Chapter 1


Section 3: Two Pieces of the Puzzle

“In the last three decades in his life, Einstein failed to create the unified field theory largely because he abandoned his conceptual approach, resorting to the safety of obscure mathematics without any clear visual picture.”

Michio Kaku


The incompatibility between general relativity and quantum mechanics is the spark behind our investigation. Our inability to augment and piece together these fragments is the reason that we haven’t been able to formulate a picture of reality that encases all known phenomena. We are conceptually adrift, incapable of uniting all of Nature’s dissonant details, and without a trustworthy map for our journey. Our goal is to come into possession of a complete map.

The incompatibility between the two fragmentary descriptions of Nature we use today is reflected in the fact that the Western intellectual world has acquired its heritage from two distinct intellectual modes – ways of thinking that can be traced back to independent historical and geographical origins. These modes set the foundations for how we formulate concepts and relate to the external world. Because their constructions are different, the two modes often misinterpret each other. One of those modes germinated modern science while the other gave birth to the mythological texts of the great Western religions. Because of this, many people consider these modes of thought diametrically opposed. But this conclusion fails to recognize the symbiotic contributions that these modes make to our evolving worldview.

The first mode, which is passed down from the Greek tradition of thought, assumes that ultimate reality possesses permanent physical characteristics. This approach is concerned with unmasking the ultimate nouns of reality and mapping Nature based on the permanent and unchanging parameters of those nouns. It is classical by design and assumption, and it emphasizes a spatial dependence for reality. It assumes that if you remove space from the framework, reality dissolves — literally nothing remains. But with space, objects can possess definite properties: position, mass, extension and so on.

The second tradition, the Hebraic mode of thought, assumes that ultimate reality, that which is to be considered real, is an action — a verb. [12] Reality, according to this way of thinking, must be explained and mapped through interactions, evolution, and change. It follows that the forms of Nature are born of interplay — which means that change is the only immutable, fundamental construct of Nature. Consequently, this view cannot describe Nature without action — without time.

Following the Greek tradition of thought, science has achieved many breakthroughs. Atomic theory has followed the cascading structure of matter down to smaller and more fundamental parts. It has found that all the objects we experience around us, the air, water, rocks, trees, dogs, and humans, are all composed of atoms. Furthermore, we have determined that every atom is made up of more fundamental parts, namely protons, neutrons, and electrons, and that protons and neutrons are in turn constructed of even finer and more basic parts called quarks. More recently, string theory has suggested that all primary particles are made of tiny strings whose different vibrational modes cause all the varying masses, charges, and spins found in matter. The search for these hypothetical strings represents the ultimate goal of the reductive Greek tradition — to discover the ultimate noun from which the universe is constructed.

The Hebraic tradition is built upon an entirely separate foundation. Its time dependent framework underlies the ideologies of the great Western religions, which often label the fundamental verb of Nature as ‘God’. The philosophy of this view organizes reality into a construct of fundamental interactions. Therefore, in order to accurately depict Nature, this mode concentrates on discovering and understanding the most elemental verb.

History has seen many conflicts that stem from the foundational differences between these two modes of thought. Supporters of each camp have long argued that either the Greek tradition or the Hebraic tradition must be right. But modern discoveries suggest that Nature is surprisingly a mixture of the two. In fact, when Einstein married space and time into a single entity called spacetime, the spatially focused framework of the Greek tradition became melded with the temporally focused framework of the Hebraic tradition. It now appears that — with no space, we have no time, and with no time, we have no spatial forms. Without spacetime our physical reality possesses no description.

Somehow the Greek and Hebrew traditions were both right.

As it turns out, the two traditions were also both right in another way. The Greek tradition claims that ultimate reality is classical — that the base constituents of Nature possess definite properties like position and velocity at all times, and that every action in Nature is strictly deterministic (see Chapter 17). The Hebraic tradition, represented most formidably in science by quantum mechanics, claims that ultimate reality is probabilistic (see Chapter 12) — that before an event occurs, a range of possibilities exists for the outcome of that event — meaning that definite properties are replaced by probabilities of properties.

The framework we are about to construct will show that although these two claims appear to be strict opposites, from another perspective they can, in fact, both be seen as correct. (See Chapter 18) To discover that vantage point we are going to challenge one of humanity’s oldest assumptions about space and time. We are going to assume that instead of being a continuous medium, space is a superfluid medium composed of quantized units.

The level of understanding that we are looking for requires us to properly follow questions that are capable of guiding us to a deeper understanding of Nature. But to do this we need to be able to identify which questions are relevant. This sort of proper identification was Einstein’s shining strength. He was able to focus in on the three most important issues of his day (Is the fundamental structure of matter continuous or atomic? Can Nature’s laws of motion and Maxwell’s equations of electromagnetism be reconciled? And, is light quantized?) He then used these questions to author an entirely new construction of physical reality. If we are to complete that process then we too must properly identify questions capable of revealing Nature’s deeper structure. For this purpose let us continue reviewing the route of our scientific journey thus far and then discuss how to make the next conceptual leap.

The most satisfying aspect of Newtonian physics was that it gave us intuitive access to the world around us. Now that we have discovered phenomena in Nature that Newton’s model cannot account for, we are obligated to search for a new physics. Einstein dethroned the framework of Newtonian physics by introducing curved spacetime, which allows us to partially visualize curved spacetime. But Einstein didn’t replace Newton’s model with another “complete” and intuitive model. We can only access his curvature in a dimensionally reduced form and his model does not (even non-intuitively) account for quantum mechanical phenomena (new discoveries in his day). Still, thanks to Einstein we can now at least partially visualize the world of general relativity. As a result, the mysterious nature of the universe can now be mapped and intuitively accessed, at least in part, instead of being left entirely in the hands of confusing and often conflicting mathematics.


Figure 1-10 Classic “warped space” or “rubber sheet” diagram. A two-dimensional slice of space warping into some “other” dimension. This is a traditional depiction. Notice that the third dimension – the dimension that the plane of space is curving into, is unlabeled.


Einstein did make an attempt to satisfy our intuition by offering a partial model of warped spacetime, but this explanation was dimensionally incomplete. The math he used was remarkably elegant, but the picture he associated with that math was only capable of mapping one plane of reality at a time. (Figure 1-13) In spite of this, it is important to remember that the monumental breakthrough Einstein brought to humanity developed not from mathematical formulae or trial and error, but from a clear, visually intuitive picture in his mind. Mathematics and observations later solidified his conceptual solutions, but those equations and measurements hold little value compared to the deeper understanding and pictorial insights that remain their foundation. [13]

One way to attempt to complete this map and to extend the reach of our intuition is to, once again, challenge our assumptions about what space and time are. The reward for undertaking this task comes from the possibility of completing Einstein’s attempt to regain a complete and intuitively accessible framework of Nature.


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