volume II: Synopsis
section III: Modern Physics
page 24: Meaning
The Universe, as we see it, has grown enormously over the last century. Modern cosmology reveals a Universe which is very large and very old, and appears to have evolved from a structureless point, the initial singularity). Gravitational singularity - Wikipedia
This scenario is modelled using the general theory of relativity published by Einstein in 1916. The special theory of relativity tells us how things look in a Universe where everything is moving at a uniform velocity. There is (by definition) no force (and no acceleration) between inertial frames. General relativity - Wikipedia
Einstein wished to extend this theory to include force and acceleration. The seed of the general theory was for Einstein 'the happiest thought of my life': 'if a person falls freely he will not feel his own weight. I was startled. This simple thought made a deep impression on me. It impelled me toward a theory of gravitation'. In 1907, Einstein realized that all natural phenomena could be discussed in terms of special relativity except gravitation. Wikiquote - Einstein's happiest thought
Putting this idea into mathematical form was not easy, and required a change from the Cartesian coordinates used by Newton to Gaussian coordinates. Newton imagined an absolute space and time coordinate system which enabled him to give a name ('coordinate') to every point in the solar system. Einstein, following Gauss, imagined that the Universe is in effect its own coordinate system, so that we work with 'intrinsic' coordinates. This opened the way to treating the geometry of the world as a dynamic rather than a static entity. Gaussian curvature - Wikipedia The mathematical theory needed to develop this view came from the geometry of dynamic spaces invented by Riemann. Riemannian geometry - Wikipedia
The study of the Universe requires the identification of fixed points or invariances that stay the same as the system around them changes. As I walk, lots of muscles move, but the lengths of my leg bones remains constant. Gaussian coordinates enable us to define the structure of a space by measuring the distances between observable events in the space.
Although Gaussian coordinates are intrinsic, they still involve the duality of knower and known. We use coordinates as a known system in order to study an unknown one. The relationship between them we call meaning or mapping. The coordinate system in general relativity Einstein calls the 'reference mollusc' by which I understand him to mean the soft and flexible parts of a mollusc rather than the hard and rigid parts. Einstein
After a lot of work, Einstein found the gravitational field equation, which in its simplest form reads G = T. G is the Einstein tensor which encodes the metric structure of space. T is the 'stress energy' which encodes the distribution of mass-energy in space. Space-time intervals in the Universe depend on the energy density in the neighbourhood. Einstein field equations - Wikipedia, Pais
Although Einstein's equations are rather rich and complex, they result from a very simple mathematical constraint: the transformation between any two systems of Gaussian coordinates should be continuous and differentiable and leave the the interval between any two points unchanged. This idea is called 'general covariance'. General covariance is a statement about meaning or mapping. Broadly, to truly represent the world as languages (coordinate systems) change, the words used to express the representation (another coordinate system) must also change in order to respect the invariance of a reality independent of coordinates. Metric tensor - Wikipedia
Mathematically, a function is said to be continuous if its input and output are coupled so that small changes in input yield small changes in output, input and output tending to zero together. The differential equations of the general theory of relativity represent fixed points in the continuous dynamics of the Universe. Relativity is a classical theory and has proven very hard to reconcile with quantum mechanics. Continuous function - Wikipedia
The general theory is the theory of dynamic space, and it tells us that the Universe does not have a fixed size: it is either expanding or contracting. Observation shows that it is expanding, and careful mathematical analysis of the theory suggests that the Universe started from a structureless point. But we have a problem here. Gravitation is always attractive so how does it make the Universe expand? Hawking & Ellis
On this site we are trying to model the Universe as a computer network, so we ask ourselves how do we interpret the classical continuity that lies at the heart of general relativity in terms of communication and computation? Continuity means symmetry, the equivalent of nothing happening, no change. This is consistent with the observation that gravitation sees everything simply as a quantity of energy.
Energy is conserved,which in quantum mechanical terms means that no matter when we look at the Universe, the overall rate of activity, measured in quanta of action per unit of time, is the same.
Let us guess that quantum mechanics does not see the difference between potential and kinetic energy. Gravitation, which emerges from quantum mechanics with the origin of space, does. We can interpret Einstein's equation to mean that the potential energy of a spatial structure is equal to the kinetic energy that exists in that space.
Now we assume that the Universe has evolved by natural selection since the very beginning. Natural selection picks out those systems which are optimized for survival. Let us further guess that the efficacy of the Lagrangian method in physics is a consequence of this optimization. Natural selection - Wikipedia, Lagrangian - Wikipedia
Hamilton's principle tells us that Nature tends to favour situations where the action (which can be measured in units of Planck's contant) is stationary. The action is the time integral of the Lagrangian. Let us assume here that the action of the Universe is stationary because the Lagrangian of the Universe is zero, implying that its kinetic and potential energy are (integrated over time) equal. This is the simplest interpretation of Einstein's field equation. Action (physics) - Wikipedia, Hamilton's principle - Wikipedia
Gravitation introduces interaction between inertial frames, thereby differentiating the frames and creating space. The invariant that defines the structure of quantum mechanics is the quantum of action. The differentiation of the Universe into space and time introduces the measures of rate of action per unit time (frequency) and action per unit space (momentum). In special relativity space and time and momentum and energy transform in the same way: they are mathematically indistinguishable. This situation describes life in an inertial frame.
We can imagine the initial singularity as inertial by definition, since there is nothing else to perturb it. Now let it communicate with itself, thus copying itself. For the copy to exist, it must be differentiated from the orignal and let this differentiation be by putting the copy in a different place, which in the inertial world means moving at a different velocity. The change of velocity implies force and changes in the kinetic and potential energy of the child frames. The symmetry of the initial inertial frame is broken to make two interacting frames. We imagine this process to continue indefinitely subject only to conservation of action, energy and momentum to give us the spacetime manifold we now enjoy.
We can express this 'classical' description in network terms. Networks grow by copying themselves. The copies then communicate, the network equivalent of a force. As the network continues to proliferate, the rate of communication between the different sources may vary, giving rise to different fores between them.
Symmetry breaks to create differentiation, communication and meaning. The classical theological version of this model is the model of the Trinity developed by Thomas Aquinas. Aquinas 160
To support this picture we have the second law of thermodynamics: overall, entropy never decreases (and mostly increases). What is entropy? A count of states, that is a count of differentiation. As the Universe differentiates, generating more fixed points , its entropy increases. Second law of thermodynamics - Wikipedia
We can communicate with one another because we share a common code or language. When I say 'I feel sad' you know what I mean because you have felt sad too. And so with all the communications that we have with one another. Meaning is made possible by shared experience. It may be one of the complex feelings that surround our reproductive activity, the simple statement 'this is a brick' or the most general protocol: I follow the rules of quantum mechanics.
[revised 24 May 2013]