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the spectrum of the volume is discrete. That is, the volume can only be made up of “discrete packets,” somewhat similar to the energy of the electromagnetic field, which is also formed of “discrete packets”: photons.
This is the light of our soul animating our 5 senses through our nervous system
The nodes of the graph represent the discrete packets of volume and, as in the case of photons, can only have certain sizes, which can be computed using Dirac’s general quantum equation.* 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. Every node of the graph is a “quantum particle of space.” The structure that eme...
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On the left, a graph formed by nodes connected by links. On the right, the grains of space that the graph represents. The links indicate the adjacent particles, separated by surfaces.
A link is an individual quantum of a Faraday line.
Now we can understand what it represents: if 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...
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Area is not continuous; it is granular. There is no such thing as an arbitrarily small area.
This is our conscious coming into contact with another consciousness; with or without a body... Think of our ancestors, or of family that have pased on, yet remain in our hearts and minds from time to time. "We don't remember days... We remember moments, which through the electromagnetic force of their soul ~ igniting of a moment shared long ago, bringing it into our present embodied moment.
Space appears continuous to us only because we cannot perceive the extremely small scale of these individual quanta of space, just as when we look closely at the cloth of a T-shirt, we see that it is woven from small threads.
The idea that measuring length, area, and volume is a question of counting individual elements had been proposed in the nineteenth century by Riemann himself.
The mathematician who developed the theory of continuous curved mathematical spaces was already aware that a discrete physical space is ultimately more reasonable than a continuous one.
To summarize, the theory of loop quantum gravity, or “loop theory,” combines general relativity with quantum mechanics in a rather conservative way, because it does not employ any other hypotheses apart from those of the two theo...
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General relativity taught us that space is something dynamic, like the ...
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Quantum mechanics teaches us that every field of this sort is “made of quanta,” has a...
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We expect “quanta of gravity,” just as there are quanta of light, quanta of the electromagnetic field, and just as particles are quanta of quantum fields. But space is the gravitational field, and the quanta of the gravitational field are “quanta of space”: the granular constituents of space.
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.
Loop theory describes this atomic and granular quantum structure of space in a pr...
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by applying the general equations of quantum mechanics written by Dirac to Einste...
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In particular, loop theory specifies that volume (for example the volume of a given cube) cannot be arbitrarily small. A minimum volume exists. No space smaller than this minimum volume exists. There is a m...
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But is this what truly happens in nature? Are there intervals between Achilles and the tortoise that can be arbitrarily short? Does it really make sense to talk of a billionth of a billionth of a billionth of a millimeter, and then to think of dividing it again, a further innumerable number of times? The calculation of the quantum spectra of geometric quantities indicates that the answer is negative: arbitrarily small chunks of space do not exist. There is a lower limit to the divisibility of space.
It is at a very small scale indeed, but it is there. This is what Matvei Bronštejn had intuited in the 1930s. The calculation of the spectra of volume and area confirms Bronštejn’s idea and frames it in a mathematically precise manner.
Without experiments and mathematics, we would never have understood what we have understood. Yet we develop our conceptual schema for understanding the world by exploring new ideas, but also by building on the powerful intuitions of giant figures from the past.
A spin network represents a quantum state of the gravitational field: a quantum state of space, a granular space in which area and volume are discrete.
Figure 6.4 A spin network
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.
Yet gravity travels at same speed as light? Hmmm
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 adjacen...
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