2 − c2 t2.' back |
Newton's Laws of motion - Wikipedia, Newton's Laws of motion - Wikipedia, the free encyclopedia, 'Newton's laws of motion are three basic laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows: Law 1. A body remains at rest, or in motion at a constant speed in a straight line, unless acted upon by a force. Law 2. When a body is acted upon by a force, the time rate of change of its momentum equals the force. Law 3. If two bodies exert forces on each other, these forces have the same magnitude but opposite directions.' back |