Fields of Color

The Theory That Escaped Einstein

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Who Killed Schrodinger's Cat?

In 1935 Erwin Schrödinger described a hypothetical experiment to show that something is incorrect with the traditional analysis of Quantum Mechanics.

One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following device (which must be secured against direct interference by the cat): in a Geiger counter there is a tiny bit of radioactive substance, so small that perhaps in the course of the hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer which shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The [wave-function] of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts. [1]

Schrödinger's cat quickly emerged as the most famous example of what is now called the measurement problem, "the most controversial problem in physics today", [2] with more than 30 youtube videos dedicated to it. (Less well-known is that Einstein suggested a similar bomb experiment to make the same point, stating "a sort of blend of not-yet and already-exploded systems [can not be] a real state of affairs". [3])

The measurement problem arises because QM does not supply a picture of reality when no one is looking. Instead we have particles that are neither here nor there, states that are in superpositions, and equations that only give probabilities. The majority of physicists believe that these superpositions are real, and some even accept that the cat can be both half dead and half alive. Then there are physicists who prefer not to talk about reality.

I am a positivist who believes that physical theories are just mathematical models we construct, and that it is meaningless to ask if they correspond to reality, just whether they predict observations.-- Stephen Hawking. [4]

Something was obviously missing.

That something came along later on in the form of Quantum Field Theory-- a theory that does offer a picture of reality, even when no one is looking. However there are various explanations and understandings of Quantum Field Theory, while some physicists reject it completely. For instance, N. David Mermin wrote in Physics Today, "I hope you will agree that you are not a continuous field of operators on an infinite-dimensional Hilbert space, [5] and Meinard Kuhlmann wrote in Scientific American, "quantum field theory ... sounds like a theory of fields. Yet the fields supposedly described by the theory are not what physicists classically understand by the term field". [6]

Between those who approve Quantum Field Theory, most follow Richard Feynman's approach based on particles and virtual particles, while Julian Schwinger's (and Sin-Itiro Tomonaga's) version, which is based only on fields, is much less well-known. [7] Surprisingly enough, Frank Wilczek discloses that Feynman later changed his mind:

Feynman told me that when he realized that his theory of photons and electrons is mathematically equivalent to the usual theory, it crushed his deepest hopes ... He gave up when, as he worked out the mathematics of his version of quantum electrodynamics, he found the fields, introduced for convenience, taking on a life of their own. He told me he lost confidence in his program of emptying space. [8]

Although both methods lead to the identical equations, the physical pictures are quite different. It is Schwinger's Quantum Field Theory that we refer to in this article, but because this variation is so little known, we must first give a brief description.

Definition of field. A field is a property of space. This idea was proposed by Michael Faraday in 1845 as an explanation for electric and magnetic forces. Yet the concept that space has properties was not easy to acknowledge, so when James Maxwell predicted the presence of EM waves in 1864, an ether was created to carry the waves. It took many years before the ether was dispensed with and physicists approved that space itself has properties:

Read the entire article here. 

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"SPOOKY ACTION AT A DISTANCE" IS NOT SO SPOOKY

"Spooky action at a distance", as Einstein called it, refers to the experimental fact that particles can have an effect on each other instantly, even when separated by substantial ranges. For example, if two photons are produced together in what is referred to as an entangled state and the angular momentum of one of these is changed, then the angular momentum of the other one will adjust in a corresponding fashion at the same time, no matter how far apart the particles are. This "spooky" behavior has been known for almost a hundred years and still is a source of confusion.

Yet there is an idea in which the result is not spooky, but rather a natural consequence. I'm referring to Quantum Field Theory, which identifies a world made only of fields, with no particles. What we consider a particle is really a part, or quantum, of a field. Quanta are not localized like particles, but are spread out through space. For example, photons are parts of the electromagnetic field and protons are parts of the matter field. These quanta evolve in a deterministic way as per the fundamental field equations and there is a term in these equations that restricts the speed of propagation to the velocity of light.

However the QFT equations don't tell the whole story. There are events that are not described by the field equations-- for example, when a field quantum transitions energy or momentum to another object. This event is non-local in the sense that the change in, or even disappearance of, the quantum occurs instantly, no matter how spread-out the field may be. It can also happen with two entangled quanta-- no matter how much they are separated. In QFT, this is essential if each quanta is to act as a unit, as per the fundamental basis of QFT.

There is a major distinction between quantum collapse in QFT and wave-function collapse in QM. The previous is an actual physical change in the fields while the following is a change in our knowledge. Despite the fact that we don't have a theory to describe quantum collapse, there is nothing irregular about it. To quote from Fields of Color: The theory that escaped Einstein:

In QFT the photon is a spread-out field, and the particle-like behavior occurs because each photon, or quantum of field, is absorbed as a unit ... It is a spread-out field quantum, but when it is taken in by an atom, the entire field vanishes, no matter how spread-out it is, and all its energy is deposited into the atom. There is a big "whoosh" and the quantum is gone, like an elephant vanishing from a magician's theater.

Quantum collapse is not an easy concept to accept-- perhaps more difficult than the concept of a field. Here I have been working hard, trying to persuade you that fields are a real property of space-- indeed, the only truth-- and now I am requesting you to accept that a quantum of field, spread out as it may be, instantly vanishes into a tiny absorbing atom. Yet it is a process that can be envisioned without inconsistency. In fact, if a quantum is an entity that lives and dies as a unit, which is the very meaning of quantized fields, then quantum collapse must occur. A quantum can not divide and put half its energy in one place and half in another; that would violate the basic quantum principle. While QFT does not provide a breakdown for when or why collapse occurs, some day we may have a theory that does. In any case, quantum collapse is necessary and has been confirmed experimentally.

Some physicists, including Einstein, have been troubled by the non-locality of quantum collapse, declaring that it goes against a fundamental postulate of Relativity: that nothing can be sent out faster than the speed of light. Now Einstein's postulate (which we must remember was only a guess) is indeed valid in relation to the evolution and propagation of fields as described by the field equations. However quantum collapse is not described by the field equations, so there is no reason to expect or to insist that it falls in the domain of Einstein's postulate.

Read more here!

[rodneybrooks32]

Dear New York Times

In the article ("With faint chirp, scientists prove Einstein correct", p. A1, 2/12/16) we review that black holes were part of Einstein's theory. The truth is considerably contrary. "Einstein argued vigorously against black holes [as] incompatible with reality" (see "Black Holes" by R. Anderson) and his rivals held back their acknowledgment for many years.

Einstein was also mistaken when he rejected Quantum Field Theory. According to his biographer A. Pais," QFT was repugnant to him". This is ironic because QFT, and only QFT, clarifies and resolves the paradoxes of Relativity and Quantum Mechanics that most people struggle with (see "Fields of Color: The theory that escaped Einstein" by this writer).

Possibly the greatest irony is the statement, "according to Einstein's theory, gravity is caused by objects warping space and time". Even though that is what everybody thinks today, the actuality is that Einstein recognized gravity as a force field, similar to electromagnetic fields, except that it is generated by mass, not charge. That an oscillating mass generates gravitational waves is no more incomprehensible or surprising than that electromagnetic waves are created when electrons move back and forth in an antenna. To Einstein, curvature was actually a consequential outcome, similar to the alterations in space and time generated by motion according to his Special theory of Relativity.

Black holes. Contrary to numerous reports, black holes were not part of Einstein's idea. In fact Einstein argued vigorously against black holes [as] incompatible with reality, and his opposition held back their approval for many years.

Recap. Gravitational waves are easy to understand if you recognize gravity as a force field, similar to the electromagnetic field (QFT). And while the contraction effect is more subtle, it is not that much different from the F-L contraction that has been recognized for over a hundred years.

Read more here...

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New Physics Theory Solves Paradoxes

By Rodney Brooks

For one hundred years, most people have seen it impossible to understand physics. Examples include Joseph Heller ("writhing in an exasperating quandary over quantum mechanics"), Bill Clinton ("I hope I can finally understand physics before I leave the earth", Richard Feynman ("One had to lose one's common sense"), and even Albert Einstein ("fifty years of pondering have not brought me any closer to answering the question, what are light quanta?).

Julian Schwinger's Contribution to Physics

And yet, there is an idea that makes perfect sense and can be understood by anyone. This theory, with roots in the 1930s, was eventually developed by Julian Schwinger, who once had been considered "the heir-apparent to Einstein's mantle". This success occurred a number of years after Schwinger had already attained physics fame for solving the "renormalization" problem, described by the NY Times as "the most important development in the last 20 years" and was duly awarded the Nobel prize.

Nevertheless for Schwinger this was not good enough. He believed that Quantum Field Theory, as it stood at that point, was still lacking. Schwinger's target was to integrate matter fields and force fields on an equivalent basis. Following numerous years of hard work, he released a collection of five papers entitled "The theory of quantized fields" in 1951-54.

Physicists have been battling a particles-vs.-fields battle for over 100 years. There have been three "rounds", beginning when Einstein's concept of light as a particle (called photon) triumphed over Maxwell's belief that light is a field. Round 2 happened when Schrödinger's hope for a field theory of matter was overcome by the particle-like behavior that physicists could not ignore. And round 3 occurred when Schwinger's field-based solution of renormalization was superseded by Feynman's easier-to-use particle based approach.

For that reason, and others, Schwinger's final development of Quantum Field Theory, which he regarded as far more important than his Nobel prize work, has been unfortunately neglected, and is indeed not known to most physicists-- and to all of the general public.

Fortunately there are signs that QFT, in the true Schwingerian sense is reemerging, so in this sense it is a "new" theory There have been several books and articles, such as "The Lightness of Being" by Nobel laureate Frank Wilczek, "There are no particles, there are only fields" by Art Hobson, and "Fields of Color- The theory that escaped Einstein" by Rodney Brooks. The last one explains QFT to a lay reader, without any equations, and shows how this remarkable "new" theory" resolves the paradoxes of Relativity, Quantum Mechanics and physics that have baffled so many people.

Learn more here!

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GRAVITATIONAL WAVES REVEALED

By Rodney A. Brooks author of "Fields of Color: The Theory That Escaped Einstein".

The current discovery of gravitational waves at LIGO (Laser Interferometer Gravitational-Wave Observatory) has captured the imagination of the public. It will stand as one of the great feats of experimental physics, alongside the famous Michelson-Morley experiment of 1887 which it resembles. In fact by comparing these two experiments, you will discover that comprehending gravitational waves is not as challenging as you think.

Contraction. Michaelson and Morley measured the speed of light at different times as the earth moved around its orbit. To their - and everyone's - surprise, the speed turned out to be continuous, separate of the earth's motion. This breakthrough caused great consternation until George FitzGerald and Hendrick Lorentz came up with the only possible explanation: objects in motion contract. Einstein then showed that this reduction is a consequence of his Principles of Relativity, but without saying why they contract (other than a desire to conform to his Principles). In fact Lorentz had previously provided a partial explanation by showing that motion affects the way the electromagnetic field interacts with charges, causing objects to contract. However it wasn't until Quantum Field Theory came along that a full explanation was found. In QFT, at least in Julian Schwinger's model, everything is made of fields, even space itself, and motion affects the way all fields interact.

Waves. Electromagnetic waves, e.g., radio waves, have long been understood and accepted as a natural phenomenon of fields. Now in QFT gravity is a field and, just as an oscillating electron in an antenna sends out radio waves, so a large mass moving back and forth will send out gravitational waves. But it didn't take QFT to show this. Einstein also believed that gravity is a field that obeys his equations, just as the EM field obeys the equations of James Maxwell. In fact gravitational waves have been recognized by many physicists, from Einstein on down, who regard gravity as a field.

Curvature. But what about "curvature of space-time", which many people nowadays say is what causes gravity? You may be surprised to learn that's not how Einstein saw it. He thought that the gravitational field causes things, even space itself, to contract, analogous to the way motion causes contraction. In fact Einstein used this analogy to show the correlation between motion-induced and gravity-induced contraction: they both affect the way fields interact. It is this gravity-induced contraction that is sometimes knowned as "curvature".

Evidence. The first uncovering of gravitational waves was done at LIGO, using an apparatus similar to Michelson's and Morley's. In both experiments the time for light to travel along two perpendicular paths was examined, but because the gravitational field is much weaker than the EM field, the distances in the LIGO apparatus are much greater (miles instead of inches). Another difference is that while Michelson, not knowing about motion-induced contraction, expected to see a shift (and found none), the LIGO staff used the known gravity-induced contraction to observe a change when a gravitational wave passed through.

Fields of Color: The theory that escaped Einstein explains Quantum Field Theory to a lay audience, without any math. If you want to learn more about gravitational waves or about how Quantum Field Theory resolves the paradoxes of Relativity and Quantum Mechanics, read Chapters 1 and 2, which can be seen free at http://www.quantum-field-theory.net/.

http://quantum-field-theory.net/gravitational-waves-explained/

[rodneybrooks32]

The Forgotten Genius of Physics

I started my graduate study in physics at Harvard University in 1956. Julian Schwinger had just finished his reformulation of Quantum Field Theory and was preparing to teach a three-year series of courses. I sat mesmerized, as did others.

Attending one of [Schwinger's] formal lectures was comparable to hearing a new major concert by a very great composer, flawlessly performed by the composer himself ... The delivery was magisterial, even, carefully worded, irresistible like a mighty river ... Crowds of students and more senior people from both Harvard and MIT attended ... I felt privileged-- and not a little daunted-- to witness physics being made by one of its greatest masters. - Walter Kohn, Nobel laureate ("Climbing the Mountain" by J. Mehra and K.A. Milton).

As Schwinger stood at the blackboard, writing ambidextrously and speaking mellifluously in well-formed sentences, it was as if God Himself was presenting the Ten Commandments. The equations were so elegant that it seemed the world couldn't be constructed any other way. From the barest of first basic principles, he derived all of QFT, even encompassing gravity. Not only was the mathematics beautiful, but the philosophic concept of a world made of properties of space seemed to myself much more satisfying than mysterious particles. I was astonished and thrilled to discover how all the mysteries of relativity theory and quantum mechanics that I had earlier discovered so confusing vanished or were cleared up.

Regretably, Schwinger, once referred to as "the heir-apparent to Einstein's mantle" by J. Robert Oppenheimer, never brought forth the impact he should have had on the world of physics or on the public at large. It is feasible that Schwinger's very elegance was his downfall.

Julian Schwinger was one of the most important and influential scientists of the twentieth century ... Yet even among physicists, recognition of his funda ¬ mental contributions remains limited, in part because his dense formal style ultimately proved less accessible than Feynman's more intuitive approach. However, the structure of modern theoretical physics would be inconceiv ¬ able without Schwinger's manifold insights. His work underlies much of modern physics, the source of which is often unknown even to the practi ¬ tioners. His legacy lives on not only through his work, but also through his many students, who include leaders in physics and other fields.-- "Climbing the Mountain" by J. Mehra and K.A. Milton.

Schwinger is recalled primarily, if he is remembered at all, for figuring out a calculational problem with QFT referred to as renormalization, for which he shared the 1965 Nobel prize with Sin-Itiro Tomanaga and Richard Feynman. Feynman's particle-based approach, which had no theoretical base, proved to be easier to work with than Schwinger's (and Tomanaga's) field-based approach, and Schwinger's method was relegated to the archives. It is Feynman's image, not Schwinger's, that was enshrined on a postage stamp.

Nevertheless Schwinger was not content with his renormalization work:

The pressure to account for those [experimental] results had produced a certain theoretical structure that was perfectly adequate for the original task, but demanded simplification and generalization ... I needed time to go back to the beginnings of things ... My retreat began at Brookhaven National Laboratory in the summer of 1949. It is only human that my first action was one of reaction. Like the silicon chip of more recent years, the Feynman diagram was bringing computation to the masses ... But eventually one has to put it all together again, and then the piecemeal approach loses some of its attraction ... Quantum field theory must deal with [force] fields and [matter] fields on a fully equivalent footing ... Here was my challenge.-- from "The Birth of Particle Physics", ed. by Brown and Hoddeson.

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Quantum Field Theory-- A Solution to the "Measurement Problem".

Definition of the "Measurement Problem".

A notable question in physics today is "the measurement problem", likewise known as "collapse of the "wave-function". The issue developed in the early days of Quantum Mechanics as a result of the probabilistic nature of the equations. Since the QM wave-function explains merely probabilities, the result of a physical measurement can only be determined as a probability. This naturally brings about the question: When a measurement is made, at exactly what point is the ultimate result "decided upon". Some individuals thought that the role of the observer was essential, and that the "decision" was generated when someone looked. This led Schrödinger to propose his famous cat experiment to demonstrate how ridiculous such an idea was. It is not commonly known, but Einstein also proposed a bomb experiment for the very same reason, saying that "a sort of blend of not-yet and already-exploded systems. can not be a real state of affairs, for in reality there is just no intermediary between exploded and not-exploded." At a later time, Einstein remarked, "Does the moon exist only when I look at it?".

The argument persists to this day, with some people still believing that Schrödingers cat is in a superposition of dead and alive until someone looks. On the other hand the majority of people think that the QM wave-function "collapses" at some earlier point, before the uncertainty achieves a macroscopic level-- with the definition of "macroscopic" being the primary question (e.g., GRW theory, Penrose Interpretation, Physics forum). Some individuals take the "many worlds" view, in which there is zero "collapse", but a splitting into different worlds which contain every possible histories and futures. There have been a lot of experiments designed to address this question, e.g., "Towards quantum superposition of a mirror".

We will now see that an unequivocal answer to this issue is presented by Quantum Field theory. However since this theory has been disregarded or misunderstood by many physicists, we must initially specify what we imply by QFT.

Definition of Quantum Field Theory. The Quantum Field Theaory described within this article is the Schwinger version where there are no particles, there are only fields, not the Feynman variation which is based on particles. * The 2 versions are mathematically equivalent, but the concepts supporting them are really different, and it is the Feynman model that is chosen by most Quantum Field Theory physicists.

* According to Frank Wilczek, Feynman ultimately changed his mind: "Feynman informed me that when he realized that his theory of photons and electrons is mathematically equivalent to the usual theory, it crushed his deepest hopes ... He gave up when ... he found the fields introduced for convenience, taking on a life of their own.".

In Quantum Field Theory, as we will make use of the term henceforward, the world is composeded of fields and only fields. Fields are defined as characteristics of space or, to put it in a different way, space is comprised of fields. The field concept was introduced by Michael Faraday in 1845 as an illustration for electric and magnetic forces. Though the concept was not easy for people to accept and so when Maxwell demonstrated that these equations predicted the existence of EM waves, the idea of an ether was presented to carry the waves. These days, however, it is generally accepted that space can possess properties:.

To reject the ether is essentially to believe that empty space has no physical qualities whatsoever. The basic truths of mechanics do not harmonize with this view.-- A. Einstein (R2003, p. 75).

Moreover space-time in itself had come to be a dynamical medium-- an ether, if there ever was one.-- F. Wilczek ("The persistence of ether", Physics Today, Jan. 1999, p. 11).

Even though the Schrödinger equation is the non-relativistic limit of the Dirac equation for matter fields, there is an important and fundamental distinction between Quantum Field Theory and Quantum Mechanics. One illustrates the strength of fields at a given point, the other illustrates the probability that particles could be discovered at that point, or that a given state exists....

For the rest of this article visit the blog at Fields of Color.

[rodneybrooks32]

How Quantum Field Theory Solves the "Measurement Problem".

It is not usually known that Quantum Field Theory supplies a basic answer to the "measurement problem" that was examined on the September letters page of Physics Today. But by QFT I do not mean Feynman's particle-based theory; I mean Schwinger's QFT where "there are no particles, there are only fields".1.

The fields exist in the form of quanta, i.e., chunks or units of field, as Planck envisioned over a century ago. Field quanta evolve in a deterministic way defined by the field equations of QFT, except when a quantum abruptly deposits some or all of its energy or momentum into an absorbing atom. This is known as "quantum collapse" and it is not explained by the field equations. In reality there is no principle that explains it. All we understand is that the chance of it occurring depends on the field strength at a given location. Or, if it is an internal collapse, like a change in angular momentum, the probability depends on the element of angular momentum in the given direction. In QFT this collapse is a physical event, not a mere shift in probabilities as in Quantum Mechanics.

Many physicists are troubled by the non-locality of quantum collapse in which a spread-out field (or even two correlated quanta) suddenly disappears or changes its inner condition. Yet non-locality is required if quanta are to work as a unit, and it has been experimentally confirmed. It does not lead to inconsistencies or paradoxes. It might not be just what we anticipated, but just as we acknowledged that the earth is round, that the planet orbits the sun, that matter is made of atoms, we should have the ability to accept that quanta can collapse.

In some cases quantum collapse can bring about a macroscopic change or "measurement". Yet the measurement outcome, i.e., the "decision", was determined at the quantum level. Everything after the collapse follows without doubt. There is no "superposition" or "environment-driven process of decoherence.".

Use Schrödinger's cat as an illustration. If a radiated quantum collapses and deposits its energy into one or more atoms of the Geiger counter, that triggers a Townsend discharge that leads inexorably to the death of the cat. In Schrödinger's words, "the counter tube discharges and through a relay releases a hammer which smashes a little flask of hydrocyanic acid" and the cat dies. On the other hand, if it doesn't collapse in the Geiger counter then the cat lives....

For the full article visit Fields of Color by Rodney A. Brooks

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The Uncertainty Principle

The probabilistic comprehension of Schrödinger's equation ultimately resulted in the uncertainty principle of Quantum Mechanics, produced in 1926 by Werner Heisenberg. This principle states that an electron, or any other particle, can not have its particular position known, or even specified. More precisely, Heisenberg formulated an equation that relates the uncertainty in position of a particle to the uncertainty of its momentum. So not only do we have wave-particle duality to manage, we need to manage particles that might be here or might be there, but we can't say where. If the electron is actually a particle, then it only stands to reason that it must be someplace.

Resolution. In Quantum Field Theory there are no particles (stop me if you have indeed heard this before) and therefore no location-- certain or uncertain. Rather there are blobs of field that are spread out over space. Rather than a particle that is either here or here or potentially there, we have a field that is here and here and there. Extending out is a thing that only a field can do; a particle can't do it. Actually Heinsenberg's Uncertainty Principle is not much different from Fourier's Theorem (uncovered in 1807) that associates the spatial spread of any wave to the spread of its wave length.

This doesn't mean that there is no uncertainty in Quantum Field Theory. There is uncertainty in regard to field collapse, but field collapse is not identified by the equations of QFT; Quantum Field Theory can only forecast probabilities of when it occurs. Having said that there is a significant difference involving field collapse in QFT and the corresponding wave-function collapse in QM. The former is an actual physical change in the fields; the latter is only a change in our understanding of where the particle is....

For the full article visit the Fields of Color Blog.

[rodneybrooks32]

Scientific American, EINSTEIN DIDN'T SAY THAT!

In the September "Einstein" issue of Scientific American, readers are given the impression that gravity is caused by curvature of space-time. As an example, on the 1st page of that section, we read "gravity ... is the by-product of a curving universe", on p. 43 we find that "the Einstein tensor G describes how the geometry of space-time is warped and curved by massive objects", and on p. 56 there is a reference to "Albert Einstein's explanation of how gravity emerges from the bending of space and time".

In reality, lots of physicist today stress "curvature" as the definition for gravity. As Stephen Hawking penned in A Brief History of Time, "Einstein made the revolutionary suggestion that gravity is not a force like other forces, but is a consequence of the fact that space-time is not flat, as had been previously assumed: it is curved, or warped.".

The trouble is, that's NOT what Einstein said. Einstein made it quite clear that gravity is a force just like other forces, along with (obviously) specific differences. In the actual paper indicated by Scientific American ("The foundation of the general theory of relativity", 1916) he wrote," [there is] a field of force, namely the gravitational field, which possesses the remarkable property of imparting the same acceleration to all bodies". The G tensor, said Einstein "describes the gravitational field." The term "gravitational field" or just "field" occurs 58 times in this write-up, while the term "curvature" does not show up in any way (besides in relation to "curvature of a ray of light"). And Einstein is not the sole physicist who believes that. As an example Sean Carroll, a prominent physicist these days, wrote:.

Einstein's general relativity describes gravity in terms of a field that is defined at every point in space ... The world is really made out of fields ... deep down it's really fields ... The fields themselves aren't "made of" anything-- fields are what the world is made of ... Einstein's ... "metric tensor"... can be thought of as a collection of ten independent numbers at every point.-- Sean Carroll.

To suppress the field concept and emphasize "curvature" not only misstates Einstein's perspective; it likewise offers people a false or misleading knowledge of general relativity.

So where does "curvature" come from? According to Einstein (in the cited paper), the gravitational field creates physical adjustments in the length of measuring rods (just like temperature can cause such changes) and it is these changes that create a non-Euclidean metric of space. In fact, as Einstein indicated, these changes can take place even in a space which is devoid of gravitational fields-- i.e., a rotating system. He then demonstrated that this non-Euclidean geometry is mathematically equivalent to the geometry on a curved surface, which had been established by Gauss and extended (mathematically) to any amount of dimensions by Riemann. That this is a mathematical equivalence is clearly stated by Einstein in a later paper: "mathematicians long ago solved the formal problems to which we are led by the general postulate of relativity".

For the full story visit the Fields of Color Blog.

[rodneybrooks32]

When Do Fields Collapse?

A major concern in physics these days is about collapse of the "wave-function": When does it take place? There have been numerous speculations (see, e.g., Ghirardi-- Rimini-- Weber theory, Penrose Interpretation, Physics forum) and experiments (e.g., "Towards quantum superposition of a mirror") concerning this. The more extreme view is the opinion that Schrödinger's cat is both alive and dead, despite the fact that Schrödinger proposed this particular thought-experiment (like Einstein's less-well-known bomb experiment) to demonstrate how ludicrous this sort of an idea is.

The complication emerges because Quantum Mechanics can only calculate probabilities until an observation happens. Nevertheless Quantum Field Theory, which works in actual field intensities-- not probabilities, provides an uncomplicated unquestionable answer. However, Quantum Field Theory in its authentic sense of "there are no particles, there are only fields" (Art Hobson, Am. J. Phys. 81, 2013) is dismissed or misconceived by most physicists. In QFT the "state" of a system is described by the field intensities (technically, their expectation value) at every point. These fields are real properties of space that act deterministically depending on the field equations-- with one exemption.

The different is field collapse, but in Quantum Field Theory this is a really different thing from "collapse of the wave function" in QM. It is a physical event, not a change in likelihoods. It takes place when a quantum of field, regardless of how spread-out it might be, instantly deposits its energy into a single atom and disappears. (There are also other kinds of collapse, for example, scattering, coupled collapse, internal change, etc.) Field collapse is not defined by the field equations-- it is a different event, but simply because we do not possess a theory for it does not indicate it can not occur. The fact that it is non-local troubles some physicists, but this non-locality has been proven in several experiments, and it does not generate any disparities or paradoxes.

So whenever field collapse occurs, the ultimate "decision"-- the moment of truth-- is reached. This is QFT's response to when does collapse occur: when a quantum of field colapses. In the instance of Schrödinger's cat, this is when the radiated quantum (perhaps an electron) is grabbed by an atom in the Geiger counter.

Before a field quantum finally collapses, it may have interacted or entangled with numerous other atoms along the way. These interactions are defined (deterministically) by the field equations. However the quantum can not have indeed collapsed into any of those atoms, given that collapse can take place just one time, so no matter what you refer to it as-- interaction, entanglement, perturbation, or just "diddling"-- these preliminary interactions are reversible and do not result in macroscopic changes. Then, when the final collapse transpires, those atoms come to be "undiddled" and return to their undisturbed state.

To summarize, in QFT the "decision" is made when a quantum of field deposits all its energy into an absorbing atom. Besides replying to this issue, QFT also clarifies why time dilates in Special Relativity and solves the wave-particle duality issue of Quantum Mechanics. One can simply wonder the reason that this concept hasn't been welcomed and made the basis for our awareness of nature. I feel it is truly time for physicists to WAKE UP AND SMELL THE QUANTUM FIELDS.

Find out more on the blog!

[rodneybrooks32]

Book Streamlines Confusing Quantum Field Theory

The following is a current write-up written about Quantum Field Theory and the book, Fields of Color. The article appeared in the Leisure World News on September 4, 2015.

The publication "Fields of Color: The Theory that Escaped Einstein" clarifies the sophisticated Quantum Field Theory so a nonprofessional can understand it. Written by Leisure World resident Rodney Brooks, it includes no formulas-- in fact, no math-- and it utilizes colors to represent fields, which in themselves are challenging to think of. It demonstrates the field picture of nature resolves the paradoxes of quantum mechanics and relativity that have puzzled numerous individuals. It is original, comprehensive, and entertaining.

Brooks is impressed and wowed with the success of his book, that was released in 2011. He says 6,000 copies have been sold, unusual for a self-published book on physics. Additionally, the publication has a 4.4 (out of 5) star rating on Amazon with greater than 90 reader reviews-- a greater rating than Einstein's own book on relativity and more than Stephen Hawking's popular book "The Theory of Everything.".

In its essence, quantum field theory (QFT) describes a world made of fields, not particles (neutrons, electrons, protons) as most physicists conclude. However the field principle is hard to comprehend. To quote from Chapter 1 of "Fields of Color": "To put it briefly, a field is a property or a condition of space. The field concept was introduced into physics in 1845 by Michael Faraday as an explanation for electric and magnetic forces. However, the idea that fields can exist by themselves as "properties of space" was too much for physicists of the time to accept." (Chapter 1 in its entirety can be read at http://www.quantum-field-theory.net/).

Colors of Fields. Later on this idea was extended to other fields. "In Quantum Field Theory the entire fabric of the cosmos is made of fields, and I use (arbitrary) colors to help people visualize them," says Brooks. "If you can picture the sky as blue, you can picture the fields that exist in space. Besides the EM (electromagnetic) field ('green'), there are the strong force field ('purple') that holds protons and neutrons together in the atomic nucleus and the weak force field ('brown') that is responsible for radioactive decay. Gravity is also a field ('blue'), and not 'curvature of space-time' which most people, including me, have trouble visualizing.".

He carries on: "In QFT, space is the same old three-dimensional space that we intuitively believe in, and time is the time that we intuitively believe in. Even matter is made of fields-- in fact two fields. I use yellow for light particles like the electron and red for heavy particles,.

like the proton. But make no mistake, in QFT these 'particles' are not little balls; they are spread-out chunks of field, called quanta. Thus the usual picture of the atom with electrons traveling around the nucleus like little balls, is replaced by a 'yellowness' of the space around the nucleus that represents the electron field.".

Brooks' interest in physics was initially triggered when at age 14 he read Arthur Eddington's "The Nature of the Physical World." This book explains how a table is made from small atoms that consequently can be split into even tinier objects. "So this is what the world is made of," Brooks thought at the time. In college at the University of Florida he majored in mathematics with a minor in physics. He was then drafted into the army for two years.

Quantum Field Theory Answers Problem. Fast forward to graduate school at Harvard University where Brooks was a National Science Foundation scholar, majoring in physics. Throughout this time, he enrolled in a three-year formal lecture series instructed by Julian Schwinger. The Nobel prize-winning physicist had just finished his reformulation of QFT, so the timing was perfect. "I was shocked that all the mysteries of relativity and quantum mechanics that had earlier perplexed me disappeared or were resolved," Brooks says.

After receiving his Ph.D. at Harvard under Nobel laureate Norman Ramsey, Brooks worked for 25 years at the National Institutes of Health in Bethesda, Md., in neuroimaging. His 1st research study was regarding the new technique of Computered Tomography (CT), during which time he developeded the approach now known as dual-energy CT. Later, he did research on Positron Emission Tomography (PET) and ultimately in Magnetic Resonance Imaging (MRI). Altogether, Brooks published 124 peer-reviewed articles.

After he retired, he and his wife, Karen Brooks, moved to New Zealand in 2001. That was the time he became conscious of the widespread confusion about physics, particularly quantum mechanics and relativity, whilst his precious QFT that fixes the confusion was overlooked, misunderstood, or forgotten.

"Consequently I tackled the vision of illustrating the principles of quantum field theory to the public," Brooks says.

His book was initially published in New Zealand in 2010, and is presently in its 2nd edition.

In 2012, his grandchildren, who reside in Maryland called out, and he and his wife relocated to Leisure World, where he continues to work on his mission. Although Einstein ultimately came to believe that reality should consist of fields and fields alone, he wanted there to be a solitary "unified" field that would not simply include gravity and electromagnetic forces (the only two forces known back then), but would additionally include matter.

He devoted the last 25 years of his existence unsuccessfully hunting for this particular unified field theory.

Referring to the particle image that he upheld, physicist Richard Feynman once said, "The theory ... describes Nature as absurd from the point of view of common sense. And it agrees fully with experiment. So I hope you can accept Nature as She is-- absurd.".

Brooks, on the other hand, concludes his introductory chapter by saying, "I hope you can accept Nature as She is: beautiful, consistent and in accord with common sense-- and made of quantized fields.".

Read more on the Fields of Color Blog.

[rodneybrooks32]

Space-Time Curvature & Quantum Field Theory

General Relativity is the name given to Einstein's theory of gravity which was described in Chapter 2 of my book. As the theory is typically shown, it illustrates gravity as a curvature in four-dimensional space-time. Now this is an idea far outside the grasp of regular people. Merely the concept of four-dimensional space-time brings most of us to tremble ... The answer in Quantum Field Theory is simple: Space is space and time is time, and there is no curvature. In QFT gravity is a quantum field in ordinary three-dimensional space, just like the other three force fields (EM, strong and weak).

This does not imply that four-dimensional notation is not practical. It is a convenient approach of dealing with the mathematical partnership between space and time that is called for by special relativity. One could almost say that physicists couldn't live without having it. Nevertheless, spatial and temporal advancement are basically different, and I say shame on people who attempt to foist and press the four-dimensional principle onto the public as vital to the knowledge of relativity theory.

The idea of space-time curvature also had its origin in mathematics. When searching for a mathematical technique that could embody his Principle of Equivalence, Einstein was led to the formulas of Riemannian geometry. And of course, these formulas define four-dimensional curvature, for those who can easily imagine it. You see, mathematicians are not restricted by physical restraints; formulas that have a physical significance in 3 dimensions can be generalized algebraically to any variety of dimensions. But when you do this, you are actually addressing algebra (formulas), not geometry (spatial configurations).

By flexing our minds, several of us may even develop a vague mental image of what four-dimensional curvature might be like if it did exist. However, claiming that the gravitational field equations are equal to curvature is certainly not the same as claiming that there is curvature. In Quantum Field Theory, the gravitational field is just yet another force field, like the EM, strong and weak fields, albeit with an increased complexity which is shown in its higher spin value of 2.

While QFT resolves these paradoxical statements, I don't want to leave you having the notion that the theory of quantum gravity is problem-free. While computational troubles involving the EM field were conquered by the process referred to as renormalization, very similar issues involving the quantum gravitational field have not been conquered. Fortuitously they do not interfere with macroscopic calculations, for which the QFT formulas come to be identical to Einstein's.

Your choice. Once more you the reader have an option, as you did in concern to the 2 methods to special relativity. The choice is not concerning the equations, it has to do with their interpretation. Einstein's equations can be translated as suggesting a curvature of space-time, unpicturable as it may be, or as explaining a quantum field in three-dimensional space, much like the other quantum force fields. To the physicist, it really does not make much difference. Physicists are far more interesteded in solving their equations than with deciphering them. If you will allow me another Weinberg quote:

The important thing is to be able to make predictions about images on the astronomers photographic plates, frequencies of spectral lines, and so on, and it simply doesn't matter whether we ascribe these predictions to the physical effects of gravitational fields on the motion of planets and photons or to a curvature of space and time. (The reader should be warned that these views are heterodox and would meet with objections from many general relativists.)-- Steven Weinberg

And so in the event that you prefer, you can think that gravitational effects are because of a curvature of space-time (even if you can't visualize it). Or, like Weinberg (and me), you could view gravity as a force field that, just like the other force fields in Quantum Field Theory, exists in three-dimensional space and progresses in time according to the field equations.

Find out more about Quantum Field Theory at Fields of Color blog!

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Why Then is the Speed of Light Constant?

The inquiry "The reason is the speed of light constant?" is frequently asked about by those trying to comprehend physics. Google has 2760 links to that query. But the answer is so simple that a 10-year-old can comprehend it, that is, if you accept Quantum Field Theory.

Take the ten-year-old to a lake and drop a stone in the water. Show her that the waves travel through the water at a certain velocity, and tell her that this speed depends solely on the properties of water. You could release different types of items at varying places and show her that the waves travel at the same velocity, no matter the size of the item or location of the water.

Then inform her that sound travels through air with a fixed speed that depends only on the properties of air. You may wait for a thunderstorm and time the difference in between the lightning and the noise. Tell her that a whisper travels as fast as a yell. I believe a ten-year-old can easily comprehend the idea that water and air have properties that identify the velocity of these waves, regardless of whether she doesn't understand the formulas.

Anyone who can understand this can then understand why the speed of light is constant. You see, in Quantum Field Theory space has properties, just as air and water have properties. These properties are called fields.

As Nobel laureate Frank Wilczek wrote, "One of the most basic results of special relativity, that the speed of light is a limiting velocity for the propagation of any physical influence, makes the field concept almost inevitable.".

When you recognize the concept of fields (which admittedly is not an easy one), that is actually all you need to know. Light is waves in the electromagnetic field that travel through space (not space-time) at a rate dictated by the properties of space. They comply with relatively basic equations (not that you need to know them), just like sound and water waves comply with simple formulas. OK, the Quantum Field Theory formulas are a tad more difficult, but quoting Wilczek again, "The move from a particle description to a field description will be especially fruitful if the fields obey simple equations ... Evidently, Nature has taken the opportunity to keep things relatively simple by using fields.".

Even so this question can possess a different meaning: "Why is the speed of light independent of motion?" This reality was initially shown by the famous Michelson-Morley experiment, where light beams were timed as the earth revolved and rotated. The surprising outcome was that the speed of light was precisely the same irrespective of the earth's motion.

As I wrote in my book (see quantum-field-theory. net): That the speed of light should be independent of movement was most shocking ... It makes no sense for a light beam - or anything, for that concern - to travel at the identical speed no matter the movement of the observer ... unless "something funny" is going on. The "something funny" turned out to be even more surprising than the M-M outcome itself. In a nutshell, objects contract when they move! Even more specifically, they contract in the direction of movement. Think about it. If the path length of Michelson's apparatus in the forward direction contracted by the exact same amount as the extra distance the light beam would certainly have to travel due to motion, the two effects would cancel out. Actually, this is the only way that Michelson's null result could be illustrated.

Nevertheless the idea that items contract when in motion was just as puzzling as the Michelson-Morley outcome. Why should this be? Once again the explanation is provided by Quantum Field Theory. Quoting once more from my publication:.

We must recognize that even if the molecular configuration of an object appears to be fixed, the component fields are constantly interacting with one another. The EM field interacts with the matter fields and vice versa, the strong field interacts with the nucleon fields, etc. These interactions are what keeps the item together. Now if the item is moving rather quickly, this communication among fields will certainly become harder because the fields, on the average, will need to interact through greater distances. Therefore the object in motion must somehow adjust itself so that the exact same interaction among fields can occur. How can it do this? The sole way is by reducing the distance the component fields need to travel. Because the spacing between atoms and molecules, and thus the dimensions of an item, are determined by the nature and arrangement of the force fields that bind them together, the dimensions of an object must therefore be affected by motion.

It is very important to understand that it is not just Michelson's apparatus that contracted, it is anything and everything on earth, including Michelson himself. Even if the earth's speed and the consequent contraction were considerably greater, we on earth would still be ignorant of it. As John Bell wrote about a moving observer:.

But will she not see that her meter sticks are contracted when laid out in the [direction of motion] - and even decontract when turned in the [other] direction? No, because the retina of her eye will also be contracted, so that just the same cells receive the image of the meter stick as if both stick and observer were at rest. - J. Bell (B2001, p. 68).

To conclude, for individuals who would like to comprehend physics, I say use Quantum Field Theory and: WAKE UP AND SMELL THE FIELDS.

[rodneybrooks32]

EXACTLY WHAT DOES THE ELECTRON LOOK LIKE?

http://www.quantum-field-theory.net/electron-look-like/

In June, 2014, I lectured at the Physics Department of the Czech Technical University in Prague. I began by asking the question "Just what does the electron look like?", and I presented two images. The first was the familiar Rutherford image of particles orbiting a nucleus, and the second was a (very simplified) image of the electron as a field in the space around the nucleus.

Then I called for a vote. Rather remarkably just 4 individuals in the crowd selected the field picture, and not a single person chose the particle image. In other words, THEY DID N'T KNOW. So here we are, 117 years after the electron was discovered, and this highly educated group of physicists had zero idea what it looks like.

Naturally when the electron was identified by J. J. Thomson, it was naturally pictured as a particle. Nevertheless, particles are easy to visualize, while the field idea, let alone a quantized field, is not an easy one to comprehend. But this photo soon faced problems which led Niels Bohr in 1913 to propose that the particles in orbit picture must be replaced by something new: undefined electron conditions that fill the following two postulates:

1. [They] have a peculiarly, mechanically unexplainable [emphasis added] stability.

2. In opposition to the classical EM theory, no radiation takes place from the atom in the stationary states on their own, [but] a process of transition among two stationary conditions can be accompanied by the emission of EM radiation.

This led Louis de Broglie to suggest that the electron has wave characteristics. There then followed a type of battle, with Paul Dirac leading the "particle side" and Erwin Schrodinger the "wave side":.

We insist that the atom in fact is just the ... phenomenon of an electron wave caught, as it were, by the nucleus of the atom ... From the point of view of wave mechanics, the [particle image] would be simply fictitious.-- E. Schrodinger.

However the fact that a free electron imitates a particle could not be solved, consequently Schrodinger gave in and Quantum Mechanics became a theory of particles that are described by probabilities.

A 2nd battle occurred in 1948, when Richard Feynman and Julian Schwinger (together with Hideki Tomanaga) created various methods to the "renormalization" issue that plagued physics. Once more the particle view espoused by Feynman won out, in huge part considering that his particle diagrams proved simpler to work with than Schwinger's field equations. Therefore 2 generations of physicists have been raised on Feynman designs and led to trust that nature is made of particles.

Meanwhile, the theory of quantized fields was improved by Julian Schwinger:.

My retreat started at Brookhaven National Laboratory in the summer of 1949 ... Like the silicon chip of more recent years, the Feynman design was giving computation to the masses ... But inevitably one must bring it all together again, and after that the piecemeal method loses a bit of its appeal ... Quantum field theory must deal with [force] fields and [matter] fields on a fully comparable ground ... Here was my challenge.-- J. Schwinger.

Schwinger's final version of the theory was released between 1951 and 1954 in a collection of five documents entitled "The Theory of Quantized Fields". In his words:.

It was to be the purpose of further advancements of quantum mechanics that these 2 distinct timeless principles [particles and fields] are combined and become transcended in a thing that has no classical equivalent-- the quantized field that is a new conception of its own, an unity that substitutes the classical duality.-- J. Schwinger.

I believe that the primary reason these masterpieces have been ignored is that several physicists found them too hard to understand. (I know one who could not get past the very first page.).

And so the option is yours. You can assume that the electron is a particle, despite the numerous inconsistencies and absurdities, not to mention inquiries like how big the particles are and what are they constructed from. Or you could conclude it is a quantum of the electron field. The choice was described this way by Robert Oerter:.

Wave or particle? The answer: Both, and neither. You could think of the electron or the photon as a particle, but only if you wanted to allow particles act in the peculiar way explained by Feynman: appearing again, disrupting each other and cancelling out. You can also think of it as a field, or wave, but you had to keep in mind that the sensor always registers one electron, or none-- certainly never half an electron, no matter just how much the field has been broken up or stretched out. In the end, is the field just a calculational instrument to tell you where the particle will be, or are the particles just calculational tools to inform you what the field values are? Take your pick.-- R. Oerter.

What Oerter neglected to mention is that QFT describes why the detector constantly registers one electron or none: the field is quantized. The Q in QFT is extremely important.

Therefore when you take your pick, dear reader, I really hope you will never select the picture of nature that doesn't make sense-- that even its proponents call "bizarre". I hope that, like Schwinger, Weinberg, Wilczek, Hobson (and me), you will choose a truth comprised of quantum fields-- properties of space that are described by the equations of QFT, the most philosophically acceptable picture of nature that I can imagine.

Find out more on the blog for Fields of Color

[rodneybrooks32]

EINSTEIN DIDN'T STATE THAT!

Many people think that Einstein's theory of basic relativity states that gravity is due to curvature in space-time. For instance, here's a new question placed on Quora: ""Einstein tells us that gravity is motion in curved space-time, so why do scientists still refer to it a force?".

I'm sorry for screaming, but this one really makes me insane. EINSTEIN DID N'T SAY THAT! In his theory of general relativity, developed in 1915, gravity is a force field, not much different from the electro-magnetic (EM) field. It is CERTAINLY NOT four-dimensional curvature. But first a bit of history.

The field principle was presented into physics in 1845 by Michael Faraday through his studies of electric and magnetic phenomena. When James Maxell supplied equations for Faraday's field in 1864, the field view of EM forces was commonly accepted. However Isaac Newton's theory of gravity, which involved "action at a distance", stayed unchanged. Newton's theory was extremely successful, and is still taught in elementary physics programs today, but Newton was not satisfied with the concept of "action-at-a-distance", saying "That one body may act upon another at a distance, through a vacuum, without the mediation of anything else ... is to me so great an absurdity, that I believe no man who has in philosophical matters a competent faculty of thinking can ever fall into it.".

This altered, of course, when Einstein presented his theory of general relativity in 1915. In Einstein's words: "As a result of the more careful study of electromagnetic phenomena, we have come to regard action at a distance as a process impossible without the intervention of some intermediary medium ... The effects of gravitation also are regarded in an analogous manner ... The action of the earth on the stone takes place indirectly. The earth produces in its surroundings a gravitational field, which acts on the stone and produces its motion of fall ... [T] he intensity and direction of the field at points farther removed from the body are thence determined by the law which governs the properties in space of the gravitational fields themselves.".

Keep in mind that Einstein stated not a thing about "curvature". By developing formulas for the gravitational field, as Maxwell had carried out for EM forces, Einstein answered Newton's grievance about action-at-a-distance and brought the gravitational field into physics on a par with the EM field.

For individuals who don't know just what a field is, I provide this straightforward definition: A field is a property of space. There is no such thing as vacant space. You cannot have space without fields. These fields follow laws (i.e., formulas) that specify how an adjustment at one point impacts the field at adjacent points, and also how one field impacts other fields.

Find out more on the blog at Fields of Color...

[rodneybrooks32]

The Principle of Relativity - The Easy Way

In the whole history of physics there is absolutely no formula more popular than e = mc2. This connection amongst mass (m) and energy (e) was derived in 1905 by Albert Einstein from his Principle of Relativity. The derivation wasn't easy and merited a paper on its own, referred to as "Does the inertia of a body depend upon its energy content?". The formula continues to baffle and dumbfound lay folks, since in the usual particle picture of nature, it is difficult to see why there is a likeness between mass and energy.

Meanwhile, a new theory called Quantum Field Theory was created. QFT was perfected in the 1950s by Julian Schwinger in five papers called "Theory of Quantized Fields". In QFT there are no particles, there are only fields-- quantized fields. Schwinger succeeded in positioning matter fields (leptons and hadrons) on an equal footing with force fields (gravity, electromagnetic, strong and weak), in spite of the obvious differences between them. Additionally, 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 mostly forgotten.

Yet QFT has lots of advantages. It has a stronger basis than the particle picture. It explains many things that the particle picture does not, including the numerous paradoxes related to Relativity Theory and Quantum Mechanics, that have confused so many people. Philosophically, many people can accept fields as basic properties of space, as opposed to particles, whose composition is unknow. Or if there pictured as point particles, one can only ask "points of what?" And above all, QFT provides an effortless derivation and understanding of e = mc2, as follows.

Mass. In classical physics, mass is a measure of the inertia of a body. In QFT a few of the field equations include a mass term that affects the speed at which quanta of these fields evolve and propagate, slowing it down. Therefore mass takes on the same inertial role in QFT that it does in classical physics. But this is not all it does; this same phrase causes the fields to oscillate, and the greater the mass, the higher the frequency of oscillation. The result, if you're picturing these fields as a color in space (as in my book "Fields of Color"), is a kind of shimmer, and the greater the mass, the faster the shimmer. It might appear strange that the same term that slows the spatial development of a field also causes 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 ability to perform work, which is specified as exerting a force over a distance. This definition, however, does not offer much of a picture, so in classical physics, energy is a rather abstract idea. In QFT, alternatively, the energy of a quantum is determined by the oscillations in the field that makes up the quantum. As a matter of 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 precisely from the equations of QFT.

wilczek_frankWell, since both mass and energy are associated with oscillations in the field, it doesn't take an Einstein to see that there must be a relationship between the two. Actually, any schoolboy can combine the 2 equations and discover (big drum roll, please) e = mc2. Not only does the equation tumble right out of QFT, its meaning can be visualized in the oscillation or "shimmer" of the fields. Nobel laureate Frank Wilczek calls these oscillations "a marvelous bit of poetry" that create a "Music of the Grid" (Wilczek's term for space seen 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 various combos of quarks, gluons, electrons, photons, ... and allow them to settle till they reach equilibrium 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 viewed it in the publications I've read. And still I consider it 1 of the amazing accomplishments of QFT.

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