Section 2: The Sands of Space and Time
“No great discovery was ever made without a bold guess.”
By conjecturing that the vacuum is quantized I mean to assume that the medium of spacetime is a collection of quantized parts – that it is a fluid medium composed of discrete, separate pieces at its fundamental scale. In a very practical way, this suggests that spacetime is like the medium of air, which is made up of an enormous number of identical interactive particulates that move about within a deeper setting. The pieces of spacetime, which we will call quanta, are “the primordial substratum, underlying our macroscopic spacetime picture.” 
An immediate consequence of the claim that the vacuum is quantized is that the vacuum loses its ability to function as a background. In other words, if spacetime is quantized, then it cannot be the ultimate background of physical reality. By assuming that the vacuum is a medium composed of constituents that are situated in, and move through, dimensions that are not part of the x, y, z metric, we necessitate the conclusion that additional variables (additional dimensions) are physically real.
Some people find the possibility that there are real spatial dimensions in addition to x, y, z to be so radical that they dismiss it outright — in spite of the vast collection of experimental and empirical evidence that points us in that direction. Such a response is understandable, and expected, but it may also be premature and inappropriate. If we never seriously explored new perspectives, if we always allowed common experience to frame our worldview, then we would still be modeling air and water as we experience them — as continuous media instead of as collections of molecules. A model that attempted to explain all media (air, water, wood, etc.) as continuous would be far more complicated than a molecular one, and its explanatory power would severely suffer. By allowing for the existence of atoms, our model of physical reality becomes far more coherent, simple, and intuitive.
It is important that we understand the significance of this point. Although we never directly experience atoms with our senses, we believe they physically exist because their existence enables us to explain a vast array of mysterious natural phenomena. The explanatory power that comes from the assumption that the world is made of atoms is absolutely staggering. Those explanations allow us to understand: crystalline structures, nuclear fusion in the sun, friction, heat, color, chemical reactions of all sorts — like the ones that control our digestion — why the sky is blue, why Uncle Billy’s Magic Fire Dust turns flames green, how fast a receding galaxy is moving away from us, and on and on.
A beautiful, elegant model that is accessible to our intuition connects all of these phenomena, but the model itself relies on the assumption that the world is made of atoms. Once we make that assumption we find that a simple model emerges with the ability to explain a truly enormous number of natural properties and interactions. This is why several luminaries have claimed that the most important scientific idea to date is that the world is made of atoms.
“If in some cataclysm, all of scientific knowledge were to be destroyed, and only one sentence passed on to the next generation of creatures, what statement would contain the most information in the fewest words? I believe it is…that all things are made of atoms.”
Richard Feynman 
Today most of us have no difficulty comprehending atoms because we allow for the existence of a deeper background (spacetime) behind material media. After all, it is this intuitive framework that allows us to rationalize how it is that we can pass from one medium (like air) to the next (for example water) without having to reformulate our picture of reality. We simply allow the deeper medium to remain the background and we break up the respective foreground media into quantized collections that move about within that background. We imagine all the foreground media as collections of small, quantized parts, that is, atoms, molecules, etc. that move about in spacetime.
The switch to a quantized persepctive has two significant effects. First, it allows us to simplify our picture of Nature as it applies to our experiences. Second, it enables us to explain a vast range of phenomena indicative of the quantized medium, which are not necessarily linked to our common experiences. This consequently strengthens our confidence in that model.
Applying this to the medium of air, we find that high-pressure and low-pressure variances simply translate into changing densities of air molecules within the background of spacetime. (Note that if we modeled air as continuous, then we would have to introduce some sort of magical curvature tensor just to model those changes in pressure.) Temperature becomes an expression of how energetically the molecules are moving about on average, and wind becomes the net result of the collective motions of those molecules as they undergo the process of equalization from high-pressure regions toward low-pressure regions.
On the deeper level, a quantized depiction of air provides us with an explanation of its less intuitive properties, like its optical absorption and dispersion patterns (explaining, among other things, why the sky is blue), its chemical reactivity, the dynamical mechanics behind its phase transitions, and so on. Quantized models give us access to two levels of description. One level describes the macroscopic properties of the medium — pressure, density, temperature, and so on, and the other describes the microscopic, or the properties of the individual atoms or molecules that make up the medium and how they interact with each other. Both of these parts stem from the same intuitive quantized picture.
Because we are going to carry the ‘atomic idea’ further than anyone has before, it is important for us to understand that the simplification that emerges when we express different media of matter (air, water, wood, metal, etc.) as constructs of atoms, is a strong argument that those atoms physically exist in Nature. In general, this is how we test the validity of an assumption we make about the world. If a model grows out of a particular assumption and inherently explains physical reality in a more complete yet simplistic way, then the idea is to be taken seriously. As we have seen, one of the most valuable ideas ever postulated was that the world is made of atoms. In this book we are going to take that idea and extend it one step further. We are going to postulate that literally all media are composed of ‘atoms’ — discreet, quantized, interactive parts. Specifically, we are going to add spacetime (the vacuum) to our list of quantized media.
To determine whether or not this extension carries our intellectual quest in the right direction, we will have to study the model of physical reality that stems from it and check to see if that model connects an array of seemingly separate phenomena in Nature, simplifies our description of those phenomena, and gives us a way to extend our intuition deeper into the heart of physical reality’s divine form. Ultimately we are looking for an intuitive picture that unites general relativity and quantum mechanics while revealing the origins of Nature’s deepest secrets: the uncertainty principle, wormholes, dark energy, the cause of the Big Bang, what black holes are like on the inside, how the constants of Nature were determined, etc. We are looking for ontological access to these mysteries. If the framework that grows out of our new assumption does not grant us this access, then it will be appropriate to dismiss the quantization claim altogether. But if a simplistic, encapsulating framework does emerge, and if it gives us an intuitive understanding of those phenomena, then we will gain confidence in the idea that spacetime is quantized.
When Islamic philosophers historically debated the possibility of an underlying atomic structure for space and time they envisioned atomic space to be something like a chessboard with no “interstitial voids” between the atoms of space. This atomic model was incapable of even approximating the Pythagorean theorem, which was esteemed as “the best attested theorem in mathematics,” which led them to reject atomism.
According to chessboard atomism the length of the inscribed hypotenuse must be equal to the number of atoms (cells) that sum down the diagonal of the triangle (4). But according to the Pythagorean theorem that length should be the square root of the sum of the two shorter sides squared. (Figure 4-1) This incompatibility is an artifact of the chessboard atomic model.
The situation changes, however, when quantization is understood to mean that the vacuum is a medium composed of quanta that are dispersed throughout a superspatial background. This dispersion allows the Pythagorean theorem to be regained as a macroscopic identity, in the absence of density gradients (curvature).
Figure 4-1 Islamic chessboard atomism vs. a proposal with interstitial voids.