Canonical copies of the two program papers live on Zenodo under CC BY 4.0. The other papers on this page are site papers, not deposits. Each of those has a “Read on this page” button, because a PDF download is blocked inside the preview. 2026a and 2026b are not replaced.
Shields 2026a · Working paper · v1
Individual Completion of Metastable Decay: A Constructive Program after Einstein's Reply to Criticisms
Will Shields · 12 September 2026
Predictive primitive. Converts Einstein’s 1949 successor-theory demand into a number: the first-event time T*(S). States axioms A1–A6, builds the Rank-1 analog, and orders the empirical sequence.
Abstract
Einstein's 1949 Reply to Criticisms does not propose a hidden-variable dressing of the existing quantum formalism. It states a successor-theory demand: a complete description of the individual situation whose laws, per se, have nothing to do with statistics; statistical quantum theory would then stand to that description as statistical mechanics stands to classical mechanics. This paper converts that demand into a predictive primitive for the case Einstein used as his example—the decay of a metastable individual and the mark it writes. The primitive is a first-event time T*(S) fixed by a complete individual state S. Laboratory preparations specify only a coarse cell S_coarse; the unread remainder S_perp decides the instant. A deterministic analog (metastable well plus a finite Fourier background with definite phases) is integrated: specified phases yield a unique T*; unstructured phases yield a waiting-time histogram; partial readout of phases narrows Var(T*). The program is thereby empirically constrained without being forced to sit Bell's examination for local completions of the quantum correlators. Nuclei are not the first test. Characterized analog systems are.
- Einstein 1949 Reply
- incompleteness
- individual description
- metastable decay
- arrival time
- field ontology
- analog tests
- Concept DOI
- 10.5281/zenodo.22717069
- MD5 of PDF
- 4475c8057d78a962aec68700efe1379d
Contents
- §1 The problem as Einstein stated it
- §2 Two texts, two examinations
- §3 Axioms of individual completion
- §4 The prediction primitive
- §5 A constructive analog
- §5.1 Dynamics
- §5.2 Two individuals, one coarse well
- §5.3 Unread remainder and the statistical shadow
- §5.4 Conditional narrowing
- §6 From analog to field
- §7 An empirical sequence
- §8 What the program refuses
- §9 Relation to neighboring programs
- §10 Conclusion
Shields 2026b · Working paper · companion · v1
Completion, Not Unification: Einstein's Field Program as a Template for Individual Description
Will Shields · 12 September 2026
Jurisdiction. Separates Einstein’s completion from postwar unification-as-quantization. Keeps unified field theory as the type of completion he would accept, not as a prophecy of quantum gravity.
Abstract
Postwar physics uses unification for a family of projects that keep the quantum formalism as the form of the fundamental laws and join gravity, or the remaining forces, to that formalism. Einstein used the same word for a different project: a complete individual description in spacetime, one field rather than two, particles and instruments not foreign to the field, and statistical quantum theory demoted to the role statistical mechanics plays inside classical mechanics. This companion paper separates those projects. The target argued in the preceding paper is completion of the individual situation, not a marriage of general relativity to the existing quantum algorithm. Einstein's unified field theory is nonetheless not optional furniture. It is the type of completion he would accept. One may retire his particular continuum if a better primitive appears; one may not replace his demand with quantization-as-unification and still claim his program. Contact with already catalogued quantum statistics is a graduation constraint on any such completion, not an entrance examination written in Bell's variables.
- Einstein unified field theory
- incompleteness
- completion
- quantum gravity
- Reply to Criticisms
- individual description
- Concept DOI
- 10.5281/zenodo.22717720
- MD5 of PDF
- d588b53a5840dccd5b8666d46c44fa19
Contents
- §1 The same word, two jobs
- §2 What Einstein was unifying
- §3 What postwar unification is doing
- §4 Why the first paper was a completion paper
- §5 Why his unified field theory is still the template
- §6 Entrance and graduation
- §7 Conclusion
Shields 2026c · Working paper · exhibition · not on Zenodo · v1
The Algorithm and the Individual: Schrödinger Evolution, the Measurement Update, and What the Bell Record Does Not Display
Will Shields · 22 September 2026
Exhibition of the algorithm. Writes the Schrödinger equation, the Born rule, and the measurement update symbol by symbol, then places Einstein’s fork and the Bell record against that split. Does not replace 2026a or 2026b.
Abstract
The two program papers convert Einstein’s 1949 demand into a first-event time and locate that demand in a field completion rather than in postwar unification. They do not exhibit the predictive algorithm they refuse to treat as a complete description of one individual. This paper does. It assigns every symbol in the Schrödinger equation on a worked spin, shows why a repeatable measurement forces an update the equation cannot produce, and separates that explanatory gap from the Bell tables. The correlations in the loophole-free tests are real. A photograph of a linear superposition is not. No new experimental gap inside those tables was found. A local unread remainder of the sort defined in 2026a does not reach 2√2.
- Schrödinger equation
- measurement problem
- Born rule
- wave-function update
- Einstein 1949
- Bell inequality
- explanatory gap
- DOI
- Not deposited. Zenodo records remain 2026a and 2026b.
- Concept DOI
- —
- MD5 of PDF
- 482c2808573feaa11bbd4e273c0a3e21
Contents
- §1 How this paper sits beside the other two
- §2 The question
- §3 Objects, before dynamics
- §4 Bra-ket notation
- §5 The Schrödinger equation, each symbol assigned
- §6 The Born rule
- §7 The measurement update
- §8 Why the update is not the Schrödinger equation
- §9 Einstein’s stance
- §10 Bell, Aspect, and the loophole-free record
- §11 Where self-deception is real, and where it is not
- §12 What the program may say
- §13 Worked sheet
Shields 2026d · Working paper · not on Zenodo · v2
The Measurement Problem as Incompleteness: Why the Update Is Not a Collapse, and Why This Program Does Not Add One
Will Shields · 24 September 2026
The measurement problem, read as incompleteness. Proves on one spin that the update is not unitary, not invertible, and not entropy-preserving, then reads that split as Einstein read it: the vector does not contain the mark. No collapse is added. Does not replace 2026a, 2026b, or 2026c.
Abstract
The textbook uses two maps. Between clicks the state vector moves by a unitary group. At a click it is replaced by an eigenvector. This paper writes both maps on one spin and proves the replacement cannot be the Schrödinger equation: a nontrivial projector is not unitary, the nonselective map changes the spectrum of the density operator, and the von Neumann entropy rises from 0 to log 2. The apparatus chain and decoherence do not select a term. Einstein’s 1949 demand reads the split as incompleteness, not as a contradiction and not as a physical collapse of ψ. In this program the individual is S, not a ray. The mark is a threshold crossing of one solution. Repeatability is the solution having passed the barrier. Born weights are the unread remainder. No nuclear lifetime is computed, and the Bell record is not reopened.
- measurement problem
- projection postulate
- no collapse
- incompleteness
- Einstein 1949
- von Neumann entropy
- DOI
- Not deposited. Zenodo records remain 2026a and 2026b.
- Concept DOI
- —
- MD5 of PDF
- 4c56d66c35e2444cb79dd0fe1c8ec054
Contents
- §1 Where this paper sits
- §2 What is observed, before any vector
- §3 The spin the algebra will use
- §4 The Schrödinger equation on this spin
- §5 Born’s rule, on the same vector
- §6 The update
- §7 Proof that the update is not the Schrödinger equation
- §8 The chain does not find a place to stop
- §9 Decoherence is not a selection
- §10 Einstein’s reading
- §11 Why this program has no collapse
- §12 A crossing already does the work the projector was doing
- §13 What is not being claimed
- §14 Conclusion
- §15 References
Shields Planck · Site paper · not on Zenodo · v1
Planck’s Energy Elements: What the 1900 Derivation Does, Step by Step
Will Shields · 23 September 2026
Primary steps of the 1900 count. Writes Planck’s October interpolation and December counting argument in order, and separates that discreteness from a Fourier harmonic. The same paper linked from the History tab.
Abstract
Planck’s December 1900 derivation introduces a finite energy element so that Boltzmann’s count can be performed, then uses Wien’s displacement law to set that element proportional to frequency. The constant of proportionality is h. This paper writes the steps in order, separates them from the later phrase “act of desperation,” and separates Planck’s discreteness from the discreteness of a Fourier harmonic. The ultraviolet catastrophe is Ehrenfest’s later name for the divergence of equipartition. It was not the sentence Planck was repairing on 19 October 1900. Nothing in the derivation times the emission from one resonator.
- Planck 1900
- energy elements
- Wien
- equipartition
- h
- DOI
- Not deposited. Zenodo records remain 2026a and 2026b.
- Concept DOI
- —
- MD5 of PDF
- 5fd3b0c3934c3bb85cfaf686a8d88cbb
Contents
- §1 The quantity
- §2 19 October 1900
- §3 14 December 1900
- §4 What sort of discreteness
- §5 What he later said
- §6 What this does not do
- §7 The second derivative, written out
- §8 What this expansion does not add
- §9 References
Shields Einstein · Site paper · not on Zenodo · v1
Einstein’s Reading of Planck: The Heuristic of 1905 and the Resonator of 1906
Will Shields · 23 September 2026
1905 and 1906, against the 1949 gap. Shows what Einstein took from Planck, what he refused, and that neither paper contains the instant of one emission. The same paper linked from the History tab.
Abstract
Einstein does not inherit a finished method from Planck and drop the word heuristic. In 1905 he puts the word in the title, works in the Wien limit rather than from Planck’s full law, and concludes that radiation behaves as if its energy were in localized quanta. In 1906 he argues that Planck’s count is justified only if resonator energies are integer multiples of hν. Admiration runs both ways and does not cancel the disagreement: Planck locates h at emission and absorption and keeps Maxwell in the vacuum; Einstein treats the quantum as real and still does not possess an individual law of the emission instant. That second gap is the one open in 1949.
- Einstein 1905
- Einstein 1906
- light quantum
- Planck
- heuristic
- DOI
- Not deposited. Zenodo records remain 2026a and 2026b.
- Concept DOI
- —
- MD5 of PDF
- 1d1bb07ad191f9166ec238883c51c38a
Contents
- §1 1905
- §2 1906
- §3 What Planck and others answered
- §4 What neither paper contains
- §5 What he added before 1949
- §6 References
Shields Early · Site paper · not on Zenodo · v2
Four Calculations, 1904–1905: Fluctuation, Wien Entropy, the Photoelectric Line, and the Mean Square Displacement
Will Shields · 24 September 2026
The four calculations, not a second essay on Planck. Derives the 1904 fluctuation, the Wien entropy match, the photoelectric line, and the Brownian mean square. The disagreement with Planck stays in Einstein’s Reading of Planck and is not repeated.
Abstract
Computes four results Einstein published in 1904 and 1905. It does not repeat the essay on his disagreement with Planck. The fluctuation identity is the 1904 paper. The entropy match and the photoelectric line are sections 6 and 8 of the March 1905 paper, with Wien’s law and Lenard’s measurements as inputs. The diffusion law is the May 1905 paper. Perrin is the 1909 count, listed as a later measurement. Each source is in the reference list.
- Einstein 1901
- photoelectric effect
- Lenard
- Wien limit
- Brownian motion
- DOI
- Not deposited. Zenodo records remain 2026a and 2026b.
- Concept DOI
- —
- MD5 of PDF
- 5bfab2f50a9c8f263c47854a12842023
Contents
- §1 What is not repeated
- §2 The 1904 fluctuation
- §3 From Wien’s law to a quantum
- §4 The photoelectric line
- §5 The mean square displacement
- §6 References
Shields Special · Site paper · not on Zenodo · v1
Deriving the 1905 Transformation: From the Two Postulates to γ, and from Two Light Pulses to L/c²
Will Shields · 23 September 2026
The algebra of the June and September notes. Derives γ from the two postulates and L/c² from the pair of light pulses. Lorentz and Poincaré are credited as the neighboring sources Einstein did not cite. Not a retelling of where 1905 sits in the History tab.
Abstract
Writes the steps from the two postulates to γ, then the September note from two opposite light pulses to a mass difference L/c². The general formula E = γmc² is not attributed to that note. Lorentz 1904 and Poincaré 1905 are cited as the neighboring primary sources. The light-quantum paper is not an input.
- special relativity
- 1905
- Lorentz transformation
- inertia of energy
- DOI
- Not deposited. Zenodo records remain 2026a and 2026b.
- Concept DOI
- —
- MD5 of PDF
- 095db5eee6111d7505922510d2971a1e
Contents
- §1 The postulates, as equations
- §2 Addition of velocities
- §3 The September mass difference
- §4 What is credited, and what is not claimed
- §5 References
Shields General · Site paper · not on Zenodo · v1
The 1915 Equation and Two Numbers: Perihelion and Deflection
Will Shields · 23 September 2026
The equation, the line element, and the two comparisons. Why the Einstein tensor is divergenceless, Schwarzschild’s vacuum element, the perihelion formula that gives 43 arcseconds, and the deflection that gives 1.75 rather than the 1911 half. Not the History narrative of 1907–1916.
Abstract
Records why the left-hand side of the field equation must be divergenceless, writes the 25 November 1915 equation and Schwarzschild’s line element, and writes the perihelion advance and the light deflection that were compared with observation. Equivalence and the Entwurf appear only as the premises those expressions replaced. Sources are numbered in the reference list.
- equivalence principle
- field equation
- Mercury
- 1915
- Eddington
- DOI
- Not deposited. Zenodo records remain 2026a and 2026b.
- Concept DOI
- —
- MD5 of PDF
- f8bcec43d605e3b424c0550e6c9cbfe8
Contents
- §1 What may stand on the left
- §2 The vacuum line element
- §3 The two numbers
- §4 What is deliberately absent
- §5 References
Shields Notes · Site paper · not on Zenodo · v1
The Harmonic Radiation Notes: A Signed Series and What It Does Not Solve
Will Shields · 23 September 2026
The notes, diagnosed. Records the signed harmonic series, why an absolute value is the wrong repair, and why the series is not the ultraviolet catastrophe. The same paper linked from the History tab. The later Hamiltonian derivation lives in that tab, not in this PDF.
Abstract
Notes accumulated over several years try to replace Planck’s energy elements with a harmonic series, so that blackbody radiation would be a classical continuum and a later single-system Hamiltonian could be built outside Hilbert space. The series goes negative wherever the sine does. An absolute value would hide the sign and destroy the interference the notes also want. The convergence of Σ 1/n² is not the ultraviolet problem. The latest formula reimports the Planck factor it was meant to avoid. Read against the 1949 program, the notes are an ancestor of the Fourier remainder in the Rank-1 analog, not a path that reaches a decay time.
- harmonic series
- signed energy
- ultraviolet catastrophe
- Fourier
- Rank-1
- DOI
- Not deposited. Zenodo records remain 2026a and 2026b.
- Concept DOI
- —
- MD5 of PDF
- 2dbc28699d6b53c2fe0314f282881c77
Contents
- §1 Aim
- §2 The expressions
- §3 The sign
- §4 Two infinities
- §5 Can the radiation be fully continuous
- §6 Relation to the program
- §7 References
Shields Unified · Site paper · not on Zenodo · v1
Components of the Nonsymmetric Field: What Each Index Symmetry Was Asked to Carry
Will Shields · 23 September 2026
The components, credited, without the program essay. Writes the symmetric and antisymmetric parts, the compatibility condition, and the action, and names Eddington, the 1925–1931 attempts, Schrödinger’s affine papers, and the 1945–1955 texts. Shields 2026b is cited only as the argument this paper does not repeat.
Abstract
Writes the objects Einstein varied from 1945 to 1955 and names the earlier affine and tetrad attempts. The symmetric part was asked to be the 1915 metric. The antisymmetric part was asked to be the electromagnetic field. That identification is not a theorem, and the papers do not produce a quantized charge, a spectrum, or an emission time. 2026b’s argument about the type of completion is not repeated.
- unified field
- nonsymmetric metric
- distant parallelism
- Einstein 1955
- DOI
- Not deposited. Zenodo records remain 2026a and 2026b.
- Concept DOI
- —
- MD5 of PDF
- d76e1809412573158a8994308b7d9659
Contents
- §1 Earlier than the nonsymmetric tensor
- §2 The split
- §3 What the components do not yield
- §4 References