Limitations of science: Quantum field theory
The next article in series on “Limitations of scientific language” and limitations of theoretical models in physics. I ultimately deal with quantum field theory, which is the most advanced microscopic quantum theory developed. It can describe creation and annihilation of particles and interactions of particles by fundamental forces.
The difference between the wavefunction and the quantum field
The action of creation and annihilation are smeared out by uncertainty in position as any quantum wavefunction or field. Mathematically creation and annihilation can be constructed from complex linear superposition of position and velocity. It is impossible to create a particle with exactly precise position and velocity because of the Heisenberg uncertainty principle. Only with a precise position and not velocity. The creation and annihilation are governed by the same uncertainty principle, although as actions they can not be directly measured.
Measurement by definition and in reality (in practice) is emission and absorption of photons with probability related to structure constant as strength of the fundamental force and distance. How does kinetic energy and other terms in the Hamiltonian work in the context of quantum field theory?
Quantum field theory — Kinetic energy
How does kinetic energy or kinesis, as the motion of the elementary particle works in quantum field theory? As a first, velocity of travel of information can not be infinite — otherwise kinetic energy would be infinite.
Hamiltonian or kinetic energy K (without certain constants such as mass) describes all the possible processes that can occur in reality.
At very small distances the effect has a large probability, and the particle is zigzagging through space and the electron quantum field. Elementary particles are excitations in the quantum field.
Infinitesimal length can not be less then Planck length. So the motion of the electron is quantized, the electron is not moving continuously through space, but it is constantly being annihilated at one place and then created at another place with the infinitesimal distance.
When infinitesimal length becomes comparable to Planck length, the probability of interaction can in principle become larger then 100%, which is nonsense. At Planck length quantum theory breaks down and has to be replaced by quantum gravity.
It the context of quantum field theory the zitterbewegung process and the zigzagging motion can be interpreted as interaction of the electron with particles and antiparticles with different spin, that form spontaneously in the vacuum.
It is in accordance with zitterbewegung motion of the electron because the virtual particles can be created both forward and backwards. When the Dirac equation kinetic energy is included there is mixing between particles of different spin, so by the same process spin can also change.
Conservation of charge requires for the total charge to be the same before or after the process. Obviously the processes have to be in accordance with conservation of momentum, energy and spin. All the processes have to be in accordance with causality —but the electron fields are described by a wavefunction, as their position in space is smeared out with uncertainty.
Does the wavefunction collapse occur with these processes? Obviously (from experiments) the wavefunction does not spread with time for a long period, otherwise electrons from planet Earth would be spontaneously appearing in space. So the collapse of the wavefunction occurs one way or another, and classical universe does work as observed from classical experiments.
In quantum field theory the same Dirac equation is used, but with an important difference, the wavefunction has been promoted to a quantum electron field. When the Dirac equation gets promoted to a quantum field equation, it describes a quantized electron field and electromagnetic force — interaction between the electrons and photons. The conclusion is the same for the Dirac electron field, electrons have the same properties, only there is mixing between particles of different spin. Zitterbewegung (spin changing) for the electron is also true in quantum field theory. The electron is constantly being destroyed and created in the quantum electron field, replaced by other electrons. The real electron can interact with a spontaneously created positron/electron virtual pair as a vacuum fluctuation, by annihilating with virtual positron charge, the virtual electron becomes real. The previously real electron is annihilated.
All sorts of processes occur with different probability — in fact an infinite number of different processes can occur (creation and annihilation of particles from the standard model), with decreasing probability. The more complicated process is, the smaller the probability of occurrence is. The vacuum has complicated structure, where particles are constantly created and annihilated. It is impossible to define precise position or momentum of any particle in quantum field theory.
Elementary particles are Indistinguishable
In fact an important result from quantum field theory is that every electron is the same, different electrons can not be distinguished from each other. If the electron has interactions between other electrons, after scattering, it is impossible to distinguish which was the original electron — all combinations have to be included and probability calculated.
As I have explained in article, the virtual positron/electron pairs reduce the infinite electron charge to a measurable value by vacuum fluctuation interactions. If a virtual positron/electron pair forms in vacuum around the real electron, and the positron and electron annihilate, it is impossible to distinguish which electron was destroyed and what is the real electron that remained.
The standard: electron is a static wavefunction explanation, that does not have properties before being measured, is different with quantum field theory. The properties are still probabilistic, but interpretation different. There is a scientific requirement to with an experiment detect the zitterbewegung properties of the electron, but unfortunately it is not possible with technology now. In any case what I presented is a mathematical interpretation of kinetic energy and Dirac equation in quantum field theory.
I tried to rationalize why proper interpretation of quantum physics has to rely on quantum field theory. How successful may be of debate.
Probability and Quantum Field Theory
Reality changes dramatically with the Dirac equation and quantization of all fields. In quantum field theory everything of importance is information and probability of interaction, from which results of scattering events of collisions of particles can be calculated and compared (for example) with real events in particle collider such as the LHC at CERN. Quantum field theory calculates probability rates of decay and production modes of certain particles such as the Higgs boson. Also from these experiments masses of particles and constants of nature can be determined.
It was already determined in 19th century that charge of the electron is quantized — quantum theory was inevitable. In science all physical parameters change, one way or another, all constants that are quantized and are truly constant and dimensionless, are probability of interaction values. Indeed, eventually with development of quantum field theory the structure constant of the electromagnetic force (as a dimensionless constant) which is related to the charge of the electron, was determined to be nothing more then probability of electron emitting or absorbing a photon. The probability is the structure constant 1/137 or 0.7%.
In accordance with laws of probability, more complicated process such as one electron emitting a virtual photon and then other electron absorbs the same photon which are independent processes then the probability of such interaction with one emission and one absorption of the photon is proportional to (1/137)². The more complicated interaction, the smaller probability of occurrence is. That is why even though in the vacuum there are infinite possibilities of interaction (the electron can emit infinite number of photon), the probability is still (1/137) to the power of infinity which is equal to = 0.
Even quantum field theory has its limitations, it does not work for the gravitational field. Also, many parameters in the standard model of particle physics have to be measured experimentally — there is no explanation for their origin. Some of the constants are apparently fine tuned for life — in contradiction to Copernicus principle. Is our universe special and tuned for life? Further, fundamental forces (including gravity) mathematically have almost the same strength at Planck energy.
The electroweak theory by Weinberg and others provides an explanation of origin of the electromagnetic and weak force (which can be used to provide origin of the photon and a relation between constants and masses of other gauge bosons). The electroweak force breaks into electromagnetic and weak force by interaction with the Higgs field. Higgs mechanism provides particles mass, but the origin of the Higgs boson mass and the Higgs field is unknown.
As I have presented in ‘Limitations’ series of articles, evolution of science is a series of more complicated statements, laws, theories and models that define our reality, and that allows development of technology. As technology advances, more sophisticated experiments can be performed that reveal failures of previous theoretical models — which results in better theories. The ones I have presented are last theories that are supported by experimental data. Now, perhaps entanglement and interpretation of quantum theory might be easier to study.
