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”.


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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