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The earliest 'time loop' story I am aware of is Lester Del Rey's '...and it comes out here' from 1951. The main character is trying to invent a practical atomic generator & fails again and again. His 30-years-older self travels back in time and takes the main character a couple of centuries into the future where the generator he patented is on display; they steal the generator and take it back to the present where the main character patents it. So, who invented the generator?

I've seen copies of this story again and again over the years - I believe it was either Gardner Fox or Otto Binder who wrote a Superman's Pal Jimmy Olsen story using the idea, and that bugs me because I hate Superman's Pal Jimmy Olsen.

Does anyone know of a story that pre-dates 1951?

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1935: "The Man Who Met Himself", a short story by Ralph Milne Farley (pseudonym of Roger Sherman Hoar); first published in the August, 1935 issue of Top-Notch magazine; reprinted in Farley's 1950 time-travel collection The Omnibus of Time. This story was part of my answer to the question What was the first Time-Travel story to involve gambling?.

Review at the Internet Time Travel Database:

Among physicists, the most favored resolution to time-travel paradoxes is a world of one fixed landscape of time and its events. Time travel may be possible, but if so, the Karma will conspire to have only those events that have been written into the landscape to occur. Heinlein’s “—All You Zombies—” may be the pinnacle of such stories, but Farley’s is the earliest case that I’ve read to present a clear deterministic time loop along these lines. In the story, Boston stock broker Dick Withrick is on a 1935 tiger hunt in Cambodia when he runs into a strangely familiar (and slightly older) man who warns him, “As you value your freedom, do not touch the machine—” And yet, he does touch the machine, taking him back to 1925 so he (in the company of his Buddhist Abbot host) can relive the decade of financial turmoil.

The time loop is described in this excerpt::

Not a single flaw in his time-traveling. Not a single puzzling or preposterous thing about it, except for one question: Whence came the time-machine which he had found in the Cambodian jungle?

He put that question to the parchment-faced old Abbot.

Yama Toga laughed. "Perfectly simple," he asserted. "It is now locked up, oiled, and in good condition, in some hiding-place of mine, unrevealed to you; is it not?"

"I suppose so," Withrick admitted, "although I haven't seen it since I left it in the woods the day I back-tracked in time."

"1935 will arrive," the Abbot continued, an inscrutable smile playing about his Oriental features. "A young American named Richard Withrick will come up the trail, bound on a tiger-hunt. I shall have the time-machine taken back to the proper place, several days in advance. One of your beaters will discover it. Dono Dal will explain to this other you how to operate it."

"But how will Dono Dal know? An ignorant lesser priest like he!" Withrick interjected.

"Ah! You have already told me his exact words, many times. I have written them out on palm-leaves, and have drilled and drilled the stupid Dono Dal in them, until he is letter-perfect. When the proper hour decreed by fate arrives, he will recite his little piece. The cycle will be complete."

"But what if he makes a mistake?"

"He will not make a mistake. What is written, is written."

"But you haven't yet told me where the time-machine came from!" Withrick exclaimed, exasperated.

"You yourself brought it here out of 1935.'

"But where did it come from originally?" Withrick persisted.

"There never was any 'originally'," the yellow-robed old Buddhist patiently explained. "You flew the time-machine backward through time from 1935 to 1925. And that is why I now have the machine all available, to plant so that it will be found by you in 1935."

"To fly it back again to 1925?" Withrick added, interrogatively.

"No. Nothing of the sort. There is no round-and-round circle of events; no repetition. Merely one closed cycle. One overlapping of events for only ten years. One Richard Withrick, with ten years of his life folded together in the middle. One time-machine, found in 1935 and brought back to 1925 — found in 1935 because brought back to 1925. That is all."

"But who made it in the first place? — Oh, skip the 'in the first place'. Just plain: who made it?"

"No one. It was never made. There never lived, and never will live a man who could make a time-machine. Time-traveling is impossible. You yourself have accomplished this impossible feat, because you found, in 1935, the time-machine which you yourself brought into 1925 out of the future. And when 1935 arrives, and you have found the machine, and have flown back with it, the machine will thereby be gone forever, gone back into the past, and no time-machine will exist. It never existed before 1925 — it will not exist beyond 1935. And yet it was never created, and will never be destroyed."

"Just like Einstein's idea of the universe: finite but unbounded," Withrick gasped. "There must be some flaw in it somewhere, but I'm damned if I can figure out what it is. The only time-machine the world has ever known, or will ever know, existing for a brief space of ten years! Existing in complete circularity; existing in 1925 merely because it existed in 1935, and then was flown back ten years in time; existing in 1935, merely because carefully preserved by you for ten years."

"Well, after all, is not that the same solution as is given to the reason why anything exists? It is here because it is here."

Withrick chuckled. "We used to have a song about that, back in America," he said.

And this is the nearest that he ever came toward solving the riddle of the time-machine.

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    I'm sorry - I did not make myself clear when writing this question. My focus is on the object that in effect has no origin - the atomic generator in Del Rey's story or the book in the Jimmy Olsen story, a 'time rig' in a 1956 Silverberg story. I had never heard of 'The Man Who Met Himself', but it definitely qualifies. Feb 12, 2021 at 12:25
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In researching this answer to a different question, I came across an earlier example of a bootstrap paradox in the 1904 story The Panchronicon by Harold Steele MacKaye, available on project Gutenberg here. In this story the characters travel back from 1898 to Shakespeare's time, and in Chapter XII, "How Shakespeare Wrote His Plays", a time traveler named Phœbe, who is very familiar with his plays, offers to help him complete Hamlet's famous soliloquy in return for some help getting a message to one of her companions:

"Ay, there, and in more than this!" Phœbe exclaimed. "You have spoken of Hamlet, Master Shakespeare. Guy hath told me something of that tragedy. This Prince of Denmark is a most unhappy wight, if I mistake not. Doth he not once turn to thought of self-murder?"

"Ay, mistress. I have given Sir Guy my thoughts on the theme of Hamlet, and have told him I planned a speech wherein should be made patent Hamlet's desperate weariness of life, sickened by brooding on his mother's infamy."

"'To be or not to be, that is the question,'" quoted Phœbe. "Runs it not so?"

"This passes!" cried Shakespeare, once more all amazement. "I told not this to your friend!"

"Nor did I from Guy receive it," said Phœbe. "Tell me, Master Shakespeare, have you yet brought that speech to its term?"

"No," he replied, "nor have I found the task an easy one. Much have I written, but 'tis all too slight. Can you complete these lines, think you?"

"My life upon it!" she cried, eagerly.

He shook his head, smiling incredulously.

"You scarce know what you promise," he said. "Can one so young—a damsel, too—sound to its bitter deeps the soul of Hamlet!"

"Think you so?" Phœbe replied, her eyes sparkling. "Then what say you to a bargain, Master Shakespeare? You know where Sir Guy Fenton may be found?"

"Ay, right well! 'Tis a matter of one hour's ride."

"So I thought," she said. "Hear, then, mine offer. I must perforce convey a message straight that touches the life and honor of Sir Guy. To send my servant were over-dangerous, for there may be watchers on my going and coming. Will you go, sir, without delay, if that I speak for you the missing lines completing young Hamlet's soliloquy?"

Shakespeare looked into her face for a few moments in silence.

"Why, truly," he said at last, "I have here present business with my fellow-player Burbidge." He paused, and then, yielding to the pleading in her eyes: "Yet call it a bargain, mistress," he said. "Speak me the lines I lack and straightway will I take your word to Sir Guy."

"Now blessings on thee!" cried Phœbe. "Give me straight the line you last have written."

At once the poet began:

"When he himself might his quietus make——"

"With a bare bodkin"—broke in the excited girl. "Who would fardels bear, to grunt and sweat beneath a weary life, but that the thought of something after death—the undiscovered country from whose bourne no traveller returns—puzzles the will, and makes us rather bear the ills we have than fly to others that we know not of. Thus conscience does make cowards of us all, and so the native hue of resolution is sicklied o'er with the pale cast of thought, and enterprises of great pith and moment by this regard their currents turn awry and lose the name of action."

"No more—no more!" cried Shakespeare, in an ecstasy. "More than completely hast thou made thy bargain good, damsel unmatchable! What! Can it be! Why here have we the very impress of young Hamlet's soul—'To grunt and sweat beneath a weary life'—feel you not there compunction and disgust, seeing in life no cleanly burden, but a 'fardel' truly, borne on the greasy shoulders of filthy slaves!"

He turned and paced back and forth upon the gravel, repeating without mistake and with gestures and accents inimitable the lines which Phœbe had dictated. She watched him, listening attentively, conscious that what she saw and heard, though given in a moment, were to be carried with her forever; convinced as well that she was for something in this, and thankful while half afraid.

On its own, I suppose it might be possible to interpret this episode in terms of a changeable timeline, like a scenario where there was an original version of history where Shakespeare finished the soliloquy himself, and Phœbe only changed things by giving him his own words from a different timeline. However, there are other elements of the story that point to a fixed self-consistent timeline rather than a changeable timeline. In real-life history, a woman named Delia Bacon put forth the the theory that the works of Shakespeare were actually written by Francis Bacon, and Phœbe references this theory at the beginning of the story, before she has done any time-traveling:

"Look, Rebecca!" cried Phœbe, as she entered the door, "here's a new book Mrs. Bolton lent me to-day. All about Bacon writing Shakespeare's plays, an' how Bacon was a son of Queen Elizabeth. Do you s'pose he really did?"

During the course of the story the time travelers meet Francis Bacon, and in the final chapter he ends up accompanying them when they travel back to their own time, with the result that he himself turns out to be the originator of the Shakespeare theory, with "Delia Bacon" being his pseudonym. After that he is eager to return to his own time, having already learned of the "brilliant future" he will have after returning. So, all this suggests a fixed-history model where the effects of the trip through time were already part of the time travelers' history before they actually made the trip.

The date-recording instrument must have been deranged in some way, for when, after a great number of eastward turns around the pole, it marked the year 1898, they had really only reached 1857. Supposing themselves to have actually reached the year erroneously indicated by the recorder, they set off southward and made a first landing in Hartford, Connecticut.

Here they discovered their mistake, and returned to the pole to complete their journey in time. All but Francis Bacon. He declared that so much whirling made him giddy, and remained in Connecticut. Alas! Had Phœbe known the result of this desertion, she would never have consented to it.

Bacon, who had read much of Shakespeare while in the Panchronicon, found on returning thus accidentally to modern America, that this playwright was esteemed the first and greatest of poets and dramatists by the modern world. Then and there he planned a conspiracy to rob the greatest character in literary history of his just fame; and, under the pseudonym of "Delia Bacon," advanced those theories of his own concealed authorship which have ever since deluded the uncritical and disgusted all lovers of common-sense and of justice.

Copernicus Droop, on returning his three remaining passengers to their proper dates and addresses, discovered that his sole remaining phonograph, with certain valuable records of Elizabethan origin, had disappeared. As he owed a grudge to Francis Bacon, that worthy fell at once under suspicion, and accordingly Droop promptly returned to 1857, sought out the deserter, and charged him with having stolen these instruments.

It was not until the accused man had indignantly denied all knowledge of Droop's property that the crestfallen Yankee recollected that he had left the apparatus in question in the deserted mansion of Newington, where he had stored it for greater safety after Bacon's first unexpected visit.

Without hesitation, he determined to return to 1598 and reclaim his own. Bacon, who had learned from modern historical works of the brilliant future in store for himself in England, begged Droop to take him back; and as an atonement for his unjust accusation, Droop consented.

It is not generally known that, contrary to common report, Francis Bacon was not arrested for debt in 1598; but that, during the time he was supposed to have been in prison, he was actually engaged in building up in his own behalf the greatest hoax in history.

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