Cosmology
Cosmology
Within science, as distinct from philosophy, cosmology seeks to provide theories explaining the universe from observation of those parts we can observe. It is a peculiar subject in that we have only one sample to study and we cannot observe all of it. We are not sure, therefore, whether the discoveries we make about small parts of it lead reliably to laws that govern the universe as a whole. We certainly have made progress in this direction with relativity and quantum mechanics. However, our failure to unify these remains a concern. For this reason, it is worth considering an alternative approach that proposes special properties unique to the universe and follows their implications downwards to solutions of local problems. Eternity, for example, as a special property of the universe is one such concept.
Eternity
I will focus on a cosmology based on an atemporal, aspatial eternity existing before the creation of space and time. Such a concept suggests an approach to non-locality and requires few other assumptions. One additional one is important, however. Creation of a universe involves work and this requires energy. As there are no dimensions in this eternity, the assumption has to be made that formless energy is present, with no dimensions in space or time.
Many types of energy exist in spacetime, including gravitational energy, kinetic energy, potential energy, heat energy, elastic energy, electrical energy, radiant energy, nuclear energy, pressure energy, and mass energy. All these can change from one form into another. We can calculate the energy transferred and verify that energy is conserved. What we do not know, as Richard Feynman pointed out, is what is transferred and conserved, or its nature [5].
Properties of particular forms of energy are described by a set of dimensions. When energy is separated from its many forms, what remains is a dimensionless energy that can move from one form to another, picking up the necessary dimensions on the way. We can see the process taking place in the movement of a pendulum (or an upthrown rock). Potential energy, described within the dimensions of mass and height, is transformed smoothly and continuously into motion energy, described within the dimensions of mass and velocity. This shape-changing energy that can move freely among dimensions is the logical candidate for the formless energy of eternity.
Energy existing in space and time has an equivalent mass (M = E/c2). But this equivalence of energy and mass is gained by a factor, c (the speed of light), that includes length and time. As space and time are absent before establishment of spacetime, so too is mass, and gravity. Mass is a form of energy but the energy in eternity is by definition formless.
For the energy of eternity to gain form it has to enter spacetime. This indicates that the first step in creation of a universe is emergence of spacetime from eternity. To create a stable universe, the process must follow universal laws, such as conservation of energy, that come into existence as spacetime is formed. One can say then, that eternity contains formless energy and universal laws that gain form and expression with the creation of spacetime.
Entropy
One of these universal laws governs the way transactions involving energy can occur. The law involves the entropy in a closed system. A closed system is one in which energy does not flow in or out. Alternatively, if all of the energy entering or leaving is scrupulously accounted for, the system can be considered closed. For example, suppose we want to consider the Earth as a closed system, so that we can understand how we are using energy. We would have to account for the high temperature sunlight arriving by day and the low temperature heat radiation leaving by night. In closed systems like this, a universal law holds that no decrease in entropy can occur.
A common way of describing the effect of this law is to say that entropy nearly always increases, in the form of randomness and disorder. Anybody who has brought up children is familiar with their ability to perform this function, but such agents are not essential. Nature performs this function herself. It was first observed in steam engines, where it became clear that heat always flowed from parts at a high temperature to parts at a low temperature. Later, it was realized that using energy to get useful work involves organized energy being degraded into disorganized energy. Sunlight, generated at a high temperature corresponds to organized energy. Plants use it for their metabolism and radiate what they have left over as low temperature heat, a less organized form of energy. We describe this change in organization as an increase in entropy. Life survives on Earth by means of a steady increase in entropy that we get rid off by radiation of low temperature heat with high entropy at night, after low entropy sunlight has been processed during the say. Low entropy energy is no use for organized processes such as plant metabolism or human thought.
So overall, with entropy nearly always increasing, the universe is running down. But for this to happen, the universe must first be wound up. This means that if entropy is to continually decrease, it must start off at a very low level, preferably zero. A statistical way of describing entropy provides us with entropy units. This approach relates entropy to the amount of hidden information that governs the overall state of a system. In a gas, the overall state can be described by its temperature. The hidden information that governs temperature is in the individual location and motion of every molecule in the gas. And since location requires three dimensions to specify it, and velocity requires another three, the information for each molecule is said to be expressed in six degrees of freedom. Multiply this by the number of atoms in the gas (2.7 x 1022) and you have an estimate of the hidden information. To start a universe with zero entropy, you need a substance with zero units of hidden information.
In eternity theory, the universe emerges from a region with zero dimensions in space and time. The only information we have about the formless energy in this region is that it is there. That is, this energy has only one degree of freedom. Entropy is expressed in units as the logarithm of the total number of degrees of freedom needed to specify an overall state like temperature. The entropy of the formless energy of eternity is the logarithm of one, which is zero. The proposed initial state of the universe is one of zero entropy.
Emergence of Spacetime Quanta
Our universe could have moved towards existence when a fluctuation broke the symmetry of eternity, setting off a phase change that precipitated spacetime. Such a phase change would have seen bubbles of spacetime condense out of eternity in the way droplets of dew condense out of water vapor in the atmosphere, or ice crystals grow in liquid water.
Phase changes like this are familiar in present accounts of evolution of the universe. In big-bang cosmology, the universe starts with a sudden expansion that initiates many phase changes. In one set, the four or five main forces emerge in succession. In another, a succession of matter particles emerges – quarks, protons, neutrons, nuclei, atoms, and molecules.
The cosmology that starts with eternity requires the same set of phase changes, but adds a prior one in which elementary units of spacetime emerge to form spacetime quanta. When packed together into a lattice the quanta are the building blocks for a four-dimensional spacetime. Each quantum consists of three dimensions of space and one of time. As a starting point, it is worth assuming the building blocks to be uniform and of minimum size. There would be no dimensions smaller than their dimensions.
As spacetime quanta have the minimum possible dimensions they are indivisible, otherwise their dimensions would not be minimal. That is, this approach abandons the notion of infinitely divisible space. No spatial interval can be smaller than the spatial size of a spacetime quantum; no temporal interval can be smaller than the size of the time dimension of a spacetime quantum The two intervals are related through the speed of light, which emerges as the primary universal constant. The time interval is the time taken for light to travel the smallest interval of space. As it would be absurd to have a universe with different minimum dimensions in different directions, the spacetime quanta will be spherical. Spacetime condenses out of eternity as spherical bubbles.
Because we have a stable universe, the initial phase-change that accounts for the emergence of spacetime must invoke appropriate laws governing how energy acts to stabilize the universe. These laws require energy to be conserved and free energy to be minimized. The latter requirement would cause newly born spacetime quanta to move into a closely packed lattice that minimizes the remaining energy surrounding the quanta. In effect, formless energy between quanta exerts a pressure that pulls the spherical quanta into arrays containing the least energy in the interstitial space between spheres. The effect will be the compression of the spacetime quanta into a lattice by a negative pressure, and the trapping of interstitial energy between the spheres.
In this first primordial phase change, universal constants begin to achieve expression. In the spacetime bubbles the relationship between space and time is expressed in the velocity of light, a constant that relates energy to mass (E=Mc2). The effect of mass on spacetime is expressed by the gravitational constant relating energy to attractive force. The relation of energy to radiation is expressed by the Planck constant of action (energy acting through time). These three constants determine the size of the quanta.
Properties of Quanta
Science has accepted, for the most part, that there is indeed a minimum length appropriate for the description of the physical world. Some argue that it is possible to go below this length by discovering new physical principles that lead to quantum gravity. This would lead to an alternative description to that being developed here. In the present description, spacetime quanta exhibit gravitational and relativistic effects without invoking a separate quantum gravity clause.
There is also general agreement that the logical minimal length is found in the natural units proposed by Max Planck [8]. Expressing the properties of space, these units are of fundamental interest because they are derived from the universal constants. The constants themselves are measured in units defined by arbitrary convention, such as defining the meter to be a certain number of wavelengths of a particular color of light. But the natural units are formed from the universal constants by ratios that remove the arbitrary aspect of conventional units. One effect of this is that the Planck units would be the choice for interstellar communication, if this were ever to occur.
The natural unit for spatial dimensions is the Planck area, a simple function of the three universal constants mentioned. It is the product of the Planck constant and the gravitational constant divided by the cube of the speed of light. This yields an area of 2.61 x 10-70 square meter. The current method of calculating the corresponding smallest possible length is to take the square root of the Planck area. The Planck length then becomes 1.61 x 10-35 meter. The Planck second is the time taken for light to travel the Planck length, 5.39 x 10-44 second.
These dimensions would be appropriate for cubic spacetime quanta. However, for spherical quanta the cross-sectional area of a spacetime quantum is circular. The corresponding Planck length is the diameter of that area. The Planck length therefore becomes (2 times the square root of Planck area) divided by the square root of pi:
Quantum Planck
length = 1.83 x 10-35 meter
Quantum Planck
time = 6.09 x 10-44 second
The length for the spacetime quantum is 13 per cent larger than the conventional Planck length. For either approach, the length is extremely small. Some 1019 times smaller than the diameter of a proton.
The initial event in the creation of the universe is the condensation of spacetime quanta and their formation into a lattice in which every spacetime quantum is in contact with adjacent ones. Within this lattice, matter and radiation particles, which are considered to be infinitesimal points with no dimensions, gain locality and movement . Their effective direction of movement is from one quantum to another through a point of contact between the spheres. No other movement through space between quanta would be possible, because that would require passage through the interstitial energy. There, the effective distance would be indeterminate, possibly smaller than the assumed minimum interval in space and time. Instead, the particle simply disappears from one spacetime quantum and appears in the next, in an interval no shorter than the smallest unit of time.
The result is that the direction of movement of particles in the lattice is set by the contact points between quanta. In a closely-packed regular lattice, a quantum would have 12 contact points with other quanta. However, the lattice will not be regular. The current expansion of the universe shows that space expands uniformly throughout its volume, indicating that new quanta appear between existing quanta. This will increase the randomness of contact points and of directions of movement between quanta.
A particle transfers between quanta in a restricted number of directions and those directions are unlikely to conform to the direction in which it is traveling. It would have to find a zig-zag route with an average direction corresponding to, for example, the straight line path expected of a photon of light. So the spherical quanta and their limited number of contacts, would add randomness to the movements and interactions of particles.
Initial Expansion of Spacetime
We see galaxies moving away with speeds relative to us that increase with their distance. The rate of expansion suggests that it started with a unique event that occurred about 13.8 billion years ago. On the basis of the present properties of matter distributed throughout the universe, the generally accepted pattern of expansion involves a very rapid early phase, described as inflation. The expansion subsequently slowed to the speed we see today. I suggest that the beginning of the inflationary phase was the initial emergence of spacetime by the rapid creation of spacetime quanta in an expanding sphere. I have looked at a rate of addition of quanta that involves doubling the number of existing quanta in the sphere diameter each Planck second. This rate would be faster than simple doubling like 1, 2, 4, 8, 16 . . . type. Instead the population of quanta along a diameter would have an increase of the form 1, 3, 8, 16, 27 . . . As a rough approximation the total number of quanta in the spherical spacetime lattice would be increasing at 6 times this rate, but the volume increase would be pulled down by the effect of negative pressure compressing the lattice into a fully-packed state.
The first ten Planck seconds of the universe are referred to as the Planck epoch. In this interval the diameter of the spherical lattice would have increased to about 60,000 Planck lengths. In the next two Planck seconds the diameter would increase to over 500,000 Planck lengths, or 9.5 x 10-30 meters. It was probably sometime towards the end of this initial expansion that formless energy flowed into spacetime. Gaining dimensions, it acquired mass.
Then, two forms of expansion took place. One was the continued expansion of spacetime, the other was the new expansion of a mass of energetic particles thrust into spacetime and moving randomly within it. The initial inrush of energy into spacetime would create an expanding volume of energetic particles. General relativity suggests that this might be accelerated further by the negative pressure exerted by interstitial energy. At the same time, the continuing inflow of energy and its conversion into particles would cause the mass in spacetime to increase, giving rise to a growing gravitational force. This inward force would pull particles back through the lattice into clumps, slowing their outward expansion.
Gravity not only exerts a force on energetic particles, it affects the structure of spacetime itself. It therefore slows the initial expansion of spacetime as well. If this slowing did not occur, spacetime would have expanded to a diameter of 14 centimeters by 4.3 x 10-42 seconds. We do not know the actual expansion rate of spacetime during this era, but current cosmology envisages that the universe of energetic particles reached a diameter of the order of 14 cm some 10-35 seconds after its creation in a big bang, resulting from a corresponding increase in the volume of spacetime. Inflation is seen as a sudden, vast increase in the rate of expansion of the universe after the Planck era. In contrast, the picture presented here is of a slowing down of a much faster rate of expansion after the Planck era. The retardation is brought about by the creation of mass and the consequent gravitational force putting the brakes on the speed of expansion of spacetime and of the population of energetic particles. In both scenarios the inflationary period of expansion has the important result of rendering the distribution of matter in the universe uniform at very large scales. The type of structure we see today.
The energy of eternity gains mass in the form of energetic particles moving through the newly formed lattice of spacetime quanta. Their random paths through the lattice cause small clumps of particles to form. These produce concentrations of mass higher than the average around them. Because gravity is an attractive force proportional to mass, it automatically magnifies these small perturbations. Small clumps pull other particles to themselves and grow larger. In a slowly expanding universe the clumps would grow very large, move apart and lose contact with each other. As a result, their separation would become too great for their temperatures to come into equilibrium. Huge variations of temperature would occur among distant parts of the universe.
Such variations are not detected. Instead, the average temperature of the universe across the whole sky is incredibly uniform, with fluctuations being confined to a few hundred thousandths of a degree. Such uniformity requires a very rapid inflationary expansion, before large-scale variations in mass grow out of miniscule random quantum fluctuations and become isolated in spacetime. What remains is a uniform distribution of random fluctuations spread uniformly over spacetime. After the extremely short period of very rapid inflation, the expansion in spacetime slows to about the rate we see today. Later, the small fluctuations remaining form the seeds for galactic structures created as gravity continues to exert its clumping effect.
Dark Energy
It is generally agreed that after inflation, expansion of the universe continues at about the rate we see now in the recession of the galaxies, with some slowing occurring as gravity dominates in one period and some acceleration appearing later. This later acceleration may result from the growth in the volume of interstitial energy as spacetime continues to expand.
The energy in the space between spherical quanta continues to exert a negative pressure, even when the quanta have reached the most efficient packing possible. According to Einstein's equations of general relativity, negative pressure has the effect of a repulsive form of gravity. That is, it exerts an expansive force. So as the population of quanta swells in numbers and volume, the negative pressure, which is proportional to the quantity of space, increases. But after the initial inrush of energy into spacetime has ceased, gravity does not increase. It is proportional to the amount of mass-energy present and stays constant. Then the negative pressure of interstitial space acts like a form of dark energy, overcoming the inward pull of gravity and speeding up expansion of the universe.
Spacetime Quantum Lattice
If the proposed action of formless negative pressure were fully effective in pulling the spacetime quanta together, it would yield a regular lattice in which the maximum space, 74 per cent, would be taken up by the spacetime quanta and 26 per cent would be occupied by the formless energy of eternity [6]. In a closely packed regular lattice, a quantum would have 12 contact points with other quanta. (I assumed an initial growth from six points on the assumption that a regular lattice would not form spontaneously.) In a random lattice, the quanta would occupy only about 64 per cent of the space, with formless energy occupying 36 per cent, and the number of contacts points any one sphere may experience varying. In fact, the lattice probably has a high degree of randomness as a result of continued insertion of new quanta within it. Such randomness would make the path of a particle more tortuous (Figure 1).
Figure 1. An artist’s impression of a cross-section of a lattice with some irregularities. Movement of particles between spacetime quanta takes place at the contact points, producing a degree of randomness in their motion. Dislocations in the lattice increase the randomness.
Such randomness does not appear at the macro level. The random disturbances occurring within the infinitesimally small dimensions of the lattice are evidently overcome in some way, because we see that light and other particles do in fact travel in straight lines. So the assumption must be that particles are operated on so as to follow at the macro level the specific path demanded by the forces acting on them. Such randomness as remains is evident only over very small distances. But it can be observed when a light beam is tightly restricted in diameter and held to very low intensity. As Richard Feynman put it “. . .the idea that light goes in a straight line is a convenient approximation to describe what happens in the world that is familiar to us;”.[7] The small deviations have to be taken into account at scales found within an atom.
In fact, as the scale is decreased still further, down below the diameter of a neutron or proton, the randomness in the lattice has a greater effect. In this region, the deviations caused by the lattice cannot be rendered visible. If they could be, then they would appear more and more erratic as the area of view decreased, but each random movement is limited to the dimensions of the quanta.
The quanta are extremely small, less than 10-34 meter, but the elementary particles moving through them have, theoretically, no size at all. Because of their zero size, the position of fundamental particles is known only to the accuracy of being somewhere within the space defined by a spacetime quantum. There is an inherent uncertainty in particle location. But elementary particles collide within the interval provided by a single quantum by virtue of being there for a Planck second. The collision results then spread in the next time step to other quanta.
When integrated into a closely packed lattice, the quanta provide the extended dimensions required to provide the possibility of action. They make possible movement of fundamental particles from one location to another and permit action between different locations. But they restrict movement through space and time to discrete, finite steps.
Waveforms
My concept of time is that as the quanta assembled into a lattice their time dimensions became synchronized. From the concept that space and time emerged in the form of spacetime bubbles, the conclusion might have been drawn that a random foam appeared. However, this would not lead to an orderly, stable universe, because in every instant it would be impossible to forsee in what stretch of past or future time the next instant would be. A more reasonable assumption is that in these bubbles the relationship between space and time is constant and expressed in the velocity of light, and that the time component of each quantum is moving forward across the minimum step in time. A transition from one quantum to the next takes an elementary particle to the next time step. The transitions are synchronous with the time steps of the lattice as a whole. The lattice is moving forward synchronously in time.
The transition of a particle from one spacetime quantum to another takes place at the speed of light. Particles achieve lower average speeds by staying longer than the minimum before making the next transition. Protons in the Large Hadron Collider, for example, would pause nine Planck seconds within every billion Planck seconds. Most matter particles move at slower speeds with many more pauses in quanta. Presumably these pause intervals are spaced with even probabilities through time. The effect is to create a waveform in which the time frequency of the pauses is inversely related to the speed of the particle.
An analogous stationary waveform is created within the space of the contiguous lattice interstices surrounding spacetime quanta. This space surrounds the quanta with the energy of eternity. However, this energy now has a degree of locality in that it is confined within specific dimensions. Before entering the interstitial space, this energy of eternity had no form and no dimensions -- it was in a region where all space was the same space and all time was the same time. It becomes surrounded by spacetime, but unlike the partitioning of spacetime, the interstitial space presents a region that is continuous throughout the emerging universe. Being continuous, a significant feature of the interstitial energy is that it is sculpted into a spatial, stationary waveform in three dimensions, created by the curved spaces between spherical quanta. This stationary waveform in space can adopt any frequency by subtraction of its occupation of specific spatial elements.
My suggestion is that it is these two waveforms that give rise to familiar types of quantum phenomena, as described in the next section.
12/16/2015