Conversely, I read a sci-fi novel about a spaceship which was outfitted with a jump drive which essentially teleports the ship instantly from one point in space to another. So the spaceship goes off on its maiden voyage, jumps across thousands of light years and back… only to discover that jumps don’t happen “instantly” after all and thousands of years have passes back on Earth. So the actual speed of the trip was equal to the speed of light, from Earth’s point of view, even though the astronauts were not aware of the passage of time. BTW, their first clue that something was amiss was the fact that when they set coordinates to get back to their starting point, the entire solar system wasn’t there anymore. They assumed their targeting scanners were miscalibrated but the truth was that the solar system had moved along in its path through the galaxy.
The OP wonders if time travel would move you through space but in this story space travel moved you through time.
In your example, you’re only changing one of many intertial values a very tiny fraction. (walking at 3kph?)
The Earth has a rotational velocity of 1,674 kph at the equator. It orbits the Sun at an average speed of almost 30 km/sec. The Sun moves at 220 km/sec relative to the center of the galaxy, or 370 km/sec relative to the cosmic microwave background radiation. The Milkway Galaxy is moving 552 km/sec towards the Great Attractor. (And the universe itself is expanding at 67 km/sec per Megaparsec. Dunno if that matters… )
The premise of most time machine stories, the user is transported through any amount of time near instantly. So, your DeLorean leaps ahead (or back) in time 30 years. The Earth has moved (relative to the CMBR) quite a bit of distance in that time.
Do you believe that the “law of conservation of inertia” alone compels the DeLorean to appear in the same spot it was/will be in 30 years?
As others have posted above he real problem is that there is no fixed reference frame with which to define, “the same place”. With respect to certain reference frame you are moving with respect to others you are stationary. Along with that is the question of momentum. When you reappear are you going at the same relative speed according to your reference frame? Also do you experience any accelerations as you travel back? Without knowing how precisely you are planning to violate the laws of physics its hard to determine what happens.
One possible scenario is that as you travel backwards you maintain the same velocity relative to any inertial reference frame but with a negative time vector. So if respect to a given frame your time machine was traveling 2 mph forward and then went back in time 10 hours, you would find yourself 20 mph behind where you were according to that reference frame. But if you also imagine gravitational acceleration is going to also behave the same way such that you get the same acceleration as you would before but just with a negative time, then it is entirely possible that you would end up pretty much in the same place you were relative to the planet, sun and star system as you were before you left (at least for small jumps). Perhaps someone with a better understanding of general relativity than I can help to see if this works out if we view gravity as warped spacetime.
Although it’s one of those movies you need to watch about 4 time with a annotated concordance to figure out what the hell happened.
All frames of reference are relative, but IIRC the “simple” Relativity calculations involve an inertial frame of reference… i.e. you continue in your frame of reference with no acceleration. Introduce acceleration and the calculations become far more complex.
Right off the bat, the circular motion of standing on a rotating earth, or the circular motion of orbiting the sun, are forms of acceleration. Technically, the motion of the solar system in the Milky way is likely also acceleration because the stars are circling the center of the milky way. As a result, your position is constantly changing, and not just that, your frame of reference is constantly changing due to acceleration - so any 'all is relative" arguments got a lot more complicated. Your inertial frame at any time is the tangential path you are on at that instant, where you would be flung away along if gravity disappeared. Plus, there’s the effect of gravity itself which according to Einstein is indistinguishable from acceleration.
I know nothing about wormholes, but one assume they exist in a local inertial frame of reference?
Beyond that, we’re still back to the premise - it’s your time travel story to write, pick the rules (or gloss over them) that make the story work as conveniently as possible.
I’m picturing a time traveler, cocky with the accuracy of his relativistic inertial frame calculations, making the first jump a day previous in time, but flying off in some arbitrary direction at 20,000 miles per second upon arrival.
You misunderstand. People talk about closed timelike curves because they’re necessary for what people actually mean when they say “time travel”: If you don’t have them, then you’re just doing the equivalent of re-setting a clock, not actually traveling through time at all. But while a timelike curve can be the worldline of a particle, it’s not actually required that it be so, and certainly not required that it be the worldline of the time traveler. In fact, a closed timelike curve cannot be the worldline of any traveler who came from outside the time machine, since such a traveler would have an open end to his worldline from when he entered.
Likewise, wormholes are not the only posited means of time travel. Any device which allows for FTL travel would also allow for time travel, and vice-versa: This also includes, for instance, the Alcubierre warp drive. Of course, none of these phenomena have been shown to exist, and so far as we know all of them would require the existence of “exotic matter” with negative mass.
FLT travel would enable reversals of causality, true enough; but it most certainly involves movement in space as well as time, so the question in the original post is answered. You can’t ‘stand still’ on the surface of a planet and travel backwards in time: you have to go somewhere in space.
If the time travel mechanism is one where you move in tiny time jumps such that gravity still affects the time traveler, you might get away with it. However if the ground eroded out from under you the time machine would fall also. One would need a pretty nifty force field to let you be buried and survive also.
I vaguely remember a story about a time traveler sending himself into the future - but the effect was he went into stasis, and his body just sat in the middle of a green like a statue, visible to all, until he reached his temporal destination. Under that model no problem about flying off into space.
Would it be consistent to postulate a “pseudo-motionless” reference frame where so long as the only forces acting on an object are inertia and gravity, it’s considered to be “not moving”? So for example as long as a time traveler’s only movement was the earth’s rotation, it’s orbit around the sun, and the solar system’s drift through space, he would remain at the “same” spot relative to the Earth’s surface as he moved through time? Or does this hypothesis break down somewhere I’m not seeing?
One hypothetical form of time travel hasn’t been mentioned yet; according to Wheeler and Feynman, positrons might be considered electrons going backwards in time. If you tried to go backwards in time while standing still on the surface of a planet you would be converted into antimatter; the first thing you would encounter would be yourself, a split second before; result; gamma rays.
Maybe time machines would be useful after all - as efficient matter-to-energy converters.
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