# Sources: the reversibility objection (Thomson 1874, Loschmidt 1876, Boltzmann 1877)

All quotations are in `quotes.json`. Each one records its source URL, the local file, how the text was obtained (archive.org OCR, our own Tesseract OCR, or read from the page image), and any OCR corrections (`ocr_raw` compared with `verbatim`). All translations are ours and are labelled as such.

## What was found

### 1. Thomson, "The Kinetic Theory of the Dissipation of Energy"
- Proc. Roy. Soc. Edinburgh 8, pp. 325-334 (DOI 10.1017/S0370164600029680). Reprinted in Nature 9 (9 April 1874) 441-444 (DOI 10.1038/009441c0).
- **Date read:** Monday, 16 February 1874, with Thomson in the chair (meeting heading on p. 289; the paper is item 9 of that meeting).
- Key passages:
  - p. 325: abstract dynamics, where "any solution remains a solution when t is changed into -t".
  - pp. 325-326: the reversed universe (the bursting bubble re-forms, boulders rejoin the mountain peak, living creatures "would become again unborn").
  - p. 329: reversing every particle of a gas brings back the initial unequal temperatures.
  - pp. 329-330: imprecise reversal.
  - p. 330: 9/10 against 1/10 of the energy, and the iron bar over 1000 and 1,000,000 years.
  - p. 331: the probability figures.
- **The numbers, checked against the page image of p. 331.** The jar holds 2,000,000,000,000 O2 and 8,000,000,000,000 N2 molecules, and the region is 1/5 of the volume. The odds against all the O and none of the N being in that region form a number with "about 2,173,220,000,000 of places of whole numbers". The chance against exactly 2/10 of each gas being in the region is "only 4021 × 10^9 to 1". The Appendix on p. 333 gives log N = (10 - 26 log 2) × 10^12 = 2173220 × 10^6.
- **Caution for the page.** Thomson does *not* say that a slight error ruins the reversed motion. He says small deviations "would not obviate the resulting disequalisation", but that "the greater the number of molecules, the shorter will be the time during which the disequalising will continue". He does not discuss instability.

### 2. Loschmidt, "Über den Zustand des Wärmegleichgewichtes ... I."
- Wiener Ber. 73 (II. Abth.) 128-142. It was presented at the session of 27 January 1876, according to the session report printed in Abt. III.
- The reversal argument is on **p. 139**. We transcribed it from the ÖAW page image, including the key sentences:
  - "Offenbar muss ganz allgemein, in jedem beliebigen System, der gesammte Verlauf der Begebenheiten rückläufig werden, wenn momentan die Geschwindigkeiten aller seiner Elemente umgekehrt werden."
  - "Das berühmte Problem, Geschehenes ungeschehen zu machen, hat damit zwar keine Lösung, doch eine einfache Formulirung erhalten ..."
- The context is his gravity model. His conclusion on p. 140 is that no strict proof of uniform equilibrium temperature has been given.
- **Thomson:** Part I cites only Thomson's 1851 second-law axiom (p. 135, Trans. RSE vol. XX p. 265). Our OCR search of pp. 128-142 found no citation of Thomson's 1874 paper.

### 3. Boltzmann's reply
- "Bemerkungen über einige Probleme der mechanischen Wärmetheorie", Wiener Ber. 75 (II) 62-100. Section II runs from pp. 67 to 73.
- Key sentences, all checked against the page images:
  - p. 67: Loschmidt's theorem "ein Bedenken gegen die Möglichkeit eines rein mechanischen Beweises des zweiten Hauptsatzes involvirt".
  - p. 69: the sign of ∫dQ/T follows "nicht in dem Wirkungsgesetze ..., sondern bloss in den Anfangsbedingungen".
  - p. 70: "ein interessantes Sophisma".
  - p. 71: "unendlich vielmal mehr Anfangszustände" lead to a uniform distribution. "Der Loschmidt'sche Satz lehrt also bloss Anfangszustände kennen ...".
  - p. 72: "ausserordentlich unwahrscheinlich ... für die Praxis ... unmöglich". The oxygen/nitrogen example. Loschmidt's theorem is important "weil er zeigt, wie innig der zweite Hauptsatz mit der Wahrscheinlichkeitsrechnung in Verbindung steht". The remark about the infinitely distant past.
- "Über die Beziehung zwischen dem zweiten Hauptsatze ... und der Wahrscheinlichkeitsrechnung", Wiener Ber. 76 (II) 373-435:
  - The opening (pp. 373-374) refers back to section II of the "Bemerkungen" and quotes its lottery passage.
  - **It never names Loschmidt.** Our OCR of all 63 pages contains no "Loschmidt".

### 4. The "go ahead and reverse them" anecdote: verdict
- **The earliest printed occurrence we could actually see is Mark Kac, *Probability and Related Topics in Physical Sciences* (Interscience, 1959), p. 61.** These are the lectures from a 1957 Boulder summer seminar. The passage reads: "(To this objection Boltzmann reportedly replied 'go ahead, reverse them!')". We checked it against the page image. Kac gives no source.
- Later occurrences found through archive.org full-text search (snippets only):
  - Parry, *Many-body problems* (1969): "reportedly".
  - *The Study of Time* (1972): "reputed".
  - Davies, *The Physics of Time Asymmetry* (1974; we saw the 1977 edition).
  - Omohundro (1986), who cites "[Kac, 1959] p. 62".
  - Price (1996): "which tradition attributes to Boltzmann".
  - A 2026 paper (Shepelyansky, arXiv 2604.04879) attributes the "legend" to Mayer & Goeppert-Mayer, *Statistical Mechanics*, 2nd ed. (1977). The 1940 first edition (full OCR, archive.org) does not mention Loschmidt at all, and we could not see the 1977 edition.
- **Not found in any 1870s source examined**, including Loschmidt I, Boltzmann's "Bemerkungen" section II, and Boltzmann 1877b.
- **Not found in Boltzmann's 1895 memorial address for Loschmidt** ("Zur Erinnerung an Josef Loschmidt", Populäre Schriften 1905, pp. 228ff.). That address recalls Loschmidt's "Idee des Umkehrens alles Geschehens" (p. 231) and retells jokes from their Vienna days, but it has no such retort.
- No German-language version ("kehre sie doch um" and similar) turned up in any search.
- **Verdict:** the remark is unattested before 1959 as far as we could check, and most sources hedge it ("reportedly", "reputed", "tradition"), though Davies 1974/77 states it flatly. Present it as a later anecdote, not as a documented remark of Boltzmann's.
- We did not check the English-language book tradition before 1959 exhaustively. Google Books and HathiTrust were blocked, and Cercignani's 1998 biography could only be searched through archive.org's full-text search, which did not match the phrase.

### 5. Levesque & Verlet
- J. Stat. Phys. 72 (3-4), 519-537, August 1993, DOI 10.1007/BF01048022 (confirmed through Crossref).
- **We could not read the abstract.** Springer, ADS and ResearchGate returned bot challenges or 403/405, Crossref has no abstract, and Semantic Scholar says it is elided.
- A web-search summary mentions a "time-symmetrical integer arithmetic algorithm" (bit-reversible). It is not quoted in `quotes.json` and must be checked before use.

### 6. Zermelo 1896
- "Ueber einen Satz der Dynamik und die mechanische Wärmetheorie", Ann. Phys. (Wied. N.F.) 57, 485-494. DOI 10.1002/andp.18962930314 (Crossref numbers the volume 293).

## Access notes and failures
- **Wiener Sitzungsberichte, Abt. II:** these are not on archive.org or BHL. The Austrian Academy (ÖAW) viewer holds them as IIIF records `MN_2Abt_73_1876`, `MN_2Abt_75_1877` and `MN_2Abt_76_1877`. That source has no OCR, so we downloaded the page images (`page_images/`) and ran Tesseract with German language data (`ocr_tesseract/`, plus the combined `OAW_*_tesseract.txt` files).
  - Every key passage was proof-read against its image, except the Boltzmann 1877b opening and Loschmidt p. 135, which are OCR only.
  - Canvas numbers do not equal printed page numbers. In vol. 73, canvas 137 is p. 128, then Topsøe's plates are bound in, and canvas 156 is p. 139. In vol. 75, canvas 71 is p. 67. In vol. 76, canvas 377 is p. 373.
- **Blocked:** HathiTrust, BHL, Gallica, Google Books page text, Springer, ADS and zobodat were blocked (403, Cloudflare or bot challenges).
- **Not examined:** Loschmidt Parts II-IV. Part II is vol. 73 pp. 366-372, presented 9 March 1876. Part III is vol. 75 pp. 287-298, presented 8 February 1877. Part IV is in vol. 76.