{
    "schema": "prokopton42-public-passage-v1",
    "id": "einstein.relativity_popular_de",
    "canonical_url": "https://prokopton42.com/en/works/einstein/relativity-popular-de/reference-section-0028/",
    "language": "en",
    "title": "Relativity: The Special and General Theory, German Edition",
    "author": "Albert Einstein",
    "date": "1916",
    "summary": "In this German exposition for nonspecialists, Einstein builds relativity through trains, clocks, measuring rods, and elevators. Thought experiments replace some formalism without concealing the transformation of space, time, and gravitation.",
    "learning": "Reconstruct the relativity of simultaneity, use thought experiments as arguments, and follow the extension from inertial frames to gravitational fields.",
    "long_summary": "The first part shows why simultaneity, length, and duration depend on the state of motion while physical laws and light speed remain invariant. The second extends the reasoning to accelerated frames and presents gravitation geometrically.\n\nThe pedagogical style begins with idealized situations and then corrects classical intuition. This German manifestation preserves Einstein’s linguistic formulation; it is an exposition of theory, not a complete mathematical textbook or a diary of invention.",
    "historical_context": "The corpus manifests do not yet establish the precise place and circumstances of composition. The images below document the author’s world or the text’s transmission. They do not claim to show the exact scene of writing.",
    "material_world_label": "World of the world wars, 1914-1945",
    "material_world": {
        "technology": "Electricity, internal combustion, steel, aviation, radio, cinema, and mass production transform civilian life and warfare.",
        "science": "Relativity, quantum physics, chemistry, psychology, and genetics reshape knowledge within powerful institutions that are sometimes militarized.",
        "medicine": "X-rays, surgery, transfusion, antisepsis, and early antibiotics save more lives without universal access.",
        "transport": "Rail, cars, trams, ocean liners, and aircraft coexist. Armies mechanize mobility rapidly.",
        "agriculture": "Tractors, fertilizers, and breeding advance; rationing, blockade, and requisition expose fragile supplies.",
        "communication": "Telephone, telegraph, radio, newsreels, and newspapers reach mass audiences; propaganda and censorship use the same networks.",
        "clothing": "Suits, shorter dresses, coats, and hats coexist with uniforms and workwear. Shortages simplify cuts and materials."
    },
    "material_world_scenes": [
        {
            "asset": "/assets/timeline/landmarks/26-1939-ce/world-01.webp",
            "title": "Technology, science, and care",
            "description": "Electricity, internal combustion, steel, aviation, radio, cinema, and mass production transform civilian life and warfare. Relativity, quantum physics, chemistry, psychology, and genetics reshape knowledge within powerful institutions that are sometimes militarized. X-rays, surgery, transfusion, antisepsis, and early antibiotics save more lives without universal access."
        },
        {
            "asset": "/assets/timeline/landmarks/26-1939-ce/world-02.webp",
            "title": "Travel and communication",
            "description": "Rail, cars, trams, ocean liners, and aircraft coexist. Armies mechanize mobility rapidly. Telephone, telegraph, radio, newsreels, and newspapers reach mass audiences; propaganda and censorship use the same networks."
        },
        {
            "asset": "/assets/timeline/landmarks/26-1939-ce/world-03.webp",
            "title": "Farming and food",
            "description": "Tractors, fertilizers, and breeding advance; rationing, blockade, and requisition expose fragile supplies."
        },
        {
            "asset": "/assets/timeline/landmarks/26-1939-ce/world-04.webp",
            "title": "Clothing, women and men",
            "description": "Suits, shorter dresses, coats, and hats coexist with uniforms and workwear. Shortages simplify cuts and materials."
        }
    ],
    "intellectual_tradition": {
        "id": "science",
        "label": "Science and scientific thought"
    },
    "period": {
        "id": "contemporary",
        "label": "Contemporary era"
    },
    "languages": [
        "de",
        "en",
        "fr"
    ],
    "manifestations": [
        {
            "coverage": "complete",
            "file": "data/corpus/normalized/einstein/relativity_popular_de/representations/de.ndjson",
            "language": "de",
            "records": 76,
            "role": "complete_source_selection",
            "sha256": "8ba7b3154fc2e4fa2e842282f6965a0e5ea29cfd3067e27bfd51fede063b01bb",
            "source_id": "relativity_popular_de"
        },
        {
            "coverage": "complete",
            "file": "data/corpus/normalized/einstein/relativity_popular_de/representations/ai-generated/en-gpt-5-6-sol-corpus-passage-translation-v1.ndjson",
            "generated_on": "2026-09-11",
            "language": "en",
            "model": "gpt-5.6-sol",
            "official_status": "non_official",
            "prompt_version": "corpus-passage-translation-v1",
            "provider": "codex_subscription",
            "records": 76,
            "role": "ai_generated_translation_non_official",
            "sha256": "81515ccd119450fc9fbb127b851abe0a463f6b7252716a365ba8ecf652a03b8a",
            "source_id": "prokopton42-codex-translation:gpt-5.6-sol:corpus-passage-translation-v1",
            "translation_type": "ai_generated_translation"
        },
        {
            "coverage": "complete",
            "file": "data/corpus/normalized/einstein/relativity_popular_de/representations/ai-generated/fr-gpt-5-6-sol-corpus-passage-translation-v1.ndjson",
            "generated_on": "2026-09-11",
            "language": "fr",
            "model": "gpt-5.6-sol",
            "official_status": "non_official",
            "prompt_version": "corpus-passage-translation-v1",
            "provider": "codex_subscription",
            "records": 76,
            "role": "ai_generated_translation_non_official",
            "sha256": "13b13b02d977e51b12b3f6ec60473ab5491378e2d63c6c45f4585b73de0a2acf",
            "source_id": "prokopton42-codex-translation:gpt-5.6-sol:corpus-passage-translation-v1",
            "translation_type": "ai_generated_translation"
        }
    ],
    "concepts": [
        {
            "id": "care_of_soul",
            "label": "Care of the soul"
        },
        {
            "id": "empirical_test",
            "label": "Empirical test"
        },
        {
            "id": "equivalence_principle",
            "label": "Equivalence principle"
        },
        {
            "id": "family",
            "label": "Family"
        },
        {
            "id": "invariance",
            "label": "Physical invariance"
        },
        {
            "id": "poverty_wealth",
            "label": "Poverty and wealth"
        },
        {
            "id": "relativity_principle",
            "label": "Principle of relativity"
        },
        {
            "id": "sin",
            "label": "Sin"
        },
        {
            "id": "space_time",
            "label": "Space-time"
        }
    ],
    "source_work_ids": [
        "einstein.relativity_popular_de"
    ],
    "passages": 76,
    "word_count": 21317,
    "word_counts_by_language": {
        "de": 19174,
        "en": 21317,
        "fr": 21945
    },
    "editorial_status": "gpt_5_6_semantic_draft_v1",
    "structure": {
        "citation_scheme": "source-section-v1",
        "kind": "native",
        "levels": [
            {
                "key": "section",
                "label_fr": "Section",
                "label_en": "Section"
            }
        ],
        "leaf_fr": "Section",
        "leaf_en": "Section"
    },
    "canonical_passage_id": "passage:einstein.relativity_popular_de:section-0028",
    "canonical_ref": "section-0028",
    "canonical_parent_ref": null,
    "canonical_parent_id": null,
    "representations": [
        {
            "language": "de",
            "text": "Von K aus beurteilt ist die Uhr mit der Geschwindigkeit v bewegt; von diesem Bezugskörper aus beurteilt vergeht zwischen zweien ihrer Schläge nicht eine Sekunde, sondern 1 √ 1 − v 2 c 2 Sekunden, also eine etwas größere Zeit. Die Uhr geht infolge ihrer Bewegung langsamer als im Zustande der Ruhe. Auch hier spielt die Geschwindigkeit c die Rolle einer unerreichbaren Grenzgeschwindigkeit. § 13. Additionstheorem der Geschwindigkeiten Fizeau scher Versuch. Da wir Uhren und Maßstäbe in praxi nur mit Geschwindigkeiten bewegen können, die klein sind gegen die Lichtgeschwindigkeit c , so werden die Ergebnisse des vorigen [S. 26] Paragraphen kaum direkt mit der Wirklichkeit verglichen werden können. Da dieselben andererseits dem Leser recht sonderbar vorkommen werden, so will ich nun aus der Theorie eine andere Konsequenz ziehen, die aus dem bisher Dargelegten leicht abzuleiten ist, und die durch das Experiment glänzend bestätigt wird. In § 6 haben wir das Additionstheorem für gleich gerichtete Geschwindigkeiten abgeleitet, so, wie es sich aus den Hypothesen der klassischen Mechanik ergibt. Dasselbe läßt sich auch leicht aus der Galilei-Transformation (§ 11) folgern. Statt des gehenden Mannes im Wagen führen wir einen Punkt ein, der sich relativ zum Koordinatensystem K′ nach der Gleichung bewegt. Aus der ersten und vierten Gleichung der Galilei-Transformation kann man x′ und t′ durch x und t ausdrücken und erhält so: Diese Gleichung drückt nichts anderes aus als das Bewegungsgesetz des Punktes gegenüber dem System K (des Mannes gegenüber dem Bahndamm), welche Geschwindigkeit wir mit W bezeichnen, so daß man, wie in § 6, erhält: Wir können aber diese Betrachtung ebenso gut unter Zugrundelegung der Relativitätstheorie durchführen. Man hat dann in der Gleichung x′ und t′ durch x und t auszudrücken unter Verwendung der ersten und vierten Gleichung der Lorentz-Transformation . Man erhält dann statt der Gleichung (A) die Gleichung:",
            "source_id": "relativity_popular_de",
            "translation_type": "original_language"
        },
        {
            "language": "en",
            "text": "As judged from K, the clock moves with velocity v; as judged from this body of reference, the interval between two of its ticks is not one second but 1/√(1 − v²/c²) seconds, thus a somewhat longer time. As a result of its motion, the clock runs more slowly than when at rest. Here too the velocity c plays the role of an unattainable limiting velocity.\n\n§ 13. Addition Theorem of Velocities. Fizeau's Experiment.\n\nSince in practice we can move clocks and measuring rods only at velocities that are small in comparison with the velocity of light c, the results of the preceding [p. 26] section can scarcely be compared directly with reality. Since, on the other hand, they will appear quite strange to the reader, I shall now derive from the theory another consequence that follows easily from what has so far been presented and that is brilliantly confirmed by experiment.\n\nIn § 6 we derived the addition theorem for velocities in the same direction as it follows from the hypotheses of classical mechanics. It can also be derived easily from the Galilean transformation (§ 11). In place of the man walking in the carriage, we introduce a point that moves relative to the coordinate system K′ according to the equation. From the first and fourth equations of the Galilean transformation, x′ and t′ can be expressed in terms of x and t, thus obtaining: This equation expresses nothing other than the law of motion of the point relative to the system K, or of the man relative to the railway embankment. We denote this velocity by W, so that, as in § 6, we obtain:\n\nBut we can equally well carry out this consideration on the basis of the theory of relativity. In that case, x′ and t′ in the equation must be expressed in terms of x and t using the first and fourth equations of the Lorentz transformation. Instead of equation (A), we then obtain the equation:",
            "translator": "Codex gpt-5.6-sol",
            "edition": "Prokopton42 non-official AI translation, 2026-09-11",
            "source_id": "prokopton42-codex-translation:gpt-5.6-sol:corpus-passage-translation-v1",
            "translation_type": "ai_generated_translation",
            "official_status": "non_official",
            "generation_model": "gpt-5.6-sol"
        },
        {
            "language": "fr",
            "text": "Évaluée depuis K, l’horloge se déplace à la vitesse v. À en juger depuis ce corps de référence, il ne s’écoule pas une seconde entre deux de ses battements, mais 1 √ 1 − v 2 c 2 secondes, soit un temps quelque peu supérieur. Du fait de son mouvement, l’horloge marche plus lentement qu’à l’état de repos. Ici encore, la vitesse c joue le rôle d’une vitesse limite inaccessible. § 13. Théorème d’addition des vitesses. Expérience de Fizeau. Puisque, dans la pratique, nous ne pouvons déplacer des horloges et des étalons qu’à des vitesses faibles par rapport à la vitesse de la lumière c, les résultats du paragraphe précédent [p. 26] ne pourront guère être comparés directement à la réalité. Comme ils paraîtront par ailleurs fort étranges au lecteur, je vais maintenant tirer de la théorie une autre conséquence, facile à déduire de ce qui a été exposé jusqu’ici et brillamment confirmée par l’expérience. Au § 6, nous avons déduit le théorème d’addition des vitesses de même direction tel qu’il résulte des hypothèses de la mécanique classique. On peut également le déduire aisément de la transformation de Galilée, § 11. Au lieu de l’homme marchant dans le wagon, introduisons un point qui se déplace par rapport au système de coordonnées K′ selon l’équation. La première et la quatrième équation de la transformation de Galilée permettent d’exprimer x′ et t′ au moyen de x et t, et l’on obtient ainsi : cette équation n’exprime rien d’autre que la loi du mouvement du point par rapport au système K, ou de l’homme par rapport au remblai, mouvement dont nous désignons la vitesse par W, de sorte que l’on obtient, comme au § 6 : mais nous pouvons tout aussi bien effectuer ce raisonnement sur le fondement de la théorie de la relativité. Dans l’équation, il faut alors exprimer x′ et t′ au moyen de x et t en employant la première et la quatrième équation de la transformation de Lorentz. À la place de l’équation (A), on obtient alors l’équation :",
            "translator": "Codex gpt-5.6-sol",
            "edition": "Prokopton42 non-official AI translation, 2026-09-11",
            "source_id": "prokopton42-codex-translation:gpt-5.6-sol:corpus-passage-translation-v1",
            "translation_type": "ai_generated_translation",
            "official_status": "non_official",
            "generation_model": "gpt-5.6-sol"
        }
    ],
    "content_checksum": "61c034ae2ddee5ec79f5ebe17367198f9b103d1ef3b86487f08d8df9adf3c894"
}