Causal Dynamical Triangulation (CDT)

[Write4U]

This is derived from Asexperia's thread on "Philochrony" which discusses the properties of Time,
whereas CDT proposes a new look at the "unfolding properties of space"

Causal Dynamical Triangulation (CDT)

Causal dynamical triangulation (abbreviated as CDT) theorized by Renate Loll, Jan Ambjørn and Jerzy Jurkiewicz, is an approach to quantum gravity that, like loop quantum gravity, is background independent.

This means that it does not assume any pre-existing arena (dimensional space), but rather attempts to show how the spacetime fabric itself evolves.

There is evidence [1] that at large scales CDT approximates the familiar 4-dimensional spacetime, but shows spacetime to be 2-dimensional near the Planck scale, and reveals a fractal structure on slices of constant time. These interesting results agree with the findings of Lauscher and Reuter, who use an approach called Quantum Einstein Gravity, and with other recent theoretical work.

Introduction

Near the Planck scale, the structure of spacetime itself is supposed to be constantly changing due to quantum fluctuations and topological fluctuations. CDT theory uses a triangulation process which varies dynamically and follows deterministic rules, to map out how this can evolve into dimensional spaces similar to that of our universe.

The results of researchers suggest that this is a good way to model the early universe, and describe its evolution. Using a structure called a simplex, it divides spacetime into tiny triangular sections. A simplex is the multidimensional analogue of a triangle [2-simplex]; a 3-simplex is usually called a tetrahedron, while the 4-simplex, which is the basic building block in this theory, is also known as the pentachoron. Each simplex is geometrically flat, but simplices can be "glued" together in a variety of ways to create curved spacetimes, where previous attempts at triangulation of quantum spaces have produced jumbled universes with far too many dimensions, or minimal universes with too few.

CDT avoids this problem by allowing only those configurations in which the timelines of all joined edges of simplices agree.

See also
Physics portal

• Asymptotic safety in quantum gravity
• Causal sets
• Fractal cosmology
• Loop quantum gravity
• 5-cell
• Planck scale
• Quantum gravity
• Regge calculus
• Simplex
• Simplicial manifold
• Spin foam

https://en.wikipedia.org/wiki/Causal_dynamical_triangulation

 

[Write4U]

A supporting model is offered here.

But, like Sorkin, Loll and her colleagues found that adding causality changed everything. After all, says Loll, the dimension of time is not quite like the three dimensions of space. “We cannot travel back and forth in time,” she says. So the team changed its simulations to ensure that effects could not come before their cause — and found that the space-time chunks started consistently assembling themselves into smooth four-dimensional universes with properties similar to our own10.

Intriguingly, the simulations also hint that soon after the Big Bang, the Universe went through an infant phase with only two dimensions — one of space and one of time. This prediction has also been made independently by others attempting to derive equations of quantum gravity, and even some who suggest that the appearance of dark energy is a sign that our Universe is now growing a fourth spatial dimension. Others have shown that a two-dimensional phase in the early Universe would create patterns similar to those already seen in the cosmic microwave background.

more..... https://ronmorehead.com/the-fabric-of-reality-causal-dynamical-triangulations/

 

[Asexperia]

This is derived from Asexperia's thread on "Philochrony" which discusses the properties of Time,
whereas CDT proposes a new look at the "unfolding properties of space"

Causal Dynamical Triangulation (CDT)

Introduction

See also
Physics portal

• Asymptotic safety in quantum gravity
• Causal sets
• Fractal cosmology
• Loop quantum gravity
• 5-cell
• Planck scale
• Quantum gravity
• Regge calculus
• Simplex
• Simplicial manifold
• Spin foam

https://en.wikipedia.org/wiki/Causal_dynamical_triangulation

Very interesting, but for me space is not matter even at the quantum level. I think that gravity could be a still unknown quantum force. We must not confuse space with stellar matter.

 

[Write4U]

Very interesting, but for me space is not matter even at the quantum level. I think that gravity could be a still unknown quantum force. We must not confuse space with stellar matter.

I don't believe that CDT describes matter, but rather fundamental generic relational quantum values that answer to logical-mathematical guiding equations.

I cannot think of a better candidate for an abstract quantum than a fractal. It naturally self-forms and organizes into a homogenous geometry that allows for the emergence of the most complex patterns, based on fundamental geometric simplexes.

Simplex

The four simplexes which can be fully represented in 3D space.

In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions. The simplex is so-named because it represents the simplest possible polytope in any given dimension. For example,

• a 0-dimensional simplex is a point,
• a 1-dimensional simplex is a line segment,
• a 2-dimensional simplex is a triangle,
• a 3-dimensional simplex is a tetrahedron, and
• a 4-dimensional simplex is a 5-cell.

more .... https://en.wikipedia.org/wiki/Simplex

Fractals naturally form curved surfaces, which conforms to "curved space" while answering to very uncomplicated equations such as the "gravitational constant".

The gravitational constant (also known as the universal gravitational constant, the Newtonian constant of gravitation, or the Cavendish gravitational constant),[a] denoted by the capital letter G, is an empirical physical constant involved in the calculation of gravitational effects in Sir Isaac Newton's law of universal gravitation and in Albert Einstein's theory of general relativity.

The gravitational constant G is a key quantity in Newton's law of universal gravitation.

more.... https://en.wikipedia.org/wiki/Gravitational_constant

But also, IMO it answers to your model of philochrony as well.

It seems that all of this describes an emergent evolving object that can be measured by its dimensional expressions.
In the end it should be reducible to its most simplest forms.

I firmly believe that there is no such thing as "irreducible complexity"