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

Definition of the “Measurement Problem”.

A significant question in physics these days is “the measurement problem”, likewise known as “collapse of the “wave-function”. The issue developed in the early days of Quantum Mechanics as a result of the probabilistic nature of the equations. Because the QM wave-function describes merely probabilities, the outcome of a physical measurement can only be calculated as a probability. This naturally brings about the question: When a measurement is made, at exactly what point is the ultimate result “decided upon”. Some folks believed that the role of the observer was critical, and that the “decision” was generated when someone looked. This led Schrödinger to design his well-known cat experiment to demonstrate how ludicrous such an idea was. It is not usually 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. can not be a real state of affairs, for in reality there is just no intermediary between exploded and not-exploded.” At a later time, Einstein remarked, “Does the moon exist only when I look at it?”.

The controversy continues to this day, with a few individuals still thinking that Schrödingers cat remains in a superposition of dead and alive until somebody looks. On the other hand most people believe that the QM wave-function “collapses” at some earlier point, before the uncertainty achieves a macroscopic level– with the definition of “macroscopic” being the primary question (e.g., GRW theory, Penrose Interpretation, Physics forum). A few people take the “many worlds” perspective, in which there is no “collapse”, but a splitting into various worlds that include every possible histories and futures. There have been a lot of experiments designed to address this question, e.g., “Towards quantum superposition of a mirror”.

Schrodinger's Cat.gif

We will now find that an unequivocal solution to this question is supplied by Quantum Field theory. But because this theory has been neglected or misunderstood by many physicists, we need to initially specify what we mean by QFT.

Definition of Quantum Field Theory.
The Quantum Field Theaory referred to within this post is the Schwinger version where 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 backing them are very different, and it is the Feynman model that is chosen by the majority of Quantum Field Theory physicists.

* According to Frank Wilczek, Feynman ultimately 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 make use of the term henceforward, the world is comprised of fields and only fields. Fields are defined as characteristics of space or, to put it in a different way, space is comprised of fields. The field concept was introduced by Michael Faraday in 1845 as an illustration for electric and magnetic forces. Even so the idea was not easy for folks to accept and so when Maxwell showed that these particular equations predicted the existence of EM waves, the concept of an ether was introduced to carry the waves. These days, however, it is normally accepted that space can possess properties:.

To deny the ether is essentially to presume that empty space has no physical qualities whatsoever. The key realities of mechanics do not harmonize with this view.– A. Einstein (R2003, p. 75).

Moreover space-time on its own had emerged as 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 illustrates the strength of fields at a given point, the other describes the probability that particles could be found at that point, or that a given state exists…..

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How Quantum Field Theory Solves the “Measurement Problem”.

Max_Planck.jpg

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.

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The Uncertainty Principle

Uncertainty Principle, Fields of Color

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….

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Scientific American, EINSTEIN DIDN’T SAY THAT!

Scientific American - Einstein's theory of relativity

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?

when fields collapse, quantum field theory

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.

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Book Simplifies Complicated Quantum Field Theory

fields of color, quantum field theory, theory of relativity

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.

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 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.”.

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Space-Time Curvature & Quantum Field Theory

space-time curvature

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:

steven weinberg

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.

Learn more about space-time curvature at Fields of Color!