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.

Way Beyond Teflon

In imagining a universe filled with an invisible substance, it is natural to use air as an analogy. We then run immediately into trouble with Newton’s first law of motion, which is also an assumption in Einstein’s theories:

Every object in a state of uniform motion tends to remain in that state unless acted upon by an external force.

We know that air actively slows the movement of objects passing through it. Why aren’t moving objects slowed as they pass through Dark Energy?

One way around the problem is to assert that Dark Energy is a wall-flower: it doesn’t interact with anything else. That’s a prevalent assumption, and it causes me to remember the early history of thermodynamics. In building a theory of heat, early investigators, noticing that heat moved from place to place without changing the substance it occupied, conceived of caloric, an invisible field that permeated the spaces between atoms. That didn’t have much explanatory power, and was rapidly replaced by theories that explained heat as disordered motion of atoms.

Astrophysicists tell us that the universe is a pretty cold place – only a few degrees centigrade away from the coldest temperatures possible. Study of systems at these temperatures have revealed some amazing behaviors. For purposes of our discussion, liquid helium is an interesting example because it exhibits superfluidity, which allows objects to move through it without resistance. But superconductivity – materials that pass electricity without resistance – is another consequence of the basic principles that determine the behavior of really cold systems. Both liquid helium and superconductivity, by the way, are extremely important technologies in building facilities such as CERN.

Liquid helium is particularly simple because it bonds only very weakly, which is why it is liquid at temperatures that cause almost every other element to freeze. For illustration, I’m going to show a model system that shows atoms in a square two-dimensional lattice. The details may not apply to liquid helium, but I have reason to believe that they might to dark energy.

Imagine that we have a tank filled with liquid helium. At very cold temperatures, the atoms stack uniformly in the tank.
Super Fluid Lattice
Such arrangements are said to have high order. They are typical of crystalline materials, including many solids. One of the upshots is that it’s difficult to move a single atom without moving the entire collection. That’s because gravity presses the volume into a compact mass, which means that that atoms are compacted slightly, and therefore repelling each other. So moving one helium atom causes the atom it’s moving towards to move away. The cold here is important: if the lattice were vibrating somewhat, there would be little gaps that could absorb some of the distortion, and so the parts of the lattice could change independently. It’s the lack of such vibrations that forces the lattice as a whole to respond to changes.

Now let’s imagine that we place an impurity into the lattice.
Impurity in Super Fluid
This time a slight distortion of the arrangement will occur. The atoms nearest the impurity will indeed shift their positions slightly. Since the atoms at the walls of the container can’t move, they will tend to remain in place. So the distortion will be localized. What’s interesting to consider is what might happen if two defects are created. Will the disturbance to the lattice be minimized if the defects are brought together, or if the lattice acts to separate them? The astute student of physics will see that this thought leads to a model for gravity.

Now let’s propose that somehow our impurity begins to move.
Slow Impurity
How will the lattice react? Well, again, the atoms at the walls can’t move. The impurity will push against the atom in front of it, and leave a gap behind it. So long as the speed of the impurity is much less than the speed of the sound in the lattice, it is only the nearest atoms that will be disturbed. Obviously, the solution to restoring the order of the lattice is for the forward atoms to migrate to the sides as the impurity passes, displacing the atoms already on the side so that they fill the gap left by the passing impurity. When they reach the back, the atoms will come to rest by giving their energy back to the impurity. This is the essence of superfluidity: the impurity loses energy to the lattice only temporarily.

What is interesting to note is that in quantum mechanics, when calculating collisions between two charged particles, we have to assume that the particles are constantly emitting and re-absorbing photons. This is analogous to the situation in the superfluid: the impurity is constantly losing energy and then regaining it.

Finally, let’s consider an impurity moving closer to the speed of sound in the lattice. In this case, the distortions affect more than the nearest atoms, and the circulation becomes more widespread.
Fast Impurity
It’s important to note that energy is stored in the circulatory motion of the helium atoms. They are moving, just as the impurity is moving – but in the opposite direction, of course. The closer to the speed of sound, the more energy is stored in the circulation. This means that it becomes harder and harder to make the impurity move faster as it moves more and more nearly at the speed of sound.

In Special Relativity, Einstein showed that particles become harder and harder to accelerate as they come closer and closer to the speed of light. The relationship is (m0 is the mass of the particle at rest):

m = m0/(1-v2/c2)1/2

Again, we see some strong correspondence between superfluidity and the behavior of particles in both special relativity and quantum mechanics. The big difference is that, while Richard Feynman famously stated that quantum mechanics was merely a mathematical procedure without any explanation, when applying the superfluid analogy to dark energy, it seems that at least some previously mysterious quantum and relativistic phenomena are simple to understand.

For more on models of particle mass, see That’s the Spirit.

Einstein is So 20th Century

In the two centuries between Newton and Einstein, arguably the greatest physicist of the 19th century was the Scotsman James Clerk Maxwell. Maxwell made fundamental contributions to thermodynamics, the study of how gases, liquids and solids change when ambient conditions (such as temperature and pressure) change, and how to convert heat to work. One of the results was an understanding of the propagation of sound waves through the air. But Maxwell also applied the new mathematics of differential calculus to create a unified theory of electricity and magnetism. These are the famous “Maxwell’s Equations” that predict the existence of electromagnetic waves, which we see as “light”.

Maxwell saw the relationship between electromagnetic waves and water and sound waves. Being steeped in a mechanical analysis of the world, he was unsatisfied with his abstract mathematical theory, and invested time in building a mechanical model of the “aluminiferous ether” – the medium in which light waves traveled. Having spent years studying his equations and their predictions, I am fascinated by claims of his success. It’s a magical world in which the linear motion of charges creates rotary magnetic effects. My understanding is that the model was not simple, but contained complex systems of interlocking gears.

Now Maxwell’s work was not merely a curiosity – it was the basis for the design of communication networks that broke down distances with the enormous speed of light. More than anything else, this has brought us into each other’s lives and helped to create the sense that we are one human family. (The social and psychological reaction to that reality is complex, and we’re still growing into our responsibilities as neighbors. In The Empathic Civilization, Jeremy Rifkin offers a hopeful analysis of the transition.)

So the world of scientific inquiry hung on Maxwell’s words, and in America, two of them, Michelson and Morley, designed an experiment to detect the presence of the ether. If the ether filled all of space, the Earth must be moving through it. Therefore the speed of light should change depending upon the motion of the observer through it. The analogy was with water waves: an observer moving along with a water wave doesn’t experience its disturbance – while one moving against it feels its disturbance enhanced. This is an example of Newton’s laws concerning the change of reference frames.

Since the Earth rotates around the sun, light emitted from the Earth in a specific direction relative to the sun should have a different speed at different times of the year. To test this hypothesis, Michelson and Morley built a sensitive instrument that compared the speed of light travelling in two perpendicular directions. As the Earth varied its motion through the ether, the pattern of dark and light on a screen was expected to shift slowly. Strangely, the result was negative: the image did not change.

The conclusion was that there was no ether. This was a real crisis, because Maxwell’s Equations don’t behave very well when trying to predict the relationship between observations made by people moving at different speeds. To understand how really terrible this is, consider: in Maxwell’s theory, charges moving through empty space creates a rotary magnetic field. But what if the observer is moving along with the charge? The charge no longer appears to move, so the magnetic field disappears. How can that be possible?

This was the challenge taken up by the Dutch physicist Henrik Lorenz. He analyzed the mechanical properties of rulers and clocks, which are of course held together by electromagnetic forces, and discovered a magical world in which rulers change length and clocks speed up and slow down when the speed of the observer changes.

This was the context in which Einstein introduced his theory of Special Relativity. He did not really add to the results of Lorenz, but he simplified their derivation by proposing two simple principles: First, since the vacuum is empty, we have no way of determining whether we are moving or not. All motion is relative to an observer (thus the title: Special Theory of Relativity), and so no observer should have a preferred view of the universe. The second was that the speed of light is the same to every observer. Einstein’s mathematical elaboration of these principles unified our understanding of space and time, and matter and energy. Eventually, General Relativity extended his ideas to include accelerating observers, who can’t determine whether they are actually accelerating or rather standing on the surface of a planet.

Special and General Relativity were not the only great theories to evolve in the course of the 20th century. Quantum Mechanics (the world of the microscopic) and Particle Physics (describing the fundamental forces and how they affect the simplest forms of matter) were also developed, but ultimately Einstein’s principles permeated those theories as criteria for acceptance.

Then, in 1998, studies of light emitted from distant supernovae seemed to indicate that something is pushing galaxies apart from each other, working against the general tendency of gravity to pull them back together. The explanation for this is Dark Energy, a field that fills all of space. This field has gravitational effects, and its effects in distorting the images of distant galaxies have been observed. However, this field cannot be moving in all possible directions at all possible speeds. Therefore, it establishes a preferred reference frame, invalidating Einstein’s assumptions.

Working physicists resist this conclusion, because they have a means of accommodating these effects in their theories, which is to introduce additional mathematical terms. But science is not about fitting data – it is about explaining it. Einstein used his principles as an explanation to justify the mathematics of his theories. When those principles are disproven, the door opens to completely new methods for describing the universe. We can travel as far back as Maxwell in reconstructing our theories of physics. While for some that would seem to discard a lot of hard work done over the years between (and undermine funding for their research), for others it liberates the imagination (see Generative Orders as an illustration).

So, for example, why didn’t Michelson and Morley detect the ether? Maybe ether is more like air than water. Air is carried along with the Earth, and so the speed of sound doesn’t vary as the Earth moves about the sun. Maybe dark energy, which Maxwell knew as the ether, is also carried along with the Earth. Maybe, in fact, gravitation is caused by distortion in the Dark Energy field when it is bound to massive objects.

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.