In our blog we have tried to analyze collision experiments from the particle viewpoint. Our photograph model of quantum field theory claims that deep down the processes happen in classical mechanics. It is the path integral which makes the processes to look like wave phenomena.
Meinard Kuhlmann (2020) has written a detailed account about various standpoints in quantum field theory. Paul Dirac and Richard Feynman supported particle interpretations, Wolfgang Pauli a field interpretation. The string model (some people call it a theory) has a string interpretation.
Feynman diagrams describe events in the momentum space. There are no spatial locations in the diagrams, nor points in time. In this sense, the diagrams are a pure field interpretation.
Our view in this blog has been that we must work in the position space and use a particle interpretation to gain more insight on events, and possibly remove divergences from Feynman integrals.
Ontology of quantum field theory is unclear
Meinard Kuhlmann writes about the unclarity of the "existing things" in quantum field theory, that is, the ontology.
In this blog we have been perplexed by the ontology. Does quantum field theory study:
1. classical particles,
2. classical fields,
3. quantum fields with the creation and the annihilation operators and a Fock space,
4. virtual particles,
5. wave functions,
6. path integrals, or
7. measurements?
Or maybe Hilbert spaces, operators, or algebras?
In addition, is it just a perturbative theory, or a general physical theory?
Many confusions arise from the ontology. For example, the Unruh effect definitely does not exist in classical fields. Could it exist in quantum fields?
Hawking radiation definitely does not exist in classical fields. Could it exist in quantum fields?
What is the vacuum energy per cubic meter? Classically it is zero. Is it infinite in quantum field theory?
The ontology problem exists in ordinary quantum mechanics, too: it is the wave-particle duality.
The electron clearly is a "particle"
Charge conservation requires that the number of electrons does not change spontaneously. Quantization of charge requires that electrons do not break up.
Dirac formulated his equation in the way that there is a probability density for the location of the electron, and probability is conserved.
The electron is very much a particle. We can look at the path of an electron in a cloud chamber and see it drawing a line there.
The Schrödinger equation has had great success in explaining natural phenomena. The electron is a particle in the equation, moving under a potential.
A rotating electric dipole falling in a gravitational field; is the photon a "particle"?
An observer in free fall measures the dipole emitting right-handed photons of a fixed frequency.
An observer far out in space measures red-shifted photons of varying frequencies. Some of the photons are left-handed, because the dipole sends a "chirp" and the Bogoliubov transformation turns the handedness of a small number of photons in a chirp.
It is the general spirit of quantum mechanics to make a minimum number of assumptions about a system before a measurement is made. It would be wrong to say that the photons "existed" before any measurement. The "charge" to make the photons, that is, the energy, did exist. Before the measurement, there was a superposition of states of the various locations of the "charge".
If an excited hydrogen atom sends a photon, and we measure afterwards the recoil of the atom, then after the measurement it is safe to say that a photon particle is flying somewhere in space.
If we have an electron in our hand and wave the hand, the electron classically sends a very complex electromagnetic waveform with various frequencies. Should we say that the electron sent a set of photons which was completely defined immediately after the hand waving?
Again, the spirit of quantum mechanics is to make the least assumptions before a measurement is made. It sounds wrong to claim that the set of photons is defined before a measurement. Usage of a creation operator sounds wrong because it seems to assume that the set of photons is definite and determined before they are measured.
Creation operators are a form of a hidden variable model - assuming that some property is defined before a measurement.
The photon may be a particle, but in most cases we do not know how many and what frequency photons exist in an experiment.
The photon clearly is a particle in a digital camera or Compton scattering
If the photon is not a particle, how does it then appear as a single pixel in the image sensor of a digital camera?
In Compton scattering, a classical particle seems to collide with the electron. If the photon were a wave, why would it imitate a classical particle in a collision?
Is the virtual photon in a Coulomb scattering Feynman diagram a "particle"?
In his 1949 paper, Richard Feynman derives the virtual photon from the Fourier decomposition of the 1 / r Coulomb potential.
The QED lagrangian talks about the electromagnetic field A interacting with the Dirac field, but nowhere it is defined where we get A from. How does a Dirac electron wave generate A? If the electron wave packet is far away, we can calculate A classically. How to calculate A when the electron wave packet is all around?
The particle status of a virtual photon is much less clear than the status for a real photon. The alternative is just to use the Coulomb classical potential.
In an earlier blog post we wrote about an electric field bending a beam of electrons. The phenomenon is easy to understand with a potential and the Schrödinger equation. But it is hard to use the concept of a virtual photon to explain the electron paths. The reason probably is that the bending is not a perturbative phenomenon. The path of every electron gets bent with a 100% probability. Then it is not a "perturbation". Incidentally, a particle moving in the gravitational field of a macroscopic object, that is, curved spacetime, is not under a "perturbation" either. Has this been overlooked by researchers?
Virtual photons seem to exist in "perturbations" only. They are a useful concept in Feynman diagrams, but probably just fiction as "particles".
Steven Weinberg's view
Steven Weinberg (1996) writes about the history and philosophy of quantum field theory.
Weinberg tells us that in the 1960s he did not like the path integral approach of Feynman, because an objective of quantum field theory was to work with fields only - no particles.
Weinberg strongly supports the regularization / renormalization machinery of quantum field theory.
Weinberg writes that the standard quantum field theory is an inevitable consequence of Lorentz covariance, quantum mechanics, and the cluster decomposition principle, which requires that distant experiments give uncorrelated results. But then he admits that the string model (which some people call a theory) does satisfy the above principles without being a quantum field theory!
Weinberg says that a weakness of quantum field theory is that it is just a perturbative theory.
Our blog studies various problems in mainstream quantum field theory: the need for regularization / renormalization, the obscure status of Unruh and Hawking radiation, non-renormalizability of gravitation, and failure to handle a simple non-perturbative situation like an electron beam in a static electric field. Steven Weinberg seems to have a practical attitude: if the theory agrees with the empirical data, then it is ok.
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