Chapter 1

Section 4: Fitting the Pieces Together

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

Since 1905, we have been trying to explain the beauty of Nature without so much as a pic­ture. 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 pic­ture. In order to attain this pic­ture, this all-encompassing frame­work, we must learn to open our eyes to entirely new dimen­sions. We must return to a con­cep­tual approach and, once again, rethink the very para­me­ters of space and time.

Let’s see where this inquis­i­tive freedom can take us.

[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.

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

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 14^th 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.