Twelve papers. Four research traditions. Follow the idea back to its source.
What is observable? What is assumed? Which calculation connects the two? Read Feynman, Einstein, Bohm and Dirac through original visual studies that keep those questions open.
Original research by R. P. Feynman. Publisher access conditions may apply.
Original qualitative diagram. Space-time diagrams organise contributions to a quantum-electrodynamic calculation. Internal lines encode mathematical propagators, not directly observed tracks.
R. P. Feynman · 1982 Schematic
Let the simulator share the physics.
Feynman examines the difficulty of simulating quantum systems with classical computers and motivates quantum-mechanical simulation.
q.Which resources must a simulator preserve to reproduce a physical system?
Original research by R. P. Feynman. Publisher access conditions may apply.
Original qualitative diagram. Feynman examines the difficulty of simulating quantum systems with classical computers and motivates quantum-mechanical simulation.
02 / Einstein
A. Einstein · 1905 Schematic
Energy arrives in quanta.
The light-quantum hypothesis connects radiation energy to frequency. The photoelectric relation provides one testable consequence; light also exhibits interference.
q.Which observation calls for a particle-like description of radiation?
Original research by A. Einstein. Publisher access conditions may apply.
W is the work function; emission requires hν ≥ W in this ideal model. Original qualitative diagram. The light-quantum hypothesis connects radiation energy to frequency. The photoelectric relation provides one testable consequence; light also exhibits interference.
A. Einstein · 1905 Computed
Random motion, measurable order.
Brownian motion links statistical displacement to diffusion and molecular-scale thermal agitation. Ensemble spread grows even when the mean displacement is zero.
q.How can irregular motion provide quantitative evidence for molecules?
Original research by A. Einstein. Publisher access conditions may apply.
⟨x²⟩ = 2Dt (one dimension); zero mean displacement.
An analytical ensemble relation for free diffusion with constant D; time and squared displacement are in consistent arbitrary units. Not a measured trajectory or atomistic simulation.
A. Einstein · 1905 Schematic
Time belongs to a measurement procedure.
Special relativity connects inertial frames through the Lorentz transformation. Clock synchronisation and the invariant speed of light reshape simultaneity.
q.Which events are simultaneous—and according to which inertial frame?
Original research by A. Einstein. Publisher access conditions may apply.
Original qualitative diagram. Special relativity connects inertial frames through the Lorentz transformation. Clock synchronisation and the invariant speed of light reshape simultaneity.
03 / Bohm
D. Bohm · 1952 Schematic
A wave and a configuration.
Bohm develops a formulation with definite particle positions guided by the wavefunction. It is an interpretation with a specified dynamics, not a classical trajectory picture.
q.Which parts of a theory are observed, and which describe its ontology?
Original research by D. Bohm. Publisher access conditions may apply.
Original qualitative diagram. Bohm develops a formulation with definite particle positions guided by the wavefunction. It is an interpretation with a specified dynamics, not a classical trajectory picture.
D. Bohm · 1952 Schematic
Measurement enters the dynamics.
The second paper treats measurement and the relation to the usual quantum predictions. Agreement relies on the quantum-equilibrium distribution, not arbitrary hidden-variable states.
q.If predictions agree, what would distinguish interpretations experimentally?
Original research by D. Bohm. Publisher access conditions may apply.
Original qualitative diagram. The second paper treats measurement and the relation to the usual quantum predictions. Agreement relies on the quantum-equilibrium distribution, not arbitrary hidden-variable states.
Y. Aharonov & D. Bohm · 1959 Computed
A phase carries the enclosed flux.
The Aharonov–Bohm effect is a prediction of standard quantum mechanics, not unique evidence for Bohm’s interpretation. The relative phase of coherent alternatives can depend on enclosed magnetic flux even when the accessible paths lie in a field-free region.
q.What is physically testable when a potential depends on a gauge choice?
Idealised two-path interference. Here x is dimensionless position in fringe-period units; φ = qΦ/ℏ uses SI units with signed charge q and oriented magnetic flux Φ. The chosen plus sign defines the path/charge convention; changing flux by a phase of 2π repeats the pattern.
04 / Dirac
P. A. M. Dirac · 1927 Schematic
Radiation joins the quantum description.
Dirac treats emission and absorption using a quantum account of radiation and its interaction with matter. The sketch marks a transition, not a calculated rate.
q.What changes when radiation itself becomes part of the quantum system?
Original research by P. A. M. Dirac. Publisher access conditions may apply.
Original qualitative diagram. Dirac treats emission and absorption using a quantum account of radiation and its interaction with matter. The sketch marks a transition, not a calculated rate.
P. A. M. Dirac · 1928 Computed
Relativity meets the electron.
Dirac’s first-order matrix equation, H = cα·p + βmc², incorporates electron spin through its spinor structure. The dispersion relation shown here is relativistic but not unique to Dirac’s equation. Its energy structure has positive and negative branches; the later antiparticle interpretation is not a direct reading of this graph.
q.What additional structure is required when a wave equation is relativistic?
Original research by P. A. M. Dirac. Publisher access conditions may apply.
E±(p) = ±√(p² + m²), with c = 1.
Relativistic free-particle dispersion, not a numerical solution of the Dirac spinor equation. Branch colour indicates energy sign, not probability.
P. A. M. Dirac · 1931 Schematic
Consistency constrains charge.
Dirac explores how magnetic monopoles would constrain electric charge through quantum consistency. This is a theoretical condition, not evidence that monopoles have been detected.
q.Can a consistency requirement explain why an observable comes in discrete units?
Original research by P. A. M. Dirac. Publisher access conditions may apply.
Original qualitative diagram. Dirac explores how magnetic monopoles would constrain electric charge through quantum consistency. This is a theoretical condition, not evidence that monopoles have been detected.
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Connect a paper to a testable question.
Move from a historical formulation to a bounded model: specify the assumptions, compute a reference, and identify what evidence would change your conclusion.