So what would be the behavior of the universe if space was in fact quantized? How would it differ from a universe in which the three dimensions of space were a continuum?and then proceeded to describe a single quantum of space, a minimal volume. In particular, I asserted that there is no such thing as a singularity: there is a maximum energy that can fit in a minimal volume. I further postulated that these quanta of space are exclusionary: no two quanta of space could occupy the same volume.
These quanta of space would not be reacting to the whole universe. Each quanta of space would only interact with its immediate neighbors. In three dimensions of space, each could have a maximum of twelve immediate neighbors - but only if they are packed together as tightly as possible. In that special case, these quanta of space would be lined up in neat rows familiar to anyone who has seen a stack of oranges or cannonballs.
Before I go further: I keep using the phrase "quanta of space" over and over. I want to include the term "space" to differentiate it from the word "spacetime", which I will cover later. However, "quanta of space", while accurate, is unwieldy to write (and read) over and over. Therefore I will substitute another term which means the same thing, and use iota instead henceforth. The plural of iota is iotas.
This fully-packed arrangement of iotas is very low entropy. If any one iota is even just slightly out of place, the arrangement loses symmetry, and several iotas will have eleven neighbors instead of twelve.
In a fully packed arrangement, the volume of space inside the iotas accounts for just under 75% of the total volume. In this arrangement, each iota is constrained in place by its neighbors. Less-full packings of spheres which still constrain each sphere in all directions can cover as little as 65% of the available volume.
These less-full arrangements are also low-entropy in a different way than the fully-packed arrangement. In the less-full arrangement, if one iota is even slightly out of place, then that can open up enough contiguous volume that a new iota can fit inside the pack.
So to the properties of a single iota that I outlined above, add this new postulate: if enough contiguous volume becomes available between iotas for one Planck time, a new iota will be incorporated into the universe at that location.
We know our universe is expanding. If the above postulate is right, then it means that new iota are being incorporated into the universe all the time, everywhere. However, they are not being incorporated into the universe at the same rate everywhere. Volumes where the iota are tightly packed would incorporate new iota at a slower rate than volumes where they are more loosely-packed. In fact, as long as a region of space remained fully-packed with iota, new iota could not be incorporated at all.
Let's imagine the universe at the moment of the Big Bang if space is quantized. All of the mass/energy of the whole universe, all 10^53 kg of it, would be packed into about 10^61 or so iota in a fully-packed cluster about 10^-20 m across. To any iota inside that cluster, there would be an indeterminate period of time where absolutely nothing happened. No energy could move from one iota to any of its neighbors, because each is already as full as it can get, and none of them can move because they are all completely constrained in position by their neighbors. Any iota on the periphery of that cluster that was not completely full of energy would not be able to move any energy to any of its neighbors inside the cluster, as they are already full, nor could they move energy to any empty neighbors outside the cluster either, as it is in the ultimate gravitational crunch. Neither are any iota further out interacting in any way with the cluster, as all the energy available for any interaction is already inside the cluster.
To any iota, the only other things that exist are its neighbors. To those iota inside the cluster, there are only identical full neighbors; from the point of view of each of those iotas, each one can legitimately be considered the center of the universe; there's no way to tell, and no differences between any of these iotas. For those on the periphery, there are only those neighbors with energy. Any iota outside that periphery cannot interact with anything inside (no information can ever pass from them to the inside as there is none available outside), so from the point of view of the cluster those exterior iotas are irrelevant and may as well not exist at all.
This arrangement of all the mass/energy in the universe in a tiny cluster of iotas is simultaneously stable and low-entropy. It is stable because there would be no way to observe the passage of time; nothing would change. The only way it becomes unstable in any way is if there is some intrinsic property of iotas causing them to jiggle and jostle with their neighbors at a scale smaller than the iotas themselves, which in turn causes the very unlikely event that enough volume opens up between iotas for one Planck time for a new iota to be incorporated into the cluster.
Although that event is extremely unlikely under those conditions, once it does happen after an indeterminate time, everything changes. The new iota is empty of energy, and does not necessarily have 12 neighbors. With its incorporation into the universe, symmetry is broken, energy can flow from its neighbors into the new iota, and the iotas are not as fully constrained. This opens up new gaps into which more new iotas can be incorporated into the universe. This becomes a runaway process as the symmetry breaks all over the entire cluster of iotas. Bang.
The first new iotas to appear also happen to be the most loosely-packed of all the iotas in the cluster. It thus becomes easier for new iotas to be incorporated into the universe close to where the original symmetry-breaking iotas appeared. These would be the start of the great voids which dominate most of the volume of the universe. However, this incorporation process was happening all over the entire cluster the moment the symmetry was broken.
This symmetry breaking was not an information signal, limited to the speed of light. It wasn't like the new iota shoved the old iotas out of the way and the shove was transferred from iota to iota. The iotas were already full of energy, and no information could pass from one full iota to another full iota. Instead, the shape of the universe itself changed. It expanded. However, for any location where no new iotas appeared, nothing changed at all. If an iota didn't get any new neighbors, then from its perspective it didn't move at all, even as the universe as a whole expanded. The universe couldn't collapse back on itself because it was no longer tightly packed and new iota were being incorporated too quickly, everywhere in all directions. The less tightly-packed it became, the faster new iota could be incorporated. It is this period of time in the early universe that Alan Guth called Inflation.
One of the main ideas of the Big Bang theory is that the universe started out as a single point. I am arguing that there is no such thing as a singularity, and as a result the universe started as a small object of roughly spherical shape about 10^-20 meters across. Guth proposed Inflation as a way to get around having gravity immediately slamming the universe back into a singularity immediately after the Big Bang.
Using R=cT as a formula for the radius of the universe, with c the speed of light and T the age of the universe, and V=(pi/3)*R^3, it is easy to see that a doubling in the age of the universe means an increase in the number of iota by a factor of 8; as the universe doubles in age, for every iota at the start there are seven more at the end. The roughly 10^61 iotas present at the moment of the Big Bang would have become roughly 10^62 iotas one Planck time later. Expressed in Planck times, the universe is roughly 8x10^60 Planck times old; that's only 202 doublings in age since the first Planck time. The inflation at the start does not require a new force, just the available gaps between now no-longer-aligned iota.
Under this scenario, it is possible to have a cyclic universe; a Big Crunch would, after some indeterminable passage of time, eventually become a Big Bang.
This idea also implies that the Big Bang was not a singular event 13.8 billion years ago or so. Instead, the Big Bang is a continuous process, occurring even now, still incorporating new iotas into iota-sized gaps in the volume of the universe. As the universe expands, if an iota does not acquire a new neighbor than from its perspective it has not moved at all. If it does get a new neighbor, there is no way for that iota to tell if the neighbor is new to the universe or if one of its old neighbors shifted position slightly, and again from that iota's perspective it has not itself moved at all. The expansion of the universe thus does not require energy. We have been calling this process Dark Energy, but it is the ultimate free lunch.
A new iota is empty. It has no mass. It only defines a volume that had not been defined by prior iota. It is only the pre-existing iotas which can contain energy. And since the new iotas are being produced more quickly in volumes where they are not packed as tightly, it is clear that iotas will be most tightly packed around iotas which contain mass/energy. This is what we observe as the warping of space by mass.
Which brings me to a possible test for the idea of quantized space. The red-shift of light from distant galaxies depends on their radial velocity relative to the observer (us). This follows a fairly predictable relationship, with the most distant galaxies moving away from us the fastest. It works out to about 70 kilometers per second of relative velocity per megaparsec of distance (about 3.26 million light years). That value is the Hubble Constant.
Most of the volume of the universe is great voids. These can be thought of sort of like the bubbles in a bubble bath. The soapy film that marks the boundaries of the bubbles would be galaxies. Where four bubbles meet, you have the highest concentration of galaxies, but where only three bubbles meet the galaxies form long strings. And it is these long strings of galaxies that could provide the test of the theory. We can measure the velocities of these galaxies relative to us by looking at their red shift. What we need to calculate is the velocities of these galaxies relative to each other and see if they too follow that 70km/sMPc rule.
If space is quantized and volumes where iota are loosely packed gain new iotas more quickly than more densely packed volumes, then the great voids should be expanding faster than the rest of the universe as a whole. If so, then the long strings of galaxies where three voids meet should exhibit a much higher velocity relative to each other than the Hubble rule would dictate. If that is the case, then the Great Attractor may not be an attractor at all, but a consequence of new iotas being produced faster in voids than in galaxies, so that space would appear to be expanding faster in one direction than another for our local group of galaxies.
To be continued in part 3.
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