# How Quantum Field Theory Solves the “Measurement Problem”.

It is not usually recognized that Quantum Field Theory gives a simple answer to the “measurement problem” which was discussed on the September letters page of Physics Today. But by QFT I do not mean Feynman’s particle-based theory; I imply 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 pictured over a century ago. Field quanta evolve in a deterministic way defined by the field equations of QFT, aside from when a quantum abruptly deposits some or all of its energy or momentum into an absorbing atom. This is called “quantum collapse” and it is not defined by the field equations. As a matter of fact there is no principle that describes it. Everything we understand is that the likelihood of it occurring depends upon the field strength at a given location. Or, if it is an interior collapse, like a shift in angular momentum, the likelihood depends on the component 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 bothered by the non-locality of quantum collapse in which a spread-out field (or perhaps two correlated quanta) unexpectedly vanishes or transforms its internal state. Yet non-locality is needed if quanta are to work as a unit, and it has been experimentally proven. It does not result in inconsistencies or paradoxes. It may not be what we anticipated, but just as we accepted that the world is round, that the planet orbits the sun, that matter is built from atoms, we ought to be able to acknowledge 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.”.

Take Schrödinger’s cat as an example. If a radiated quantum collapses and transfers its energy into 1 or more atoms of the Geiger counter, that starts a Townsend discharge that leads inexorably to the demise of the cat. In Schrödinger’s words, “the counter tube discharges and through a relay releases a hammer which shatters a little flask of hydrocyanic acid” and the cat dies. On the other hand, if it does not collapse in the Geiger counter then the cat lives.

Obviously we don’t know the outcome until we look, but we never know anything until we look, no matter if it’s throwing dice or picking a sock blindfolded. The fate of the cat was determined at the time of quantum collapse, just like the result of throwing dice is determined when they hit the table and the color of the sock is determined when it is taken out of the drawer. After the quantum collapse there is no entanglement, no superposition, no decoherence, only ignorance. What could be easier?

Along with delivering a simple solution to the measurement problem, Quantum Field Theory offers a reasonable explanation for the paradoxes of Relativity (Lorentz contraction, time dilation, etc.) and Quantum Mechanics (wave-particle duality, etc.). It is regrettable that so few physicists have accepted QFT in the Schwinger sense.

# The Uncertainty Principle

The probabilistic translation of Schrödinger’s formula ultimately brought about the uncertainty principle of Quantum Mechanics, formulated in 1926 by Werner Heisenberg. This principle specifies that an electron, or any other particle, can not have its specific position known, or even pointed out. More exactly, Heisenberg derived a formula 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 take care of, we must take care of particles that might be here or may be there, but we just 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 hence no position– certain or uncertain. Alternatively there are blobs of field that are spread over space. As opposed to a particle that is either here or here or perhaps there, we have a field that is here and here and there. Extending out is one thing that only a field can do; a particle cannot do this. Actually Heinsenberg’s Uncertainty Principle is not very different from Fourier’s Theorem (found in 1807) that relates the spatial spread of any wave to the spread of its wave length.

This does not mean that there is no uncertainty in Quantum Field Theory. There is uncertainty in relation to field collapse, but field collapse is not explained by the equations of QFT; Quantum Field Theory can just predict probabilities of when it happens. Nevertheless there is a significant distinction between 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 precisely where the particle is….

# Scientific American, EINSTEIN DIDN’T SAY THAT!

In the September “Einstein” issue of Scientific American, readers are granted 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 emphasize “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 issue is, that’s NOT what Einstein said. Einstein made it quite clear that gravity is a force just like other forces, along with (of course) specific distinctions. In the actual 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 term “curvature” does not appear whatsoever (besides in relation to “curvature of a ray of light”). And Einstein is not the only physicist who thinks that. For instance Sean Carroll, a prominent 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 emphasize “curvature” not only misstates Einstein’s view; it also gives individuals an incorrect or misleading understanding of general relativity.

So where does “curvature” come from? According to Einstein (in the cited paper), the gravitational field causes physical adjustments in the length of measuring rods (just like temperature can cause such changes) and it is these changes that produce a non-Euclidean metric of space. In fact, as Einstein pointed out, these changes can take place even in a space which is devoid of gravitational fields– i.e., a rotating system. He then proved that this non-Euclidean geometry is mathematically equal to the geometry on a curved surface, which had been developed by Gauss and extended (mathematically) to any amount of dimensions by Riemann. That this is a mathematical equivalence is distinctly 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 my complete article on the disparity of Einstein’s theory of relativity visit the blog at Fields of Color.

# When Do Fields Collapse?

A main question in physics these days concerns collapse of the “wave-function”: When does this occur? There certainly 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”) about this. The most extreme perspective is the view that Schrödinger’s cat is at the same time alive and dead, although Schrödinger proposed this particular thought-experiment (like Einstein’s less-well-known bomb experiment) to demonstrate how absurd such an idea is.

The problem happens because Quantum Mechanics can only calculate probabilities until an observation occurs. Nonetheless Quantum Field Theory, which works in actual field intensities– not probabilities, supplies an uncomplicated unequivocal answer. Sadly, Quantum Field Theory in its authentic 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 explained by the field intensities (technically, their expectation value) at each and every point. These fields are real properties of space that act deterministically depending on the field equations– with one exception.

The exemption is field collapse, but in Quantum Field Theory this is a remarkably different thing from “collapse of the wave function” in QM. It is a physical event, not a change in chances. It occurs when a quantum of field, regardless of how spread-out it may be, instantly transfers its energy into a solitary atom and vanishes. (There are also additional kinds of collapse, like scattering, coupled collapse, internal change, etc.) Field collapse is not described by the field equations– it is a different occurrence, but simply because we don’t have a theory for it does not mean it can’t happen. The fact that it is non-local bothers some physicists, but this non-locality has been demonstrated in several experiments, and it does not lead to any inconsistencies or paradoxes.

So whenever field collapse happens, the ultimate “decision”– the defining moment– is reached. This is QFT’s answer to when does collapse occur: when a quantum of field colapses. In the scenario of Schrödinger’s cat, this is when the radiated quantum (perhaps an electron) is captured by an atom in the Geiger counter.

Just before a field quantum finally collapses, it could have interacted or entangled with a lot of other atoms along the way. These interactions are illustrated (deterministically) by the field equations. But the quantum can not have indeed collapsed into any of those atoms, for the reason that collapse can take place just one time, so no matter what you refer to it as– interaction, entanglement, perturbation, or just “diddling”– these initial interactions are reversible and do not bring about macroscopic changes. Then, when the ultimate collapse takes place, 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 replying to this question, QFT additionally explains why time dilates in Special Relativity and resolves the wave-particle duality issue of Quantum Mechanics. An individual can simply think about why this particular theory hasn’t already been welcomed and made the basis for our knowledge of nature. I feel it is truly time for physicists to WAKE UP AND SMELL THE QUANTUM FIELDS.

Find more on the Fields of Color Blog!

# Book Simplifies Complicated Quantum Field Theory

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

The book “Fields of Color: The Theory that Escaped Einstein” streamlines the complicated Quantum Field Theory in order that a nonprofessional can grasp it. Written by Leisure World resident Rodney Brooks, it contains no formulas– as a matter of fact, no math– and it utilizes colors to represent fields, which in themselves are hard to think of. It demonstrates the field picture of nature resolves the paradoxes of quantum mechanics and relativity that have perplexed a lot of individuals. It is original, detailed, and interesting.

Brooks is impressed and satisfied with the success of his book, that was published in 2011. He states 6,000 copies have been sold, out of the ordinary for a self-published book on physics. In addition, the publication has a 4.4 (out of 5) star rating on Amazon with much more than 90 reader reviews– a higher score than Einstein’s own book on relativity and above Stephen Hawking’s popular book “The Theory of Everything.”.

In its essence, quantum field theory (QFT) defines a world made of fields, not particles (neutrons, electrons, protons) as most physicists conclude. Nevertheless the field principle is hard 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 principle was expanded 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 initially triggered when at age 14 he read Arthur Eddington’s “The Nature of the Physical World.” This publication illustrates how a table is made of small atoms that in turn could be split into even tinier objects. “So this is what the world is built 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 2 years.

Fast forward to graduate school at Harvard University where Brooks was a National Science Foundation scholar, majoring in physics. During the course of this time, he went to 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 excellent. “I was astounded that all the paradoxes of relativity and quantum mechanics that had earlier perplexed me evaporated or were settled,” 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 was regarding the new method of Computered Tomography (CT), during which time he devised the procedure now called dual-energy CT. Then, he did research on Positron Emission Tomography (PET) and lastly in Magnetic Resonance Imaging (MRI). All in all, Brooks published 124 peer-reviewed articles.

Once he retired, he and his spouse, Karen Brooks, relocated to New Zealand in 2001. That was when he became conscious of the prevalent confusion about physics, specifically quantum mechanics and relativity, whilst his cherished QFT that resolves the mystification was disregardeded, misconceived, or neglected.

“Consequently I undertook the mission of clarifying the principles of quantum field theory to the general public,” Brooks says.

His book was first released in New Zealand in 2010, and is currently in its 2nd edition.

In 2012, his grandchildren, who live in Maryland called out, and he and his wife moved to Leisure World, where he moves ahead to work on his mission. Though Einstein eventually came to believe that reality should include fields and fields alone, he preferred there to be a solitary “unified” field that would not merely consist of gravity and electromagnetic forces (the only two forces recognized back then), but would additionally contain matter.

He invested the last 25 years of his life unsuccessfully looking for this unified field theory.

Referring to the particle image 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 contrary, 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.”.

Find out more on the Fields of Color Blog.

# Space-Time Curvature & Quantum Field Theory

General Relativity is the title given to Einstein’s theory of gravitational force that was illustrated in Chapter 2 of my book. As the theory is normally shown, it illustrates gravity as a curvature in four-dimensional space-time. Now this is an idea far over and above the reach of regular individuals. Simply the idea of four-dimensional space-time causes most of us to tremble … The answer in Quantum Field Theory is straightforward: Space is space and time is time, and there is no curvature. In QFT gravity is a quantum field in regular three-dimensional space, the same as the other 3 force fields (EM, strong and weak).

This does not indicate that four-dimensional notation is not useful. It is a practical approach of addressing the mathematical relationship between space and time which is needed by special relativity. One may almost say that physicists could not live without it. Nevertheless, spatial and temporal evolution are fundamentally different, and I say shame on those who try to pass off and force the four-dimensional idea onto the general public as important to the awareness of relativity theory.

The concept of space-time curvature likewise had its origin in mathematics. When looking for a mathematical method that could embody his Principle of Equivalence, Einstein was led to the equations of Riemannian geometry. And yes, these formulas explain four-dimensional curvature, for individuals who can easily visualize it. You see, mathematicians are certainly not restricted by physical restrictions; equations that have a physical meaning in 3 dimensions may be generalized algebraically to any variety of dimensions. But when you do this, you are definitely managing algebra (equations), not geometry (spatial configurations).

By stretching our minds, some of us are able to even create a faint mental image of what four-dimensional curvature would resemble if it did exist. Nonetheless, stating that the gravitational field equations are equivalent to curvature is certainly not the same as saying that there is curvature. In Quantum Field Theory, the gravitational field is just an additional 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 declarations, I really don’t wish to leave you having the thought that the theory of quantum gravity is problem-free. Whilst computational troubles concerning the EM field were overcome with process called renormalization, very similar challenges involving the quantum gravitational field have not been overcome. Thankfully they do not actually interfere with macroscopic calculations, for which the QFT formulas become identical to Einstein’s.

Your choice. Once again you the reader have a choice, as you did in concern to the two approaches to special relativity. The choice is not regarding the formulas, it is about 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, just like the other quantum force fields. To the physicist, it really doesn’t make much difference. Physicists are much more concerned with solving their formulas rather than with interpreting them. If you will permit 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

Thus in case you prefer, you can think that gravitational effects are due to a curvature of space-time (even if you can’t picture it). Or, like Weinberg (and myself), you may see gravity as a force field that, like the other force fields in Quantum Field Theory, exists in three-dimensional space and progresses in time according to the field equations.

# Why Then is the Speed of Light Constant?

The question “Reasons why is the speed of light constant?” is often questioned by those making an effort to comprehend physics. Google has 2760 links to that query. Yet the explanation is so simple that a 10-year-old can understand it, that is, if you accept Quantum Field Theory.

Bring the ten-year-old to a pond and drop a rock in the water. Show her that the waves move through the water at a particular velocity, and explain to her that this speed depends solely on the properties of water. You might release different types of items at varying sites and show her that the waves move at the exact same speed, regardless of the size of the item or location of the water.

Then tell her that sound travels through air with a fixed rate that depends only on the properties of air. You could await a thunderstorm and time the difference between the lightning and the sound. Advise her that a whisper moves as quick as a yell. I believe a ten-year-old can understand the principle that water and air have properties that determine the speed of these waves, regardless of whether she does not understand the formulas.

Anybody who can comprehend this can then understand reasons why the speed of light is constant. You see, in Quantum Field Theory space has properties, exactly as air and water have properties. These properties are knowned as 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.”.

As soon as you accept the concept of fields (which admittedly is certainly not an easy one), that is actually all you need to recognize. Light is waves in the electromagnetic field that travel through space (not space-time) at a speed directed by the properties of space. They abide by reasonably simple formulas (not that you have to understand them), just as sound and water waves abide by basic equations. OK, the Quantum Field Theory formulas 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.”.

Nevertheless this inquiry can have a different meaning: “Why is the speed of light independent of motion?” This particular fact was first illustrated by the renowned Michelson-Morley experiment, in which light beams were timed as the earth revolved and rotated. The shocking result was actually that the speed of light was exactly the same despite the earth’s movement.

As I wrote in my book (see quantum-field-theory. net): That the speed of light must be independent of movement was most surprising … It makes no sense for a light beam – or anything, for that matter – to journey at the identical speed no matter the movement of the observer … except if “something funny” is taking place. The “something funny” turned out to be even more astonishing than the M-M result itself. Essentially, 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 device in the forward direction contracted by the exact same amount as the extra distance the light beam would certainly have to travel due to movement, the 2 effects would cancel out. In fact, this is the only way that Michelson’s null result could be explained.

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

We need to acknowledge that even if the molecular configuration of an object seems stationary, 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 holds the object together. Now if the object is moving really quickly, this interaction among fields will become more difficult since the fields, on the average, will need to interact through greater distances. Thus the object in motion ought to in some way adjust itself to ensure that the exact same interaction between fields can occur. How can it do this? The only way is by decreasing 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 measurements of an item must therefore be impacted by motion.

It is very important to comprehend 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 a lot greater, we on earth would continue to be unaware of it. As John Bell discussed 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 individuals who would like to comprehend physics, I say use Quantum Field Theory and: WAKE UP AND SMELL THE FIELDS.