Why Relativity Breaks the Schrodinger Equation by Richard Behiel (2023)
Source. Take a plane wave function, because we know its momentum perfectly. Apply a constant voltage to an electron. You can easily bring it beyond the speed of light at about 255.5 keV.Adds special relativity to the Schrödinger equation, and the following conclusions come basically as a direct consequence of this!
Experiments explained:
- spontaneous emission coefficients.
- fine structure, notably for example Dirac equation solution for the hydrogen atom
- antimatter
- particle creation and annihilation
Experiments not explained: those that quantum electrodynamics explains like:See also: Dirac equation vs quantum electrodynamics.
- Lamb shift
- TODO: quantization of the electromagnetic field as photons?
The Dirac equation is a set of 4 partial differential equations on 4 complex valued wave functions. The full explicit form in Planck units is shown e.g. in Video 1. "Quantum Mechanics 12a - Dirac Equation I by ViaScience (2015)" at youtu.be/OCuaBmAzqek?t=1010:Then as done at physics.stackexchange.com/questions/32422/qm-without-complex-numbers/557600#557600 from why are complex numbers used in the Schrodinger equation?, we could further split those equations up into a system of 8 equations on 8 real-valued functions.
Equation 1.
Expanded Dirac equation in Planck units
. Quantum Mechanics 12a - Dirac Equation I by ViaScience (2015)
Source. PHYS 485 Lecture 14: The Dirac Equation by Roger Moore (2016)
Source. Theoretical framework on which quantum field theories are based, theories based on framework include:so basically the entire Standard Model
The basic idea is that there is a field for each particle particle type.
E.g. in QED, one for the electron and one for the photon: physics.stackexchange.com/questions/166709/are-electron-fields-and-photon-fields-part-of-the-same-field-in-qed.
And then those fields interact with some Lagrangian.
One way to look at QFT is to split it into two parts:Then interwined with those two is the part "OK, how to solve the equations, if they are solvable at all", which is an open problem: Yang-Mills existence and mass gap.
- deriving the Lagrangians of the Standard Model: why do symmetries such as SU(3), SU(2) and U(1) matter in particle physics?s. This is the easier part, since the lagrangians themselves can be understood with not very advanced mathematics, and derived beautifully from symmetry constraints
- the qantization of fields. This is the hard part Ciro Santilli is unable to understand, TODO mathematical formulation of quantum field theory.
There appear to be two main equivalent formulations of quantum field theory:
Quantum Field Theory visualized by ScienceClic English (2020)
Source. Gives one piece of possibly OK intuition: quantum theories kind of model all possible evolutions of the system at the same time, but with different probabilities. QFT is no different in that aspect.- youtu.be/MmG2ah5Df4g?t=209 describes how the spin number of a field is directly related to how much you have to rotate an element to reach the original position
- youtu.be/MmG2ah5Df4g?t=480 explains which particles are modelled by which spin number
Quantum Fields: The Real Building Blocks of the Universe by David Tong (2017)
Source. Boring, does not give anything except the usual blabla everyone knows from Googling:Quantum Field Theory: What is a particle? by Physics Explained (2021)
Source. Gives some high level analogies between high level principles of non-relativistic quantum mechanics and special relativity in to suggest that there is a minimum quanta of a relativistic quantum field.