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Underlying all spaces is a regular network. A spatial network is defined by rules indicating how each point should connects to its adjacent points. Change the connectivity rules and the dimension of the space changes. Putting a few additional random connections in the above lattice will create a fractional dimensional space like a 3.4 dimensional space.
Space Itself is Formed from a Bi-Directional Network
Space Itself is Formed from a Bi-Directional Network
(July 7, 2022) Space itself is best seen as being the average background noise of the quantum network. Space is not fundamental for two reasons. The first is because it can be defined as being a regularly connected network. Networks can even define fractional spaces and higher dimensional spaces. The second is that it will change in order to keep events consistent as shown by Einstein's Theory of General Relativity.
The creation of the universe probably should not be seen as the creation of something from nothing but as the sudden crystallization of part of the underlying randomly connected divine network into a regular spatial network. As the universe expands most of its spatial network is gradually returned to its randomly connected state.
Don Lincoln of Fermilab near Chicago provides an introduction to wave interference and particles.
Quantum Mechanical Network is Assembled from Quantum Wave Interference
Quantum Mechanical Network is Assembled from Quantum Wave Interference
Networks as causal connections were a part of the Ancient Pagan Paradigm of the Neolithic farmers. The idea that things can only interact if they are connected is as valid now as was then. Yet the modern quantum mechanical network which guides matter is not hierarchical going from divine source to the material realm but instead is self-assembled on the fly using the divine realm as its eternal substrate. The quantum mechanical wave functions assemble the space-time network by wave interference.
This network assembly idea gained traction with the work of Richard Feynman on Quantum Electrodynamics after World War 2. His "Sum over Paths" formulation of quantum mechanics became the standard after he used it to developed Quantum Electodynamics (for an easy and non-mathematical introduction see Feynman, 1985). In this approach all possible pathways of light are considered and only those which don't cancel out provide the most probable network paths along which a casual event will occur. Physicist, Michio Kaku puts the significance of Feynman's pathing approach this way and the parenthesis are his:
The power of Feynman's "sum over paths" is that today, when we formulate GUT theories, inflation, even string theory, we use Feynman's "path integral" point of view. This method is now taught in every graduate school in the world and is by far the most powerful and convenient way of formulating the quantum theory. ... (When I first learned of Feynman's point of view as a graduate student, it changed my entire mental picture of the universe. Intellectually, I understood the abstract mathematics of the quantum theory and general relativity, but it was the idea that I am in some sense sniffing out paths that take me to Mars or the distant stars even as I walk across the room that altered my worldview). (Kaku, page 164)References
Feynman, R.P. (1985) QED - The Strange Theory of Light and Matter; Princeton University PressReferences
Kaku, Michio (2005) Parallel Worlds - A Journey through Creation, Higher Dimensions, and the Future of the Cosmos. Random Hous
Don Lincoln of Fermilab near Chicago describes an experiment showing how distant events can affect the structure of the universe.
Underlying Quantum Network can Change Instantaneously Across the Whole Universe
Underlying Quantum Network can Change Instantaneously Across the Whole Universe
(July 7, 2022) Studies of quantum entanglement show that the structure of the quantum network and its provided event constraints in one location of the universe can change instantaneously based upon changes in another part of the universe.
Quantum mechanical field waves partly exist outside of space-time as evidenced by their use of imaginary numbers in their equations to represent a temporary hidden dimension. These waves thus are not limited to the speed of light limitation. These wave fields don't become real again until their end result is mathematically squared removing any reference to that hidden dimension.
The curve defined by y = 1/x provides a good example of the properties of a continuum because it is symmetrical around point (x=1, y=1). If a curve is thought to consist of a number of finite points then as many points exist between 0 and 1 and between 1 and infinity. This contradiction means we cannot think of continuums as composed of such points. Instead points are markers extracted as needed from the continuum. A point can always be extracted from between any two other points. In physics numbers are just labeled points extracted from a continuum having values greater than and lessor than other points. This is why mathematics works so well in describing reality.
The Foundation of Reality is the Continuum
The Foundation of Reality is the Continuum
(July 7, 2022, updated March 26, 2025) Perhaps everyone has heard of the time-space continuum from Einstein's Relativity Theory. This is the foundation of the universe and mathematics because it has the property that some smaller interval always exists. If a system needs it then it can pop into existence. The classic example of a continuum is the mathematical curve defined by 1/x shown to the left. Because the curve is symmetric around the point (1,1) as many points can exist between 0 and 1 as between 1 and infinity.
With no hard minimum length, lengths can only be defined in a relative fashion by ratios from geometry or from wave functions (musical harmonics, quantum mechanics). That is, by comparison of a reference length to another. The reference length can be called 1. All other numbers can then be defined by a ratio making process. Mathematics can thus be used to approximately describe the workings of continuums.
Historically, this insight was first made by the Pythagoreans. The first Pythagorean who wrote anything down seems to be the Greek Philolaus who began his book (only now exists in small fragments) with a bold statement about this insight:
- Nature (physis) in the world-order (cosmos) was fitted together out of things which are unlimited and out of things which are limiting, both the world-order as a whole and everything in it. (Fr. 1)
Here the continuum is called an "unlimited" and the "limiting" processes were the ratios defined from geometry and musical harmonics.
References
References
Stanford Encyclopedia of Philosophy - Philolaus (Sept 2003, revised September 2024). Online at: https://plato.stanford.edu/entries/philolaus/
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