22 Dec 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 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.