A Fractal Foam Model of Universes

Cosmic Foam and Ether Foam

The Sloan Digital Sky Survey (SDSS) has mapped about half a million galaxies in 3D, revealing a picture which resembles a giant bubble bath. This is what I call our cosmic foam. A median-size bubble in our cosmic foam is roughly 10²⁴ meters across and is surround by relatively thin walls, each containing hundreds or thousands of galaxies. The picture at right depicts a cross section of our cosmic foam roughly as wide as the visible universe. If it appears .1 meter across on your screen, then it is reduced in scale about 10^-27 to 1.

In FFMU, the cosmic foam of our universe is the ether foam of a super-universe, and the ether foam of our universe is the cosmic foam of a sub-universe. So when you look at this picture of our known universe, you could just as well be looking at our ether foam magnified in scale about 10³² to 1. At this magnification, an electron would be about 10¹⁰meters across—one tenth as wide as Earth's orbit around the sun. So there is plenty of room for several more layers of complexity within an electron or a quark before we reach the smallest fundamental particle in our universe.

Presumably, these three—sub-universe, our universe and super-universe—are part of an infinite scale-wise sequence, but that must always remain a matter of philosophy and religion—not science.

Expansion

Space is expanding. Some astrophysicists claim that other factors, besides Doppler effect, are responsible for the cosmological redshift. I allow that other factors may contribute to the redshift, but for my model to work, some expansion is necessary. "Space is expanding," is not the same as, "The universe is expanding." An infinite universe can't get bigger, but its space can expand. The Hubble constant, H₀, is now widely believed to be approximately 2.4 x 10^-18/sec. If it remained constant at that rate, the distance between distant galaxies would double about every 9 billion years. The volumetric expansion rate is three times the linear expansion rate; so the volume of a region, defined by comoving boundaries, will double about every 3 billion years. [Calculation.]

The space in our universe is expanding, and that is equivalent to our measures of distance shrinking, relative to the cosmic foam, while remaining a constant size relative to the ether-foam. The expansion of space in the sub-universe causes the expansion of space in our universe; the expansion of space in our universe causes the expansion of space in the super-universe.

One only has to listen to the head on a glass of beer to know what happens when a foam expands. (Technically, the beer is drained out of the head by gravity making the bubble walls thinner.) As our space expands, the bubble walls of our cosmic foam are stretched thinner and thinner until they reach the limit of their tensile strength. Then, one by one, great walls of galaxies rupture; cosmic-foam bubbles pop! Not to worry! It’s not the end of everything. Maybe “pop” isn’t the right word; it takes billions of years for one of these bubbles to pop. If we knew what to look for thru our telescopes, I am pretty sure we could see cosmic-foam bubbles popping all around us; they’ve been doing it for ever.

Just in the last 3 billion years, the total volume has doubled. How does that relate to the number of cosmic-foam bubbles? If the volume of a median-size cosmic-foam bubble remains constant (big unfounded assumption), then we must have half as many of them now (in a well defined region) as we had 3 billion years ago. Half as many bubbles means half as many bubble walls; so half of the bubble walls that existed 3 billion years ago have since popped. That's a lot of popped bubble walls, so the evidence should be plentiful all around us—if only we knew how to recognize it! We do see plenty of colliding galaxies. Unfortunately, we don't see galaxies accelerating away from the middle a ruptured wall. The reason we don't see that is the fact that we have only one measure of relative velocity, namely Doppler shift, and that only relates to radial velocity. Our 3D map of galaxies is a map of redshift, which is incorrectly presumed to be a map of radial distance. If we see a popping bubble wall slanting away from us, the galaxies on the far side should be redshifted significantly more than those on the near side, and the difference is disproportionate to the small difference in distance.

Bubbles pop chaotically, which is significantly different from randomly. But let us suppose, for now, that the bubble sizes are random, having a mean, median and mode. A more rigorous approach should be reserved for a time when a mathematician shows interest in refining the model. By “median-size”, I mean that half the volume of a region is contained in bubbles larger than the median size. The median size cosmic-foam bubble (in the present epoch) is probably the same everywhere within our knowable universe; but in relatively small regions the median size varies significantly. There may also be significant variations at distances far beyond the Hubble limit, but those must always remain unknowable to us. Note that we observe distant galaxies as they were at an earlier era, when the median cosmic-foam bubbles were smaller.

We should expect our ether foam to be fundamentally similar to our cosmic foam, although we have no way of knowing how old the sub-universe is. If the sub-universe is much younger than our own universe, then its cosmic foam (our ether foam) should resemble the state of our cosmic foam in a much earlier epoch. If the sub-universe is so young that its galaxies have not yet spread apart enough to leave voids surround by walls of galaxies, then we must ask whether the term "cosmic foam" even applies to the sub-universe. It could be in a different phase than our own cosmic foam, and our own cosmic foam may have gone thru many phase transitions to get where it is today. Conceivably, such phase transitions in the sub-universe might significantly alter the laws of physics in our universe.

Space expands when the number of ether-foam bubbles in a region of space (defined by the presence of comoving objects) increases. The number of median-size ether-foam bubbles between the ends of a meter stick is a function of time—probably a very simple function. In keeping with Occam’s razor, I choose to assume, for the time being, that this function is a constant. If so, even though new bubbles are continuously popping up (explained in next paragraph) within the boundaries of a meter stick, the total number of ether-foam bubbles within the meter stick remains constant. I’ll stick with that assumption until it leads to a contradiction or paradox.

Time inversion

Speaking of paradox: When the membrane between two cosmic-foam bubbles disappears, two bubbles become one, representing a decrease in the number of cosmic-foam bubbles. A bubble pops in the sub-universe’s cosmic foam, and that increases the number of bubbles in our ether foam; otherwise our space would be shrinking, not expanding. There must be an inversion of time between adjacent universes to resolve this paradox. As our universe is getting older, the sub-universe is getting younger. Cosmic-foam bubbles pop; ether-foam bubbles un-pop! Thus, expansion of space determines the direction of time's arrow.

This is a new wrinkle on the second law of thermodynamics. Time inversion turns increasing entropy into decreasing entropy. Not that the greater physical universe is a closed system, but if it were closed, that would be no obstacle to decreasing entropy. Each universe outputs its entropy to the next larger-scale universe, and time inversion converts that to and input of extropy.

Space is equivalent to energy

The expansion of our space doesn’t just drive the expansion of space in the next universe; it drives everything in between! Here’s how that happens: When a cosmic-foam bubble wall pops, the galaxies in that wall accelerate away from the rupture toward the edges, gaining tremendous momentum and energy along the way. Momentum and energy are conserved by radiating outward thru the cosmic foam. A positive pressure p-wave radiates like ripples on a pond in the plane of the ruptured wall. The pair of bubbles, newly joined into one long bubble, shortens to find a new equilibrium; this radiates a pair of negative pressure p-waves perpendicular to the plane of the ruptured wall.

Due to time inversion, p-waves in the ether foam converge—seemingly at random—and their considerable energy goes into the un-popping of an ether-foam bubble. Thereby, dark energy is converted to new space. I call these p-waves “dark energy” because the term was invented by mainstream astrophysicists to explain the recent discovery of the acceleration of the expansion of space. I don’t know how much energy is involved, but it probably fits the general formula: E = kVρ(c_g)².

[V is the volume of new space created; k is an unknown constant; ρ is the inertial density of the ether; c_lis the speed of light; c_g is the speed of gravity.] Notice the similarity to Einstein’s famous equation, E = mc²; kVρ is an inertial mass, and c_g is a velocity.

For a median-size ether-foam bubble, my initial guess is that V is about one Planck volume (~10^-105 m³); k is probably one; ρ might be somewhere between 1 and 10¹⁸⁰ times the density of our universe (probably closer to the latter); and c_g might be between c_l and >10¹⁰c_l. So the dark-energy equivalent of a cubic meter of space is probably somewhere between an electron volt and all the matter-energy in the known universe. I have a feeling it’s closer to the latter than the former.

If k = 1, you get E = Mc_g²; unfortunately, we don’t know what mass we’re talking about, nor do we know the speed of gravity, which is somewhere between c and infinity.

Shaken, not stirred

I am only guessing that these dark-energy p-waves propagate at the speed of gravity, c_g, which might vary in inverse proportion to the local median bubble size. Since cosmic-foam bubbles vary greatly within our own tiny corner of our universe, I assume the same is true of ether-foam bubbles. The variation is probably random (or chaotic), with large variability in small regions but homogeneity on larger scales. Large-scale variations most likely would be observable if they exist within a Hubble limit of Earth; they might have the general appearance of gravity hills and valleys, but they would not be associated with any mass; they would be stationary relative to the ether, and therefore probably relative to the CMB radiation. I doubt if there are any such variations within a Hubble limit of Earth, but given the infinite size of our universe, it seems likely that they do exist somewhere, but well beyond the knowable universe.

When a p-wave enters a blob of smaller bubbles, it slows, transferring momentum to the blob, which is knocked out of its equilibrium position; when the p-wave leaves the blob, it recovers that momentum, leaving the blob out of equilibrium. The blob then accelerates back toward its equilibrium position, producing transverse s-waves, which propagate at the speed of light perpendicular to the path of the p-wave, which continues at the speed of gravity.

So dark-energy p-waves produce high-energy s-waves. If this mechanism is real, I would expect it to produce either one full-cycle of an s-wave, i.e., motion to one side, then to the other side and back to neutral, or it may be only a half-cycle s-wave. However, I am not convinced that any such mechanism actually exists in the present epoch, because it suggests that all of space should glow with high-energy photons—perhaps in the range of cosmic rays. Perhaps that process ended when our universe was quite young. For now, I just don’t know what else might be the ultimate source of s-waves.

Historical note:

In the early stages of developing my model, I thought the momentum imparted to blobs might stir up the ether, causing the blobs to migrate thru the foam. I thought blobs, themselves, were fundamental particles. I also thought some blobs caused fission and fusion of p-waves of specific energies. This might not be entirely wrong, so anyone seeking to improve upon the model might occasionally reexamine those bits of film from the cutting room floor.

Yes, a photon is an s-wave, and the ether is a solid. As James Clerk Maxwell said, over a century ago, if there is an ether, it must be a solid, because electromagnetic waves are transverse, and only a solid can be a medium for transverse waves. The term “solid” has nothing to do with lack of emptiness; if it did, there would be no such thing. Every solid is mostly empty space; sheer strength is what makes it solid. Even though each ether-foam bubble is mostly empty subspace, the tiny fraction that is filled with sub-universe matter has a tremendous amount of inertia. The waves that carry soooo much energy in our universe scarcely wiggle the sub-universe galaxies; the amplitude is probably a tiny fraction of a Planck length. Conceivably, a sub-universe galaxy might have as much inertial mass as the equivalent galaxy in our universe. One cubic meter of the ether foam might have a googol times more inertial mass than all the galaxies and dark matter in our known universe. The ether has no gravitational mass because it is the medium of gravity.

Cause of gravity

Nicolas Fatio de Duillier, in 1688, and Georges-Louis Le Sage, in 1748, described a mechanism which they hoped would eventually explain the cause of gravity. They thought gravitons are ultra-small ultra-fast particles which form a perfect gas; gravitons, they said, are randomly scattered by all massive particles; the scattering makes the particles appear dark to one another against a uniform; therefore, gravitons push massive particles toward one another. This reasoning is flawed because random scattering alone cannot result in a net exchange of momentum. If enough gravitons were absorbed to account for gravity, each massive particle would absorb the energy-equivalent of its own mass in less than a picosecond. Recent attempts by VanFlandern to refine the mechanism have supposed that a tiny fraction (1 in 10²⁰, as calculated by Slabinsky in an article in Pushing Gravity) of the gravitons must be absorbed to impart momentum, and the rest are randomly scattered. The “elysium”, VanFlandern’s light carrying medium, carries away the energy of the absorbed gravitons or somehow transfers it to the scattered gravitons.

I propose several major changes to Fatio/Lesage. First, I substitute p-waves for gravitons. Second, I propose interaction between p-waves and s-waves, resulting in an orderly bending, rather than random scattering. Because the bending is orderly, it produces an imbalance of momentum without significant exchange of energy between p-waves and s-waves. The s-waves are thus bent into orbit around one another, converting their energy to mass. This may eventually account for not only gravity but all of the forces and particles of nature; the details of this process have yet to be worked out.

Interaction between s- and p-waves

S-waves pass thru one another without changing course; the same is true of p-waves. I am going way out on a limb, however, to postulate that an s-wave can exchange momentum with a p-wave. The character of the exchange depends upon the wavelengths and wave forms. The simplest case is a collision between single half-wave pulses. The s-wave is a motion of the ether to one side and back to neutral; the p-wave is a motion of the ether opposite the direction of propagation and back to neutral. The portion of a p-wave that passes thru the head of the s-wave gets nudged in one direction; the part that passes thru the tail of the s-wave gets nudged in the opposite direction. If the p-wave is in the plane of the s-waves polarity, the direction of the p-wave will therefore be altered with a corresponding change of momentum; equal and opposite momentum is imparted to the s-wave. This momentum exchange results in groups of s-waves orbiting one another; these are the most fundamental particles of matter—even more fundamental than quarks.

Free s-waves can have any energy and wavelength, but there is some sort of exclusion principle governing the formation of particles—just as the Pauli exclusion principle governs the orbitals of atoms. The realm of analog physics from the sub-universe thus yields to the realm of quantum physics in our universe.

These particles either attract or repel one another, depending on their phase relationships. The s-waves continue to orbit one another at the speed of light while the group is more or less stationary; and thus, the energy of the s-wave is converted to mass. Everything in our universe consists of s-waves and p-waves; every force in our universe results from exchange of momentum between s-waves and p-waves.

Full circle

Each species of particle is a strange attractor. Quarks are one class of strange attractors. Leptons, meson, and bosons are in another class. Roughly five orders of magnitude larger in scale, you get atoms and molecules. Another five orders of magnitude larger, you get microbial life. At each level of complexity, the smaller attractors group to form more complex attractors. Larger still, you get planets, solar systems, galaxies and the cosmic foam. Then the whole sequence repeats in the next universe.