Suppose I hop in my TARDIS or DeLorean and want to go back and buy that HEMI powered Daytona for $4000 or ahead and get that anti-gravity flying bike.
Wait a minute…
The Earth spins on it’s axis, orbits the Sun, and travels around the Milky Way galaxy…a galaxy which is racing away from other galaxies. This spot (Pats the ground at my feet) here and now is located at a completely different location in the universe at a different time in the future or past.
But WAIT!
According to Relativity, there is no privileged frames of reference: one could describe a stationary Earth with spacetime cork-screwing around it.
With the above two postulates in mind, could step inside my time machine on the corner of 123 Main Street, move the lever ahead or behind 50 years, and still step back out onto 123 Main Street?
I have traveled through time from 1954 to post this answer:
Yes, you could do it. Why? Because your time machine doesn’t actually transport you through time, except the usual 1 second per second, so when you step out, it’s still 2017.
Sci-fi writers have recognized the problem (some of them, anyway) and simply assume that whoever is clever enough to build a time machine is clever enough to design one that uses the current location as the origin of their coordinate system. You also have to take the speed of the rotation into account so you don’t wind up traveling at 1000MPH.
This was discussed in detail in the below thread. With fictional time machines, backward time travel is so difficult that if someone could make the time part work, the spatial adjustments would likely be solvable. E.g, TARDIS stands for Time And Relative Dimensions In Space. However to simplify the narrative, the spatial adjustments are often not covered in fictional accounts.
Those are two different problems, and being clever enough to solve one problem in no way indicates that you are clever enough to figure out the other. It’s like telling a tale about building a ship fast enough to travel to the surface of our sun and back within a week without even mentioning how it is the ship didn’t get destroyed once it got near the sun.
As it happens, I just read a science fiction novel where this spatial motion was used in combination with backwards time travel. In that novel there was a limitation of the time travel mechanism in that it could only transport objects backwards in time a couple of nanoseconds. But because of the effects of the earth/sun/galaxy/etc’s rotation, in those few nanoseconds the new object would show up a couple of feet away from the original - which still existed.
It’s not quite like that. Building a ship that travels to the sun and back in one week is only 300 miles per second. To be launched next year, Solar Probe Plus will travel up to 120 miles per second and come within 3.67 million miles of the photosphere, 1/10th Mercury’s distance from the sun. That is well within the sun’s corona, or upper atmosphere: Parker Solar Probe - Wikipedia
We already have the technology to make a spacecraft go 300 miles per sec if there was a compelling need, and probably get even closer to the sun. So we can already do both of those.
By comparison, backward time travel (if possible at all) would likely require harnessing fantastic, mind-bending energies and forces, such as creating an artificial wormhole. It might also require understanding and manipulating exotic matter. It would not be done via alchemy, some magic incantation or a clever gadget. Since time and space are intertwined, in general controlling one is controlling the other.
If Larson was still working that would be a great cartoon. “Having tried a trip of fifteen minutes, Professor Benson discovers he overlooked an important factor in designing his time-travel belt.” with a lab-coated guy floating in space looking at a receeding Earth.
And yet you’ve been pulled along with that spot to its new location as it travels forward through time normally. If one is postulating a system of time travel that allows going forward at a faster rate than normal or backward at any rate, it seems easy enough to handwave some similar form of continued gravitational attachment such that the earth does not disappear out from under you.
Or you might make millions of micro-jumps: you jump ahead or back in time by a microsecond – presuming this takes you less than a microsecond to do (otherwise you’re a time-machine on a treadmill) – and look around for the spot you want to occupy. With luck, it hasn’t gone too far away…
If you take a relativistic view then the Universe is described in terms of events and details like spatial and temporal position depend on coordinate systems. Time travel in relativistic terms is usually seen as the existence of closed timelike curves (CTCs). I.e. when it is possible for an observer to reach the same event multiple times at different points along their timeline.
One way to do it would be to say that part of the way the time machine works is that as part of the time travel process spacial location is effected by gravity and velocity but in reverse, and that the gravitational components are adjusted at all points in the travel to account for the past positions of matter. For a time traveler in a stable orbit, this should put him exactly where he was relative to all heavenly bodies when he comes back, but probably won’t work for a person on the surface since it won’t adequately account for the force exerted by the ground.
Nitpick: this isn’t quite true. Acceleration is NOT relative, so there is a real discernable difference between an Earth rotating and revolving and a stationary Earth with the rest of the universe spinning around it. Or, another way to say it: all non-accelerating frames of reference are equally privileged, but accelerating ones aren’t.
Not only would you have to account for changes in position, you’d have to account for changes in velocity as well. If I set my time machine to 6 months in the future, even if I manage to stay put in the same spot on the Earth, I’ll still be moving 70,000 mph in the direction opposite that the Earth is moving due to its orbital motion.
Actually, if you really want to bend the math well beyond the breaking point, you can treat the universe as spinning around a stationary earth, and GR deals with it just fine. It’s INSANE, but it really does work.
(The Bad Astronomer pointed this out, in response to the loonies who believe that the earth does not rotate.)
I’m not at all sure, though, that this can generalize to more complex motion, such as a satellite around the moon, which goes around the earth, which goes around the sun, which goes around the galaxy… Once you start adding these up, “simple” (!) GR transpositions don’t work.
