# Time travel coordinates

My problem is as follows:

• mr Average Joe has designed a device for time travel in his garage/basement
• at the moment he has sent the device forward in time (for testing purposes) a couple of times (first time a full second, afterward parts of a second -- smallest time setting is 0.01s), the biggest problem being the fact that the device appears at seemingly random places in or outside the testing grounds

The question:

• how would one set (or fix) the coordinates for the destination in space and time? (Given the fact that the earth rotates around its axis and the Sun, what would be a plausible set of coordinates for the device?) (If one takes into account only the rotation of the planet, one would reasonably expect to be in the same position if he/she travels 24h forwards or backwards in time -- but the Earth's rotation is not the only movement which needs to be taken into account)

• it's a device which can be portable (it just requires a power supply , wall socket would be enough)
• it creates a 'bubble' around the device, with a radius that can be set (and, of course, limited by the amount of power available)
• the 'bubble' dissipates as soon as the 'travel' is finished
• travel time is instantaneous to anyone/anything inside the 'bubble'
• after solving the coordinates problem, the device can be used as a teleportation device by setting the time at the minimum setting and modifying the coordinates
• it was built by cleverly combining off-the-shelf available technology

• current time, current world
• no aliens

This is my first post, so be gentle with me :D

If you feel that the post needs clarifications, please let me know.

EDIT: Some issues that need to be clarified:

• Joe needs to know the position before leaving, in order to avoid plunging into the depths of space or into the/a Sun.
• The device has a capacitor-type power source, meaning it charges when plugged in and can release the power all at once (much like a camera flash).
• It could possibly be modified to do 2 jumps and automated to return to the same location, but i'd try to avoid that, because obtaining the power for the next jump is an important part of the plot...
• building a ship or other vessel to contain the device and the traveler is a no-go, as would be over the character's budget (ans would spoil the science)
• the device pops in and out of time (tardis-like) but instantaneous, it does not travel the whole length of time (this avoids a lot of issues like: what happens if one travels backwards before the time of the machine, what happens if he travels to a time where he's already inside the machine?)
• the 'beacon' idea sounds nice, but one would have to somehow read the position of the beacon before travelling (see the first point in edit)
• the 'extra dimension' approach also sounds nice, but I would try to keep it as close to reality as possible, otherwise i could go all gunslinger -- The Dark Tower is one of my favorite reads
• the device adjusts for velocity (if it starts as stationary, upon arrival at the destination is still stationary)
• Does it also adjust velocity? if it travels 6 months into the past and gets the position on earth correct and the position relative to the sun correct does it also adjust velocity or does it suddenly find itself traveling 130,000 km per hour because the earth is now moving in the opposite direction? Also there's also the solar systems movement around the center of the milky way and the milky ways movement around the local supercluster. Jul 22 '15 at 11:56
• definitely +1 for noticing the spacial offset! Jul 22 '15 at 11:59
• Standard question for a teleportation device: what happens if it tries to "boink" its way into a solid object? Jul 22 '15 at 13:30
• Also, in some ways this question seems to presuppose that there's such a thing as an absolute frame of reference, a.k.a "the ether". The reason for the device appearing somewhere weird during testing is presumably because the Earth has moved "a bit" in the time it takes to travel--but relative to the Andromeda galaxy, for instance, the Earth has moved a whole lot more than that. If your machine somehow traveled through all the times in between its endpoints, rather than "boinking" from time to time in a discontinuous faction, it might just end up where it needs to be naturally. Jul 22 '15 at 13:35
• Perhaps you could assume it follows the geodesic. Then the only question is where on Earth it ends up. Jul 22 '15 at 17:23

The biggest issue you're going to have here is with absolute vs relative co-ordinate systems. If the time machine is getting its co-ordinates relative to the earth/the sun/the centre of the galaxy then this becomes a computational problem of 'where will the thing I want to be on be at the time I want it to be there'. The choice of object for your frame of reference may cause this to be a chaotic relationship, in which case you can only really guess at the location, and longer trips (in both time and space) will lead to bigger disparity between where you want to be and where you end up.

For example: If the reference point is the centre of the Earth you can trace a circle around the axis of rotation intersecting with your destination, spin the circle for an amount of time and then aim for where your destination will be. If you take the centre of the Earth/Moon system as your point then this becomes much harder, you'll end up tracing ellipses and all sorts to get to the right place. If you take the Sun? Well, the sheer number of things in the solar system that could perturb Earth relative to the Sun by the few meters it could take to accidentally place you in a wall makes it almost impossible.

In the second instance if you're using an absolute reference system then.. erm.. You're boned. We experience things from a relative perspective. It's the way it goes. If there is some form of universal absolute co-ordinate system then you're not going to be able to exploit it without accidentally dropping into the endless void between galaxies first.

My recommendation here (which may be a non-starter based on how you're defining your time-travel paradigm) is to 'stutter' your time machine ahead of you, getting it (or a version of you) to gather the necessary jump adjustments and send the information back to itself before it jumps. This way a trillion iterations of your time machine jumping, correcting, jumping, correcting etc etc can occur before the actual jump is completed to within acceptable parameters for drift. At that point you're free to define whatever co-ordinate system you like, relative to whatever frame you like. You can even get the machine to travel until it matches a particular image, if you like, and because you can send out decillions of parallelised time machines it can perform a brute force search of the universe.

EDIT: I think some more explanation of the stutter-search concept is required.

Lets assume that I want to travel to a location on the Earth's surface 20 years in the future. I need to choose a method of maintaining location that makes sense, so I choose GPS signals. (A local, Earth only system likely to last the next 20 years). Obviously getting straight there requires some form of vector, but I don't know the correct vector.

So: I set my time machine to jump forwards a millisecond, measure the change in GPS position and send the information back. Then, using the information gained from the future, the machine (that hasn't actually jumped yet due to my abuse of paradoxes) calibrates a jump for the correct GPS co-ordinates 2 milliseconds in the future. It measures the change in GPS position from the expected and sends it back to itself.Then, using the information gained from the future, the machine (that hasn't actually jumped yet due to my abuse of paradoxes) calibrates a jump for the correct GPS co-ordinates 3 milliseconds in the future... You can see where this is going.

The trick to understanding this is that the signals used by the machine to get from place to place don't have to match a set of arbitrary co-ordinates. They have to match the signals used by the machine to get itself to the place you want to go. As you can use the machine to basically brute force a navigation solution you don't need any form of co-ordinates, as long as you have a way of identifying where it is you want to go.

Examples or potential navigational aids include but aren't limited to: GPS, image recognition, accelerometers, radiation sources, star-maps, thermal monitors and impact detection. The last two are especially useful in that you can use your pre-jump machines to avoid any tricky things like reappearing inside walls or suns, and if you want to 'stay where you are' you can calibrate for jumping forwards while maintaining constant pressure on the base of the machine.

The combination of the above can be used to let your machine 'feel' its way through time and space to your final destination, at which point it can transmit the finalised jump 'vector' back to itself and execute it.

Of course this needs some rather odd time travel logic to be allowed, but what the heck, we're allowing an average guy to build a perpetual-motion-infinite-energy-unstoppable-force-breaks-conservation-of-energy-momentum-and-causality-time-machine BREATH out of parts from radioshack.

• Brute-forcing the universe does sound like a good idea (BIG GRIN). Let's assume Joe here can automate 2 jumps (one going and one coming back), he would still need to be able to get some coordinates of the point the device goes to, in order to calculate the spatial offset. And he needs more than 2 points (a beacon and the delta-time). And it's not really a perpetual-motion-infinite-energy-unstoppable-force-breaks-conservation-of-energy-momentum-and-causality-time-machine (copyright to you on that), as it needs to be plugged in to start :P Jul 22 '15 at 14:01
• There is a practical matter to be discussed for your stutter-step technique: GPS measurements aren't instantaneous. You need to listen for at least one repetition of the code sequence from each satellite to provide accurate autocorrelation locking, and that takes a minimum of 1 msec. On the other hand, if Joe Average has a brilliant friend or teenage son, an expected curve of locations can be generated, with something like GPS used to fine-tune it. Jul 22 '15 at 16:31
• Something little known but the GPS system we use isn't only GPS. For high precision work (or flying), GPS systems often rely on ground correction stations. This give local corrections to the signals received by the GPS satellites and can provide a 10x (or maybe more) improvement in position resolution. Jul 22 '15 at 20:08
• This might actually make the time traveling story more interesting. In that going to space-time locations you have already traveled past is quick and easy. Going to new ones takes careful time and planning. No jumping back to the Jurassic era on a lark in this fictional Universe. It also makes jumping back before GPS more problematic than later times. Jul 22 '15 at 20:11
• @leftroundabout: There's also no such thing as a perfectly accurate theory. If we're positing that time travel is not only possible but easily achievable then we're already messing around at some pretty fundamental levels. Even the rules we've written about the universe are relative to our experiences. Just as our brains aren't wired to handle free-form time travel, we're similarly unequipped to deal with absolute anything. Hence my 'even if there is' comment. Even if in this story there is some form of awesome absolutism revealed by the toaster, we won't be able to make sense of it. Jul 24 '15 at 8:36

## In the real world this is irrelevant...

The question is irrelevant because there is no such thing as absolute reference frame. You can not move. You can only move from respect to something. We feel like we can determine an absolute location in space-time because of our tendency to choose the Earth as our frame of reference. This is a flaw that mislead a lot of people before Special Relativity was discovered.

You have either to decide an arbitrary frame of reference or to abandon the question.

If you decide there is an absolute reference frame in your world then you will get in trouble* since you're denying the principles of the Special Relativity which leads to Einstein's General Theory of Relativity.

That being said, you still should choose Earth's surface as your "absolute" reference frame and say everything is moving but the center of the Earth (this is pretty arbitrary and awfully wrong but... this is what Aristotle thought in is time after all). With a rotating Earth and Earth's center as your absolute reference frame everything is much simpler: you just have to figure out how fast Earth rotate and compute your future position according to this angular rotation.

All your problems are gone if you choose your machine to be the center of the Universe but... well I am pretty sure this prospect will not seem "logical" to your readers.

Choosing the sun as your absolute reference frame makes your problem much more complex.

*: Since everything is rotating relative to the Earth we are able to say that both speed and acceleration can be absolutely measured. Since Earth is at the center of the universe, there will be things that are far enough from Earth and will have a faster than light angular momentum. Light can't be the speed limit and things become much more complex...

• That may be fine for the machine, but not for a person in the machine... People have an annoying tendency to complain when dropped in inconvenient places, like massive rock, volcanoes, empty space and such. Jul 22 '15 at 14:04
• Why would it be like this? There is NO absolute referential. Jul 22 '15 at 16:46
• Having a preferred (but not absolutely absolute) reference frame is my pet idea for avoiding causalty violations in ftl travel. It would be the reference frame of the object in hyperspqce enabling transit, not a feature of spqcetime itself. Jul 22 '15 at 19:57
• Didnt Spock help Scottie get around this when he told Scottie of future Scottie's teleportation formula that treated the ship as stationary and the whole of space as moving? Aug 26 '15 at 22:18

Only you can tell if this would work for your story, but what if the time machine didn't actually disappear while it does its time travelling?

Instead of Doctor Who-esque machine that pops in and out of time, it would be more like having a fixed portal you come through to another time - as long as the other end of the portal is still working.

This limits the use of the device, of course, but limitations are usually great for a story. The obvious points to consider:

• Unless you maintain that the machine can propagate itself backwards in time, you can't travel further in the past than the time the machine was created.
• The time machine exists between the points in time you're travelling - this means that in can be tampered with in the meantime, and you wouldn't be able to do much about it. And of course, this includes others being able to use the device, not just you.
• As many similar magic devices, this could be used to create a free source of infinite energy. Careful :)
• The machine needs to be incredibly durable and reliable to be of use if you want long time travels. Repeating last thursday would be fine, traveling a few years or decades is probably still doable, but thousands of years is a lot trickier. Millions and billions seem to be outright out, unless you make the time machine a "fixed" event in spacetime.

Considering the machine as something fixed in spacetime could allow travelling further into the past than the machine was created; imagine the moment the machine was created and started, it suddenly has always been there, since the creation of the universe, up till the universe dies. It's immovable, indestructible, a permanent feature of the spacetime itself. It is timeless, following geodesics in space-time. Of course, this still means that while the device cannot be destroyed or moved, it's possible to, say, flood it in an ocean, or cast it in concrete. And of course, the chic sci-fi favourite, thrown into a Sun or a black hole. You might want to make extra provisions if you want the travelling to be safe :)

And of course, the usual time travel cautions apply as well. You're bound to break a lot of physical laws unless you make special provisions to ensure strict consistency at all times. Breaking the universe is rarely a good idea.

Many different ways to approach this, some better than others:

• Coordinates are absolute: simplest to understand, but hard to apply and in reality there's no such thing because relativity. I think it's not worth the trouble.

• Coordinates relative to a celestial body: could be the surface or center of the Earth, Sun, Galaxy, local cluster, etc. Pros: simple, can be calculated, small errors create interesting stories. Cons: can't teleport inside moving (or moved) structures, there will always be small drifts, geological changes lead to disasters.

• Coordinates relative to an arbitrary anchor point: the anchor could be a physical object, like the teleportation pad, a building or a macguffin. Less calculations, more stable along geologically long periods (assuming the anchor survives), moving anchors can be a plot point. Requires separate device or landmark.

• "Do what I mean": the system looks into the user's mind, simulates many different destination points and selects the one that would make the user most satisfied. Always works (unless you don't want it to, e.g. the AI rebels), but requires a pretty important separate device.

• Median particle position: look at the destination in the present, identify all particles inside bubble-sized area. Travel in time, locate previously identified particles, take median position (and orientation). Hard to explain, but exceedingly stable and works without additional devices. Allows time-teleportation inside moving/moved structures, across geological changes, etc. The planet could have been blown up and you would still arrive at somewhere (in space, probably, but somewhere). Basically, track the destination across time.

You say it requires a power socket. If that is the case then you had better make the power socket the reference frame otherwise it will unplug itself as soon as it starts up.

This may provide your solution. Reinforce the power socket and the lead and by that means tether the machine to the wall. That way it can travel in time but it will be prevented from travelling in space.

Keeping the tether from breaking will be the tricky part. The wall end of the lead will be travelling forward in time at a standard speed of 1. The other end will be time-travelling faster or even in a negative direction. There will be a whole new theory of physics needed to work out how the speed of time travel varies along its length.

If you can tether the machine to the wall socket then be careful going backwards in time because it will meet itself. If it stops, this will cause it to explode itself. If you are going forward in time make sure you are paying the electricity bill by direct debit and there's plenty in the bank. You don't want to get cut off.

• Depends if it uses energy constantly throughout its trip, or just instantaneously at the point of departure. It could "fire" itself through time. Or it could have batteries/capacitors that discharge gradually during the trip. Jul 23 '15 at 6:02
• It could have one burst, but then need another to slow down. Or have one burst, and then when it stops, the physical connection to the wall is what anchors you in space, not the power. Jul 24 '15 at 12:50

Naive Approach

A naive approach would be to make the time travel coordinate system be similar based on a quadruple of $[{X, Y, Z, Time}]$. This would require being able to calculate the location of the destination to a ridiculously high degree of accuracy across incredible distances, while taking into account the spin of the earth, the wobble of the earth, the orbit of the earth, the movement of the sun through the galaxy and the movement of the galaxy through the broader galactic cluster. That's really difficult for any kind of long movements. (Perhaps this might be useful to your story, to have a limitation precluding long trips?) Any other coordinate system based on a $[{0,0,0,0}]$ will have these same kinds of issues.

Brute Force

One answer proposes a 'stutter-step' approach to moving forward or backward in time. This is equivalent to calculating the 10 million Fibonacci term by first calculating from 1 to 9,999,999. It can be done but it's not elegant, when an alternative exists to calculate the 10 millionth term directly as shown in the the below equation.

$Fib(n) = \frac{1}{\sqrt(5)} ((\frac{1+\sqrt5}{2})^n-(\frac{1-\sqrt5}{2})^n)$

Let's not take the long way 'round.

Direct Calculation

Let's assume that this time machine has access to many of the other dimensions proposed by string theory and that travel by way of these other dimensions is feasible. Note that a higher dimension can "look in" on the dimension below it. A line can see all of a point. A 3rd dimension observer can see all of a 2D square. So, a 5th dimensional observer should be able to see everything contained in our $[{X, Y, Z, Time}]$ quadruple. From this 5D perspective, placing an object in a 4D location should be easy since all the information about that quadruple is open to inspection. Movement of the time machine through the 5th (or higher) dimensions to an exact destination should be instantaneous and danger free since the exact circumstances at the arrival point are known.

I've had this idea for a while, and I'm pretty sure it didn't originate with me, but here goes.

Joe's time machine travels through time at a rate, eg 1 hour outside per 1 second inside. The rate can vary, of course, but from the time machine's perspective, its transit is not instantaneous.

From outside the time machine, the machine is "present" to a degree proportional to its time-speed. For example, if the machine is travelling 110 minutes per 100 minutes it experiences, it would be visible, if a bit transparent, and would be solid...ish. At near-real-time speeds, the machine would be soft, easily damaged by a physical force. A hammer would more easily dent its metal shell than when the machine was inactive.

As the machine's time-speed got further away from real-time, from outside it would be more and more transparent and less and less solid until it was impossible to detect. From inside, it would remain 100% solid.

Because the machine is still present in the world, it would be affected by gravity and the electromagnetic forces that hold matter as we know it together. In practical terms, it would re-appear in the same geographic location that it left, because it was really there the whole time.

At first you would think that at any real time-speed, the machine's apparent weight due to gravity would crush it. But just as the machine is less present in the normal flow of time, Earth's gravity has a proportionally smaller effect on the machine. From the machine's perspective gravity remains 1G. Same thing with its contact with the ground below it.

If an object was placed where the machine was before activating, the machine would be pushed out of the way to accommodate it, but relatively slowly/weakly. So if a person walks through the space, they have almost no effect on the machine. But put a chair there and leave it in the exact same place for a few months, and the machine would feel a bump as the box "appeared" in its space.

One could also make their time machine with wheels, and drive it around while also traveling in time. For whatever features were reasonably constant, the machine could drive on them as normally as in normal time. Moving things passing through the machine would jostle it a bit, and being less noticeable as the machine traveled faster through time.

This opens up some interesting possibilities if the machine is set to travel slower than real-time. From the machine's perspective, the universe would fade and become less solid. From outside, the machine would become impossibly solid.

This also has really strange implications for traveling backwards in time, at least near the start and end points. The machine would arrive in the past instantly, and a ghost of it would exist in the same location, fading away into the future as the backwards-traveling machine decelerated to normal, forward-moving time. It would also instantly disappear from the present instantly after "accelerating" through slower than real-time (and everything that that implies).

This might make traveling backwards in time have a difficult-to-surmount barrier similar to the sound barrier for planes; early time machine prototypes simply couldn't break through the 0 seconds per 1 second barrier.

Joe discovered after some experimentation (involving a high-speed camera both inside and outside the device) that his initial prototype was jumping around because it accelerated through time too fast, and the air pushing into its space would jostle it enough to physically move it to another nearby location. It was actually worse when he made it "jump" forward by .01 seconds, because its "jump" really consisted of a sharp acceleration and another sharp deceleration, both of which had to occur in roughly .0001 seconds from the device's perspective. Once he figured out the device was experiencing time subjectively (rather than traveling instantaneously), he soon figured out how to slow the acceleration to a reasonable level, and his device started fading into existence in the same location it had faded out a few minutes prior.

• Slower than real time, from outside, the machine would become impossibly solid. I'm now picturing the black monolith in 2001:A Space Odyssey. Jul 22 '15 at 22:25
• I never understand how this idea is supposed to work. It just makes the "overlapping with other matter upon arrival" problem even worse, extending it to the entire journey.
– zeta
Jul 23 '15 at 4:01
• It's hard to imagine that the mchine should soften so much as to be "ghostlike" and allow objects to pass through it when at the same time it does not fall trhough the ground (this is a common problem with many "ghost" and "can go through walls" stories) Jul 23 '15 at 10:06

Your underlying assumption is that the machine is able to change it's time coordinate without effecting its spacial coordinate, and that it therefore get's left behind as the earth spins on its axis and orbits the sun. However, this assumes that the sun is tied the origin of the entire universe and provides a reference to some absolute coordinate system...

firstly, you have forgotten that the sun orbits the galaxy, that galaxies tend to swing around centres of gravity caused by galaxy clustering, and that all of space is expanding.

Secondly, there is no absolute coordinate system. All space and time and motion is relevant to the observer.

When 'not timetravling' our position evolves over time relative to everything else according to the rules of causality. We cannot make any intelligent prediction as to what location in space a time travel device would link to because it is a fictional device, not even loosely supported by any physical laws. HOW does it create this link? Tell me that and I can try to predict where it would end up, or how to make it turn up where you want.

My simple solution is: Assume that the time machine is affected by gravity.

Why is it that when you walk across the room you don't suddenly find yourself floating in space because the Earth has moved along its orbit around the Sun? It's because you move with it, dragged along by gravity.

Assume that the time machine doesn't literally disappear and reappear at another time, but that it moves through time, still on the Earth the whole time and affected by gravity.

Would it really work like this? I have no idea. To the best of my knowledge no one has any idea how a time machine could actually work. So for an SF story, you can make up anything that makes the story work. (Actually you can throw things in an SF story that totally contradict all known science, like saying that a starship can travel faster than light, or that a politician might live up to his campaign promises, if it helps to make the story work.)

i like BoppreH's idea of an arbitrary anchor point, but i might extend it by making the machine itself the anchor. that is to say, the 0-0-0 origin of your target time is where the machine would have been if it had not jumped through time.

for jumping into the future, that would generally be the same spot on earth. of course, things get interesting if you fail to predict an earthquake or zoning law that would have moved the machine. for the past, the origin point is simply wherever the machine was at that point in the past (making 0-0-0 a bad idea). on the other hand, collisions could be mitigated by swapping whatever happens to be in the target bubble. so when you go back in time to spot x, that stuff at spot x goes forward in time to compensate.

another alternative is to combine the arbitrary anchor object and a mean particle position. so you could target for example a gold coin. when you jump back in time far enough, you end up at the mean location of all the mass in that gold coin from before it was mined (ie underground). travelling forward in time essentially makes the coin a moving target until such time as it is melted down or otherwise destroyed.

combining all three ideas could be very interesting. imagine that when you go forward in time, the matter at your target location is swapped back in time to the present. then, to satisfy causality that matter would be forced to find it's way back to the target location over the intervening time period to form a loop. this could essentially make the target location origin simply the most likely place for all that matter to re-accumulate. quantum uncertainty would simply chose a place in a relatively predictable region much like electrons occasionally resolve into particles at a particular location. choosing locations further away from that most-likely origin could place additional strain on the predictability of the universe by forcing the matter to re-accumulate in increasingly less likely arrangements. pushing far enough away from the origin could cause quantum effects to grow to classically observable scale (e.g.spontaneous creation of particle-antiparticle pairs happening several grams at a time).

+1 for the question. I have long thought that the question of spacial coordinates to be the biggest hurdle to time travel. Who would want to travel ahead or back in time even one day and arrive in the vacuum of space?

Create a beacon

You will need actually set of four, I will call the whole set as a beacon. Beacon is located on earth and is unmovable. The time machine will align the destination with origin in space relative to the beacon. This will however limit range of when the time machine can travel. You won't be able to travel back in time before the time machine and beacons were constructed, also you won't be able to travel too far into to future either unless you solve maintenance of the beacon.

The origin is a point on the surface of the Earth (perhaps the current resting point of the time machine), and the vertical axis is aligned with the direction of the Earth's magnetic field or gravitational pull or something like that.

Maybe general relativity affects the time machine somehow - helps it work, so that would explain how it's able to detect the earth's gravity - and therefore presence - even while in transit.

The time machine may seem like it's teleporting through time, but actually there's a technobabbular phlebotonic energy-data capacitance which maintains a presence at a fixed geographic position between source and destination. Joe doesn't notice it because he is modulated into data for the journey (though he does know about it since he's the one who designed the thing), the same way as spacial teleporters don't notice their data packets being transmitted through space. The same energy-data-thingy could be moved (maybe at speed of light) for the spacial teleporter.

So the time machine doesn't have to know the position of Earth because it's being carried with Earth even as it journeys through time. It either can fix itself to the Earth as it moves or it is fixed as naturally as Joe is while standing in his garage.

For a very detailed paper on orbital paths, download the PDF here.

The following process should provide accurate enough coordinates provided Joe stays on Earth and doesn't travel more than 50,000 years from present day. If this isn't good enough for Joe, I suggest he use what he has to befriend Stephen Hawking.

1. Calculate the Milky Way's position. Wikipedia provides methods for 2 common frames of reference.

2. The Sun's orbit around the Milky Way is circular, with a diameter of 26,000 light years and a speed of 782,000 km/hour.

3. Find Earth's orbital position: Eccentricity is currently 0.017, and this should remain true for 50,000 years in either direction from now.

4. The destination's position relative to the center of the Earth is a vector with a length of the Earth's radius (6371 km) + destination's altitude above sea level. The angle of the vector is based on time of day (milliseconds passed / 86,400,000 x 360).

If you've kept your frames of reference straight the whole way through, you should have the correct rotation so that your initial velocity matches that of Earth's where you arrive. I think. To be safe, double check with Hawking.

What if you simply break your trips into multiple parts. Build a spaceship around your time machine. It doesn't need to be fancy, just a pressure vessel with some external cameras on it and a power source. Now whenever you need to travel a substantial amount of time, jump to the time you want, but simply ballpark your coordinates in space to be somewhere nearby Earth. You'll wind up somewhere in near Earth space. Then after a few seconds the time machine can get its bearings using the external cameras and will calculate the relative positioning and velocity of wherever it wants to go and make a microsecond jump to teleport to that place.

So you make one long jump forward or backwards in time which will be relatively easy because you can use estimates of your targets position to make sure you show up near it but not in it. Then you make a short lateral hop through space once you have calculated your target's exact relative position and velocity.

For traveling super long distances in space and time you can split the trip into as many jumps as necessary to make sure you don't get lost or wind up in the center of a sun.

• Don't forget he's Joe, the regular guy. He doesn't have access to fancy equipment or technology. Anyhow, to build on your idea, the vessel would need a power source (for the jumps and cameras), air, temperature control, etc. This would inquire big costs for poor Joe, not to mention that the device itself would need a lot more power to encompass the bigger vessel. Jul 22 '15 at 14:46
• Won't the time machine always have to bring a power source with it if travels to any place and time that doesn't have a wall outlet? Life support is optional because ideally you would only be in space for a few seconds at most so you don't need to worry about CO2 buildup or heating or cooling. The biggest costs in terms of size and complexity would be the external cameras and the computers to perform the calculations which would need to be very technologically advanced, but you could always make your first jump, take pictures, then hop back and do the calculations at home. Jul 22 '15 at 16:51

If you can let go of the "instantaneous" experience of the contents of the machine as it travels through time, then instead of programming spatial coordinates to "jump" to, a traveller could simply pilot the machine and adjust its position as they observe the world change around them.

This assures your machine won't end up e.g. phasing into a rock formation that's been long eroded (and therefore couldn't be accounted for in data available in the present), as well as assuring it's still on the planet and ends up precisely where it's intended too. Furthermore, with this approach time travel isn't limited by something as dry as the traveller's abstract mathematical skills (or reliance on a supercomputer) and confidence in data, but instead by the traveler's ability to observe, react, and navigate as the world changes around them.

In a previous answer I mused on how a time travel machine would stay put.

Even if your time machine idea doesn't work that way, it is a good way to plot coordinates. Similarly to how time for space travel is defined as the center of the sun imagined as a point mass (or something like that) you need the same way of noting time at different gravitational potentials and velocities. In fact, space travel has a position system too. Why not just adopt the same system?

Similar to the other answers, you want your co-ordinate system to be relative in some way. The intuitive answer, especially for Joe, would be to have it relative to your current position. However as the other questions point out, how do you define where your current position will be in t time.

Instead of co-ordinates measured as a single $[x,y,z,t]$ vector, I suggest that you calculate your future position as the sum of all forces acting upon the device modelled for time t.

Each of these forces would be modelled as either relative to a point, e.g. gravitational forces relative to the center of mass of their bodies, or acting from a constant relative direction e.g. a push.

This should take into account the 'general case' however if anything unpredicted occurs such as foreign bodies hitting the earth and changing it's orbit or sea levels changing, cliffs being eroded. Then Joe could find himself in a sticky situation. But that's more likely to give you some nice plot/discussion points.

If Joe wishes to adjust his future/past location, he should specify a force which will move that location as desired.

Calculating the coordinate may be hard. But there is a way to avoid needing to calculate. If you do not move too fast in time you can drive to your destination like a car would in fast forwarded movie. This is also easy to automate even with very low tech equipment.

Others have suggested similar things but not exactly in these words, or reasoning. My point being that this is how i would approach the problem at least until I get enough experience in predicting and verifying that my predictions are correct. I would like to avoid finding myself 1/2 rotation of earth, or even outside the solar system. Who knows what can happen in this move, or how it might react to coordinates.

Sure this would limit the viability and speed of general teleporting. But lets face it, you are much happier if you get there in one piece. Rather than lost in space, or worse.

Be cautious.

Here's a thought- have a few trials where your device blinks out of time/space for a set period with a beacon, each trial being a different length of time. Acquire that signal upon reentry and begin building a non relative map of the local universe.

• How would that solve OP's problem?
– L.Dutch
Oct 5 '19 at 14:24