Spin Networks and Foams

In the ongoing quest to explore the mapping between the parsimonious NPQG point charge universe and the patchwork quilt of effective theories of physics, let’s take a quick spin through the landscape of spin networks and spin foams.


In physics, a spin network is a type of diagram which can be used to represent states and interactions between particles and fields in quantum mechanics. From a mathematical perspective, the diagrams are a concise way to represent multilinear functions and functions between representations of matrix groups. The diagrammatic notation often simplifies calculation because simple diagrams may be used to represent complicated functions.

Roger Penrose is credited with the invention of spin networks in 1971, although similar diagrammatic techniques existed before his time. Spin networks have been applied to the theory of quantum gravity by Carlo Rovelli, Lee Smolin, Jorge Pullin, Rodolfo Gambini and others.


I’ll start with notes and commentary on this excellent Carlo Rovelli talk via Oxford Mathematics.

  • Title : Spin networks : the quantum structure of spacetime from Penrose’s intuition to Loop Quantum Gravity
  • @10:00 Carlo describes space between his hands. He talks about removing the air from this volume, removing the photons, removing the fields and what remains being space.
    • This abstraction is lacking and incorrect. First of all, good luck removing the particles that actually implement spacetime aether. Those super lightly interacting particles permeate everything, including Carlo’s waving hands. Those particles also generate fields, and those aren’t removable either. This gets to the fundamental misconception of the vacuum and more specifically the quantum vacuum as some sort of emptiness out of which pair production can occur and into which annhilated particles can disappear.
  • Spin networks attempt to bridge a key aspect of general relativity to a key aspect of quantum mechanics.
  • Key aspect of space :
    • Space, as measured by distances and angles of rotation, is a continuous geometry in general relativity, yet space is a curvy geometry, as described with a pseudo-Riemannian manifold.
    • NPQG is based on a continuous Euclidean geometry of 1D time and 3D space.
  • Key aspect of quantum :
    • Probability : we can not know sufficiently about the state of the world to predict with certainty.
    • Relationality : we measure properties via an intermediary, an observational apparatus
    • Discreteness : things are discrete, they can only take certain values.
    • NPQG critique : quantum mechanics, in a colossal failure of imagination, calls an end to the investigation upon reaching a difficult step where things are fuzzy yet we sense discreteness.
  • “There is a precise sense in quantum mechanics where the angles between two objects are not continuous, but are discrete.”
    • This occurs when we consider the angle as being between the axis of rotation of each object.
    • In classical mechanics the axis of rotation and the corresponding angular momentum vector can orient in continuous geometry.
    • This is simple to explain in NPQG, where everything we are talking about is based upon structures of spinning point charges. It is natural for these structures to form repetitive patterns and to align sub-structures within an object and between objects according to the dynamical field effects of the structures themselves. Stated simply, there are certain discrete configurations, positions, or orientations which are selected by nature.
    • Carlo links the concept of the velocity of the rotation to the discrete (quantum) nature of the angular momentum magnitude and direction.
    • When Carlo said velocity he is moving his index finger around in a circle. What is he tracing? Maybe the electron in its wave equation orbital? He says “given the mass of it you have certain discrete velocities possible”. Yeah, he is probably several assembly steps of structure above the point charges.
  • Carlo says Roger had the intuition that if the angular momentum vectors are quantized in magnitude and angle that space itself may also be quantized as well.
  • Carlo describes at a high level how spin network angles are determined combinatorically with simple operators applied to the spin network. It is an unpacking of the representation theory of a rotation group.
  • What does a spin network, or rotation group, correspond to? Is it a standard model structure such as a quark, electron, or photon? From an NPQG perspective, this seems like such an odd approach to the problem because it is conducted in a dark cave with no knowledge that everything is constructed from point charges. Still, let’s press on, it is possible that there is a simple mapping and that would be huge.
  • That covers the 1971 paper by Sir Roger. Then in 1995 spin networks were applied to Loop Quantum Gravity.
  • Carlo goes on to describe how each node in the spin network corresponds to a small chunk of spacetime volume. Noether cores can be considered to be a small chunk of spacetime volume. Do these map to each other? Do the edges in the spin network correspond to transfers of angular momentum between Noether cores?
  • Note that in the NPQG point charge universe, Euclidean time and space is permeated with Noether cores over vastly wide range of energy scales and corresponding volumes. Some of these Noether cores are adorned with personality charges and these are the fermions. Other Noether cores are energized in a way to take on a planar orientation and contra-rotate on the same axis with an anti-Noether core and we call these photons. Photons are very good at shielding their energy so they appear massless. A structure that is similar to the photon but has less energy is the neutrino and it is more wobbly and less capable of energy shielding than a photon and thus its apparent energy (i.e., mass) fluctuates. The spacetime aether particles have extremely low apparent energy and a very small volume. I can vaguely see how spin networks have some hints of this overall landscape, but it seems like an enormous cognitive chasm between the two.

In physics, the topological structure of spin foam consists of two-dimensional faces representing a configuration required by functional integration to obtain a Feynman’s path integral description of quantum gravity. These structures are employed in loop quantum gravity as a version of quantum foam. Spin networks provide a language to describe the quantum geometry of space. Spin foam does the same job for spacetime.

Wikipedia – spin foam

Quantum foam (also known as spacetime foam or spacetime bubble) is the quantum fluctuation of spacetime on very small scales due to quantum mechanics. Matter and antimatter are constantly created and destroyed. These subatomic objects are called virtual particles.[1] The idea was devised by John Wheeler in 1955.

Wikipedia – quantum foam

Neither of these concepts of a “foam” at a quantum level capture the idea of immutable point charges which are forming the structures which are then modeled as a foam. The foam is at an ontological level several assembly steps above base nature.

Our quest is to find mappings between the point charge universe and extant theory. This post was a quick tour through spin networks. I see hints but no clear linkages to the point charges universe. No doubt those mappings exist and some portions of spin networks and loop quantum gravity will be leverageable in the point charge era.

The universe is a giant soup of structures built from point charges simply being point charges. And all these structures are constantly interacting, especially locally. The problem calls for a geometry that is flexible and can describe dynamical structure formation, interaction, and reaction in an infinite scale charged N-body problem.

J Mark Morris : Boston : Massachusetts