E = mc2
Einstein's Great Equation,
The Men and Women who Helped Discover it
and Kabbalah
1905 is considered the Annus Mirabilis - the miracle year of physics. In it, Albert Einstein, employed as a patent clerk in Bern Switzerland, wrote not one, not two, not three, but five seminal papers that were published in renowned journals of their day. Each one unto itself revolutionized the world of physics. What an amazing achievement of human creativity!
The last paper - only 3 pages in length - provides the most famous equation of our time, E = mc2. One hundred and one years later we are still exploring and discovering the implications of this formula for the physical, engineering, and biological sciences. But its significance doesn't stop with these sciences or even philosophy - we are seeing more clearly than ever before how this simple yet complex equation impacts metaphysics and spirituality.
Some background into how Einstein arrived at his Big Idea
Sir Isaac Newton (1642 - 1727) - the great physicist, mathematician and mystic (he wrote as much or more about the Bible than science), father of Newton's three laws, the concepts of inertia, momentum, the differential calculus and who explained how objects are attracted to each other via gravitation, recognized that not only science, but all endeavors of human ingenuity and achievement are possible because of those true pioneers who came before, sacrificing much to advance the human condition.
Newton said "If I have seen farther than most it is because I have been able to stand on the shoulders of giants" and this of course was no less true for Einstein in his time as well as for each one of us today.
David Bodanis, author of the book "E = mc2" breaks the equation down into it's four constituents: E standing for energy, m for mass, c representing the speed of light (standing for the Latin word "celeritas" - meaning "swiftness") and the squaring of c - that is c times c. He then explains where and how the conceptual idea for each, in Einstein's day, came from.
Recently the PBS affiliate in Boston produced a wonderful TV documentary called "Einstein's Big Idea" based on Bodanis' book. The show included vignettes of several key individuals in the history of science who achieved revolutionary understandings of these components of the equation E = mc2. Their stories are poignant, ironic, some tragic, all amazing. (You can order the video/DVD from the WGBH Boston website).
Let's briefly explore what they learned and how this "set the table" for Einstein's subsequent work in putting together the components they helped to illuminate.
E - Michael Faraday
We learn about the energy part of E = mc2 through Michael Faraday - an Englishman who lived in the early 19th century (1791 - 1867). Faraday had a keen and unwavering fascination with electrical phenomena. He was a contemporary of the Italian scientist deVolta (for whom the unit of electromotive force, the Volt, is named) and of the French scientist Jean Ampere (for whom the unit of electrical current is named). In those days it was believed that electricity was a kind of fluid that flowed through wires.
As a young man, Faraday was not trained as a scientist and thus was not a member of the scientist's "club." He spent years toiling to become one though. His ideas attracted the attention of the eminent British chemist Sir Humphry Davy. Davy was like a rock star of his era and right before his well-attended public discourses he frequently imbibed on nitrous oxide - laughing gas!
Davy eventually offered Faraday a job in his lab and he flourished, eventually overtaking the master in terms of public recognition. Faraday came to understand how electricity flowing through a wire influences (moves) a nearby compass needle - a perplexing problem at the time. He reasoned there must be an "energy" that flows around the wire, perpendicular to the electrical flow that can influence a magnetic body.
What he had discovered was the existence of an electric field which interacts with a magnetic field. He later turned the problem on its head by showing that a magnetic field can cause a thin wire attached to a battery to rotate around a fixed point with the field. That was the basis of one of the greatest inventions of the post-industrial age - the electric motor. In this way Faraday was able to "command" the conversion of one form of energy to another - electric to kinetic energy of movement.
So Faraday was able to "marry" electricity and magnetism. Next came the question of the very nature of light. Faraday became convinced that light exists as an interaction between the electric and magnetic fields. But he lacked the appropriate mathematical background to demonstrate what the exact relationship is.
C - James Clerk Maxwell and Heinrich Hertz
It took a young mathematical genius by the name of James Clerk Maxwell (1831 - 1879), now well known to all college physics majors, to show the relationship between the electric and magnetic fields. Faraday came to know and work with Maxwell in Faraday's later years. The young prodigy eventually conceived of a series of mathematical relations, known as Maxwell's Laws, that explain exactly how the electric and magnetic fields of energy are interconnected, intertwined as one if you will.
What "fell out" of those equations was a number - a constant which was recognized by both Maxwell and Faraday as the speed of light - referred to as 'c'. That speed is 300,000 meters per second in a vacuum but here's the peculiar, paradoxical thing about that speed: it is constant throughout the universe. Even if one were to travel at 299,999 meters per second next to a light beam traveling in the same direction, one would still measure the light beam's speed as 300,000 meters per second relative to themself!
For the next 70 odd years physicists would simply remain perplexed about this because it was in exact opposition to Newton's concepts of absolute motion and velocity, until Einstein outlined his theory of special relativity and cleared up this paradox.
Maxwell's seminal contribution was the realization that light is an electromagnetic wave phenomena. From that was born the concept of the electromagnetic spectrum of which visible light is a small portion (it includes x-rays, gamma rays, microwaves, radio waves, etc.). Another contemporary, Heinrich Hertz (when you talk about the speed of your PC's CPU you are paying tribute to Mr. Hertz!) was able to demonstrate how electromagnetic energy can be transmitted and induce a current across a gap of several yards. He also discovered the photoelectric effect accidently - the subject of another of Einstein's 1905 papers. Both achievements remain profound phenomena in our current everyday lives!
m - Antoine Lavoisier - mass accounting
Lavoisier (1743 - 1794), an aristocratic Frenchmen who studied law and bought shares in a major tax-collecting company, lived during the time of the French revolution and died because of it. At the age of 25 Lavoisier was elected to the French Royal Academy of Sciences for an essay he wrote on a method for providing street lamps! For 6 days a week he administered his tax-collecting machinery for the King. His main civic achievement was to build a wall around Paris using collected taxes, to keep out foreigners.
But Lavoisier also had a passion, obsession really, for matter - objects of all kinds. He wanted to understand how matter, in all its forms exists and how it changes when it interacts with certain kinds of energy such as heat (burning), chemical or mechanical. The major question on his mind was whether or not the total amount of matter in the universe is fixed - that is, is matter either created or destroyed?
In his spare time Lavoisier built a sophisticated lab - that was managed by his talented and devoted wife Marie Anne - to study matter and it's transformations into various forms, for example what happens to wood when it is burned? Lavoisier wanted to know if matter, mass is destroyed or lost in such an action. Another question was - if you leave a piece of iron outside in the elements to rust, does it disintegrate and lose mass or does it gain mass (the latter - it gains mass due to chemical combination with oxygen)?
He developed very precise weighing scales for his experiments using contained systems. In this way he could measure precisely the byproducts of both chemical and mechanical operations on matter. He was therefore applying energy to matter to determine whether the latter is conserved. He was able to determine that when water is separated into oxygen and hydrogen through the electrolysis process that the summated mass of the resulting constituents is almost equal to the water, minus roughly the amount of energy needed to separate the elements.
Unfortunately at age 51, Lavoisier was tried, convicted and guillotined one day during the French Revolution - turned in by a jealous competing scientist. His contributions to our present day notions of matter (and those in Einstein's day) reflect a tremendous advancement of physics as we understand it today.
c2 - Emilie du Chatelet - defying Newton in favor of Leibniz
Clearly a child prodigy, Emilie du Chatelet (1706 - 1749), born of aristocracy, married a wealthy soldier at 19 - a marriage of convenience. Her translation of Newton's Principia Mathematica into French is still the standard used today. At age 27, a mother of three, she engaged in a close partnership and affair with the famous writer, Voltaire.
They shared many interests - in particular the world of scientific ideas of their time. Together they turned her husband's chateau into a major French base for scientific research and learning. Emilie's driving question was about the very nature of energy. At that time, different manifestations of energy were believed to be separate, unconnected, for example heat vs. wind energy.
Clearly, movement was an important component of most every source of energy. Newton believed that kinetic energy was proportional to an object's mass times its velocity (what we refer to today as momentum). However, one of Newton's main rivals, Gottfied Leibniz, the co-inventor with him of the calculus, had demonstrated theoretically that this energy is related to mass times velocity squared (mv2).
Emilie was able to recreate and extend experiments in which weighted balls were dropped or thrown onto a clay surface. By measuring how far the balls embedded themselves into the clay she proved that Newton's hypothesis was incorrect and that Leibniz was right! Since the speed of light, c, is just another kind of velocity, albeit a constant one in a vacuum, Du Chatelet's confirmation of E = mv2 helped Einstein put in place the c2 component of the great equation.
Einstein puts it all together - in his head
From these various pieces of the puzzle Einstein was able to put together E = mc2. In his 1905 paper he actually stated it in terms of mass as m = E/c2. Looking at the equation both ways allows one to see the equivalence of mass and energy through the connecting "bridge" of light. Einstein was able to achieve this intellectual pillar of our age through the medium of thought, visualization and creative expression. He asked many "what if" questions and performed "thought experiments" such as "what would I see if I were traveling on a light beam?"
With the help of first wife Mileva (checking through his math) and numerous conversations with his best friend Michelle Besso, he one day arrived at the "aha" moment that put all the pieces together. The rest, as they say is history. Einstein unveiled the truth - truth that is still and ever unfolding - that E and m exist in a reciprocal, feedback inter-relationship that goes beyond the apparent linear mathematical formalism of the equations themselves. And at the very heart of this relationship is light.
Prolog: Lise Meitner goes Fission!
The story of Lise Meitner, born Jewish in Austria in 1878, provides an intriguing postscript to the story of E = mc2. She received her doctorate in Vienna from the great physicist Ludwig Boltzmann. She went to Berlin in 1907 to study with Max Planck and following that began to work with a chemist, Otto Hahn, a collaboration that continued for nearly 30 years. Their work involved the study of radioactive substances including uranium.
In 1938 following the Nazi annexation of Austria, Lise was forced to leave everything behind and escape to Sweden. All her work was left behind but she was able to stay in touch with Hahn on their important experiments. The experiments involved the bombardment of uranium with neutrons. They had expected that heavier elements than uranium would result as the neutrons would get embedded in the atomic nuclei.
Instead, lighter elements such as barium were produced with measurement of substantial heat energy given off. This was a huge puzzle until Meitner and her nephew Otto Frisch put it all together. In an aha moment she realized that as the uranium nuclei increased in size momentarily - the nuclei would split and give off energy. Thus she discovered the process of nuclear fission.
Furthermore she recognized that the energy given off satisfied E = mc2 when all the energy and mass "accounting" was tallied. Hence her discovery was effectively the first empirical confirmation of Einstein's great equation. Unfortunately for all of Meitner's troubles she received nothing: Hahn was awarded the Nobel Prize in physics in 1945, and it is only in recent years that Meitner's genius has been more fully recognized.
E = mc2: A metaphor for the relationship between form and non-form
Physicists understand E = mc2 as expressing a reciprocal relationship between energy and matter. A certain quantity of matter contains within it an equivalent amount of energy and vice versa, that reciprocal relationship being "mediated" by the constant value of the speed of light, c, squared.
In nature, we see that certain elementary particles come together, completely transforming into energy, as in electron-positron "annihilation" in which a gamma ray results. Conversely, a gamma ray can spontaneously "create" a positron and an electron. Matter seemingly created from energy. When matter is converted into energy a great deal of it is released because of the large value of c2, as seen in either a fusion reaction (as occurs in stars) or the fission of Uranium (as occurs in an atomic bomb).
In spiritual circles there is a tendency to say "all is energy" and that matter is a form of "stuck" energy. However, E = mc2 is yielding new insights about this that hearken back to ancient wisdom! Looking at the equation one realizes that the equivalence of matter and energy brings to mind the "Law of 3." This law says that two substances join to form a third thing that is more than the linear sum of the two - the whole is more than the sum of its parts. A new synthesis emerges.
A simple example is the chemical combination of hydrogen and oxygen to form water. Water is completely different than its constituent elements - a liquid being formed from two elemental gases. In the case of E = mc2 energy and matter are no longer viewed as distinct - they are rather two aspects of a "higher" (different) reality. Let's refer to it as enermatter for the moment. Perhaps, the primordial atom that exploded in what we now refer to as the Big Bang was an enermatter body.
If we conceive of matter as form and energy as non-form, E = mc2 represents the nonlinear merging of form and non-form into a united, unified whole. Hence dualism and holism exist simultaneously - an apparent paradox in the "mundane" 4 dimensional world of our everyday existence, but not a paradox when we go beyond 4D to the 2 to 12 dimensional world of DNA, the 10-26 dimensional world of strings, and even beyond dimensional conceptions to the Endless worlds of Kabbalah.
The Star of David, The Tree of Life, The Cross, and E = mc2
The merging of form and non-form has always been deeply embedded in the significance of the Star or Shield of David. Each equilateral triangle representing not only the Law of 3, but also an expansion to infinity. One triangle, extending downward, represents heaven reaching to Earth and the other, Earth reaching up to Heaven. Both triangles, pointing in opposite directions, merge in the middle where heaven and "Earth" come together to form a new unity. The similarity to E = mc2 is clear: the merging of heaven and earth - non-form and form into a new synthesis.
This has always been the quintessential truth of Kabbalah as represented in Judaism by the Sh'ma prayer - "Hear O Israel, the Lord our God, the Lord is One." It is also the basis of the symbol of the cross - the merging of humanity and divinity - God descends toward Earth, humanity ascends toward heaven where they cross and merge!
The joining together of male and female - which produces an offspring, as represented by the right (male), left (female) and center (offspring) pillars of the Kabbalistic Tree of Life is also a symbolic representation of the most famous equation of our time - the merging of form and non-form out of which new creation is born. The story of E = mc2 was one brought back into this world by roughly equal numbers of men and women.
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