# Chapter 1

## Section 2: Our Maps, a Brief History

Our ideas, concepts, explanations, and questions are encased within a mental framework — a picture of reality that structures our interpretation of the world around us. This framework is the foundation by which we understand physical reality and the filter by which we process our sense of self. The model, however, is not static — it evolves over time.[3] As an example of this, consider the celestial model that the Greeks used for thousands of years to explain the heavens (Figure 1-1). In the first incarnation of this model the universe was conceptualized as closed, which meant that it had a natural finite limit, and the world was believed to be flat. In this picture the outer boundary of the knowable universe was depicted as a great sphere that encircled the Earth. This sphere was understood to be the edge of the universe. All the stars in the heavens were believed to be embedded in this sphere.[4] As it rotated, this sphere would continuously drag the stars within it from the eastern horizon to the western horizon.

Figure 1-1 An early map of the heavens

This geocentric model of the universe was the map by which humans understood the heavens. It became known as the Ptolemaic model because it was popularized when Claudius Ptolemy published “Almagest” circa 150 A.D. In its first incarnation, it explained the observed daily and yearly motions of the stars, and portrayed the universe as finite and permanent. But it was not yet complete. In order to explain the observed motions of the Sun and the Moon two more celestial spheres had to be included in the model (Figure 1-2).

Figure 1-2 The three levels of heaven.

Although this change complicated the model, it was generally well accepted because the existence of three celestial levels intuitively jived with humanity’s experience of the heavens. The Sun, the Moon, and the stars each belong to their own order of brilliance, therefore, many people found it easy to accept that they also belong to their own celestial sphere. These ‘three levels of heaven’ portrayed the universe in keeping with the Ptolemaic belief, which held that circles and spheres were the geometries of the divine. This sentiment has been preserved in the texts of the great Western religions.

This tri-layered depiction of the cosmos [5] was believed to be a complete model until some curious minds pointed out that five special ‘points of light’ moved about in the heavens independent of the three celestial spheres. Although they appeared to be stars, these small lights did not remain fixed within the sphere of stars. Because of this, these lights were given the name planet (the Greek word planete means wanderer and planan means to lead astray.) The motions of these ‘planets’ were complex and difficult to describe. They drifted about the heavens, moving from constellation to constellation, and sometimes even reversed their directions. To the fastidious observer they “seemed to move of their own volition, which is perhaps why they were identified with gods.” (Stewart 2006)

The presence of these ‘gods’ meant that the celestial model needed some reconstructing. In other words, the motions of these planets (Mercury, Venus, Mars, Jupiter, and Saturn) [6] severely complicated the celestial model (Figure 1-3). In order to describe all heavenly motions the model now required seven levels (which became the seven days of the week) in addition to the original outermost sphere of stars.[7] This reconstruction presented a problem because there was no longer intuitive support for that number of levels. The heavens were no longer simple, intuitive, or what mathematicians would call ‘beautiful’. These additional levels did produce a map that enabled mankind to account for all the heavenly motions that had been observed, and this account even allowed mankind to continue seeing himself as the center of the universe, but there was still a problem. This multi-leveled map of the heavens was getting fairly ugly, Nature was getting increasingly complicated.[8]

Figure 1-3 The seven levels of heaven.

Parsimony, a foundational principle of science, encourages us to look for elegance and simplicity in our descriptions of Nature. Indeed, the well-known precept of Occam’s Razor [9] forces us to consider simplicity over complexity (all other things being equal). Such considerations led a Polish man by the name of Nicolaus Copernicus (1473-1543) to challenge the multi-leveled Ptolemaic model in favor of a simpler description — one that depicts that the Earth revolving around the Sun (a heliocentric model) instead of the Sun revolving around the Earth.[10] But, fearing that his work would lead to professional ridicule and “controversy” among the masses, Copernicus refrained from bolstering his idea. Almost one hundred years later an Italian astronomer named Galileo Galilei (1564-1642) recognized the mathematical simplicity and beauty of Copernicus’ heliocentric model and publicly supported it. In response to this the Catholic Church sentenced Galileo to a life of confinement, but the church was unable to completely suppress this beautiful idea. The seeds of curiosity had been planted and the heliocentric model began gaining ground.

“Copernicus, that fool, who would reverse the entire art of astronomy…
Joshua bode the sun and not the earth to stand still.”

Martin Luther

At this point in time, the assumption that the Earth was flat had long been under attack. The Greeks noticed that when a ship approached, they first saw its sails coming over the horizon and only later saw its hull. They recognized that if the Earth were flat this wouldn’t happen. Navigators had also observed that the position of the North Star changed in the night sky as they traveled north or south. Near the equator, the North Star (Polaris) lies on the horizon, but as one approaches the North Pole, the North Star is found higher and higher until it lies directly overhead. In fact, this occurrence is what defines latitudinal position. If you are at 45° north then the North Star will appear 45° above the horizon from your position. If the Earth were a flat disk it would be very difficult to explain this phenomenon.

Another observation that argued for a spherical Earth, rather than a plate shaped Earth, was made by Aristotle in 340 BC. In his book On the Heavens he noted that during lunar eclipses (when the Moon passes into Earth’s shadow) the shape of Earth’s shadow is always round. But if the Earth were a flat disk its shadow would not always be round — unless the eclipse always marked identical alignments between the Sun, Earth, and Moon – they don’t. This, he argued, meant that the Earth must be a sphere.

These arguments, which favor a spherical geometry for the Earth, do not necessarily contradict the Ptolemaic celestial model since one could simply replace a flat Earth with a spherical Earth inside the model (Figure 1-4). The seven levels of heaven would remain identical. However, there is a physical difference that separates the Earth-centered model from the heliocentric model. One of the requirements of the heliocentric model is that the Earth itself must be spinning about its own axis, whereas in the Earth-centered model the heavens are spinning around the Earth. Therefore, in order to determine which model is correct, all one has to do is come up with an experiment capable of proving that the Earth is either stationary or spinning. Can you think of an experiment that is capable of this differentiation? (Figure 1-5)

Figure 1-4 Holding on to a flat Earth.

Figure 1-5 Do the heavens rotate or does the Earth spin?

Today, we can observe such an experiment first hand in planetariums and many science and technology museums around the world. It consists of a large pendulum suspended from the ceiling that is swinging back and forth and slowly knocking over the Dominos that encircle it (Figure 1-6). Scientists call this a Foucault pendulum because in 1851, the French physicist, Jean-Bernard-Léon Foucault was the first to construct such a pendulum at the Pantheon in Paris. To see how this simple set-up can distinguish a spinning Earth from a stationary one, let’s imagine taking a Foucault pendulum to the North Pole during the season of perpetual night (the northern hemisphere’s winter). When we get there we observe that the stars are constantly and slowly circling about us in a clockwise manner. In order to determine whether this apparent motion is due to a spinning Earth or to the spinning heavens, all we have to do is align the plane of our pendulum’s swinging motion with any star we fancy (Figure 1-7). As the hours pass, we discover that the motion of the pendulum remains aligned with the star we’ve chosen, but the orientation of the swinging pendulum, with respect to the ground, changes over time. In fact, it will make a complete cycle in one day (Figure 1-8).

 Figure 1-6 Foucault’s pendulum (doubleclick image to start/stop animation)
 Figure 1-7 Spinning heavens (doubleclick image to start/stop animation) If the stars are spinning around the Earth, then the pendulum’s motion will always trace out the same path above the ground.
 Figure 1-8 Spinning Earth (doubleclick image to start/stop animation) If the Earth is spinning and the stars are fixed, then the pendulum’s motion will change with respect to the ground.

Since there are no identifiable forces pushing or pulling on the pendulum’s orientation, we must conclude that the stars are fixed, that the pendulum’s orientation is not changing, and that its apparent motion is due to the spinning of the Earth beneath it. From this conclusion we are compelled to accept the validity of the heliocentric model. A new perspective must be embraced.

The heliocentric revolution introduced a major shift away from a culturally entrenched medieval worldview—a worldview dominated by hierarchical submission, unquestioning duty, and faith; where the ‘levels of heaven’ were seen as depicting the importance of hierarchical social order. Under the old ‘levels of heaven’ model it was natural to succumb to the idea that birthright determined your fate because a similar fixed hierarchy was seen reflected in the heavens. Each celestial body remained forever entrenched in its own domain.

With the new model, humanity was no longer at the center of the universe, and the reasoning individual was no longer restricted by caste. Objective, methodical reason, and rational inquiry replaced unquestioning faith as the path to truth. “Fear” in God was replaced by the courageous goal of discovering the laws of Nature (God). This transition gave birth to a new era, fueled by the power of human reason, with the goal of lifting the great veil to improve the human condition.

The great human quest now had a vessel—a method for discovering truth—that had been forged by the accumulation of history’s highest insights. Like the ship of Neurath’s simile, which is continuously being built and repaired by the sailors it is carrying across the sea, the vessel of science is capable of improving its methodology as it assists our exploration of the realms that lie beyond the reach of our senses.

In many ways, the first official captain of that modern vessel was Sir Isaac Newton. Newton was born one year after Galileo died. He grew up to become the world’s first theoretical physicist (although, in his day, the profession was called “natural philosopher.”) During Newton’s remarkable life, he arithmetized the Cartesian system (developed by René Descartes) and captured the heliocentric framework within this powerful formulation. Because of its precise predictive power, Newtonian mechanics overthrow the Ptolemaic model and was officially accepted as the new, universal and complete model (map) of physical reality.

Newton’s model simplified the natural realm into a deterministic picture governed by a few interlinked rules. It gave us more than the ability to explain and predict observations (orbiting bodies, colliding bodies, etc.) in terms of forces, accelerations, velocities, mass, position, and so on. It provided an elegant unification of natural phenomena.

For example, before Newtonian mechanics the phenomenon of motion and the phenomenon of heat were considered unique and separate. The Newtonian lens reveals a relation between the two because it explains heat in terms of the average motion of atoms in a medium, and sound in terms of how collective molecular motions contribute to propagating distortions in a medium.

Phenomena that had long been thought to have completely separate origins were tied together by a deeper understanding of Newton’s laws of motion. (Feynman 1988, 4) This bolstered the possibility that Nature is logically composed and that it is ultimately comprehensible. Of course, this wasn’t the end of the story. As we looked closer and closer into Nature we began to find phenomena that could not be explained by Newton’s map.

Meticulous observations, like the discovery of Mercury’s perihelion advance (first observed in the 1840s) really called the validity of Newton’s map into question. The perihelion is the location on a planet’s elliptical orbit that is closest to the Sun. If there were nothing else in the solar system besides the Sun and Mercury then the orientation of Mercury’s elliptical orbit would remain fixed in space. But in our solar system, which has many other massive bodies, the combined gravitational fields interact in such a way as to cause all the elliptical orbits to precess. (Figure 1-9) For Mercury, this precession moves the perihelion ahead of where Newtonian mechanics says it should be by about 43 seconds of an arc per century (3,600 arc seconds equals one degree.)

Newtonian mechanics predicts that Mercury’s orbit should precess at a rate of 532 arc seconds per century, yet it precesses at a rate of 575 arc seconds per century. When astronomers first discovered this discrepancy they assumed that it was due to an undiscovered planet gravitationally tugging on Mercury — similar assumptions had led to the discovery of Neptune. Urbain LeVerrier first described this effect in 1859, calculating where the mystery planet should be and named it Vulcan after the Roman god of fire.

Figure 1-9 The precessing perihelion of Mercury.

For the next 20 years astronomers from around the world searched for a planet inside the orbit of Mercury. Observing such a planet is rife with difficulties. It requires pointing your telescope at or near the Sun, which leaves you susceptible to the production of false reflections inside your optics. It is also very difficult to distinguish a round sunspot from a planet in transit. Over the years, as we might expect, many false sightings were reported.

As the years passed, more and more observations amassed that challenged the completeness of Newton’s map. Then, in 1915, Einstein formulated a new map (general relativity) that predicted Mercury’s perihelion advance without any reference to another planet. With this stroke of genius Newton’s old map was officially dethroned. But Einstein’s new map is only partially intuitively accessible, and it does not accurately map the microscopic realm. Despite its successes, this new model leaves us hungry for a more complete answer.

Since the fall of the Newtonian classical perspective we have been walking deeper and deeper into a jungle of confusion — discovering more and more aspects of Nature that defy the intuition of our old map. We no longer have a complete map of Nature’s parameters. What we have instead are two maps (models) that are, at best, approximations, or fragments, of a larger, complete picture of Nature. The ultimate dream of a physicist is to discover the complete picture – a map that naturally fits together the predictions of quantum mechanics with the explanation of general relativity.

The theory of general relativity (a theory can also be referred to as a map or a model) builds a picture from which we can partially explain the macroscopic (large scale) world, including Einstein’s discoveries of warped spacetime, black holes, time dilation, and so on. This is a rich and beautiful theory, but its explanatory power remains fragmented. There are two reasons for this. First, as it is presented Einstein’s map can be only partially used to intuitively penetrate the phenomena it describes. Second, the theory cannot be extended to accurately describe the microscopic realm.

On the other hand, Nature’s microscopic realm is exclusively translated to us via the mathematics of quantum mechanics. Statistically this quantum formalism makes predictions that are fantastically accurate, but conceptually it remains extremely fragile. Quantum mechanics is plagued to the core with conceptual difficulties. Different foundational assumptions can be used to derive the same formalism, each with their own take on the nature of reality. As a consequence, we have no consensus concerning the interpretation of the theory or its foundations. As Claude Cohen-Tannoudji states “a really satisfactory and convincing formulation of the theory is still lacking.” (p. ix, Franck Laloë)

“Anyone who is not shocked by quantum theory does not understand it.”

Niels Bohr, 1927

“Nobody understands quantum theory.”

Richard Feynman, 1967

The conceptual difficulties beneath quantum mechanics originate from the object it uses to describe physical systems – the state vector $latex | \psi \rangle$. Classical mechanics describes a system by directly specifying the positions and velocities of its components, while quantum mechanics replaces those attributes with a complex mathematical object $latex | \psi \rangle$, providing a relatively indirect description. What exactly does it mean to say that a system is better represented by a state vector than by a specification of its component’s positions and velocities? What does a state vector represent in reality?

The most difficult part of “really understanding” quantum mechanics is figuring out the exact status of $latex | \psi \rangle$. Does it describe physical reality itself, or does it convey only some (partial) knowledge that we might have of reality? Is it fundamentally a statistical description, describing ensembles of systems only? Or does is describe single systems, or single events? If we assume that $latex | \psi \rangle$ is a reflection of an imperfect knowledge of the system, then shouldn’t we expect that a better description exists, at least in principle? If so, what would this deeper and more precise description of reality be? (Franck Laloë, p. xii)

So far quantum mechanics has not been able to touch base with an intuitive representation. It fails to even partially provide a conceptual picture because, apparently, it is only equipped to speak about the world statistically. If what we are after is a conceptual picture, then we are going to have to discover a structure beneath quantum mechanics that is responsible for its peculiar effects. The question is, does such a structure actually exist?