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 [7]
As we warm up to this idea, let’s consider the fundamental properties of a quantized structure. First we will note that if the medium of spacetime is composed of quantized entities, then it will appear continuous and smooth from large scales, but it will reveal an atomic structure on the scales approaching the size of the individual quanta that make it up. The combined interactions of these quanta are observed macroscopically as an average. It is this averaging process that produces the familiar continuous image of spacetime that we experience.
Averages are useful for describing many effects, but by design, they dissolve the underlying details of the entity we mean to understand. Therefore, our familiar image of spacetime, the result of an averaging process, is incapable of expressing the details of the fundamental entity, which constructs the dimensions of our reality.
To make this clearer, let’s consider the medium of air, which has approximately 1025 molecules per cubic meter. When we describe a macroscopic property of such a medium, such as airflow, our description involves a great deal of averaging and approximating. As a result, we should expect that any mathematical equation charged with relating a macroscopic description of a system to us, like aerodynamics, would inherently be incapable of portraying the more fundamental physical laws that govern the makeup and interactions of the individual particles of which that description (airflow) ultimately depends upon. The equations of aerodynamics are therefore only capable of giving us a very limited understanding of the medium they relate to. [8] What does this mean? It means that in a very real way quantum mechanics may be more akin to thermodynamics (the study of macroscopic properties that emerge from particulate systems) in the sense that it describes physical reality in an averaged state, rather than on a deeper, more detailed level.
In addition to the descriptive dilution that occurs from the averaging process, there is a fundamental difference between the definition of position and distance that develops as we move from a continuous to a quantized fabric of spacetime. We will discuss this difference in greater detail in Chapter 6, but for now it will suffice to say that when space itself is quantized, spatial locations can be no more precise than the scale of the individual quanta. A consequence of this is that precisely mapped distances between two positions are ever-changing in magnitude and orientation because the quanta that define those positions are always in motion and shuffling about.
There are many modern discoveries that can be considered evidence that spacetime is composed of elemental, discrete parts. We are going to discuss some of those discoveries. If you have no problem with the conjecture that spacetime is quantized then you could skip past the following discussion, to the end of this chapter, without losing continuity. If, however, you would like to be introduced to some of the evidence that supports this claim before you dive into the framework that stems from it, then the following discussion should provide an adequate introduction. All of the discoveries about to be discussed will be examined in further detail once we have explored our new model.
A handful of supportive evidence comes from the following discoveries:
- The universe is nonlocal.
- The uncertainty principle dominates the microscopic realm.
- Early on, the cosmos as a whole underwent phase transitions.
- Quantized spacetime resolves the blackbody ultraviolet catastrophe.
- Matter is ultimately composed of discrete quantum values.
- The entropy of a black hole is proportional to the area of its event horizon.
- Black holes exist (which requires discontinuity in the fabric of spacetime).
- There is an overabundance of ultrahigh-energy cosmic rays reaching the Earth.
There are many more discoveries that are supportive of our claim, but this is more than enough to get us started. Let’s examine each of the discoveries and discuss exactly how they are suggestive of a quantized fabric of spacetime.
The first piece of evidence from our list comes from the fact that the universe possesses a nonlocal quality. In a local universe all mapped positions are static and objects can only directly affect things that are next to them. More specifically, the time it takes for something to affect anything spatially separate from it is limited by the speed of light. In a universe ruled by locality nothing can instantaneously affect something else that is spatially distant from it. That’s the sort of thing that we might expect but surprisingly we have observed that, on the microscopic scales, our universe does not behave in this manner. In fact, as we approach the Planck scale our universe becomes entirely nonlocal!
To understand how a nonlocal universe implies a molecular structure for its fabric, let’s imagine water at the molecular scale, and then define a sense of distance by the number of water molecules between two points (molecules). Since the molecules are actively moving around we will observe that our defined distance between any two points (two molecules that we arbitrarily selected) does not remain constant. The number of molecules between the two molecules we chose will change from moment to moment. Since we have defined the distance between our two molecules as a discrete sum of the other molecules that are positioned between our arbitrarily chosen points, or locations of interest, the distance between those locations will be found to spontaneously jump between whole number multiples of the distance value assigned to one water molecule. This is how comparisons are made in discrete manifold systems – overriding the need to perform comparison through arbitrary measurement. Also, since position can only be defined at each water molecule, the very notion of motion takes on a discrete character.
From interaction to interaction, all of the constituents making up the medium shift their relative orientation, making this model an example of a nonlocal map. Because the map is defined by interacting quantum units, the meaning of ‘next to you’ loses its consistency near the quantum scale – because position itself is defined by the arrangements of the molecules. Therefore, the observation that our universe is nonlocal directly infers that the medium of spacetime is quantized.
In further support of this, we have the foundational principle of quantum mechanics called the uncertainty principle. This principle points out that uncertainty in space and time is always present, but it becomes significant only on the microscopic scales. In a nonlocal universe this is exactly what we would expect. On quantum scales the individual pixels of Nature’s picture 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) become astounding and confusing. But, if our map portrays a quantized structure, then all of those effects become inherent necessities with simple explanations. What this means is that the quantization of spacetime produces a map of Nature that automatically demystifies the quantum world and eliminates the absurdities within it.
Our next clue that spacetime is quantized comes from the realization that the cosmos as a whole can undergo phase transitions. Cosmological theories invoke phase transitions, and their associated increase in symmetry and entropy, in their models of the early universe. Although it is not always recognized, these phase transitions are indicative of a molecular, or quantized, medium. To explore why, let’s consider the phase transitions of water.
Water can go through phase transitions from ice to water to steam (Figure 4-1). Yet all three phases share the same molecular composition — H2O. [9] The phase of water that possesses the least entropy (the least disorder) and the least symmetry is ice. 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
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Liquid – Water
Positive ends tend to |
Gas – Steam
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No preferential alignment Figure 4-1 The phases of H2O.
It follows that if the universe 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. This is the case because phase transitions are always associated with molecular or atomic arrangements. In addition to this we find 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 the empty space of that region 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
The blackbody ultraviolet catastrophe also argues for a quantized structure underlying spacetime. A blackbody is an idealized object that absorbs all incoming light without reflecting it. As it continues to absorb light it heats up and 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 smooth on all scales and therefore produces a continuous spectrum of allowed values of energy in light). Such calculations predict a far greater contribution to the blackbody radiation in the shorter wavelengths (higher energies like ultraviolet) than is actually observed (Figure 4-2).
Figure 4-2 Black Body Radiation and the Black Body Catastrophe.
What we see is that the very short wavelengths contribute less than we expect, 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 a quantized spacetime structure, 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)
“…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 [10]
Max Planck effectively quantized the effects of spacetime (at least mathematically) 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. Unfortunately, Planck believed that this quantization was some sort of a mathematical trick necessary to produce results in agreement with observation, rather than a real property of light or spacetime. It wasn’t until Einstein’s remarkable year that quanta became known as real physical entities instead of mathematical abstractions. [11]
Since then, modern theories have routinely needed to evoke Planck’s constant to describe the properties of spacetime on the microscopic scales because the microscopic realm simply turns out to be partitioned into discrete units. For example, the spin of elementary particles comes in multiples of a specific fixed quantity (1/2h). [12] Electric charge (e) sums as integer values of 1.6021765814 Coulombs, which is equal to жħ/lp Ap μ0 , [13] magnetic flux (Φ) comes in quantum multiples of 2.0678337218 x 10-13 Webers, (which is equal to ħπ/e), conductance (G0) comes in quantum multiples of 7.74809173326 x 10-5 S (which is equal to e2/πħ , the magnetic moment (μB) comes in quantum multiples of 9.2740094980 x 10-24 A/m2 , (which is equal to multiples of eħ/2me), and, of course, the j and m of angular momentum, and the energy eigenstates for atomic harmonic oscillations also exist as discrete quantum values in Nature.
All of these clues echo the need to reveal a quantized structure underlying the smooth appearance of familiar spacetime. There are many more clues suggestive of this. For example, Jacob Bekenstein and Stephen Hawking discovered that the entropy of a black hole is proportional to the area of its event horizon. This tells us something about the parameters of spacetime itself since the maximum entropy a region of space can possess is equal to the entropy contained within a black hole of that size. Familiar objects, both macroscopic and in relatively flat spacetime, possess entropy bounds in proportion to their volume. But extremely curved regions like black holes or single quanta of space (both of which are pure expressions of space) have entropy that is proportional to their surface area. Specifically, their entropy equals their surface area, in multiples of the Planck area, divided by 4 and multiplied by the Boltzmann constant. (The Boltzmann constant (k) is used in descriptions of particulate systems like gasses.) Therefore, a black hole’s entropy can be visualized as the number of discrete Planck areas that can be arranged on the surface of its event horizon. We will discuss black holes and their entropy in greater detail in Chapter 15.
This suggests that there is in fact a minimum discrete unit of space, and that each fundamental unit carries a single unit of entropy. It follows that from the perspective of spacetime nothing, even in principle, [14] can occur within one of these quanta because any such evolution would support an increase in entropy, which would in turn require that the entropy of a black hole exceed the maximum limit of entropy in any region of space. This evoked minimum discrete size for the constituents of space is the reason that black holes have fixed entropies proportional to their surface areas, and not volume-proportional or infinite entropies. Also, since this entropy bound dictates a discrete minimum unit of space, it infers that the number of constituents within a black hole of a given size is finite.
Therefore, a black hole must be composed of a finite number of parts, and that total number of parts must be less than the number of constituents that we would expect from volume-proportional entropy. Consequently, the entropy bound discovered by Bekenstein and Hawking in the 1970s suggest that our universe is composed of elemental discrete entities. [15] Looking closely at black holes we find that this is not really all that surprising. In general, black holes represent a severe conflict with the very notion of continuous space. If space and time were smooth and continuous then no matter what scale we considered them on they would retain the exact same identity and structure. The existence of just a single singularity demands discontinuity in the fabric of spacetime. It follows that if there are rips in the fabric of spacetime at any level, then that fabric can no longer be accurately described as fundamentally smooth and continuous.
This means that the mere existence of black holes is suggestive of a spacetime that is composed of discrete quantum entities. Such a condition would require spacetime to behave like a fluid on macroscopic scales, which 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)
The last piece of evidence from our list centers on the overabundance of ultrahigh-energy cosmic rays that we receive on Earth. 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 a ‘graininess’ would ease the passage of high-energy particles. (Kunzig 2004, 60)
In other words, 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) In the end, this heightened sensitivity would alter the journey of these photons as they propagate across the universe by effectively reducing the amount of space they interact with during that trek. Another way to say this is that these perturbations effectively 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 because 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.
By themselves any of these arguments should be compelling enough to warrant a thorough investigation of spacetime’s potential quantum structure, but when we consider all these arguments together (and by no means have we considered them all) the case for the quantized nature of spacetime stands very strong. With this footing, we shall now begin our construction of a model of physical reality that takes into account spacetime’s quantized structure. [16]
What we are about to do is unique. All past models have failed to propose the literal physical quantization of the fabric of spacetime but rather a metaphorical or mathematical one. As a result, none of them have achieved the ability to extend themselves into visually comprehensive maps – they offered no intuitive connection. Because of this they have existed in mathematical form alone, and consequently do not allow us access to Nature’s deepest secrets.
This is why we are motivated to introduce quantum space theory (qst). It lets us do what so many have said is impossible by showing us physical reality in eleven dimensions. It allows us to complete Einstein’s work by attacking the problem with the same style that guided him to a deeper understanding of Nature. Einstein took the first step by atomizing the world of matter. Now it is up to us to take the next step by quantizing spacetime.
“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.” (Isaacson 2007, ??)
It is time for us to take that final step, to finish Einstein’s work, and to visualize how Nature appears in higher dimensions. So, if you were taught that visualizing more than three dimensions 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,” [17] to our sensory experience. Through this we shall gain the potential to discover Nature’s complete form.
“There lies the high adventure for later generations, often mourned as no longer available. There lies great opportunity.”
E. O. Wilson [18]
From the forthcoming book:
Einstein’s Intuition
by Thad Roberts
Represented by
Sam Fleishman
Literary Artists Representatives
New York, New York
NOTES:
[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] Jan Ambjørn, Jerzy Jurkiewicz and Renate Loll, ‘The Self-Organizing Quantum Universe,’ Scientific American July 2008, pp. 42-49.
[8] Here I find it interesting to examine the Latin derived word ‘surd’ which is defined as a ‘fundamental unit, indivisible,’ in relation to the word ‘absurd’ which is defined as ‘the quality or condition of existing in a meaningless or irrational world.’ This seems to be suggestive that a rational world must be built from fundamental, indivisible units — otherwise an absurdity develops – and I find this to be a very interesting development within the English language. It seems to mimic some of the old Pythagorean claims, which might have more to do with reality than history has thus far recorded.
[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] ‘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.
[11] 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.
[12] This is also equal to multiples of π/ħ.
[13] (ж) is a unitless number equal to 3.02822121 x 10 -1 . See chapter 16.
[14] In relation to the familiar four dimensions of spacetime (x, y, z and t).
[15] See also: James Owen Weatherall, ‘The Tabletop Universe,’ Popular Science, May 2008, pp. 72-76.
[16] It is important to point out that formulating a model that mathematically incorporates quantization is not in and of itself groundbreaking. Coming up with a visual model capable of physically doing this is what is groundbreaking. Some examples of theories that mathematically address quantization can be found in Appendix A.
[17] 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.
[18] E. O. Wilson, Consilience, p. 295.