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volume II: Synopsis

part III: Modern Physics

page 22: Quantum field theory

Quantum mechanics, like Newtonian mechanics, provides a general paradigm for the study of motion. Newtonian mechanics struck trouble when it came to deal with electromagnetism. This problem ultimately led to the development of quantum theory. Quantum theory, in its turn, revealed itself to be very difficult to harmonize with Einstein's special theory of relativity. Quantum field theory has evolved to deal with this difficulty and provides us with a fairly comprehensive picture of the Universe at a small scale: the Standard Model. Standard model - Wikipedia

The essential content of the special theory of relativity is that the fixed points of physics (incuding the velocity of light and the space-time interval) are the same in all inertial frames of reference. What changes is how things in one frame of reference look when viewed from another frame of reference in relative motion. This change affects not only human observers but all interactions, which may be seen as communications between different particles. It is a constitutive feature of the Universe, coupled to the delay in communication between different points in the Universe. It seems that all things 'observe' and 'act' upon one another as though special relativity were true for them. The same is true for us. Almost every meeting involves consideration of travel times. Special relativity - Wikipedia

We move from one frame of reference to another via a Lorentz transformation. The Lorentz transformation couples what we see to what is actually happening in the local rest frame of the event we are watching. The actual structure of the Lorentz transformation is based on the axiom that the velocity of light is the same for all observers. Communication carries us between frames moving at all relative velocities (upper limit, c).

To simplify the problem of gravitation, Newton assumed instantaneous action at a distance. Not only does modern physics hold that no action is instantaneous, it also holds that interactions only occur when the space-time distance between the agents is zero. All communication in the Universe is mediated by particles moving from one point to another.

Aristotle understood change to mean that matter lost one form and gained another. Quantum field theory takes a similar approach. Being a formal theory, it is not concerned with matter. Instead it says that change occurs when one form is annihilated and another created. There is a certain energy associated with each form, and energy is conserved, placing a constraint on the forms that may be created. When an atom emits a photon, that photon is emitted with a certain energy (frequency) related to the electronic transition that created it. When the same photon is captured by another atom, it is annihilated, passing its energy to another transition.

Quantum mechanics defines a form as an eigenfunction of the operator representing the formal change. In non-relativistic quantum mechanics, everything may be considered as acting at a point in space. Quantum mechanics sees only time and energy, and it allows us to assign energies to eigenfunctions, often quite precisely. Our knowledge of eigenfunctions is ultimately deduced from measurements of the energy associated with them. Three dimensional space emerges from quantum mechanics when we take the relationship between energy and special relativity into account. Zee

One consequence of the special theory is the equivalence in interactions of mass and energy expressed by the famous formula E = mc2. Energy may be created out of massive particles, and massive particles may be created out of energy. Quantum field theory describes this process of the creation and annihilation of particles, telling us how frequently it will happen and what can be created from the annihilation of what. The nature and rate of creation and annihilation in space-time is controlled by fields, which are probability functions whose domain is space-time, telling us how probable it is that a particular event will occur at a certain place and time, rather like the weather bureau. In a way fields play the role of God, but they exist within, rather than outside, the Universe.

There are four fields, called gravitation, electromagnetic, strong and weak. Gravitation is responsible for the overall structure of the Universe described by the general theory of relativity. The electromagnetic field, carried by the photon, and its interactions with electrically charged matter, is described by quantum electrodynamics. Both gravitation and electromagnetic fields have unlimited range, and so can be sensed at the macroscopic level. We are all familiar with the pull of gravity which keeps us on the earth, and have played with magnets, so feeling an electromagnetic field. Peskin & Schroeder, Electromagnetic force - Wikipedia, Gravitation - Wikipedia

The other two fields, strong and weak, have extremely short range, but are nevertheless essential to the functioning of the Universe. Quantum field theory shows how the particles of the Universe form a complete set, spanning all possible communications of all possible information. Strong interaction - Wikipedia, Weak interaction - Wikipedia

Here we think of each field as a communication channel defined by a certain communication protocol. The overall structure of the Universe may be conceived as a network of fermions communicating by exchanging bosons with one another. Fermions define the structure of the universe through the exclusion principle, which says no two fermions can occupy one quantum state. They must spread out, like the electrons in an atom. In the Universal network, fermions are the sources, bosons are the messages. Fermion - Wikipedia, Boson - Wikipedia

In a complexifying universe, distinction is equivalent to separation in space or time. The messages we receive from the Universe are written in space. By connecting them together into models, we learn to decode these messages. Much of this decoding is already built into us, since we have evolved to live in the world described by field theory.

(revised 23 May 2013)

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Further reading

Books

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Peskin, Michael E, and Dan V Schroeder, An Introduction to Quantum Field Theory, Westview Press 1995 Amazon Product Description 'This book is a clear and comprehensive introduction to quantum field theory, one that develops the subject systematically from its beginnings. The book builds on calculation techniques toward an explanation of the physics of renormalization.'  
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Zee, Anthony, Quantum Field Theory in a Nutshell, Princeton University Press 2003 Amazon book description: 'An esteemed researcher and acclaimed popular author takes up the challenge of providing a clear, relatively brief, and fully up-to-date introduction to one of the most vital but notoriously difficult subjects in theoretical physics. A quantum field theory text for the twenty-first century, this book makes the essential tool of modern theoretical physics available to any student who has completed a course on quantum mechanics and is eager to go on. Quantum field theory was invented to deal simultaneously with special relativity and quantum mechanics, the two greatest discoveries of early twentieth-century physics, but it has become increasingly important to many areas of physics. These days, physicists turn to quantum field theory to describe a multitude of phenomena. Stressing critical ideas and insights, Zee uses numerous examples to lead students to a true conceptual understanding of quantum field theory--what it means and what it can do. He covers an unusually diverse range of topics, including various contemporary developments,while guiding readers through thoughtfully designed problems. In contrast to previous texts, Zee incorporates gravity from the outset and discusses the innovative use of quantum field theory in modern condensed matter theory. Without a solid understanding of quantum field theory, no student can claim to have mastered contemporary theoretical physics. Offering a remarkably accessible conceptual introduction, this text will be widely welcomed and used.  
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Links
Boson - Wikipedia Boson - Wikipedia, the free encyclopedia 'In particle physics, bosons are particles with an integer spin, as opposed to fermions which have half-integer spin. From a behaviour point of view, fermions are particles that obey the Fermi-Dirac statistics while bosons are particles that obey the Bose-Einstein statistics. They may be either elementary, like the photon, or composite, as mesons. All force carrier particles are bosons. They are named after Satyendra Nath Bose. In contrast to fermions, several bosons can occupy the same quantum state. Thus, bosons with the same energy can occupy the same place in space.' back
Electromagnetic force - Wikipedia Electromagnetic force - Wikipedia, the free encyclopedia 'In physics, the electromagnetic force is the force that the electromagnetic field exerts on electrically charged particles. It is the electromagnetic force that holds electrons and protons together in atoms, and which hold atoms together to make molecules. The electromagnetic force operates via the exchange of messenger particles called photons and virtual photons. The exchange of messenger particles between bodies acts to create the perceptual force whereby instead of just pushing or pulling particles apart, the exchange changes the character of the particles that swap them.' back
Fermion - Wikipedia Fermion - Wikipedia, the free encyclopedia 'In particle physics, fermions are particles with a half-integer spin, such as protons and electrons. They obey the Fermi-Dirac statistics and are named after Enrico Fermi. In the Standard Model there are two types of elementary fermions: quarks and leptons. . . . In contrast to bosons, only one fermion can occupy a quantum state at a given time (they obey the Pauli Exclusion Principle). Thus, if more than one fermion occupies the same place in space, the properties of each fermion (e.g. its spin) must be different from the rest. Therefore fermions are usually related with matter while bosons are related with radiation, though the separation between the two is not clear in quantum physics. back
Gravitation - Wikipedia Gravitation - Wikipedia, the free encyclopedia 'Gravitation, or gravity, is a natural phenomenon by which physical bodies attract with a force proportional to their mass. Gravitation is most familiar as the agent that gives weight to objects with mass and causes them to fall to the ground when dropped. Gravitation causes dispersed matter to coalesce, and coalesced matter to remain intact, thus accounting for the existence of the Earth, the Sun, and most of the macroscopic objects in the universe.' back
Special relativity - Wikipedia Special relativity - Wikipedia, the free encyclopedia 'Special relativity . . . is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein (after the considerable and independent contributions of Hendrik Lorentz, Henri Poincaré and others) in the paper "On the Electrodynamics of Moving Bodies". It generalizes Galileo's principle of relativity—that all uniform motion is relative, and that there is no absolute and well-defined state of rest (no privileged reference frames)—from mechanics to all the laws of physics, including both the laws of mechanics and of electrodynamics, whatever they may be. Special relativity incorporates the principle that the speed of light is the same for all inertial observers regardless of the state of motion of the source.' back
Standard model - Wikipedia Standard model - Wikipedia, the free encyclopedia 'The Standard Model of particle physics is a theory that describes three of the four known fundamental interactions between the elementary particles that make up all matter. It is a quantum field theory developed between 1970 and 1973 which is consistent with both quantum mechanics and special relativity. To date, almost all experimental tests of the three forces described by the Standard Model have agreed with its predictions. However, the Standard Model falls short of being a complete theory of fundamental interactions, primarily because of its lack of inclusion of gravity, the fourth known fundamental interaction, but also because of the large number of numerical parameters (such as masses and coupling constants) that must be put "by hand" into the theory (rather than being derived from first principles) . . . ' back
Strong interaction - Wikipedia Strong interaction - Wikipedia, the free encyclopedia 'In particle physics, the strong interaction (also called the strong force, strong nuclear force, or color force) is one of the four fundamental interactions of nature, the others being electromagnetism, the weak interaction and gravitation. As with the other fundamental interactions, it is a non-contact force. At atomic scale, it is about 100 times stronger than electromagnetism, which in turn is orders of magnitude stronger than the weak force interaction and gravitation. ' back
Weak interaction - Wikipedia Weak interaction - Wikipedia, the free encyclopedia 'Weak interaction (often called the weak force or sometimes the weak nuclear force), is one of the four fundamental forces of nature, alongside the strong nuclear force, electromagnetism, and gravity. It is responsible for the radioactive decay of subatomic particles and initiates the process known as hydrogen fusion in stars. Weak interactions affect all known fermions; that is, particles whose spin (a property of all particles) is a half-integer.' back

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