Chapter 1

 

Section 4: Fitting the Pieces Together


“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

 

Today’s most advanced theories (superstring theory, M-theory, loop quantum gravity, supersymmetry, etc.) have all been unsuccessful at unifying quantum mechanics and general relativity. Mathematical attempts to meld these two descriptions — to reduce the four forces of Nature into an all-encompassing framework, have produced equations so long and complex that no one entirely understands them. As Brian Greene puts it,

“the mathematics of string theory is so complicated that, to date, no one even knows the exact equations of the theory. Instead, physicists know only approximations to these equations, and even the approximate equations are so complicated that they as yet have been only partially solved.” (Greene 2003, 19)

It’s like having a gargantuan set of digital code with no information on how to translate that information into a picture. What’s even more disturbing (or intriguing) is the fact that the supercomputers we have tasked with analyzing the structure of these codes have determined that patterns are only available for translation in higher dimensions. This suggests that Nature’s complete picture may in fact exist within a framework possessing more than the familiar dimensions. What could this possibly mean? How can we ever expect to understand something that is described in more than three space dimensions?

As we ponder that question let’s recall that Einstein’s view of gravity also requires (albeit subtly) the introduction of more dimensions. (See Chapter 9.) It describes gravity as a geometric effect – a consequence of the way massive objects distort the shape of spacetime. Distorted spacetime alludes to the existence of additional dimensions because those distortions extend into something other than the familiar three spatial dimensions. But these additional dimensions are not physically real — or are they? We might allow them to exist in the abstract mathematical sense, but it’s impossible to visualize more than three dimensions. Isn’t it? They can’t physically exist — can they? Even if they do exist, how could we ever understand them? Even Einstein had to suppress a familiar dimension of space in order to visualize the dimension of curvature for a plane, so how can we ever hope to visualize many dimensions at once?

This kind of thinking is exactly what is holding us back. It is our belief that we can simultaneously visualize only three spatial dimensions at once (length, width, and height) that is keeping an intuitive picture of reality hidden from us. Once we cross this chasm, Atlantis will no longer be able to hide. And from the vantage of Atlantis the mysteries of Nature will be revealed.

In our four-dimensional (three space dimensions and one time dimension) models of physical reality, space and time are still laced with confusion. We can’t even explicitly define them. But, as we will soon discover, in a higher-dimensional realm space and time gain simple and powerful definitions. In fact, with the ability to transcend the dimensional barrier, it becomes readily obvious that Nature’s framework is eleven-dimensional. Matter, energy, and the forces of Nature (including gravity) become simple derivatives of this multidimensional ballet.

 

“All the great empires of the future will be empires of the mind.”

Winston Churchill, 1953

 

Just as I cannot meaningfully express the beauty of the fountain of Buckskin Gulch, without appealing to human senses and portraying some sort of image, we cannot comprehend Nature’s deepest beauty without discovering its deeper structure. In this book I aim to expose at least one new way of looking at the world, a way that I believe makes room for the currently unexplained mysteries in physics (wave-particle duality, the uncertainty principle, nonlocality, dark energy, dark matter, etc.). The set of assumptions that give rise to that new perspective get us beneath both general relativity and quantum mechanics, bringing us to a richer understanding of the phenomena captured by both.

In order to attain this picture, map, or all-encompassing framework, we must return to a conceptual approach and, once again, rethink the very parameters of space and time. To accomplish this task let’s examine how great thinkers have done this in the past and then see where our inquisitive freedom can take us. If the specific picture we explore falls short, then the procedure we are about to follow should give us all the tools we need to discover a better one.

 

[Continue to Chapter Two]


 

 

From the forthcoming book:

Einstein’s Intuition
by Thad Roberts

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


NOTES:

[1] This quote originally comes from an article written by Einstein that was published in Forum and Century Magazine in 1931.

[2] Einstein explained the important distinctions between these two approaches in a 1919 essay he wrote called “Induction and Deduction in Physics.”

“The simplest picture one can form about the creation of an empirical science is along the lines of an inductive method. Individual facts are selected and grouped together so that the laws that connect them become apparent… However, the big advances in scientific knowledge originated in this way only to a small degree… The truly great advances in our understanding of Nature originated in a way almost diametrically opposed to induction. The intuitive grasp of the essentials of a large complex of facts leads the scientist to the postulation of a hypothetical basic law or laws. From these laws, he derives his conclusions.” Einstein, “Induction and Deduction in Physics,” Berliner Tageblatt, December 25, 1919, CPAE 7:28; “Einstein,” Walter Isaacson, p. 118.

[3] As an early example of this, let’s consider the Pythagoreans — a secret group who followed a mysterious figure from Greek mathematics named Pythagoras (c. 475 B.C.). The Pythagoreans thought that the whole of the cosmos could be described in terms of the whole numbers: 1, 2, 3, etc. This underpinned their understanding of physical reality and guided their inquiries about the natural realm. Eventually, however, this led to problems. Around 500 B.C. arguments ensued within the Pythagorean circle about a number that is now known as the square root of two (). The Pythagoreans were concerned with this number because of its geometric significance. They had initially assumed that the value of  could be described as a ratio of two whole numbers, but a clever argument was made that disallowed this possibility. According to legend, this argument was constructed by Hippasus of Metapontum, who had been ordained to the inner circle of the cult. Hippasus’ argument meant that the Pythagoreans had to accept the fact that the square root of two could not be expressed as a fraction of integers.

Tragically with the birth of irrational numbers came the death of their discoverer. To the Pythagoreans, irrational numbers represented an idea so dangerous that it created a crisis that reached to the very roots of their cosmology. In an attempt to somehow make this crisis go away and to insure that Hippasus wouldn’t be able to divulge the secret to someone outside their circle, the Pythagoreans abducted Hippasus and drowned him on the high seas.

Today irrational numbers and many other profound ideas are so completely integrated into our formalization of mathematics that it is easy to overlook how valuable the information we have inherited is. Men and women have dedicated their lives, and some have lost their lives, attempting to give us the ideas that outline our modern world — ideas like the square root of two. The concept of ‘zero’ is another one of those ideas. In its early history the Catholic Church banned Hindu-Arabic numerals – the 0 through 9 we use today – throughout much of Italy until the fourteenth century because it regarded the concept of zero as dangerous to its theology. Richard Elwes, “From e to Eternity,” New Scientist, July 2007: 38. p. 38; Stephen Hawking, God Created the Integers; Jared Diamond, ‘Guns, Germs, and Steel, p. 235.

[4] The naked eye can see up to 7000 stars in the darkest and clearest skies.

[5] The word ‘cosmos’ comes from the Greek word kosmos, which means ‘the ordered whole’, or ‘world’.

[6] Uranus is barely visible to the naked eye. Usually only the trained observer can find it. That is why it is not included in this list. Neptune cannot be distinguished without magnification.

[7] As a reflection of how significant these curiosities have been to mankind, note that the objects occupying their own celestial level in the Ptolemaic model are still reflected in our modern days of the week.

Day of the Week Celestial Body
English Spanish English Spanish
Sunday Domingo Sun Sol
Monday Lunes Moon Luna
Tuesday Martes Mars Marte
Wednesday Miercoles Mercury Mercurio
Thursday Jueves Jupiter Júpiter
Friday Viernes Venus Venus
Saturday Sabado Saturn Saturno


The days of the week were originally named after these heavenly bodies by the Babylonians. The Romans adopted this representation. We quite literally have a 7-day week because of this model. The week was set up so that each day was spent in worship of a corresponding level of heaven – as each level was occupied by a different god. Saturn occupied the highest of those levels, which is why Saturn-day (Saturday) was the most holy day — the day everyone went to church. In 321 A.D. Emperor Constantine switched the Sabbath to Sunday instead of Saturday. Before all of this the Romans were also using an eight-day week (the seven levels of heaven plus the eighth level of background stars).

English retained its reflection of the seven levels of heaven, but some of the gods were switched for their local counterparts — the Anglo-Saxon words for the gods of Teutonic mythology. Mars was switched with Tiu or Tiw, the Anglo-Saxon name for Tyr, the Norse god of war. Odin or Woden replaced Mercury and Woden’s day eventually became Wednesday. Jupiter, also called Zeus, was switched out with his lightning bolt throwing counter part Thor. So Jove’s day became Thor’s day (Thursday). Friday was derived from Frigg’s day after the goddess Frigg, who like Venus represented love and beauty in Norse mythology.

[8] Religious texts that stem from this era, such as the Koran, reflect these changes by their mention of the ‘seven levels of heaven’. Older texts still hold onto the ‘three levels of heaven’.

[9] This maxim asserts that assumptions introduced into an explanation must not be multiplied beyond necessity. This is often stated as: all else being equal the simplest explanation is usually the correct one. It is attributed to the 14th century logician and Franciscan friar William of Occam (Ockham was the village in the English county of Surrey where he was born). Parsimony has become a reliable tool of modern science. In fact, modern hypothesis can, in general, be effectively evaluated for merit based on their elegance, simplicity and beauty. Our experiences have taught us that a theory which successfully mimics Nature is, at least in some mathematical, symmetrical way, simple, elegant and beautiful. In this, it has proven to be an extremely useful guide, but it is still no substitute for insight, logic and the scientific method. “As arbiters of correctness only logical consistency and empirical evidence are absolute.” Einstein artfully stated his version of Occam’s Razor as: “Everything should be made as simple as possible, but not simpler.”

[10] Aristarchus of Samos first proposed the idea of a heliocentric universe in the third century B.C.

[11] For simplicity we are ignoring air resistance and currents. The experiment will be even more precise if we perform it within a vacuum.

[12] For an in-depth analysis of this division of thought see: Thorlief Roman, Hebrew Thought Compared with Greek (New York: W. W. Norton & Company, 1970).

[13] In the fall of 1919, Einstein received an urgent telegram informing him that astronomers had observed evidence of the bending of light by the Sun’s gravity, validating a key prediction of his general theory of relativity. He handed the cable to a student, who began congratulating him. “But I knew that the theory is correct,” he interrupted, and she asked, what if the observations had disagreed with his calculations? “Then I would have been sorry for the dear Lord,” Einstein answered. “The theory is correct.” Richard Panek, ‘The E Factor,’ Discover, March 2008, pp. 20-21.



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