Addendum 111 — The Objectification of the Unreadable

Why Bottom-Up Causal Stories Remain Useful After Their Causal Inversion

Abstract

Scientific laws and mechanisms can be remarkably useful even when their bottom-up causal interpretation is wrong. Why? R²D starts from the count relation: an enclosing boundary defines its measurable states, transition classes, and compatible subordinate realizations. Addendum 105 establishes the resulting top-down organizing causal priority. A subordinate realization cannot primitively cause the enclosing classification that gives that realization its microstate identity. A molecular motor can realize muscle contraction; it cannot define the muscle-level possibility structure and direction that its action is supposed to explain. [1, 2, 10]

When the organizing relation is unreadable from a chosen boundary, scientific narratives often put an object in its place. A motor pulls a muscle, a particle travels between detections, a world branches, a string makes a horizon, unseen matter holds a galaxy, dark energy pushes space, a graviton carries gravity, an inflaton starts expansion, or a virtual particle mediates an interaction. The objects play the role of protagonists. Their equations can organize and predict observations while the story that gives those protagonists primitive causal agency remains a just-so reconstruction of an omitted relation.

The first error is objectification of the unreadable: the omitted organizing relation is made to look like the action of a readable protagonist. Some protagonists are model labels assigned unestablished physical occupation; the molecular motor is an observed local object assigned an unearned organizing role. The second error is causal inversion: that protagonist is said to generate the enclosing statehood on which its proposed causal role depends. The equations are preserved. What R²D disproves is the attempted bottom-up causal explanation of an enclosing count relation by its own subordinate realization. The same argument applies to causal molecular mechanisms and to the eight other projections examined below. [1, 2, 10]

111.1. The Count Proof Comes Before the Protagonist

At an operative count boundary \(B\), let \(\mathfrak M_B\) denote its complete compatible subordinate realizations and let \(\mathcal M_B\) denote its readable macrostates. The classification and its compatible fibers are

\[ \pi_B:\mathfrak M_B\longrightarrow\mathcal M_B, \qquad F_{B,i}=\pi_B^{-1}(i), \qquad W_{B,i}=|F_{B,i}|. \]

These definitions distinguish possibility from occupation. The cardinality \(W_{B,i}\) counts how many realizations are compatible with state \(i\). It does not say that each compatible realization, or each label used to calculate that cardinality, is a separately occupied occurrence. When an occurrence is read at \(B\), its state identity is defined by the operative classification at \(B\); resolving a subordinate identity changes the operative read. [1, 2]

For any admissible formal transition set \(T_B\subseteq\mathfrak M_B\times\mathfrak M_B\), the same classification partitions transitions:

\[ T_{B,i\to j}=T_B\cap(F_{B,i}\times F_{B,j}), \qquad T_B=\bigsqcup_{i,j\in\mathcal M_B}T_{B,i\to j}. \]

A transition within \(T_{B,i\to i}\) does not change macrostate \(i\). A transition counted as \(i\to j\) already depends on \(\pi_B\) for its macrostate-transition identity. One member of a fiber cannot be the primitive cause of the fiber’s definition; one transition in a classified set cannot be the primitive cause of the classification under which that transition counts. Recursive replacement adds the physical read rule: the enclosing occurrence and a resolved subordinate identity are not the same operative state read. This is the top-down result established in Part I and Addenda 103 and 105. It concerns organizing causality, not a mechanical push downward. [1, 2, 10]

Ten distinguishable binary peers make the point without any physical law. Before a flip, the ensemble boundary defines \(W(10,0)=1\) and \(W(9,1)=10\). A flip can realize the step $ (10,0)(9,1)$; it does not create the ten compatible assignments for its destination. The exact native multiplicity ratio is \(10\). Giving an individual coin credit for producing that possibility structure would reverse the count dependency. [1, 10]

Thus the invalid claim is definite: a law that assigns primitive causal creation of enclosing organization to subordinate objects or events contradicts the state architecture that gives those objects and events their subordinate count meanings. A law’s accurate calculation of local events is a separate achievement.

111.2. Why a Disproved Causal Story Can Still Work

Let \(\mathcal R\) be a model’s representation space, \(x\in\mathcal R\) a model label, and \(\mathcal F\) its rule for producing a readable quantity \(D\):

\[ \mathcal F(x)=D. \]

The equality says what the representation predicts or fits. Stable enclosing compatibility can yield stable correlations among the readable subordinate results even when the enclosing relation is absent from \(\mathcal F\). This is why a local mechanism, field equation, or statistical law can work. Its predictive success does not reverse the dependency established in §111.1. [1, 10]

To turn the model into a story about an occupied protagonist, one must identify an operative boundary \(B_x\) under which \(x\) is a readable physical state and establish its occurrence there. In audit notation, the claim being added has the form

\[ \iota_{B_x}(x)=j\in\mathcal M_{B_x} \quad\text{and}\quad O_{B_x}(j)=1. \]

Here \(O_{B_x}\) is an audit notation for an asserted occurrence, not a new primitive R²D law. One would then have to relate that local state to a compatible realization class at \(B\) without treating the two boundary reads as the same state identity. If \(x\) is merely a fitted number, internal line, or term in a sum, \(\iota_{B_x}\) has not even been defined. If several labels name possible alternatives, assigning them to one domain does not assert that each occurred. A successful read at \(B\) is not an occupation map for \(x\) at \(B_x\).

The non-entailment is elementary. Keep \(\mathcal F\), \(x\), and the successful read \(D\) fixed. One description stops at \(\mathcal F(x)=D\); another adds a specified identity map and occurrence assertion. Both contain the same successful read. The latter assertion therefore was not derived from the former equality. Even an explicitly postulated occupied protagonist does not gain primitive causal priority over the classification that defines it.

Where the protagonist is inferred from a model, this is the first crossing, from mathematical representation to physical state identity. Where an object is locally observed, its local occupation needs no invention; the error begins when its local identity is carried unchanged into the enclosing read and made the author of that read. The second crossing makes the protagonist the primitive cause of the enclosing organization under which it was given its count identity. In R²D that reverses the formal dependency:

\[ \text{enclosing classification and compatibility} \longrightarrow \text{compatible subordinate realization}, \]

whereas the inverted account assigns the compatible realization the job of primitively defining its own enclosure. These are two different errors. One can use the equations without making either. [1, 2]

The protagonist is useful because it gives a compact, repeatable script for calculating what will be read: this thing moves, binds, pulls, pushes, branches, or exchanges something. That script can guide interventions and predictions. Its causal completion is a just-so story when the unreadable organizing relation is silently replaced with an object whose alleged independent occupation or causal sufficiency was inferred from the very read it was invented to explain. More accurate predictions strengthen the law as a read; they do not turn that circular inference into a proof of bottom-up causality.

111.3. The Cross-Domain Ledger

The test can be applied without pretending that the nine examples possess the same empirical status or mathematical object. In the molecular case the object is readable at its own boundary; in other cases the protagonist is inferred from a model or an inaccessible read. The causal promotion is the common point.

Case	Read or calculated result	Causal protagonist	Added causal or occupation claim
Molecular mechanism	Protein transitions, chemistry, force, and shortening	Myosin motor and proposed power stroke	An independently acting motor originates muscle-level organization and direction.
Quantum particle	Detector counts, spectra, or interference relations	Persistent particle and path	The represented path belongs to one occupied microscopic object beneath the unchanged quantum read.
Everettian worlds	Quantum component and decohered record structure	Branch or emergent pattern	Each represented component is a separately occupied world.
Causal strings	Leading entropy agreement for a selected BPS sector and black-hole horizon	String or D-brane state label	That label is an occupied complete horizon realization.
Dark matter	Gravitational discrepancy represented under a selected calibration	Apparent source term or dark component	The inferred term is independently occupied unseen matter.
Dark energy	Expansion relation represented with a \(\Lambda\) term	Effective energy density or field	The fitted term is an occupied substance that pushes expansion.
Graviton	Measured gravitational-wave signal and quantized-field calculations	Quantum of a metric perturbation	The detected wave establishes occupied gravitons as its primitive cause.
Inflaton	Early-universe observables fitted in an inflationary model	Scalar field \(\phi\) and potential \(V(\phi)\)	The model field is identified as an occupied cosmic cause by the fit alone.
Virtual particle	Scattering amplitude containing internal propagators	Internal particle line	The internal term is an occupied traveler between the external events.

An entry in this ledger is an audited inference, not an assertion that every researcher who uses that mathematics makes it. The calculation can be retained while the added protagonist story is tested. In some rows the problem is an unwarranted occupation; in the molecular row an already observed local object is assigned causal authorship of its enclosing organization.

111.4. Molecular Mechanisms: The Protagonist Is Visible, the Organization Is Not

Muscle makes the error plain because the motor is not imaginary. Myosin changes conformation; nucleotide chemistry, motor occupancy, force, and muscle shortening can be measured under their respective reads. A kinetic model can predict how those measurements vary together. Disrupting myosin can prevent contraction. These results establish that motors participate in and locally realize the change. They do not show that a motor defines the muscle-level ensemble’s state classes, compatible motor arrangements, or the directional conditions under which work is done. [1, 10]

The story “myosin pulls actin, therefore myosin causes muscle contraction” casts the motor as a protagonist. Observed conformational changes make the story compelling; the unreadable part is the entire enclosing compatibility relation that makes this local action one realization of a directional muscle state. The proposed power stroke can be an effective description of a molecular step and still fail as the causal explanation of the enclosing organization. The molecule is real at its own boundary. Its claimed independent authorship of the muscle boundary is the projection error. [1, 10]

The same narrative move appears in reaction mechanisms. Collision sequences, bond rearrangements, and measured rates can describe how a selected reaction is locally realized. They do not, as sequences of subordinate protagonists, define the enclosing thermodynamic relation that makes one reaction direction more supportable than another. A catalyst can change rate without changing the equilibrium relation under fixed conditions. Thus one experiment can display the mechanism’s practical utility and the distinct enclosing relation that its bottom-up causal story omits. [1, 10]

R²D’s count order is

\[ \text{enclosing compatible possibilities and directional relation} \longrightarrow \text{molecular occupancy and local realization} \longrightarrow \text{muscle-level read}. \]

The arrows mark boundary-relative organization and realization, not a hidden force. A molecular kinetic law is useful because the realizations are regular. Treating those regularities as proof that a motor creates the enclosing possibility landscape is the just-so addition. A better motor model may refine the predictions; it does not change the direction of definitional dependence. [1, 2, 10]

111.5. The Quantum Side: A Particle or a World Is Added to the Read

Addendum 102 distinguishes a recorded particle-like outcome from an independently persistent miniature object beneath the quantum readability horizon. At that horizon recurrence remains readable while the associated subordinate distinguishability and continuous trajectory geometry are not readable as the same occupied count state. The detector record is a new boundary-defined distinction. Assigning one unchanged microscopic trajectory to the unreadable side is the particle identity promotion. Giving that projected particle responsibility for defining the enclosing quantum state is the subsequent causal inversion. [3]

Addendum 108 applies the first crossing to Everettian worlds. A measurement representation may have the form

\[ |\Psi\rangle =c_A|A\rangle|D_A\rangle|E_A\rangle +c_B|B\rangle|D_B\rangle|E_B\rangle, \qquad \langle E_A|E_B\rangle\simeq0. \]

The expression and environmental orthogonality describe the represented record components. The assertion that each component is a separately occupied world introduces an occurrence for each component. Linearity and suppression of interference do not define those occurrences. If “world” is a name for a robust pattern in the representation, its pattern status remains a representation claim. Calling the patterns separately occupied makes the first crossing. [4, 11]

The imagined particle is cast as a miniature actor beneath a detector read; Everettian worlds are cast as a population of actors beyond one record. In both stories the unreadable relation is given an occupied protagonist by the representation. Neither a trajectory nor multiple occupied worlds follows from the respective calculation alone.

111.6. The Gravitational Horizon: A Count Is Not a String Occupation

The string-theory example supplies an especially sharp count comparison. In the original Strominger–Vafa construction, a specified fixed-charge BPS sector is counted in a weak-coupling description. In the relevant large-charge regime its leading logarithmic growth agrees with the area entropy of a five-dimensional extremal black hole. That agreement is a substantive result. Addendum 109 separates the unsigned degeneracy, the protected weighted index, and the horizon’s compatible realization fiber; an agreement in leading logarithms is not an identity of the three sets. [5, 12]

Let \(d_q\) be the selected BPS degeneracy and let \(W_H(q)\) be the compatible count at an operative horizon boundary \(B_H\). If the horizon area is physically calibrated as a read of that compatible count, the proposed R²D correspondence concerns leading entropy growth,

\[ \ln d_q\sim\ln W_H(q)\sim\frac{A_H(q)}{4G_5}, \]

with the physical area calibration and the stated regime understood. It does not supply a state-by-state map \(\iota_H\) carrying each counted string-state label to a complete occupied element of \(\pi_H^{-1}(i_H(q))\). Declaring such a label an occupied horizon state is the first crossing. Calling it the primitive cause of horizon classification is the second. The gravitational horizon retains a distinguishable area/count read while directed enclosing recurrence is unreadable; the selected string count reads the retained result, not the missing recurrence itself. [5]

111.7. Dark Matter: An Inferred Source Is Not an Occupied Component

Part IV §10.35 and Addendum 110 exhibit an exact source–calibration equivalence within the stated simple gravitational relation. Write one observed acceleration in two ways:

\[ g_{\mathrm{obs}} =\frac{G_nM_b}{r^2} =\frac{G_{n-1}M_{\mathrm{dyn}}}{r^2} \quad\Longrightarrow\quad M_{\mathrm{DM}}^{\mathrm{app}} :=M_{\mathrm{dyn}}-M_b =\left(\frac{G_n}{G_{n-1}}-1\right)M_b. \]

Under the Canon’s invariant dimensionless gravitational-calibration hypothesis, \(G_n/G_{n-1}=(\rho_{n\mid n-1}^{\Phi})^{-2}\). The difference \(M_{\mathrm{DM}}^{\mathrm{app}}\) is a well-defined source read under the selected calibration. Its definition is not an occurrence or material-identity measurement. Calling it occupied unseen matter is the first crossing; making that assigned matter the primitive source of the enclosing gravitational organization is the second. [6]

Part IV also writes the mismatch as an effective areal calibration. The exact scalar equivalence identifies a place where the source term can arise without a second occupied component. Its application to the combined galaxy, lensing, cluster, structure, and cosmological observations is a larger physical construction than this equation. Addendum 110 separates those two propositions rather than retracting either one. [6, 13]

111.8. Dark Energy: Moving a Term Does Not Create a Substance

In the cosmological field equation, the same \(\Lambda\) term can be displayed on the geometric side or written as an effective source:

\[ G_{\mu\nu}+\Lambda g_{\mu\nu} =\frac{8\pi G}{c^4}T_{\mu\nu} \quad\Longleftrightarrow\quad G_{\mu\nu} =\frac{8\pi G}{c^4} \left(T_{\mu\nu}+T_{\mu\nu}^{(\Lambda)}\right), \qquad T_{\mu\nu}^{(\Lambda)} :=-\frac{\Lambda c^4}{8\pi G}g_{\mu\nu}. \]

This relocation is exact algebra within the selected field equation. Neither side of the equality defines a new occupied material state. High-redshift supernova observations constrain the expansion history; fitting a positive \(\Lambda\) in a chosen cosmological model is a physical result of that model. Identifying the effective source with an independently occupied substance called dark energy is a further physical assignment. Saying the substance is the primitive cause that pushes the cosmological boundary repeats the second crossing. [7, 14]

Part IV §10.37 and Addenda 53 and 63 already put \(\Lambda\) downstream of cosmological boundary and reference-area relations. They also keep the actual acceleration problem distinct from Part IV’s simpler dark-matter source–calibration equation. This addendum does not turn that distinction into a single unproved equation for both phenomena. [7]

111.9. Graviton: A Measured Wave Is Not a Quantum Occupation Count

The 2015 LIGO observation was a recorded gravitational-wave strain consistent with a binary-black-hole waveform. The detector read establishes a wave signal and constrains its source model. A perturbative quantum-gravity description may write a metric as a background plus a perturbation, \(g_{\mu\nu}=\bar g_{\mu\nu}+h_{\mu\nu}\), and quantize modes of \(h_{\mu\nu}\). Graviton lines and quantum corrections then have a defined role within that calculation. [8, 15, 16]

The occurrence claim is different: “this wave measurement establishes occupied graviton quanta, whose independent action generates the gravitational relation.” A measured macroscopic strain is not a measurement of the occupation number of any specified quantized mode. The wave read supplies neither a map from the mode labels into the complete compatible realizations at a gravitational count boundary nor an occurrence for each supposed quantum. The mode-to-occupied-graviton step is the first crossing. Assigning those projected quanta primitive priority over gravitational boundary organization is the second. [8]

This is distinct from Addendum 109. A perturbative graviton is a mode of a quantized gravitational representation; its read and mathematics are not the fixed-charge BPS count used to match a black-hole horizon entropy. Their shared error arises only if the model label is promoted beyond what its calculation and operative boundary establish.

111.10. Inflaton: A Fitted Early-Universe Field Is Not Identified by Its Fit

In a specified single-field slow-roll representation, one may write, in natural units with reduced Planck mass \(M_{\mathrm{Pl}}\),

\[ 3M_{\mathrm{Pl}}^2H^2\simeq V(\phi). \]

The equation supplies a model relation between expansion rate and a scalar potential. CMB data constrain primordial spectra and, under stated inflationary models, the corresponding parameter space. They do not by that operation measure the occupation and identity of one particular field \(\phi\) as a preexisting cosmic agent. Promoting the model field into that independently identified agent is the first crossing. Making it the primitive source of the larger cosmological compatibility relation is the second. [9, 17]

This is a distinct problem from whether an accelerated early epoch can be represented successfully. It is also distinct from the late-time \(\Lambda\) term of §111.8. The two equations may share an accelerated-expansion form without giving their fitted terms the same boundary ownership or physical identity.

111.11. Virtual Particles: An Internal Line Is Not a Detector Event

Perturbative quantum-field calculations contain internal propagators. Schematically, a scalar propagator contributes a factor of the form

\[ D_F(q)\propto\frac{1}{q^2-m^2+i\epsilon} \]

under the stated field and conventions. An internal line represents part of a term in the scattering amplitude; an external detector event is a separately specified read. Calling the internal line an occupied particle traveling between the events promotes a computational contribution into a trajectory and occurrence that the diagram alone has not established. Calling that imagined traveler the primitive cause of the enclosing interaction adds the second crossing. [3, 18]

This entry audits a literalization of the diagram. It does not assign that literalization to every user of perturbative field theory. The amplitude calculation remains the result to preserve; the claimed occupied journey is the extra step under examination.

111.12. One Test, Different Calculations

The nine cases can now be examined with the same five questions:

1. Read: Which detector, gravitational, spectral, or cosmological distinction was actually obtained?
2. Representation: Which equation, term, basis, field, or modeled state was introduced to describe it?
3. Boundary: What operative boundary defines the proposed object’s state identity and complete compatible realizations?
4. Occupation: Is the protagonist actually occupied under that read, or is a model label being assigned physical occupation? For an observed molecule, which boundary owns its local identity?
5. Causality: Is the protagonist assigned responsibility for creating the enclosing classification or direction on which its explanatory role depends?

The first two questions preserve the genuine calculation. The third and fourth locate the boundary and any unsupported occupation claim. The fifth locates the causal inversion even where an object, such as a molecular motor, is locally observed. A numerical fit, a matched entropy, a surviving quantum branch, an internal propagator, and an effective stress–energy tensor are different mathematical achievements. None becomes a primitive causal explanation merely by being useful.

This also distinguishes a possible count, a normalized weight, and an occurrence. A large compatible multiplicity is not many occupied worlds. A probability assigned to a represented alternative is not a force causing its own possibility. Possibilities and enclosing compatibility organize what can be realized; probabilities read a specified normalized relation and do not push states into existence. Addendum 107 develops that count-type distinction separately. [2, 4]

111.13. Result and Logical Status

Formal count result. At \(B\), a compatible realization has its count identity under \(\pi_B\); \(W_{B,i}\) counts the fiber, not the number of occupied copies. A label outside that classified domain has no occupied identity at \(B\) just because a representation containing it predicts \(B\)’s read. [1, 2]

Objectification of the unreadable. An unreadable organizing relation is replaced by a protagonist: either a represented label, effective source, internal line, or branch is assigned an unwarranted occupation, or a real local object such as a molecular motor is assigned an unearned enclosing causal role. [3–6, 10]

EP causal inversion. The protagonist is said to primitively produce the enclosing statehood, compatibility, or direction that gave its local identity or model role meaning. In R²D that reverses the ownership of the state and its compatible realizations. [1, 2]

Why the laws remain useful. When enclosing compatibility is stable, subordinate realizations and their correlations are regular enough to describe, manipulate, and predict. An effective law can capture those relations precisely while its accompanying bottom-up story reverses their organizing causal order. Molecular kinetics and muscle mechanics give one directly approachable example. The other eight calculations and observations have different scopes: the simple apparent-dark-source equation and relocation of \(\Lambda\) are exact under stated premises; the BPS match concerns leading entropy; LIGO recorded a wave, not graviton occupation; CMB constraints do not identify an occupied inflaton; an internal propagator is an amplitude term. [1, 5–10, 12–18]

R²D’s common conclusion is precise: a successful law can be a useful story about readable protagonists. It does not make those protagonists the authors of the unreadable enclosing relation that makes their roles possible.

Sources

R²D sources

1. R²D Part I, §§2–5 and §7, including the EP projection discussion: boundary-relative statehood, compatible fibers, recursive replacement, the ten-coin construction, and the utility of projected laws.
2. R²D Addendum 105, “The Observational Inversion”: enclosing classification, subordinate reconstruction, and organizing causal priority. Addendum 107 (cited in Addendum 108): possibility, probability, and realized occurrence.
3. R²D Addendum 102, “Particles Are Imagined”; Part III, Chapters 9–10: quantum and gravitational readability horizons.
4. R²D Addendum 108, “A Branch Is Not an Occupied World”: branch decomposition and occurrence.
5. R²D Addendum 109, “Charge Classification Occurs Before Causal Strings”: BPS sector, protected count, horizon-compatible fiber, and the leading entropy match.
6. R²D Part IV, §§10.34–10.36, and Addendum 110, “The Inferred Gravitational Source Is Not an Occupied Object”: apparent dark source and gravitational calibration.
7. R²D Part IV, §10.37, and Addenda 53 and 63: cosmological source and fixed-reference-area projections.
8. R²D Part IV, Chapters 4–5, and Addenda 50 and 52: gravitational-wave and count-to-space projections, including the distinction between a wave read and a graviton claim.
9. R²D Part IV, Chapters 10–11: cosmological background, expansion, and physical projection.
10. R²D Addendum 103, “The Causal Implications of the Microstate Definition,” and Part IV, Chapter 9: transition classes, molecular mechanisms, muscle contraction, and the difference between effective law and organizing causality.

External primary sources

11. Hugh Everett III, “‘Relative State’ Formulation of Quantum Mechanics”, Reviews of Modern Physics 29 (1957), 454–462.
12. Andrew Strominger and Cumrun Vafa, “Microscopic Origin of the Bekenstein–Hawking Entropy”, Physics Letters B 379 (1996), 99–104.
13. Vera C. Rubin, N. Thonnard, and W. Kent Ford Jr., “Rotational Properties of 21 Sc Galaxies with a Large Range of Luminosities and Radii”, The Astrophysical Journal 238 (1980), 471–487; Douglas Clowe et al., “A Direct Empirical Proof of the Existence of Dark Matter”, The Astrophysical Journal Letters 648 (2006), L109–L113; Planck Collaboration, “Planck 2018 Results. VI. Cosmological Parameters”, Astronomy & Astrophysics 641 (2020), A6.
14. Adam G. Riess et al., “Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant”, The Astronomical Journal 116 (1998), 1009–1038; Saul Perlmutter et al., “Measurements of Omega and Lambda from 42 High-Redshift Supernovae”, The Astrophysical Journal 517 (1999), 565–586.
15. LIGO Scientific Collaboration and Virgo Collaboration, “Observation of Gravitational Waves from a Binary Black Hole Merger”, Physical Review Letters 116 (2016), 061102.
16. John F. Donoghue, “General Relativity as an Effective Field Theory: The Leading Quantum Corrections”, Physical Review D 50 (1994), 3874–3888.
17. Alan H. Guth, “Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems”, Physical Review D 23 (1981), 347–356; Planck Collaboration, “Planck 2018 Results. X. Constraints on Inflation”, Astronomy & Astrophysics 641 (2020), A10.
18. Richard P. Feynman, “Space-Time Approach to Quantum Electrodynamics”, Physical Review 76 (1949), 769–789; “The Theory of Positrons”, Physical Review 76 (1949), 749–759.