Chapter 4

Section 3: The Case for Quanta


“The holy grail… is the prediction of observable consequences derived from the microscopic quantum structure.”

Jan Ambjørn [8]


As we warm up to the idea of vacuum quantization, let’s recall that a quantized medium appears continuous and smooth from large scales, and that it best reveals its atomic properties on scales that approach the size of its constituents. A macroscopic projection of a continuous medium is created when the combined interactions of those constituents are interpreted through an averaging process.

Averages are useful for describing many effects, but by design, they dissolve the underlying details from which they rise. When averages are interpreted as macroscopic emergent properties they can be very convenient tools. But when they are mistaken as representative of the system’s fundamental character, conceptual difficulties are imported. A model that mistakes emergent macroscopic properties for fundamental ones abandons a deterministic evolution for one that can at best be understood as statistical. If the mistake isn’t noticed, then it will lead to the claim that the stochastic elements of that evolution represent something real in Nature.

If spacetime is quantized, then we should expect our familiar image of it, an image that has been distorted by an averaging process, to be incapable of accounting for characteristics that directly depend upon the system’s underlying quantized structure (like the arrangements of the quanta – its specific state). Beneath that averaged over picture is a lower level description in which each constituent of the quantized vacuum has an associated velocity vector that denotes how it is moving about in the superspatial void at a given instant. We can take an ensemble of those constituents, average over their vectors and represent the combined tendency of that region with a state vector $latex |\psi\rangle$. But if we make the mistake of using that average as a fundamental descriptor, instead of seeing it as an emergent property, we end up with a vague theory that is subject to a wide variety of equally valid and nebulous interpretations. The possibility that modern quantum physicsists have made this very mistake strongly motivates our investigation of vacuum quantization.

Several other quirks of Nature lead us down the road of vacuum quantization. For example, the discovery that the universe does not conform to local realism opens the door to additional variables, which can be accounted for by the additional dimensions necessitated by a quantized vacuum. Local realism combines the expectations of locality and realism.

Locality is a very general and basic concept in physics that predates both Galilean and Einstein’s relativity. It encodes the idea that the mutual influence of events decreases when their distance incresases; that the mutual influence of events directly depends upon their spatial seperation. This purely spatial notion (no time is needed) is one of the foundations of all experimental sciences. (Laloë p. 52)

Realism is the view that the world described by science represents the real world in a mind-independent way. A scientist might believe that the formalism of quantum mechanics directly represents reality, that it tells us something about what is out there and gives us real insight into reality, or a scientist might believe that the current quantum formalism provides a blurred representation of Nature and that a deeper level more accurate description exists beneath it. Either way, a realist holds to the idea that the model describes reality on some level; that what is being described actually exists independent of our consciounsess of it.

Famously, Bell’s theorem indisputably shows that we cannot coherently assume local realism and, at the same time, that all predictions of quantum mechanics are correct. This is because a self-contradiction arises when we try to simultaneously hold to those assumptions. This conclusion stands independent of any experimental result, which means that it is a purely logical conclusion. (Ibid p. 64) (We will discuss Bell’s theorem at length in Chapter 12.)

Because the predictions of quantum mechanics have stood up against the most intricate examinations experimentalists have been able to invent, the conclusion drawn from Bell’s theorem is that Nature does not cohere to the rules of local realism. It obeys laws that are non-local, non-realist, or both. If Nature is non-realist, if our physics theories fail to map it at all, then the question remains – why do we get our predictions right? On the other hand, if Nature is non-local, then additional “elements of reality” are necessitated in order to restore realism and explain the success of our predictions. (I refer here to the EPR (Einstein-Podolsky-Rosen) ‘elements of reality,’ also known as ‘additional variables’ and sometimes misleadingly called ‘hidden variables’).

Here it become useful to recognize that the idea that nonlocal events occur in Nature is compatible with the idea that the medium of spacetime is quantized. Furthermore, vacuum quantization paves the way back to realism because it allows us to get structure beneath a smooth, averaged over, notion of the vacuum. If the vacuum is made up of parts that are mixing about, then mutual influence of events will not directly depend upon their spatial seperation. Locality will not strictly hold in the vacuum. Non-local characteristics will manifest with a dependence on resolution, showing up less and less on larger scales. And the mixing that gives rise to non-locality will be deterministically driven on a deeper level.

Going further we note that manifestations of the uncertainty principle are also compatible with a quantized vacuum. According to this principle, uncertainty in space or time is always present, and becomes more and more significant on the microscopic scales. Within a quantized vacuum this is exactly what we would expect. On quantum scales the individual pixels of Nature have dramatic effects but, like the image of a TV screen, as we zoom out from the pixilated image, individual contributions lose their potency to the average. If it is assumed that the average is a fundamental representation of the map, then effects that originate from the internal quantized structure (such as quantum jitters, quantum tunneling, and quantum entanglement) manifest as astounding and confusing. However, if we are aware of the vacuum’s quantized structure, then those effects transform into expectations.

Another hint that the vacuum is quantized can be taken from cosmological descriptions of the early universe, most famously the inflationary Big Bang model, which invoke a description of spacetime that includes phase transitions and their associated increase in symmetry and entropy. Whenever a medium is capable of undergoing a phase transition it suggests that it is atomic, molecular, or in general quantized.

For instance, consider the phase transitions of H2O. A collection of H2O molecules can undergo phase transitions transforming into ice, water, or steam. (Figure 4-2) All three phases share the same molecular composition — H2O[9] Out of these phases ice possesses the least entropy (the least disorder) and the least symmetry. The molecules of H2O inside the ice crystals are arranged in an ordered hexagonal lattice. This fixed arrangement means that the overall pattern of molecules retains its appearance only by rotations of multiples of 60 degrees. This limit on rotational symmetry means that the ice lattice has low symmetry and low entropy.

As the ice melts the molecules of water rearrange into a jumble of uniform clumps. In this state, rotating the system in any direction does not change the overall symmetry. Therefore, by melting the ice into water the system has gained symmetry and entropy. As water transitions into steam, the clumps of H2O, which tend to be arranged with the oxygen side of one molecule facing the hydrogen side of another, break up into completely random orientations. Again, this phase transition is accompanied with an increase in entropy and symmetry.

Solid – Ice

Liquid – Water

Positive ends tend to
line up with negative.

Gas – Steam

No preferential alignment
between molecules and less densely packed.

Figure 4-1 The phases of H2O.

It follows that if the vacuum is composed of quantum units, then the phase transitions it underwent early on can be explained as changes in the arrangements and associations of those quanta. Therefore, the data that suggests the universe, as a whole, has undergone phase transitions inadvertently supports a framework wherein spacetime is a medium composed of discrete quanta. Phase transitions have a natural association with molecular or atomic arrangements. Additional support of this comes from the discovery that the quantum mechanical description for regions of space, called fields, respond to temperature changes just as ordinary matter does. If we increase the temperature of a region of space, we find that the amplitude of the field undulations within that region of empty space increases in the same manner that the atomic motions of a gas increases when heated.


“The universe as a whole acts somewhat like a gas.”

Neil DeGrasse Tyson [10] 

Another quirk of nature that points towards the possibility of a quantized vacuum is known as the blackbody ultraviolet catastrophe. A blackbody is an idealized object that absorbs all incoming light without reflecting it, heats up, and then begins to emit light. The character of the light it emits is entirely dependent upon its temperature. The ‘catastrophe’ comes from a conflict with observation that arises when one calculates the amplitude of expected emission for the wavelength spectrum (assuming that spacetime is smoothly connected on all scales and therefore allows a continuous spectrum for energy). Such calculations predict a far greater contribution to the blackbody radiation in the shorter wavelengths (higher energies like ultraviolet) than is actually observed. (Figure 4-3)


Graph of black body radiation and the ultraviolet catastrophe

Figure 4-3 Black Body Radiation and the Black Body Catastrophe.


Very short wavelengths contribute less than expected, that is red contributes more than blue, which is why fires are commonly more red than blue. The most important thing to note about all of this is that if we recalculate blackbody radiation allowing for quantization (of light’s substrate – spacetime), then the discrepancy vanishes. When we do this the ultraviolet catastrophe is automatically resolved because only certain wavelengths (colors) are allowed. This restriction explains why hot objects radiate as they do. When a blackbody is heated, the first visible color it radiates is red because the energy packets of red light are the smallest energy packets in the visible light spectrum. With more heat, higher-energy colors (shorter wavelengths) can be emitted as the discrete (quantized) value of energy for each successive color is reached. (Zukav 1980, 50-51)

Max Planck took a step quite similar to this when he suggested that light could only be delivered in quantized units. This fundamental unit, now called Planck’s constant h, restricts the possible values for the frequency of light to whole number multiples (1hf, 2hf, 3hf, 4hf, 5hf…). Intermediate values of that energy, according to Planck, cannot occur. This is exactly what we would expect if we started from the assumption that space is quantized.

“…the hypothesis of quanta has led to the idea that there are changes in Nature which do not occur continuously but in explosive manner.”

Max Planck [11]


Unfortunately, Planck believed that the quantization inherent in his math was some sort of mathematical trick necessary to produce results in agreement with observation. He didn’t see it as representing a real property of light or the substrate it propagates through. It wasn’t until Einstein’s remarkable year that light quanta became thought of as real physical entities instead of mathematical abstractions. [12] And it wasn’t until now that the quantization of light was explained in terms of the vacuum’s quantum structure.

There are other reasons to doubt the continuity of space. Black holes represent a severe conflict with the notion of continuous space. The existence of just a single singularity demands discontinuity in the fabric of spacetime. In other words, if there are rips in the fabric of spacetime at any level, then that fabric can no longer be accurately described as smooth and continuous everywhere. The existence of black holes is, however, compatible with the idea that the vacuum is a medium that behaves like a fluid on macroscopic scales. Taking this claim seriously would explains why Theodore A. Jacobson, Renaud Parentani, and their colleagues found that “the propagation of sound in an uneven fluid flow is closely analogous to the propagation of light in curved spacetime… [This] suggests that spacetime may, like a material fluid, be granular and possess a preferred frame of reference that manifests itself on fine scales…” (Jacobson and Parentani 2005, 70)

We might also note the observation that the Earth receives an overabundance of ultrahigh-energy cosmic rays. Calculations based on special relativity predict that these extremely energetic cosmic rays should only rarely reach Earth because they lose energy as they travel through space. But a Japanese observatory has seen more of these rays than the calculations (based on a continuous metric of spacetime) allow for. Theorists, such as Amelino-Camelia, think that this excess is evidence that spacetime is granular because ‘graininess’ would ease the passage of high-energy particles. (Kunzig 2004, 60)

If spacetime is quantized on the Planck scale, then it can be said that on this scale its geometry (its connectivity) fluctuates. High-energy photons, which have the shortest wavelengths, would be more sensitive to these geometric perturbations for the same reason that “a baby stroller with small wheels is more sensitive to the shape of the pavement than a Mack truck with large tires.” (Atwood, Michelson and Ritz 2007) This heightened sensitivity would alter the journey of these photons as they propagate across the universe by reducing the amount of space they interact with during that trek. Another way to say this is that these perturbations shorten the distance that high-energy photons need to travel as they speed across the galaxy to our detectors. This would explain why we see more high-energy photons than we otherwise would from distant sources – they have actually traversed less space than expected. It also explains why we see the exact number of photons that we originally expected to see in the lower-energy range (longer wavelengths) from those same sources.



Section 4: The Investigation Begins


Any of these arguments should be ontologically compelling enough to warrant a thorough investigation of the axioms we use to define spacetime’s structure, but when we consider all these arguments together (and by no means have we considered them all) the possibility that spacetime is quantized is quite intriguing. With this footing, we shall now begin our construction of a model of physical reality that takes into account spacetime’s quantized structure.[13]

What we are about to do is unique. To the best of my knowledge, all past models have failed to propose the literal physical quantization of the fabric of spacetime. Any axiomatic sets that have attempted to incorporate quantization into their metric have done so either metaphorically or merely mathematically. As a result, none of those investigations have achieved the ability to extend themselves into visually comprehensive maps and, therefore, do not offer intuitive access to Nature’s deepest secrets.

This is the motivation for introducing quantum space theory (qst). We shall now attempt to gain intuitive access to Nature’s clandestine mysteries by starting over with the axiom that the vacuum is a superfluid that is composed of quantized units. The hope is that this foundation will enable us to make sense of the conundrums of modern physics, that it will guide us toward a deeper understanding of Nature.

“If you really want to grasp the truth with both hands you have to be willing to completely let go of everything you know.”
David Cantu


“If at first, the idea is not absurd, there is no hope for it.”

Albert Einstein


In the last years of his life, Einstein proposed giving up the idea that space and time are continuous, but the imagination of his youth had faded and he was unable to visualize such a structure. In reference to this he said, “I cannot imagine how the axiomatic framework of such a physics would appear… But I hold it entirely possible that the development will lead there.” He also said, “I consider it quite possible that physics cannot be based on the field concept, that is, on continuous structures.”[14] Einstein quantized the world of matter, now it is up to us to see what happens when we extend that quantization to the vacuum itself. It is time for us to further Einstein’s work, and to visualize how Nature appears in higher dimensions.

If you were taught that visualizing more than three dimensions of space simultaneously is impossible, then note that you are about to do the impossible. We are about to discover the framework of quantum space theory and break the Euclidean limitations that have, until now, kept our intuition at bay. We are about to explore a dimensionally richer map that is capable of translating the great beyond, or as Karl Jaspers might call it, “authentic reality,” [15] to our sensory experience. We are going to set our heading towards a new isle of thought.


“There lies the high adventure for later generations, often mourned as no longer available. There lies great opportunity.”

E. O. Wilson [16]





From the forthcoming book:

Einstein’s Intuition
by Thad Roberts

Represented by
Sam Fleishman
Literary Artists Representatives
New York, New York




[1] Gary Zukav, Dancing Wu Li Masters – An Overview of the New Physics, p. 207.

[2] If you count the chirps from a single cricket during the span of 15 seconds and add 39 to the number, you will end up with a number that corresponds to the temperature in degrees Fahrenheit. For example, 33 chirps in 15 seconds plus 39 equals 72 degrees.

[3] Evidently this concoction originated from Jimmy Kirkman, the state’s paleontologist, but I’m not sure if ‘uncle Billy’ had any relation to Jimmy. Martha worked with Jimmy but we all knew him because he would participate in our digs from time to time.

[4] The sky over Grand Staircase Escalante is nearly the darkest in the country. In fact, it is hardly distinguishable from the sky that stretches over the nearby Natural Bridges National Monument, which was the first park to receive the designation of “International Dark Sky Park” from the IDA (International Dark-Sky Association). The only other park to receive this designation in the U.S. is Cherry Springs State Park in Pennsylvania. On the Bortle scale, which correlates pristinely dark skies to the number one and inner-city light polluted skies to the number nine, Natural Bridges is rated a class 2.

[5] Manfred Requardt, ‘A Geometric Renormalisation Group in Discrete Quantum Space-Time,’ arXiv : gr-qc/0110077v3 25 Mar 2003, p. 4.

[6] Richard Feynman, Lectures on Physics, Introduction; Alex Stone, “The secret Life of Atoms — Until Recently We Couldn’t Even See Them,” Discover, June 2007, p. 52.

[7] Avicenna, 1983, ‘Shifa’’, Kitab as-Sama’ at-tabi’i,’ S. Zayed (ed.) Cairo: The General Book Organization.

[8] Jan Ambjørn, Jerzy Jurkiewicz and Renate Loll, ‘The Self-Organizing Quantum Universe,’ Scientific American July 2008, pp. 42-49.

[9] Ice has as least 20 different forms. The dominant crystalline structure of ice found on Earth is called 1h (pronounced “one H”). It is a hexagonal structure in which the molecules have regular spaces between them creating a low density of 0.53 ounces per cubic inch. (A cubic inch of water weighs 0.58 ounces.) The empty space in the lattice structure of ordinary ice (1h) makes it possible to rearrange the lattice in 16 different ways corresponding to 16 different crystalline structures (1h – 16h). At temperatures colder than -36.4° F, water can take on a cubic structure 1c. There are also three principal forms of amorphous ice, which are usually found in interstellar space.

[10] Neil DeGrasse Tyson, ‘Death By Black Hole,’ p. 180.

[11] ‘Neue Bahnen de physikalischen Erkenntnis,’ 1913, trans. F. d’Albe, Phil. Mag. Vol. 28, 1914; Gary Zukav, Dancing Wu Li Masters – An Overview of the New Physics, pp. 50-51.

[12] In 1905, the year often referred to as his annus mirabilis, Einstein used what little spare time his job as a Swiss patent clerk afford him to rewrite the way humanity would see the world. He submitted his ideas to the Annalen der Physik in hopes of gaining enough recognition to earn him a teaching position. Evidently he really wanted the job. The following is his work:

– On March 17, 1905 he submitted his first paper of the year titled, “On a Heuristic Point of View Concerning the Production and Transformation of Light.” Heuristic means a hypothesis that serves as a guide and gives direction in solving a problem but is not considered proven. Today this paper is commonly referred to as his photoelectric effect paper.

– His second paper was completed on April 30, 1905, submitted to the University of Zurich on July 20, 1905, revised and then submitted to the Annalen der Physik on August 19, 1905. It wasn’t published until January of 1906. The paper was titled “A New Determination of Molecular Dimensions.” In it, Einstein assumed molecules were real physical entities and he calculated their size.

– On May 11, 1905 Einstein completed his third paper but waited until August to submit it. In this paper Einstein used Brownian motion to verify that the world is made of atoms — something that was highly debated until then.

– Einstein’s fourth paper was titled “On the Electrodynamics of Moving Bodies.” The Annalen der Physik received this paper on June 30, 1905. This landmark paper gave birth to special relativity and it forever shattered the notion of universal time.

– Almost as an after thought, Einstein wrote another paper as an addendum to the fourth. In this paper titled “Does the Inertia of a Body Depend on Its Energy Content?” Einstein penned the most famous physics equation of all time: .

(The full equation is  where λ = 1/ Ö(1- v2/c2).)

This paper was received by the Annalen der Physik on September 27, 1905. (Walter Isaacson,Einstein, p. 94, 101-105, 127, 138, 577.) (Friedrich Hasenöhrl, an Austrian physicist published the equation  a year before Einstein, but he failed to relate it to a principle of relativity.)

Although all of these ideas were groundbreaking, the one Einstein eventually received the Nobel Prize for was his paper on the photoelectric effect – not his theory of relativity. “Bitter nationalist sentiments of the post-World War I era played a role, but basically relativity proved to be too radical a concept for the Nobel committee. In eleven different years, Einstein was nominated over and over only to be rejected. One Nobel committee member wrote, ‘Einstein must never receive a Nobel Prize even if the entire world demands it.’ The world did demand it, and Einstein was awarded the 1921 Nobel Prize for his contributions to physics and for his 1905 paper on the photoelectric effect. He showed that light behaves not only as a wave but also as a stream of particles, or quanta. The committee directed Einstein not to mention relativity in his acceptance lecture. He did so anyway.” Heidi Schultz, “Nobel Efforts,” National Geographic, May 2005.

[13] Some examples of theories that mathematically address quantization in one way or another can be found in Appendix A.

[14] Abraham Pais, Subtle is the Lord, Oxford University Press, New York, 1982.

[15] See “The Way to Wisdom,” by Karl Jaspers, translated by Ralph Manheim (New Haven, Conn.: Yale University Press, 1951) Chapter IV, “The Idea of God,” pp. 39-51.

[16] E. O. Wilson, Consilience, p. 295.

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