qed-0

Abbreviations

• ED = (classical) electromagnetism/electrodynamics
• QED = quantum electrodynamics
• QM = quantum mechanics
• SR = special relativity
• QFT = quantum field theory

Synonyms

• (quantum, subatomic, microscopic) scale

“study” = “area concerned with…”, “discipline”, “area”, “field” Basically, TM uses “X studies Y” to refer to what (Y) a certain “area” (X) pertains to, including its objects of interest, tools it employs to investigate and understand these objects, etc.

Iterations

Convergences.

v2

1. Special Relativity (SR) is the most accurate kinematic framework for flat spacetime; at low energies, it reduces to Newtonian mechanics, but at higher energies (associated with motion at about 0.1 or more), SR becomes necessary to accurately describe phenomena.
2. Quantum Field Theory (QFT) is a theoretical framework that accounts for phenomena at the quantum (subatomic) scale along with relativistic phenomena, which treats fields - not particles - as the fundamental objects (as opposed to the particle), with particles reinterpreted as quantum excitations of those fields.
3. Electromagnetism (EM) is the term encapsulating all phenomena associated with electric and magnetic fields and their interactions.
4. Electrostatics and magnetostatics study a subset of EM phenomena, involving static (stationary) electric charges, and magnets (respectively), and their fields.
5. Electrodynamics (ED) studies a subset of EM phenomena, involving dynamic (moving) charges and magnets (and their fields). ED is inherently relativistic because Maxwell’s equations are Lorentz covariant (don't fully understand this statement) - or, simply, since light is an EM wave, and relativity is based on treating the speed of light as constant, ED/EM is naturally relativistic (want to refine this statement).
6. A quantum (plural: quanta) is a discrete, indivisible unit of a physical quantity (e.g. energy, angular momentum, charge). One such quantity is the excitation of a field, and a quantum of this is a particle (better way to phrase this?).
   1. So, a particle is one specific kind of quantum - a field quantum ?.
7. Quantum Mechanics (QM) studies quanta (quantum particles). More specifically, QM describes how a quantum’s state (which includes observables such as spin, polarisation, energy level, etc. - but more generally, position and momentum) (which includes its position and momentum) evolves over time.
   1. QM uses 2 objects in particular: states and operators. So, instead of the vector representation of observables used in classical mechanics (does classical mechanics include equivalents to other observables like spin, polarisation, energy level?), QM represents observables as operators (in the form of Hermitian matrices) which act on states in Hilbert space, where each state represents either (1) 1 particle or (2) an N-particle system ? best way to describe.
   2. Typically, QM can be framed in 3 “pictures”. In the Schrodinger picture, the operators are time-independent and states evolve with time. In the Heisenberg picture, the states are time-independent and the operators evolve with time. In the interaction picture, a combination of these approaches is used.
   3. The Schrodinger equation is a differential equation describing how a state evolves in time under a particular operator - the Hamiltonian. ? The Hamiltonian encodes the energy of the system (or state ?) and when it acts on the state, it yields a description of how it evolves over time a very shaky statement made with minimal confidence - want to understand exactly what the Hamiltonian represents, and what function it serves
8. QM is non-relativistic - it deals with slow or stationary (basically, low energy) quantum objects. Hence, QM cannot be used to give a comprehensive, consistent account of ED phenomena (i.e., light and its interactions with matter?).
   1. The QM formalism assumes a fixed number of particles; this assumption is consistent with the low-energy regime, because particle creation/destruction requires energies on the order of $m{c}^2$ (mass-energy), which only becomes accessible at high, relativistic energies. So, QM does not handle the creation/destruction of particles, which happens naturally in the high-energy relativistic regime of ED.
9. ED is deterministic, hence it cannot be used to illuminate (probabilistic) QM phenomena.
   1. Since ED is a deterministic theory, it cannot be applied to phenomena at the quantum scale because at this scale, particles behave probabilistically in that their positions and momenta cannot be determined precisely, simultaneously.
10. Since QM and ED are incompatible - due to not sharing properties of relativity (Lorentz invariance) is it correct to say they do not "share the property of relativity"? and determinism/probabilism - another theory/approach is necessary to accurately, holistically describe EM phenomena at the quantum scale, which takes the form of Quantum Electrodynamics (QED).
    1. QED is a unification of classical ED, SR and QM. These are unified via QFT (of which QED is an instance).
11. QED removes the “action at a distance” from classical ED (and classical EM) by incorporating (virtual?) photons as particles that mediate interactions between charged particles. Photons are the gauge boson associated with the electromagnetic force.
12. The central particles of QED are electrons and photons. Electrons are the “matter particles” (fermions) and photons are the “force-carrying particles” (bosons).

v1

1. Special Relativity (SR) studies phenomena occurring at or around the speed of light (generally, 0.1c or more).
2. A Quantum Field Theory (QFT) is a theory of a set of phenomena (is there a more fitting term than "set of phenomena", like force, quantity, etc.?) that accounts for phenomena at the quantum scale (is there a more fitting term than "quantum scale"?), along with relativistic phenomena, which is achieved by relying on the field as a fundamental object (as opposed to the particle Is there another kind of object that would make sense to base a theory like this on, or is field vs particle the only sensible choice?).
3. Electromagnetism (EM) is the term encapsulating all phenomena associated with electric and magnetic fields and their interactions.
4. Electrostatics and magnetostatics study a subset of EM phenomena, involving static (stationary) electric charges, and magnets (respectively), and their fields.
5. Electrodynamics (ED) studies a subset of EM phenomena, involving dynamic (moving) charges and magnets (and their fields). Since light is an EM wave, ED is inherently relativistic.
6. Quantum refers to the smallest component of an observable/quantity (such as light, energy, matter), such that it cannot be considered to “break into” anything smaller. The plural is quanta. A quantum is a particle (or, is it a packet of energy, and the more accurate term for what I'm referring to is "quantum particle"?).
7. Quantum Mechanics (QM) studies quanta (quantum particles). More specifically, QM describes how a quantum’s state (which includes its position and momentum) evolves over time.
   1. QM uses 2 objects in particular: states and operators. So, instead of the single vector (or just vector, without the "single" prepend?) representation of position and momentum used in classical mechanics, QM represents position and momentum as operators which act on states, where each state represents 1 particle.
   2. Typically, QM can be framed in 3 “pictures”. In the Schrodinger picture, the operators are time-independent and states evolve with time. In the Heisenberg picture, the states are time-independent and the operators evolve with time. In the interaction picture, a combination of these approaches is used (how exactly, TM is currently unsure).
   3. The Schrodinger equation encodes the link between operators and states (or is it just one operator and one state?) for one particle.
8. QM is non-relativistic - it deals with slow or stationary (basically, low energy) quantum objects. Hence, QM cannot be used to illuminate ED phenomena, as ED concerns light, which is relativistic by definition.
   1. QM assumes low-energy (or assumes constant number of particles involved?), so it does not handle the creation/destruction of particles, which happens naturally in the high-energy relativistic frame (better term than "relativistic frame"?) of ED.
9. ED is deterministic, hence it cannot be used to illuminate (probabilistic) QM phenomena.
   1. Since ED is a deterministic theory (is ED considered a theory, or field, or what?), it cannot be applied to phenomena at the quantum scale because at this scale, particles behave probabilistically ? in that their positions and momenta cannot be determined precisely, simultaneously.
10. Since QM and ED are incompatible - due to not sharing properties of relativity (relativistic-ness?) and determinism/probabilism - another theory/approach is necessary to accurately, holistically describe EM phenomena at the quantum scale, which takes the form of Quantum Electrodynamics (QED).
    1. QED is a unification of classical ED, SR and QM. These are unified via QFT (of which QED is an instance).
11. QED removes the “action at a distance” from classical ED (and classical EM) by incorporating photons as particles that mediate interactions between charged particles.
12. The central particles of QED are electrons and photons.
    1. Here, do electrons represent matter? Would it be more accurate to say that the central particles are photons and any charged particle (including electrons, but also e.g. protons)? What would other charged particles even be?