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Started reading
December 7, 2025
This permanent doubt, the deep source of science.
quantum mechanics and general relativity, taken together, imply that there is a limit to the divisibility of space. Below a certain scale, nothing more is accessible.
the key to understanding the physics of these solutions lies in the points where these lines intersect. These points are called “nodes,” and the lines between nodes are called “links.” A set of intersecting lines forms what is called a “graph,” that is to say, a combination of nodes connected by links,
it is in the nodes of the graph, not in the lines, that the volume of space “resides.” The lines “link together” individual volumes sitting at the nodes.
Volume is a geometrical quantity that depends on the geometry of space,
Volume is therefore a property of the gravitational field,
Every node n in the graph has its own volume vn: one of the numbers in the spectrum of the volume. The nodes are the elementary “quanta” of which physical space is made.
you imagine two nodes as two small “regions of space,” these two regions will be separated by a small surface. The size of this surface is its area. The second quantity, after the volume, which characterizes the quantum webs of space, is the area associated with each line.* The area, just as in the case of the volume, is a physical variable and has a spectrum that may be calculated using Dirac’s equation.* Area is not continuous; it is granular.
The central prediction of loop theory is therefore that space is not a continuum, it is not divisible ad infinitum, it is formed of “atoms of space,” a billion billion times smaller than the smallest of atomic nuclei.
The crucial difference between photons, the quanta of the electromagnetic field, and the nodes of the graph, the “quanta of gravity,” is that photons exist in space, whereas the quanta of gravity constitute space itself. Photons are characterized by “where they are.”* Quanta of space have no place to be in, because they are themselves that place. They have only one piece of information that characterizes them spatially: information about which other quanta of space they are adjacent to, which one is next to which other. This information is expressed by the links in the graph. Two nodes
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what matters is not how things are, but rather how they interact. Spin networks are not entities; they describe the effect of space upon things.
space is not actually formed by a single specific spin network, but rather by a cloud of probabilities over the whole range of all possible spin networks.
As we abandon the idea of space as an inert container, similarly we must abandon the idea of time as an inert flow, along which reality unfurls.
In a certain sense, space no longer exists in fundamental theory; the quanta of the gravitational field are not in space. In the same sense, time no longer exists in the fundamental theory: the quanta of gravity do not evolve in time. Time just counts their interactions.
On the surface of Earth, for instance, the North Pole and two points on the equator can make a triangle with three sides of equal length and three right angles—something that clearly cannot be done on a plane.
But the main reason why Schrödinger’s wave is a bad image of reality is the fact that when a particle collides with something else, it is always at a point: it is never spread out in space like a wave. If we conceive an electron as a wave, we get in trouble explaining how this wave instantly concentrates to a point at each collision. Schrödinger’s wave is not a useful representation of reality: it is an aid to calculation that permits us to predict with some degree of precision where the electron will reappear. The reality of the electron is not a wave: it is how it manifests itself in
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