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: An Introduction to Quantum Field Theory, 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 5 April 2020)
