Hoisting by Einstein’s Petard

While often cited as an authority in particle physics and cosmology, Einstein didn’t win the Nobel Prize for his work on relativity. That was considered too controversial at the time. Rather, he was awarded the prize for two papers that forced physicists to shift their understanding of waves.

As I’ve pointed out before, the mathematics of waves is seductive. By assuming that a phenomenon is uniformly smooth at any magnification, we are allowed the use of powerful mathematical tools such as differential equations and Fourier analysis. But it comes with a big assumption: that the things described have no structure inside of them.

Einstein’s two papers undermined that assumption. One paper forced the conclusion that light waves were composed of particles called “photons.” The second forced a recognition that water waves were composed of molecules.

Then he spent the rest of his life pursuing a grand theory of physics that assumed that space was uniformly smooth. Go figure, and take note: he failed in his quest.

So have all the others that followed in his footsteps.

In essence, all that I am asking in my New Physics page is that we imagine that space has structure. I’m hoisting Einstein on his own petard.

That’s the Spirit

We’ve been building a model of the universe with superfluid dark energy, and introducing a “cold” alternative to the Big Bang theory. The model includes a possibility for gravitational attraction between defects in the lattice. Given that there are three other forces at play in the universe (electromagnetism and the “weak” and “strong” interactions), the model is obviously incomplete.

I’m going to throw out a model here that manifests interesting and theoretically relevant behaviors. I am certain that the model is incomplete – my sense is that the dark energy lattice itself has complex structure (I refer the reader to the image on the Generative Orders proposal). But the suggestions here should be enough to stimulate innovative thinking.

So what we need to propose is a model for our defects. It’s interesting to consider the defect to be a self-repellant loop that gets pinned to a node in the dark energy lattice. Now the lattice is going to tend to corral the expansion of the loop along a particular axis. The energy driving the expansion will eventually be spent in pushing the dark energy particles apart. We can imagine thus that the loop will oscillate back and forth, as indicated below with “right” and “mid” views. We can imagine the “left” configuration by rotating the “right” configuration through half a circle.

Right Thread
Mid Thread

Now let’s suppose that each point in the lattice can anchor up to two loops. How this is feasible is open to exploration. One way is for the dark energy to have structure itself. For example, it might be a little circle. Now there will be oscillation patterns that will minimize the interaction between the two threads. One possible pattern is shown below (the lattice is suppressed so that we can focus on the loop configurations).

Two-Thread Oscillations

We see that when one loop is clustered near the center, the other is extended. What is most important, however, is that when the sequence is followed clockwise, the pattern rotates clockwise. Reading in the reverse order reveals a counter-clockwise rotation. So this is a model for the top-like “spin” that was described earlier.

(NB: This is a terrible model of intrinsic angular momentum. A more fertile approach is to think about normal angular momentum, which arises when interacting particles are offset along the axis of approach. We then see that normal angular momentum is discretized in the lattice, because the offsets are discretized.

How is normal angular momentum conserved? Well, the model proposes that gravitation, electromagnetism and the strong interactions are all generated through the efforts of the lattice to minimize distortions. The specific character of each force reflects the degree to which a configuration of loops generates lattice distortion.

So angular momentum is conserved because the approach of the particles stores a particular type of distortion in the lattice that is released when they separate. Intrinsic angular momentum may be accommodated better by recognizing that the odd shape of the loop projections can be removed by offsetting the center of the oscillation by half a lattice point.)

Now the configuration with two loops should be fairly stable – it affects both directions equally, and so shouldn’t create too much disruption when moved. However, the configuration with one loop will tend to whip around when it moves, maybe even causing the lattice to be re-oriented locally. Given our discussion of mass, it would appear that asymmetric particles (one loop in our example) will have larger masses (disturb the lattice more when moving) than symmetric configurations (two loops in our example).

One way to minimize the impact of the asymmetric configuration might be to couple them together. This would localize the impact of the thrashing around at large distances, at least if the asymmetric configurations were synchronized in their oscillations. This models the strong force, which binds fractionally charged particles inside the proton and neutron.

Yes: what I’m suggesting is that the loops correspond to particle charges. In our two-dimensional model, only three charge states are allowed (with 0, 1 or 2 threads), because only two directions are available for oscillation. In our universe, we have three dimensions, and so four charge states are possible. This is precisely what we see in the particle zoo, and the asymmetric particles (with fractional charges: the up and down quarks, for example) have much higher masses than the symmetric particles (the neutrino and electron).

Adding a symmetric particle to a pairing of asymmetric particles might further stabilize the lattice. This is analogous to an electron bonding to a proton.

Now let’s tear our understanding of reality completely wide open: why should the loops be constrained to be bound to the dark energy lattice? What if they were able to form structures among themselves, structures that stored energy in the lattice by causing it to expand in their vicinity? Structures that could contain and process information? Structures that might even be able to open holes in the lattice that would allow particles to travel faster than the speed of light?

That’s the spirit, people.

I hope that you’re taking mind. Our brains are only interfaces to these structures. Our souls are the eternal part of us, bonding again and again to matter through our multiple lives, and using those opportunities to do a certain work on themselves.

Now I beg you, please read The Soul Comes First. While selfish configurations of spirit tend to dissipate the energy stored in the dark energy lattice, mutually supportive configurations have stored up an enormous amount of energy over time. They impose certain rules, and a failure to comply led to the destruction of the dinosaurs.

I believe in love, and I believe that at least a portion of humanity has enough maturity to master our baser urges. The Book of Revelation teaches that they will complete the work that was put before us in “Eden”. But I would like us to work efficiently to ensure that the predators, in their trashing about as they go down, are not allowed to do too much damage to the innocent.

Generative Orders Research Proposal – Part IV

Reference Model

Having advanced the principles of generative orders, we find ourselves in a situation somewhat similar to that faced by quantum theorists after wave-particle duality was advanced. A number of experiments appeared to violate the principles of Classical Mechanics (i.e. – the double-slit experiment, electronic excitations of the hydrogen atom, and the photoelectric effect). Progress was achieved by generalizing the methods of classical mechanics (Hamiltonian and Lagrange equations) into differential equations through Fourier analysis.

The problem in the case of generative orders is more difficult. The principle does not generalize existing theory into new realms of application – it serves to supplant existing theories, stretching back to Special Relativity and quantum mechanics. Additionally, the enumerated principles are abstract. They do not drive us to a specific formulation of physics in one dimension. A number of alternatives may be mathematically feasible.

Lacking a definite starting point for analysis, nothing short of an intellectual Big Bang would produce a fully elaborated theory that explains everything that is known about particle physics and cosmology. That does not exclude thoughtful exploration of specific possibilities. In this section, we consider a simple model (narrative here), elaborated to the point that conceptual correspondence with known phenomenology is established. The model is sufficient to support development of model potentials (as outlined in the research program), and therefore to advance theoretical insight and analysis methods that can be applied to other models.

  1. The initial state of the universe is a disordered but “cold” (at least as compared to Big Bang theories) collection of one-dimensional structures.
  2. Physics of one dimension includes a mechanism of segmentation (or quantization). The W/Z mass may establish a scale for this segmentation (see item 8 in this list).
  3. Folding or bonding on segmentation boundaries produces higher-dimensional structures. Geometrically, we know that triangles are the most stable of these structures.
  4. Higher-dimensional structures are self-associative, building lattices of distinct dimensionality. Tiling a plane with triangles is trivial. The structure of higher-order lattices is a an extrinsic property of the lattice potential.
  5. Lower-order lattices may exist in the empty spaces between cell layers. This is again an extrinsic property of the lattice potential
  6. Lattice formation is spontaneous. Orientation of expanding lattices is random.
  7. Surface energy at the boundaries between merging lattices of different orientation (a la grain boundaries in metals) provides the energy to compress structures into lower order, producing quasars and super-massive black holes at the center of galaxy formation. In this model, a black hole in three dimensions is a volume bounded by a two-dimensional lattice.
  8. Parthogenesis occurs through the expulsion of residual lower-order structures from the enclosed surface. In the reference model, these are one-dimensional structures (termed “threads” below). Threads may pass around the polygonal subunits of the lattice or through them. Threads that penetrate the lattice sub-units are localized, creating loci that we identify with fermions. Fermions interact strongly with similarly localized threads, giving rise to the non-gravitational forces. The potential barrier of the W and Z mass corresponds to a thread-exchange process, which requires reconfiguration of the sub-units.
  9. Captured threads locally distort the lattice. Gravity is a side-effect of the lattice energetics that localizes the distortion.
  10. Dark energy corresponds to the potential energy of lattice compression.

This illustrates how the principles of generative orders can be used to build a simple one-component model of the early universe. Geometrical models are presented in Chapter 4 of Love Works.

Certain details of particle phenomenology appear superficially to be accessible in the context of this model.

  1. Charge corresponds to the number of threads that penetrate a lattice sub-unit (which naturally has three degrees of freedom). Sign is simply a way of characterizing the tendency of fermions to attract fermions with different degrees of thread penetration.
  2. Mass arises naturally when threads pull on each other, causing the loci of thread capture to be dragged through the lattice. From the properties of the first particle family, it would appear that asymmetrical thread configurations must be more disruptive than symmetrical configurations. The equivalence of gravitational and kinetic mass is natural, as both effects correspond to lattice distortions. The equations of special relativity suggest the velocity-dependence of kinetic distortions.
  3. Particle families correspond to distortions of a particle’s lattice sub-unit from its normal configuration.
  4. Conservation of momentum could result from lattice dynamics that tends to reject disturbances, forcing energy back onto moving fermion. Analogies in material science include superfluidity and superconductivity.
  5. Light could be a self-propagating disturbance in the lattice, achievable only through fermion kinematics. Assuming that gravitational packing of particles causes re-orientation of the lattice at the surface of large bodies, the constancy of the speed of propagation is a local phenomenon (i.e. – a massive body “drags” space around with it).
  6. Light may interact with the lattice as it propagates, causing energy loss that manifests as a shift to lower frequencies. This may explain the microwave background radiation.
  7. A soul is a complex configuration of threads that are supported by but only tenuously bound to the lattice.

These configurations store energy as potential energy due to the associated distortion of the lattice.

Obviously, all of these are conceptual possibilities, whose validity can only be established through construction of a model of the energetics of the interactions between one-dimensional structures. As will become clear in the description of the research program, the list is by no means exhaustive. It is presented to provide a sense of the naturalness of fit between phenomenology and theories that might be elaborated using the principles of generative order.

Generative Order Research Proposal – Part III

Principle of Generative Order

In this section we motivate the principle of generative order and define a reference model to serve as a framework for exploring the challenges in elaborating the principle into a model capable of explaining the known characteristics of particles and their interactions.


The preceding survey of the deficiencies of GI theories, culminating with lists of unexplained first-order phenomenology and axiomatic contradictions, is a powerful motivation to search for new principles to guide the construction of alternatives. In proposing generative orders (to be developed below), the author was motivated by the following observations. The observations span the scale of phenomenology from the quantum to the cosmological, in recognition of the connection between these scales established by current physical theory.

The Preponderance of Threes

As observed, we inhabit a universe with three spatial dimensions. The three particle families (of which the first is summarized below) consist of four fermions, with three charge states (the fourth state being uncharged). Finally, the non-gravitational forces (electromagnetic, weak and color) have group-theoretical ranks of 1, 2 and 3.

Particle Mass (MeV) Charge Color Spin
n 0 0 0 ½
u 138 -1/3 1 ½
d 140 2/3 1 ½
e 0.5 -1 0 ½


Following this correspondence, it seems natural to suggest that the principles that explain our reality of threes should also be able to explain realizable physical realities based upon one, two and four and higher dimensions. This is the fundamental principle of generative order.

In the table above, it is also interesting to note other correspondences. Only fractionally charged particles (u and d) have color, and their masses are far larger than the masses of integrally charged particles (n and e). I also note that particles with odd fractional charge repel each other, but are attracted to the remaining charged particle, of even fractional charge.

Gross Cosmological Structure

Almost all galaxies have super-massive black holes at their center (Galactic Cores, or GCs). Mechanisms for ejection of GCs have been proposed to explain those that do not. In addition, the oldest objects in the universe appear to be quasars. This tends to indicate that quasars may represent the early stages of GC formation, and so that galaxies form through a sudden and enormously violent mechanism, rather than through the gradual coalescence of intergalactic gas.

Secondly, galaxies appear to be clustered on the surface of extremely large voids, lacking any visible matter, but still capable of lensing light. This indicates that the initial stages of the universe must include mechanisms that explain variations in the uniformity of space (in the sense of General Relativity, thought not necessary through the mechanisms it allows).

Core Principles

The statement of generative order provided above is weak. It admits of realities in which a three-dimensional reality is independently established, but does not co-exist with realities of higher or lower dimensionality. Lacking a dynamical result that establishes preference for a three-dimensional reality, it would seem prudent to extend the basic principle of generative order with two others. The three are then:

  1. Realizable physical laws must exist on all orders of dimensionality.
  2. Orders are compositional: elements of lower order combine to produce elements of higher order.
  3. Orders must co-exist, and transitions between orders must be related to recognizable physical phenomena.