I'm reading this book called

**Fields of Color: The theory that escaped Einstein** by Rodney Brooks about the Quantum Field Theory. The book is a dedication to the physicist Julian Schwinger who played a key role in formulating the QFT but whose work was overshadowed by Richard Feynman. Now, these two great physicists had a different approach to QFT and I guess Richard Feynman's approach became more popular eventually because it is less formal and more intuitive in the form of Feynman's diagrams. But the author argues that Schwinger's conception of quantum fields (instead of wave-particle duality of Feynman) resolves the discrepancies in quantum mechanics and Einstein's relativity.

I am really interested to know Ark's thoughts on QFT and Julian Schwinger's ideas and research and whether he sees any promise for uniting gravity and QM in these ideas. QFT has been widely tested and has produced very accurate results in experiments so it seems to be the best candidate for a Unified Field Theory.

(From Quora about the insane accuracy of QFT with experimental results - Yes, quantum field theory (QFT) has been proven many many times. It is the most accurate theory in all science. It began in 1948 as an attempt to explain the anomalous magnetic dipole moment of the electron in a mathematically consistent way.

**It succeeded extremely well. Using QFT this physical quantity can now be calculated to 13 significant digits **to 4 Feynman loops and this calculated value exactly matches the experimentally measured value. This QFT is known as quantum electrodynamics. )

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From the

**Preface **of the book:

Some time later, as a graduate student, I attended a three-year lecture series at Harvard University by Julian Schwinger. The timing was perfect. Schwinger’s development of Quantum Field Theory (QFT) had matured and he was about to publish a monumental work, “A theory of the fundamental interactions”. 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 (M2000, p. 593-4)**
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 principles, he derived the equations of QFT, even including the gravitational field. Not only was the mathematics elegant, but the philosophic concept of a world made of properties of space seemed to me much more satisfying than Eddington’s mysterious particles. I was amazed and delighted to see how the paradoxes of relativity theory and quantum mechanics that I had found so baffling disappeared or were resolved. Later on, I must admit, things got more complicated as the number and variety of fundamental fields grew, and quarks entered the scene. But to my knowledge, QFT remains as the true fabric of which the world is made. What’s more, I believe it is the only fabric of which the world could be made. 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. Instead, the more colorful and outgoing Richard Feynman came to the fore. It is his image, not Schwinger’s, that is enshrined on a postage stamp. 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.* –

**J. Mehra and K.A. Milton (M2000, p. v)**
In the 50 years that passed since my student days, I have seen very little mention of QFT in its true fields-only sense. Instead I have seen a bombardment of books and articles that keep repeating the paradoxes that people are expected to accept. Physical intuition has disappeared or, worse yet, is sneered at. Far from bringing to the public an understanding of nature, these popular books and articles have brought confusion and chaos. This hit me hard one day as I was reading Joseph Heller’s memoir, Now and Then. Heller is the author of Catch 22, one of my all-time favorites, and when I read that he tried to understand quantum mechanics and had to give it up (see quote in Chapter 1), I knew that something was badly wrong. And so I decided to write a book.

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**Chapter 8**

General Relativity
*When a journalist asked the British astronomer Sir Arthur Eddington if it was true that he was one of only three people in the world who could understand Einstein’s relativity theories, Eddington considered deeply for a moment and replied: “I am trying to think who the third person is.”* – B. Bryson (B2003, p. 124)

General Relativity is the name Einstein gave to his theory of gravity. As the theory is usually presented, gravity is said to be caused by curvature in four dimensional space-time. This is a concept beyond the reach of ordinary folks like you and me.

The non-mathematician is seized by a mysterious shuddering when he hears of ‘four-dimensional’ things, by a feeling not unlike that awakened by thoughts of the occult. — A. Einstein (E1961, p. 61)

In this chapter

**we will see that in QFT (and also in Einstein’s theory) there is no eerie fourth dimension: space is space and time is time. We will also see that gravity is caused by a force field — not curvature, and that, contrary to popular belief, QFT is compatible with general relativity.**

SPACE-TIME ISN’T 4-DIMENSIONAL
*The most challenging and non-intuitive of all the concepts in the general theory of relativity is the idea that time is part of space… Our brains can take us only so far because it is so nearly impossible to envision a dimension comprising three parts space to one part time, all interwoven like the threads in a plaid fabric.* –

**B. Bryson (B2003, p. 125-126)**
Of course space-time is four-dimensional in the trivial sense that it takes four numbers to specify when and where an event takes place, but that doesn’t mean that space and time are equivalent. In QFT, as in Einstein’s theory, space and time play separate roles in accord with our natural perceptions.

** The idea that space-time must be viewed as a four-dimensional entity was introduced by the German mathematician Hermann Minkowski. In a speech at Cologne in 1908**, he expressed this view with great eloquence:

*Henceforth space by itself, and time by itself are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality… It is only in four dimensions that the relations here taken under consideration reveal their inner being in full simplicity, and that on a three-dimensional space forced upon us a priori they cast only a very complicated projection. *—

**H. Minkowski (E1923, p. 75, 90)**
Einstein, however, did not subscribe to that view; he called it “superfluous erudition”. When adapting Minkowski’s mathematical formalism to describe the gravitational field, Einstein had to add the “imaginary” number i 1 to the time term. This makes the equations more compact and easier to work with, but Einstein was careful to distinguish the formal aspect of the notation from reality (emphases added):

*The discovery of Minkowski… was of importance for the formal development of the theory of relativity… The four-dimensional space-time continuum of the theory of relativity, in its most essential formal properties, shows a pronounced relationship to the three-dimensional continuum of Euclidean geometrical space… Under these conditions, the natural laws… assume mathematical forms in which the time coordinate plays exactly the same role as the three space coordinates. *—

** A. Einstein (E1961, p. 63)**

Einstein is saying that the four-dimensional notation is useful for physicists; it is a convenient way of handling the mathematical relationship between space evolution and time evolution that is required by special relativity. One might almost say that physicists couldn’t live without it. Nevertheless, space and time are 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.

GRAVITY ISN’T CURVATURE
In most presentations of physics today we are told that gravity is caused by “curvature of space-time”.

**This was not Einstein’s view, nor is it the view of QFT. Einstein believed that gravity is a force field, not unlike the electromagnetic field. **
*[There is] a field of force, namely the gravitational field, which possesses the remarkable property of imparting the same acceleration to all bodies.* –

**Albert Einstein (E1923, p. 114) **
The idea of space-time curvature, like the four-dimensional concept, 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. 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 dealing with algebra, not geometry.

*To those who are geometrically inclined, two dimensions is a breeze, three dimensions routine, and four dimensions impossible. But to those who think algebraically, two, three, or four dimensions are just particular examples of spaces with any number of dimensions. In this sense, Riemann was an algebraist.* –

**J. Schwinger (S1986, p. 175-176)**
Because this is such a controversial question, I will quote two more Nobel laureates who expressed similar thoughts:

*We can describe general relativity using either of two mathematically equivalent ideas: curved space-time or metric field. Mathematicians, mystics, and specialists in general relativity tend to like the geometric view because of its elegance. Physicists trained in the more empirical tradition of high-energy physics and quantum field theory tend to prefer the field view… More important, as we’ll see in a moment, 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 160 can probably tell, I’m a field man. *—

**F. Wilczek (W2008, p. 100- 101)**
*It is certainly a historical fact that when Albert Einstein was working out general relativity, there was at hand a preexisting mathematical formalism, that of Riemannian geometry, that he could and did take over whole. However, this historical fact does not mean that the essence of general relativity necessarily consists in the application of Riemannian geometry to physical space and time. In my view, it is much more useful to regard general relativity above all as a theory of gravitation, whose connection with geometry arises from the peculiar empirical properties of gravitation.* –

**S. Weinberg (W1972, p. vii, p.3) **
A physicist friend of mine put it more succinctly: “Why would God invent a different mechanism for another force?”

**GRAVITY AND QFT ARE COMPATIBLE **
It is often said that general relativity is incompatible with quantum theory. Julian Schwinger did not agree.

*[Consider] a neutral field that presumably possesses no internal properties and responds dynamically to the space-time attributes of other systems… It appears that in the hierarchy of fields there is a natural place for the gravitational field. *—

**J. Schwinger (S1957, p. 433) **
Schwinger went on to publish two papers on “The quantized gravitational field” in the Physical Review in 1963. This is not to say there is no problem with quantum gravity. Just as the QFT equations for the EM field led to infinite values, so the gravitational field equations lead to infinities, but these infinities cannot be circumvented by renormalization, as described in Chapter 6. But this does not mean that QFT and general relativity are inconsistent. It only means that the interaction of a gravitational quantum with its self-field is not described by the theory (see “The gaps” in Chapter 10). Although renormalization doesn’t work for quantum gravity, Schwinger found another way around the problem of the infinities, using a method he called source theory. Using this method, he was able to reproduce all four of Einstein’s classic results: gravitational red shift, deflection and slowing down of light by gravity, and the perihelion precession of Mercury (S1970, p. 82- 85). The neglect of source theory by the physics community was a major disappointment for Schwinger:

*The lack of appreciation of these facts by others was depressing, but understandable* —

**J. Schwinger (S1970, Preface). **
So once again, you the reader have a choice, as you did in regard to the two approaches to special relativity. Einstein’s equations can be interpreted as describing a curvature of space-time, unpicturable as this may be, or as 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:

*The important thing is to be able to make predictions about images 162 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.)* –

**S. Weinberg, (W1972, p. 147) **
You can believe that gravitational effects are caused by curvature of spacetime if you want or, like Einstein, Weinberg, Wilczek (and me), you can view gravity as a force field that exists in three-dimensional space and evolves in time according to the gravitational field equations.

**SUMMARY**

1. In QFT, space is the same three-dimensional “Euclidean” space that we intuitively believe in, and time is the same time that we intuitively believe in.

2. The gravitational field is a force field like the other force fields, but with a higher spin, or helicity, of 2. Four-dimensional curvature is best left to the physicists who find it useful in their calculations.

3. General relativity is compatible with QFT, at least in Schwinger’s formulation. However, unlike the equations for the EM field, the gravity field equations cannot be renormalized and calculations cannot be made at the quantum level.