Looking at the Principle of Relativity the Easier Way

In the entire history of physics there is no equation more famous than e = mc2. This partnership amongst mass (m) and energy (e) was derived in 1905 by Albert Einstein from his Principle of Relativity. The derivation wasn't easy and warranted a paper by itself, referred to as "Does the inertia of a body depend upon its energy content?". The equation continues to baffle and dumbfound lay people, since in the usual particle picture of nature, it is difficult to see exactly why there is an equivalence between mass and energy.

In the meantime, a new theory called Quantum Field Theory was created. QFT was perfected in the 1950s by Julian Schwinger in 5 papers called "Theory of Quantized Fields". In QFT there are no particles, there are only fields-- quantized fields. Schwinger succeeded in placing matter fields (leptons and hadrons) on an equal footing with force fields (gravity, electromagnetic, strong and weak), despite the obvious differences among them. Moreover, Schwinger established the theory from fundamental axioms, as opposed to Richard Feynman's particle picture, which he justified because "it works". Regrettably it was Feynman who won the battle, and today Schwinger's method (and Schwinger himself) are mainly forgotten.

Yet QFT has lots of benefits. It has a stronger basis than the particle picture. It describes lots of things that the particle picture does not, including the numerous paradoxes connected with Relativity Theory and Quantum Mechanics, that have puzzled so many people. Philosophically, lots of people can accept fields as basic properties of space, instead of particles, whose composition is unknow. Or if there visualized as point particles, one can only ask "points of what?" And above all, QFT offers an easy derivation and understanding of e = mc2, as follows.

Mass. In classical physics, mass is a measure of the inertia of a body. In QFT some of the field equations contain a mass term that impacts the rate at which quanta of these fields evolve and propagate, slowing it down. Thus mass takes on the same inertial role in QFT that it does in classical physics. But this is not all it does; this exact same phrase causes the fields to oscillate, and the greater the mass, the higher the frequency of oscillation. The result, if you're imagining these fields as a color in space (as in my book "Fields of Color"), is a kind of glimmer, and the greater the mass, the quicker the glimmer. It might appear unusual that the same term that slows the spatial development of a field also provokes it to oscillate, but it is actually straightforward mathematics to show from the field equations that the frequency of oscillation is given by f = mc2/h, where h is Planck's constant.

Energy. In classical physics, energy means the capability to perform work, which is specified as applying a force over a distance. This definition, however, does not offer much of an image, so in classical physics, energy is a rather abstract idea. In QFT, on the other hand, the energy of a quantum is established by the oscillations in the field that comprises the quantum. In fact, Planck's famous relationship e = hf, where h is Planck's constant and f is frequency, found in the centennial year of 1900, follows directly from the equations of QFT.

Well, since both mass and energy are associated with oscillations in the field, it does not take an Einstein to see that there must be a connection between the two. In fact, any schoolboy can combine the two equations and find (big drum roll, please) e = mc2. Not only does the formula tumble right out of QFT, its significance can be imagined in the oscillation or "shimmer" of the fields. Nobel laureate Frank Wilczek calls these oscillations "a marvelous bit of poetry" that produce a "Music of the Grid" (Wilczek's phrase for space viewed as a lattice of points):.

"Instead of plucking a string, blowing through a reed, banging on a drumhead, or clanging a gong, we play the instrument that is empty space by plunking down different combos of quarks, gluons, electrons, photons, ... and let them settle till they get to balance with the spontaneous activity of Grid ... These resonances represent particles of different mass m. The masses of particles sound the Music of the Grid.".

This QFT derivation of e = mc2 is not typically known. In fact, I have never seen it in the books I've read. And still I consider it just one of the great accomplishments of QFT.

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Einstein and Newton Followed Similar Paths in Their Gravity Theories

When one looks at the paths that Newton and Einstein followed while pursuing their theories of gravity, one is struck by the many coincidences: the unexplained data on orbits, the sudden insight about falling objects, the need for a new mathematics, the calculational difficulties, the retroactive agreements, the controversy, the problem-plagued expeditions, and the final triumph and acclaim. Both men had worked in the same eccentric and lonely way, divorced from other scientists, armed with a great feeling of self-reliance while struggling with new concepts and difficult mathematics, and both produced earth-shaking results. One can’t help but wonder if these two greatest of scientists, born 237 years apart, were “relativistically related”, conceived as twins in some ethereal plane in a far-off galaxy and sent to earth to solve a matter of some gravity.

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Mass in Quantum Field Theory

The tale of exactly how the gravitational field entered into physics and quantum field theory is a remarkable one, entailing apples and moons, predictions and confirmations, problem-plagued expeditions, and the two greatest scientific geniuses of all time. And it might not have happened if not for the Great Plague.  Read more, Fields of Color - The Theory That Escaped Einstein

Einstein Rejects Quantum Field Theory

Einstein scraps QFT. In spite of his quest for a singular field theory, Einstein shot down Quantum Field Theory after querying a friend, Valentin Bargmann, to grant him a private tutorial on the matter. This is not shocking; at the time Quantum Field Theory was simply neither comprehensive nor a success, nor was Bargmann its best spokesperson. We need to also look at Einstein's great skepticism of the QM theory that came before Quantum Field Theory-- a wariness based upon its probabilistic attributes.(In QM one could never say exactly where a particle is, simply that it has a certain probability of being here or there.) This particular randomness was actually unconformable to Einstein and resulted in his famous remark, "I can not believe that God plays dice with the universe.".

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Quantum Field Theory and Einstein

Once Einstein began to work on gravity in 1907, science had come a long way from the days of Newton. Not only had electrical energy and magnetism been identified, but the idea of an electromagnetic field had substituted action-at-a-distance and was on the edge of replacing the ether. This led naturally to gravity likewise being seen as a field. After all, why would nature use a field for one force and action at a distance for another? There had likewise been fantastic developments in astronomy, partially because of Newton's new telescope. Two more planets had been discovered, with only Pluto remaining to be discovered (and later "benched"). However there still were no gravitational field equations-- the sine qua non of a true field. There additionally was a small issue pertaining to the orbit of the planet Mercury.

http://www.quantum-field-theory.net/science-einstein/

At age fourteen, I came across Arthur Eddington's work The Nature of the Physical Universe. I was excited with the notion that a table is in fact not a solid piece of furniture. If one could possibly look closely enough, said Eddington, beyond the power of any type of microscopic lense, one would certainly observe that it is comprised of atoms so tiny that we can hardly grasp their tinyness. These atoms consequently are comprised of in fact, tinier nuclei, and these consequently are comprised of particles called neutrons and protons, with tiny electrons zooming about in orbits like miniature solar systems. "So that is what the world is made of!" I presumed, and this was my intro to physics. Of course it didn't occur to me then to question exactly what these electrons, protons and neutrons are comprised of.

Some years afterwards, as a Harvard graduate student, I was fortunate enough to attend a three-year lecture series by Julian Schwinger. The timing was perfect. Schwinger's advancement of Quantum Field Theory (QFT) had progressed and he was about to publish a magnum opus, "A theory of the fundamental interactions". I sat enthralled, as did others.

"As Schwinger stood at the blackboard, writing ambidextrously and speaking mellifluously in well-formed sentences, it was as if God Himself was handing down the Ten Commandments. The equations were so elegant that it seemed the world couldn't be built any other way. From the barest of first principles, he derived all of QFT, even including gravity. Not only was the mathematics elegant, but the philosophic concept of a world made of properties of space seemed to me much more satisfying than Eddington's mysterious particles. I was amazed and delighted to see how all the paradoxes of relativity theory and quantum mechanics that I had earlier found so baffling disappeared or were resolved." - Rodney Brooks

In the FIFTY years that had passed since my university student days, I have seen very little mention of QFT. Rather I have seen a barrage of publications and posts that keep restating the paradoxes that individuals are expected to accept. Far from giving the public a comprehension of nature, these popular books and posts have actually brought confusion and incomprehensibility.

The objective of my book, Fields of Color, is to bring to the public the exact same feeling of satisfaction that I felt in Schwinger's courses. I am also trying to resolve the paradoxes of physics that stop countless people from understanding the natural world. I hope that my endeavours will bear fruit and that the reader will come away from the book feeling that nature is not mysterious or paradoxical, but is understandable and indeed makes perfect sense. Read more at the Book's Website