The Forgotten Genius of Physics

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

Julian SchwingerAttending 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 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 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.

Unfortunately, Schwinger, once called “the heir-apparent to Einstein’s mantle” by J. Robert Oppenheimer, never had the impact he should have had on the world of physics or on the public at large. It is possible that Schwinger’s very elegance was his undoing.

Julian Schwinger was one of the most important and influential scientists of the twentieth century… Yet even among physicists, recognition of his funda­mental 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 inconceiv­able without Schwinger’s manifold insights. His work underlies much of modern physics, the source of which is often unknown even to the practi­tioners. 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 remembered primarily, if he is remembered at all, for solving a calculational problem in QFT called 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 basis, 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.

However Schwinger was not satisfied 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.

Schwinger’s final version of the theory was published between 1951 and 1954 in a series of five papers entitled “The Theory of Quantized Fields”. I believe that the main reason these masterpieces have been ignored is that many physicists found them too hard to understand. (I know one who couldn’t get past the first page.)

Schwinger went on from there to develop a new approach to Quantum Field Theory that he called source theory (and he called its practitioners “sourcerers”), which is also virtually unknown.

In addition to these momentous contributions to Quantum Field Theory, Schwinger had other accomplishments. As a 19-year old graduate student at Columbia University he was the first to determine the spin of the neutron. In 1957 he found the correct form for the weak field equations before Gell-mann and Feynman. He was the first to suggest electroweak unification, for which Sheldon Glashow, Steven Weinberg and Abdus Salam received the 1979 Nobel Prize. And he suggested the Higgs mechanism before Peter Higgs, who shared the 2013 Nobel Prize with Francois Englert.

There is no doubt that Julian Schwinger more than fulfilled his promise as “the heir-apparent to Einstein’s mantle”, and yet many physicists – let alone the general public – don’t even know his name. As I wrote in the preface to my book (see quantum-field-theory.net):

But most of all I dedicate this book to the memory of Julian Schwinger, one of the greatest physicists of all time and, sadly, one of the most forgotten. It was Schwinger who turned Quantum Field Theory into the beautiful structure that I have tried to convey to a wider public.

To Read more about Quantum Field Theory, Click Here

Quantum Field Theory – A Solution to the “Measurement Problem”

Definition of the “Measurement Problem”

A major question in physics today is “the measurement problem”, also known as “collapse of the “wave-function”.  The problem arose in the early days of Quantum Mechanics because of the probabilistic nature of the equations.  Since the QM wave-function describes only probabilities, the result of a physical measurement can only be calculated as a probability.  This naturally leads to the question: When a measurement is made, at what point is the final result “decided upon”.  Some people believed that the role of the observer was critical, and that the “decision” was made when someone looked.  This led Schrödinger to propose his famous cat experiment to show how ridiculous such an idea was.  It is not generally known, but Einstein also proposed a bomb experiment for the same reason, saying that “a sort of blend of not-yet and already-exploded systems.. cannot be a real state of affairs, for in reality there is just no intermediary between exploded and not-exploded.”  At a later time, Einstein commented, “Does the moon exist only when I look at it?

The debate continues to this day, with some people still believing that Schrödingers cat is in a superposition of dead and alive until someone looks.  However most people believe that the QM wave-function “collapses” at some earlier point, before the uncertainty reaches a macroscopic level – with the definition of “macroscopic” being the key question (e.g., GRW theory,  Penrose Interpretation, Physics forum).   Some people take the “many worlds” view, in which there is no “collapse”, but a splitting into different worlds that contain all possible histories and futures.  There have been a number 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 question is provided by Quantum Field theory. However since this theory has been ignored or misunderstood by many physicists, we must first define what we mean by QFT.

Definition of Quantum Field Theory

The Quantum Field Theaory referred to in this article is the Schwinger version in which there are no particles, there are only fields, not the Feynman version which is based on particles.*  The two versions are mathematically equivalent, but the concepts behind them are very different, and it is the Feynman version that is used by most Quantum Field Theory physicists.

*According to Frank Wilczek, Feynman eventually 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… he found the fields introduced for convenience, taking on a life of their own.”

In Quantum Field Theory, as we will use the term henceforward, the world is made of fields and only fields.  Fields are defined as properties of space or, to put it differently, space is made of fields.  The field concept was introduced by Michael Faraday in 1845 as an explanation for electric and magnetic forces.  However the concept was not easy for people to accept and so when Maxwell showed that these equations predicted the existence of EM waves, the idea of an ether was introduced to carry the waves.  Today, however, it is generally accepted that space can have properties:

To deny the ether is ultimately to assume that empty space has no physical qualities whatever. The fundamental facts of mechanics do not harmonize with this view. – A. Einstein (R2003, p. 75)

Moreover space-time itself had become a dynamical medium – an ether, if there ever was one. – F. Wilczek (“The persistence of ether”, Physics Today, Jan. 1999, p. 11).

Although the Schrödinger equation is the non-relativistic limit of the Dirac equation for matter fields, there is an important and fundamental difference between Quantum Field Theory and Quantum Mechanics.  One describes the strength of fields at a given point, the other describes the probability that particles can be found at that point, or that a given state exists.

However the fields of Quantum Field Theory are not classical fields; they are quantized fields.  Each quantum is a piece of field that, while spread out in space, acts as a unit.  It has a life and death of its own, separate from other quanta.  (This quantum nature is what leads to the particle-like behavior.)  The term quantum was introduced in 1900 by Planck, who said in his Nobel speech, “Here was something entirely new, never before heard of, which seemed called upon to basically revise all our physical thinking”.  How right he was.

Quanta can be either free or bound together.  Examples of free quanta are a photon emitted by a lamp or an electron emitted from a cathode.  Example of bound quanta are protons and neutrons in an atomic nucleus, or the electron field surrounding a nucleus.  There are also self, or attached, fields that are not quanta but are created by quanta – for example, the EM field around an electron, or the strong field around a nucleon.  These fields do not have a life of their own, but remain attached to their source.

The fields of Quantum Field Theory possess an internal property called spin or helicity.  Matter fields have a spin of ½, from which the Pauli Exclusion Principle follows, while force (or boson) fields can superimpose, even to the classical limit.  Another important feature ofQuantum Field Theory is that, like spin in QM, field strengths are described by vectors in (infinite dimensional) Hilbert space, and the dynamics of the fields are described by operators in this Hilbert space.  This means that field strength is described by a superposition of values, so when we refer to the field strength at a given point we can only speak of expectation values.  The fact that quantum,fields are different from classical fields bothers some people, but starting with the Stern-Gerlach experiment in 1922 we have had almost a hundred years to get used to the idea that physical quantities are quantized (which is what leads to the use of Hilbert space).  Of course when we take the classical limit, as we can do with force fields, the equations for the expectation value reduce to the classical equations of EM theory and General Relativity.

The fields of Quantum Field Theory behave deterministically as per the field equations, with one exception:

Quantum collapse

Quantum collapse occurs when a field quantum suddenly deposits its energy (or momentum) into an absorbing atom.  This is a very different thing from “collapse of the wave function” in QM: it is a physical event, not a change in probabilities.  When it happens the quantum, no matter how spread-out it may be, disappears from space.  While there is no theory to describe this, we must remember that it is necessary if the quantum is to act as an indivisible unit.  Collapse also occurs if some energy (or momentum) is transferred to another substance.  It can also occur with multiple quanta that are bound together, as when an atom or molecule is captured by a detector.

As stated, quantum collapse is not described by the field equations.  In fact there is no theory to tell us when, where, or how it happens.  However we know that the probability is related to the field strength at a given point.  This is troubling to some people, but even if we don’t have a theory for something, that doesn’t mean it can’t happen.  Physics history is filled with examples of observations that had no explanation or theory at the time.  Another troubling fact is that quantum collapse is non-local.  However non-locality has been proven in many experiments, and it does not lead to any inconsistencies or paradoxes.

In the many-worlds theory, there is no collapse.  Instead there is a spitting into two different worlds: one in which the transfer or absorption occurs and one in which it doesn’t.  However from the point of view of an observer in our world the effect is collapse, so whatever it is called, it is when the “decision” – the point of no return – is reached.

The solution – Quantum Field Theory

Quantum collapse is Quantum Field Theory’s answer to the measurement problem.  In the case of Schrödinger’s cat, if the radiated quantum is captured by an atom in the Geiger counter it starts an irreversible chain of events that results in the death of the cat. If it is not captured, then the cat lives (at least until the next radioactive emission occurs).

Some may now ask, OK, but isn’t it possible that the collapse/split occurs at a later time, closer to the point when a measurement (macroscopic change) occurs?  The problem is this:  These changes can not proceed further “up the line” unless energy or momentum has been transferred to an absorbing atom.  For example, in the cat experiment there can be no Townsend discharge unless an atom has been ionized, and ionization can only occur if there has been a quantum collapse.  [Is this true?]  All else then follows inevitably (with minor microscopic variations).  In Schrödinger’s words, “the counter tube discharges and through a relay releases a hammer which shatters a small flask of hydrocyanic acid” that kills the cat.  It’s like a Rube Goldberg device where you drop a ball into a chute at one end and after a series of actions, a cake appears at the other end.

Nor is there any experiment that could possibly rule out the above description of collapse/splitting.  In any experiment designed to study collapse, there must at some point be a macroscopic detection of an event.  But this detection can only determine that a collapse occurred.  It cannot determine how far up the chain of events the supposed superposition proceeded.

Quantum Field Theory is the Solution

Quantum Field Theory is an elegant theory that rests on a firm mathematical foundation.  It resolves or explains the many paradoxes of Special Relativity and Quantum Mechanics that have confused so many people.*  And as shown here, it supplies a simple and unique answer to a current problem in physics.  There are no entanglements, there are no superpositions, there are no quantum “states.  There is simply a field quantum that collapses (deposits some or all of its energy or momentum) into an absorbing atom.  And once again, the fact that we have no theory to describe this doesn’t mean it doesn’t happen.  One can only wonder why this theory hasn’t been embraced and taught in all the schools.  Maybe it’s time for physicists to WAKE UP AND SMELL THE QUANTUM FIELDS.

*see Fields of Color: The theory that escaped Einstein” by the author

How Quantum Field Theory Solve the “Measurement Problem”

It is not generally known that Quantum Field Theory offers a simple answer to the “measurement problem” that was discussed on the September letters page of Physics Today.  But by QFT I don’t mean Feynman’s particle-based theory; I mean Schwinger’s QFT in which “there are no particles, there are only fields”.1

Max PlankThe fields exist in the form of quanta, i.e., chunks or units of field, as Planck envisioned over a hundred years ago. Field quanta evolve in a deterministic way specified by the field equations of QFT, except when a quantum suddenly deposits some or all of its energy or momentum into an absorbing atom. This is called “quantum collapse” and it is not described by the field equations. In fact there is no theory that describes it. All we know is that the probability of it happening depends on the field strength at ​a given position. Or, if it is an internal collapse, like a change in angular momentum, ​the probability depends on the component of angular momentum in the given direction. In QFT this collapse is a physical event, not a mere change in probabilities as in Quantum Mechanics.

Many physicists are bothered by the non-locality of quantum collapse in which a spread-out field (or even two correlated quanta) suddenly disappears or changes its internal state. Yet non-locality is necessary if quanta are to act as a unit, and it has been experimentally proven. It does not lead to inconsistencies or paradoxes. It may not be what we expected, but just as we accepted that the earth is round, that the earth orbits the sun, that matter is made of atoms, we should be able to accept that quanta can collapse.

​In some cases quantum collapse can lead to a macroscopic change or “measurement”. However the measurement outcome, i.e., the “decision”, was determined at the quantum level. Everything after the collapse follows inevitably. There is no “superposition” or “environment-driven process of decoherence.”​​

Take Schrödinger’s cat as an example. If a radiated quantum collapses and deposits its energy into one or more atoms of the Geiger counter, that initiates 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 shatters a small 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.

Of course we don’t know the result until we look, but we never know anything until we look, whether it’s tossing dice or choosing a sock blindfolded. The fate of the cat was determined at the time of quantum collapse, just as the outcome of tossing dice is determined when they hit the table and the color of the sock is determined when it is pulled out of the drawer.  After the quantum collapse there is no entanglement, no superposition, no decoherence, only ignorance. What could be simpler?

In addition to offering a simple solution to the measurement problem, Quantum Field Theory provides an understandable explanation for the paradoxes of Relativity (Lorentz contraction, time dilation, etc.) and Quantum Mechanics (wave-particle duality, etc.).  It is unfortunate that so few physicists have accepted QFT in the Schwinger sense.

Rodney Brooks (​author of Fields of  Color: The theory that escaped Einstein)

1 A. Hobson, “There are no particles, there are only fields,” Am. J. Phys. 81, 211–223 (2013).

The Uncertainty Principle

Heisenberg - Quantum Field theoryThe probabilistic interpretation of Schrödinger’s equation eventually led to the uncertainty principle of Quantum Mechanics, formulated in 1926 by Werner Heisenberg. This principle states that an electron, or any other particle, can never have its exact position known, or even specified. More precisely, Heisenberg derived 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 deal with, we have to deal with particles that might be here or might be there, but we can’t say where. If the electron is really a particle, then it only stands to reason that it must be somewhere.

Resolution. In Quantum Field Theory there are no particles (stop me if you’ve heard this before) and hence no position – certain or uncertain. Instead there are blobs of field that are spread out over space. Instead of a particle that is either here or here or possibly there, we have a field that is here and here and there. Spreading out is something that only a field can do; a particle can’t do it. In fact Heinsenberg’s Uncertainty Principle is not much different from Fourier’s Theorem (discovered in 1807) that relates 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 described by the equations of QFT; Quantum Field Theory can only predict probabilities of when it occurs. However there is an important difference between field collapse in QFT and the corresponding wave-function collapse in QM. The former is a real physical change in the fields; the latter is only a change in our knowledge of where the particle is.

Copenhagen InstituteOut of all this uncertainty came the philosophy known as the Copenhagen school (after the great Dane, Niels Bohr) which states, to put it simply, that nothing happens until someone looks. If all we have in QM are mathematical probabilities that such-and-such will be observed, then until the observation is made, we can only talk about probabilities. As to reality, we must give up hope of understanding it. This was too much for Einstein and Schrödinger to swallow. Can it be that nothing really happens, that there are only probabilities, until someone looks? As Einstein lampooned, “Is the moon only there when we look at it?”

Einstein’s bomb. In 1935 Einstein attacked the role-of-the-observer concept by imagining a keg of gunpowder that could be triggered by the quantum instability of some particle. The quantum mechanical equation for this situation, he said, “describes a sort of blend of not-yet and already-exploded systems.” But, he added, this cannot be “a real state of affairs, for in reality there is just no intermediary between exploded and not-exploded” (I2007, p. 456).

Schrödinger’s cat. Worried that an explosion that is only half-real might not be enough to convince people of the point, Schrödinger extended Einstein’s bomb idea to an animal that, according to the Copenhagen interpretation, would be half-alive and half-dead, thereby creating the most famous cat in physics history.

Resolution. Qauntum Field Theory supplies a simple answer for Schrödinger’s cat, and also for Einstein’s bomb. There is no role of the observer.  The bomb explodes (or not) and the cat dies (or not), regardless of whether anyone looks. Field collapse does not depend on an observer. The fields evolve according to field equations and then collapse, but neither process requires that someone be there to observe it. In Schrödinger‘s hypothetical cat experiment, the radioactive nuclei do not emit particles. For example, if they are beta emitters, they emit a “yellow” electron field that slowly spreads through space. At some point in time that cannot be determined from the theory the electron field collapses into the detector and starts the chain of events that kills the cat. Until that time the cat is alive. After that time the cat is dead…

Summary. In Quantum Field Theory the paradoxes of QM have simple, almost trivial, answers:

  • There is no wave-particle duality because there are no particles, only fields. The particle-like behavior is explained by the fact that a field quantum lives and dies as a unit. This phenomenon is called field collapse
  • The Uncertainty Principle is simply a statement that fields are not localized; they spread out.
  • There is no role of the observer.  Field collapse occurs regardless of whether anyone is looking.

Is that all there is to it? Did I give too little space to discussing these “profound” paradoxes? Well, that’s really all there is to it. In Quantum Field Theory everything is fields. They spread out, they collapse, and they do all this without requiring an observer. When I hear people complaining about the weirdness and inaccessibility of modern physics, I want to ask, “What part of Quantum Field Theory don’t you understand?”

Scientific American, EINSTEIN DIDN’T SAY THAT!

Scientific American September IssueIn the September “Einstein” issue of Scientific American, readers are given the impression that gravity is caused by curvature of space-time.  For example, on the first 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 fact, many physicist today emphasize “curvature” as the explanation for gravity.  As Stephen Hawking wrote 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 problem is, that’s NOT what Einstein said.  Einstein made it quite clear that gravity is a force like other forces, with (of course) certain differences.  In the very paper cited 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 article, while the word “curvature” doesn’t appear at all (except in regard to “curvature of a ray of light”).  And Einstein is not the only physicist who believes that.  For example Sean Carroll, a leading physicist of today, 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 focus on “curvature” not only misstates Einstein’s view; it also gives people a false or misleading understanding of general relativity.

So where does “curvature” come from?   According to Einstein (in the cited paper), the gravitational field causes physical changes in the length of measuring rods (just as temperature can cause such changes) and it is these changes that create a non-Euclidean metric of space.  In fact, as Einstein pointed out, these changes can occur even in a space which is free of gravitational fields – i.e., a rotating system.  He then showed that this non-Euclidean geometry is mathematically equivalent to the geometry on a curved surface, which had been developed by Gauss and extended (mathematically) to any number 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”.

Well, you may say, if the gravitational field is equivalent to curvature of space-time, what difference does it make?  It makes a lot of difference.

First, most people cannot visualize physically four-dimensional curvature, while the fact is, they don’t have to.  The curvature of space-time, although mathematically equivalent, is not necessary for a complete understanding of Einstein’s theory.  The field concept, introduced by Faraday in 1845, is all that is needed.

Second, by eliminating or suppressing the role of the gravitational field, you destroy the great unity that the field concept brings to physics.  To quote Nobel laureate Frank Wilczek:

Physicists trained in the more empirical tradition of high-energy physics and quantum field theory tend to prefer the field view… the field view makes Einstein’s theory of gravity look more like the other successful theories of fundamental physics, and so makes it easier to work toward a fully integrated, unified description of all the laws. As you can probably tell, I’m a field man.

Finally, the theory that many physicists believe is our best and most consistent description of reality, Quantum Field theory, has once again been ignored.  For example, calling the uncertainty principle an unresolved mystery that “not even the great Einstein” could solve (p. 48), ignores the fact that in QFT it is a natural consequence of the way fields behave.  And to say (p. 34): “Relativity and quantum mechanics are just as incompatible as they ever were”, ignores the fact that they are united in Quantum Field Theory.  In August 2013 Scientific American printed an article that actually dismissed Quantum Field Theory as invalid because the fields described by the theory are not “what physicists classically understand by the term field”.  (To which one can only reply, “Duh, maybe that’s why they’re called quantum fields.”)

Please note that it is not just me who believes that the field concept is central to the understanding of general relativity.  That is also the view of, among others, Sean Carroll and Nobel laureates Julian Schwinger, Frank Wilczek, and Steven Weinberg.

When do Fields Collapse

Field CollapseA major question in physics today is about collapse of the “wave-function”: When does it occur? There have been many speculations (see, e.g., Ghirardi–Rimini–Weber theory, Penrose Interpretation, Physics forum) and experiments (e.g., “Towards quantum superposition of a mirror”) about this. The most extreme view is the belief that Schrödinger’s cat is both alive and dead, even though Schrödinger proposed this thought-experiment (like Einstein’s less-well-known bomb experiment) to show how ridiculous such an idea is.

The problem arises because Quantum Mechanics can only calculate probabilities until an observation takes place. However Quantum Field Theory, which deals in real field intensities – not probabilities, provides a simple unequivocal answer. Unfortunately, Quantum Field Theory in its true sense of “there are no particles, there are only fields” (Art Hobson, Am. J. Phys. 81, 2013) is ignored or misunderstood 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 behave deterministically according to the field equations – with one exception.

The exception is field collapse, but in Quantum Field Theory this is a very different thing from “collapse of the wave function” in QM. It is a physical event, not a change in probabilities. It occurs when a quantum of field, no matter how spread-out it may be, suddenly deposits its energy into a single atom and disappears. (There are also other types of collapse, such as scattering, coupled collapse, internal change, etc.) Field collapse is not described by the field equations – it is a separate event, but just because we don’t have a theory for it doesn’t mean it can’t happen. The fact that it is non-local bothers some physicists, but this non-locality has been proven in many experiments, and it does not lead to any inconsistencies or paradoxes.

So when field collapse occurs, the final “decision” – the point of no return – is reached. This is QFT’s answer to when does collapse occur: when a quantum of field colapses. In the case of Schrödinger’s cat, this is when the radiated quantum (perhaps an electron) is captured by an atom in the Geiger counter.

Before a field quantum finally collapses, it may have interacted or entangled with many other atoms along the way. These interactions are described (deterministically) by the field equations. However the quantum cannot have collapsed into any of those atoms, because collapse can happen only once, so whatever you call it – interaction, entanglement, perturbation, or just “diddling” – these preliminary interactions are reversible and do not lead to macroscopic changes. Then, when the final collapse occurs, those atoms become “undiddled” and return to their unperturbed state.

To sum up, in QFT the “decision” is made when a quantum of field deposits all its energy into an absorbing atom. Besides answering this question, QFT also explains why time dilates in Special Relativity and resolves the wave-particle duality question of Quantum Mechanics. One can only wonder why this theory hasn’t been embraced and made the basis for our understanding of nature. I believe it’s time for physicists to WAKE UP AND SMELL THE QUANTUM FIELDS.

Book Simplifies Baffling Quantum Field Theory

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

The book “Fields of Color: The Theory that Escaped Einstein” simplifies the complex Quantum Field Theory so that a layman can understand it. Written by Leisure World resident Rodney Brooks, it contains no equations—in fact, no math—and it uses colors to represent fields, which in themselves are hard to imagine. It shows how the field picture of nature resolves the paradoxes of quantum mechanics and relativity that have confused so many people. It is original, comprehensive, and entertaining.

quantum field theory

Brooks is amazed and delighted with the success of his book, which was published in 2011. He says 6,000 copies have been sold, unusual for a self-published book on physics. In addition, the book has a 4.4 (out of 5) star rating on Amazon with more than 90 reader reviews — a higher rating than Einstein’s own book on relativity and higher 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 believe. However the field concept is not easy to grasp. 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 this concept 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 continues: “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 first sparked when at age 14 he read Arthur Eddington’s “The Nature of the Physical World.” This book describes how a table is made of tiny atoms that in turn could 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 math 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. During this time, he attended a three-year formal lecture series taught by Julian Schwinger. The Nobel prize-winning physicist had just completed his reformulation of QFT, so the timing was perfect. “I was amazed that all the paradoxes of relativity and quantum mechanics that had earlier confused 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 first research was on the new technique of Computered Tomography (CT), during which time he invented the method now known as dual-energy CT. Next, he did research on Positron Emission Tomography (PET) and finally in Magnetic Resonance Imaging (MRI). All in all, Brooks published 124 peer-reviewed articles.

After he retired, he and his wife, Karen Brooks, moved to New Zealand in 2001. That was when he became aware of the widespread confusion about physics, especially quantum mechanics and relativity, while his beloved QFT that resolves the confusion was overlooked, misunderstood, or forgotten.

“And so I took on the mission of explaining the concepts of quantum field theory to the public,” Brooks says.

His book was first published in New Zealand in 2010, and is now in its second edition.

In 2012, his grandchildren, who live in Maryland called out, and he and his wife moved to Leisure World, where he continues to work on his mission. While Einstein eventually came to believe that reality must consist of fields and fields alone, he wanted there to be a single “unified” field that would not only include gravity and electromagnetic forces (the only two forces known at the time), but would also include matter.

He spent the last 25 years of his life unsuccessfully searching for this unified field theory.

Referring to the particle picture that he espoused, 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.”

Space-Time Curvature & Quantum Field Theory

General Relativity is the name given to Einstein’s theory of gravity that was described in Chapter 2 of my book. As the theory is usually presented, it describes gravity as a curvature in four-dimensional space-time. Now this is a concept far beyond the reach of ordinary folks.. Just the idea of four-dimensional space-time causes most of us to shudder… 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 mean that four-dimensional notation is not useful. It is a convenient way of handling the mathematical relationship between space and time that is required by special relativity. One might almost say that physicists couldn’t live without it. Nevertheless, spatial and temporal evolution are fundamentally different, and I say shame on those who try to foist and force the four-dimensional concept onto the public as essential to the understanding of relativity theory.

Riemannian GeometryThe idea of space-time curvature also had its origin in mathematics. When searching for a mathematical method that could embody his Principle of Equivalence, Einstein was led to the equations of Riemannian geometry. And yes, these equations describe four-dimensional curvature, for those who can visualize it. You see, mathematicians are not limited by physical constraints; equations that have a physical meaning in three dimensions can be generalized algebraically to any number of dimensions. But when you do this, you are really dealing with algebra (equations), not geometry (spatial configurations).

By stretching our minds, some of us can even form a vague mental image of what four-dimensional curvature would be like if it did exist. Nevertheless, saying that the gravitational field equations are equivalent to curvature is not the same as saying that there is curvature. In Quantum Field Theory, the gravitational field is just another force field, like the EM, strong and weak fields, albeit with a greater complexity that is reflected in its higher spin value of 2.

While QFT resolves these paradoxical statements, I don’t want to leave you with the impression that the theory of quantum gravity is problem-free. While computational problems involving the EM field were overcome by the process known as renormalization, similar problems involving the quantum gravitational field have not been overcome. Fortunately they do not interfere with macroscopic calculations, for which the QFT equations become identical to Einstein’s.

Your choice. Once again you the reader have a choice, as you did in regard to the two approaches to special relativity. The choice is not about the equations, it is about their interpretation. Einstein’s equations can be interpreted as indicating a curvature of space-time, unpicturable as it may be, or as describing a quantum field in three-dimensional space, similar to the other quantum force fields. To the physicist, it really doesn’t make much difference. Physicists are more concerned with solving their equations than with interpreting them. If you will allow me one more Weinberg quote:

steven weinbergThe 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

So if you want, you can believe that gravitational effects are due to a curvature of space-time (even if you can’t picture it). Or, like Weinberg (and me), you can view gravity as a force field that, like the other force fields in Quantum Field Theory, exists in three-dimensional space and evolves in time according to the field equations.

Why is the Speed of Light Constant?

The question “Why is the speed of light constant?” is often asked by those trying to understand physics. Google has 2760 links to that question. Yet the answer is so simple that a 10-year-old can understand it, that is, if you accept Quantum Field Theory.

speed of light

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 speed, and tell her that this speed depends only on the properties of water. You might drop different objects at different locations and show her that the waves travel at the same speed, regardless of the size of the object or location of the water.

Then tell her that sound travels through air with a fixed velocity that depends only on the properties of air. You might wait for a thunderstorm and time the difference between the lightning and the sound. Tell her that a whisper travels as fast as a shout. I think a ten-year-old can grasp the concept that water and air have properties that determine the speed of these waves, even if she doesn’t know the equations.

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

As Nobel laureate Frank Wilczek wrote, wilczek_frankOne 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.” 

Once you accept the concept of fields (which admittedly is not an easy one), that’s all you have to know. Light is waves in the electromagnetic field that travel through space (not space-time) at a speed dictated by the properties of space. They obey fairly simple equations (not that you need to know them), just as sound and water waves obey simple equations. OK, the Quatum Field Theory equations are a bit more complicated, 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.”

However this question can have a different meaning: “Why is the speed of light independent of motion?”   This fact was first demonstrated by the famous Michelson-Morley experiment, in which light beams were timed as the earth revolved and rotated. The surprising result was that the speed of light was exactly the same regardless 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 motion was most surprising… It makes no sense for a light beam – or anything, for that matter – to travel at the same speed regardless of the motion of the observer… unless “something funny” is going on. The “something funny” turned out to be even more surprising than the M-M result itself. In a nutshell, objects contract when they move! More specifically, they contract in the direction of motion. Think about it. If the path length of Michelson’s apparatus in the forward direction contracted by the same amount as the extra distance the light beam would have to travel because of motion, the two effects would cancel out. In fact, this is the only way that Michelson’s null result could be explained.

However the idea that objects contract when in motion was just as puzzling as the Michelson-Morley result. Why should this be? Once again the explanation is provided by Quantum Field Theory. Quoting again from my book:

Rodney BrooksWe must recognize that even if the molecular configuration of an object appears to be static, the component fields are always interacting with each other. The EM field interacts with the matter fields and vice versa, the strong field interacts with the nucleon fields, etc. These interactions are what holds the object together. Now if the object is moving very fast, this communication among fields will become more difficult because the fields, on the average, will have to interact through greater distances. Thus the object in motion must somehow adjust itself so that the same interaction among fields can occur. How can it do this? The only way is by reducing the distance the component fields must travel. Since the spacing between atoms and molecules, and hence the dimensions of an object, are deter­mined by the nature and configuration of the force fields that bind them together, the dimensions of an object must therefore be affected by motion.

It is 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 much greater, we on earth would still be unaware 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) 

In conclusion, for those who want to understand physics, I say use Quantum Field Theory and: WAKE UP AND SMELL THE FIELDS.

WHAT DOES THE ELECTRON LOOK LIKE?

In June, 2014, I gave a talk at the Physics Department of the Czech Technical University in Prague. I started by asking the question “What does the electron look like?”, and I showed two pictures. The first was the familiar Rutherford picture of particles orbiting a nucleus:

 

electron1

 

and the second was a (highly simplified) picture of the electron as a field in the space around the nucleus:

 

electron2

Then I asked for a vote. Quite amazingly only four people in the audience chose the field picture, and no one chose the particle picture. In other words, THEY DIDN’T KNOW. So here we are, 117 years after the electron was discovered, and this highly educated group of physicists had no idea what it looks like.

 

Of course when the electron was discovered by J. J. Thomson, it was naturally pictured as a particle. After all, particles are easy to visualize, while the field concept, let alone a quantized field, is not an easy one to grasp. However this picture soon ran into problems that led Niels Bohr in 1913 to propose that the particles in orbit picture must be replaced by something new: undefined electron states that satisfy the following two postulates: 

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

2. In contradiction to the classical EM theory, no radiation takes place from the atom in the stationary states themselves, [but] a process of transition between two stationary states can be accompanied by the emission of EM radiation.

This led Louis de Broglie to propose that the electron has wave properties. There then followed a kind of battle, with Paul Dirac leading the “particle side” and Erwin Schrodinger the “wave side”: 

schrodingerWe assert that the atom in reality is merely the… phenomenon of an electron wave captured, as it were, by the nucleus of the atom… From the point of view of wave mechanics, the [particle picture] would be merely fictitious. – E. Schrodinger 

However the fact that a free electron acts like a particle could not be overcome, and so Schrodinger gave in and Quantum Mechanics emerged as a theory of particles that are described by probabilities.

A second battle occurred in 1948, when Richard Feynman and Julian Schwinger (along with Hideki Tomanaga) developed different approaches to the “renormalization” problem that plagued physics. Once again the particle view espoused by Feynman won out, in large part because his particle diagrams proved easier to work with than Schwinger’s field equations. And so two generations of physicists have been brought up on Feynman diagrams and led to believe that nature is made of particles.

In the meantime, the theory of quantized fields was perfected by Julian Schwinger:

Julian SchwingerMy retreat began at Brookhaven National Laboratory in the summer of 1949… 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. – J. Schwinger

Schwinger’s final version of the theory was published between 1951 and 1954 in a series of five papers entitled “The Theory of Quantized Fields”. In his words:

It was to be the purpose of further developments of quantum mechanics that these two distinct classical concepts [particles and fields] are merged and become transcended in something that has no classical counterpart – the quantized field that is a new conception of its own, a unity that replaces the classical duality. – J. Schwinger

I believe that the main reason these masterpieces have been ignored is that many physicists found them too hard to understand. (I know one who couldn’t get past the first page.)

And so the choice is yours. You can believe that the electron is a particle, despite the many inconsistencies and absurdities, not to mention questions like how big the particles are and what are they made of. Or you can believe 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 were willing to let particles behave in the bizarre way described by Feynman: appearing again, interfering with each other and cancelling out. You could also think of it as a field, or wave, but you had to remember that the detector always registers one electron, or none – never half an electron, no matter how much the field has been split up or spread out. In the end, is the field just a calculational tool to tell you where the particle will be, or are the particles just calculational tools to tell you what the field values are? Take your pick. – R. Oerter

What Oerter neglected to say is that QFT explains why the detector always registers one electron or none: the field is quantized. The Q in QFT is very important. 

So when you take your pick, dear reader, I hope you won’t choose 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 reality made 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.