Which Sci-Fi work introduced the concept of speed-based time travel?

Question

We see speed-based time travel all the time in science fiction. It’s possibly a result of crude interpretation of Einstein’s Special Theory of Relativity which makes time a speed-dependent quantity. Some examples:

• Sonic the Hedgehog could time travel by running very fast in Sonic CD (1993) game.
• Back to the Future (1985) movie featured time travel by going 88mph.
• Superman travelled back in time to save dead Lois Lane in Superman (1978) movie. Actually, Superman has done this countless times with his super speed:
  
• In Star Trek: TOS episode Naked Time (1966), Slingshot Effect was shown which requires enormous speed. Star Trek has used Slingshot Effect countless times to time travel.
• Flash often travels back and forward in time by running very fast (Flashpoint events are results of time travel).
  

Which Sci-Fi work first showed speed-based time travel?

Answer 1

Would a science-fictional limerick count? According to the article "Humour on Einstein as expressed in limericks", this one was first published in the Dec. 19 1923 issue of Punch magazine, written by Arthur Henry Reginald Buller:

There was a young lady named Bright
Who traveled much faster than light
She set out one day,
In a relative way,
And came back the previous night.

P. 222 of Paul Nahin's book Time Machines: Time Travel in Physics, Metaphysics and Science Fiction mentions that the limerick was likely inspired by some actual results in theoretical physics papers showing that faster-than-light travel in relativity can lead to backwards causality, such as R. C. Tolman's 1917 book The Theory of the Relativity of Motion which had a section discussing the problem on p. 54 (of course, physicists usually use this theoretical result to argue that faster-than-light particles are likely impossible, not to argue for the real-world feasibility of time travel).

Answer 2

In Superman Vol. 1 #48 (September, 1947), Superman travelled through time via a "brand new super stunt," which involved him flying around in a "weird mathematical design" at super-speed, before vanishing into the "time-dimension" and materialising in the year 1776 AD.

Answer 3

Here's another example which sort of qualifies, though maybe not what the OP was looking for since the question references the theory of relativity and this story has nothing to do with it. The comical 1904 time travel story The Panchronicon by Harold Steele MacKaye, available on project Gutenberg here, is based on the idea that the passage of time is connected to the motion of the sun in the sky. So, as one character explains it, if you could travel along the surface of the Earth so that you made one complete trip around the pole each day, keeping the Sun at the same position in the sky, then "time wouldn't change" for you; and if you could circle the pole even faster than the sun (so that the sun would appear to move backwards in the sky), then you would travel back in time! So all the characters need to do is attach their ordinary vehicle, the "Panchronicon", by a 40 foot rope to an iron rod sticking out of the North pole, then ride in circles around it, "cutting the meridians" repeatedly, in order to travel back in time.

This method of time travel needn't even involve particular high speeds, but even though it's pretty silly (intentionally so, I'm sure), this story is notable as perhaps the first time travel story to feature a clear bootstrap paradox involving information that has no origin, as summarized on p. 224 of the book Time Machine Tales: The Science Fiction Adventures and Philosophical Puzzles of Time Travel--

An Edwardian literary time machine with style, the Panchronicon (literally, a ‘machine for all time’) swings on a rope tether around a steel post erected at the North Pole. By “cutting the meridians” faster than the sun does, it travels through space and time from 1898 New Hampshire to the London of three centuries earlier. Using it, a time traveler fan of Shakespeare journeys from 1898 back to the bard, who is suffering from writer’s block. There she whispers the magic lines from a play he is stuck on (lines she has memorized for her literary club meetings) into his receptive ear. Does this make Shakespeare a plagiarist? Of himself!?

Answer 4

Just to provide an early basepoint, the Cosmic Treadmill from The Flash was introduced in 1961 in The Flash #125 although he previously traveled back into the prehistoric era through running too fast in 1961 (The Flash #120).

As Kid Flash tries to pummel the giants feet, Flash manages to break free by vibrating out of the giants grasp. The sultans of speed then defeat the giant by tripping him and then tying him up with some of the steel cable that they brought along on their expedition. When they witnessed an unscheduled eclipse, it confirms Flash's theory that somehow, the entire party had been transported back in time to a prehistoric era. They further confirm this when they spot dinosaurs off in the distance. Deciding to use this extraordinary circumstance to their advantage, Flash and Kid Flash speed across the world to learn that Manners' theory is true, that South America and Africa were once connected. As coincidence would have it, they are also at the moment when the two continents are beginning to break apart.

Answer 5

I'm not sure that it entirely answers the question, but Invaders of the Infinite by John W Campbell, published in 1961 (though title page says earlier version is 1932), has its heroes travel in time due to use of a time distortion field and a space speed field and an accident during a fight with an alien ship:

Tried an experiment, and it was overly successful," replied Arcot, a worried look on his face. "I tried combining the Thessian high speed time distortion with our high speed space distortion—both on low power. 'There ain't no sich animals,' as the old agriculturist remarked of the giraffe. God knows what speed we hit, but it was plenty. We must be ten thousand light years beyond the galaxy."

When they try to return to Earth, they find they are in the distant past:

With Wade's help, and by coming to rest near several of the stars, then observing their actual motions, they were able to determine their time-status. The estimate they made finally was of the order of eighty thousand years in the past! The Thessian ship had thrown them that much out of their time.

To return to current time, they turn on the time field and sit motionless with respect to the sun:

"As to getting back—that's a question."

"Which is," added Arcot, "easy to answer now, thank the good Lord. All we have to do is wait for our time to catch up with us. If we just wait eighty thousand years, eight hundred centuries, we will be in our own time."

"Oh, I think waiting so long would be boring," said Wade sarcastically. "What do you suggest we do in the intervening eighty millenniums? Play cards?"

"Oh, cards or chess. Something like that," grinned Arcot. "Play cards, calculate our fields—and turn on the time rate control."...

...We might just as well travel slowly on the time retarder, and work on the way. I think the thing to do is to go back to Earth, or better, the solar system, and follow the sun in its path."

So, it seems that they can control their rate of time passing, but not necessarily time-travel as such, without the accident.

Answer 6

Relativistic time dilation provides a kind of one-way time travel into the future, which is featured in this story.

1931: "Out Around Rigel", a novelette by Robert H. Wilson, first published in Astounding Stories, December 1931, available at the Internet Archive, also available from Project Gutenberg. I cited this same story in my answer to the old question Earliest use of Relativity in SF?.

The narrator, Dunal, was an inhabitant of the moon, way back when it had air and water and life. He goes on a trip to Rigel with his friend Garth in a spaceship constructed by the latter, who believes that it can go faster than light:

"You see, since your mathematical friends derived their identical formulas for gravity and electro-magnetism, my job was pretty easy. As you know, a falling body follows the line of least resistance in a field of distortion of space caused by mass. I bend space into another such field by electromagnetic means, and the Comet flies down the track. Working the mercury disintegrators at full power, I can get an acceleration of two hundred miles per second, which will build up the speed at the midpoint of my trip to almost four thousand times that of light. Then I'll have to start slowing down, but at the average speed the journey will take only six months or so."

"But can anyone stand that acceleration?" Kelvar asked.

"I've had it on and felt nothing. With a rocket exhaust shoving the ship, it couldn't be done, but my gravitational field attracts the occupant of the Comet just as much as the vessel itself."

Returning alone from the trip to Rigel, Dunal finds the moon strangely changed:

With a jerk, I got to my feet and climbed up the sloping floor to the atmosphere tester. My fingers slipped off the stopcock, then turned it. And the air-pressure needle scarcely moved. It was true. Somehow, as the scientists had always told us would be the case eventually, the air on the moon, with so little gravity to hold it back, had evaporated into space.

But in six months? It was unthinkable. Surely someone had survived the catastrophe. Some people must have been able to keep themselves alive in caves where the last of the atmosphere would linger. Kelvar must still be alive. I would find her and bring her to the Comet. We would go to some other world.

[. . . .]

Then I knew.

In our argument as to the possible speed of the Comet, Garth and I had both been right. In our reference frame, the vessel had put on an incredible velocity, and covered the nine-hundred-odd light-years around Rigel in six months. But from the viewpoint of the moon, it had been unable to attain a velocity greater than that of light. As the accelerating energy pressed the vessel's speed closer and closer toward that limiting velocity, the mass of the ship and of its contents had increased toward infinity. And trying to move laboriously with such vast mass, our clocks nd bodies had been slowed down until to our leaden minds a year of moon time became equivalent to several hours.

The Comet had attained an average velocity of perhaps 175,000 miles per second, and the voyage that seemed to me six months had taken a thousand years. A thousand years! The words went ringing through my brain. Kelvar had been dead for a thousand years. I was alone in a world uninhabited for centuries.

I threw myself down and battered my head in the sand.