I don’t usually get in to philosophical scientific stuff here, but this was just too fun to write about…
image of flux capacitor intended as a joke – time dilation not included
There is a certain problem with time travel that a software engineer or sys admin will automatically understand. It has to do with relative versus absolute paths. As mentioned in the title, this applies to instantaneous time travel (time travel via time dilation does not experience this problem).
This realization came up while having an aviation discussion with AgentM regarding GPS. Somehow the idea of flying a small aircraft from today, 1,000 years in the future without GPS for navigation, came up. That led to time travel…
The problem is that the universe and everything in it is moving. A point along the equator moves, relative to the center of the earth, at 1,040 miles per hour. This means traveling 30 seconds backwards or forwards in time, to the same absolute path in space, would result in a spacial jump relative to the starting point of 8.67 miles (1,040 mph / 60 minutes in an hour / 60 seconds in a minute x 30 seconds).
All values for speeds acquired from RASC Calgary Centre. Their page on ‘how fast?’ is an awesome resource.
That’s only relative to the earth – The earth is moving through space relative to the Big Bang’s origin at 1,342,000 miles per hour. A jump in time of only a single second, with a constant absolute spacial path, puts you off course by 372.8 miles (probably miles above or below the earths surface in the process).
Let’s go back to calculus for a moment. Remember limits of functions at infinity? This is how one solves the spacial challenge of instantaneous time travel. For those who left their calculus books at home, this limit describes change as a function approaches an instant (usually as time or speed approach infinity or zero).
This becomes challenging to apply to instantaneous time travel because all physical movements known to man result in an instantaneous speed of zero. As proof, take the earths movement of 1,342,000 mph (a pretty high velocity) and divide it by infinity (what would happen at an instantaneous point in time). You get a speed of zero. Kind of like taking a picture at 1/5,000 of a second… Most everything stops. Except this is 1/infinity of a second.
This speed of zero is your relative path. A relative path of zero means your absolute path does not change, and therefore you remain in the same location while the rest of universe kept moving. A major problem.
To solve the spacial challenge of instantaneous time travel (and so you can land in the same place you jumped) one must have an instantaneous relative path that equals the function of one’s present location’s relative path to all universal factors.
Such universal factors include, but are not limited to, the earth’s rotation, the earths revolutions in the solar system, the solar systems rotation in the galaxy, and the galaxies movement in universe. Additionally, forces like black holes, comets, gravitational forces of satellites, and wind direction need to be considered.
This function becomes incredibly complicated, but let’s assume we will be capable of such calculations at or before we’re capable of making a human’s instantaneous velocity 1,342,000 mph. Manipulation of such a relative path would allow one to come out of instantaneous time travel in a completely different location, effectively teleporting.
Put simply, for successful time travel and/or teleportation, calculating the instantaneous velocity will be necessary.
I was thinking about another factor. The Earth's orbit around the Sun is not a perfect circle, it's elliptical. As I remember from my astrodynamics class, a body in orbit will sweep the same area in the same amount of time, which means in order to do that, the object must accelerate and decelerate during it's orbit. What's this mean? Well, lets say you're flying along in your fancy C-210 time machine going 150kts, and you decide to visit a specific date 1000 years in the future, assuming you factored in everything above and didn't time travel into space, you will now be subject to the difference between relative speed of the Earth's motion now and 1000 years from now.
If you leave Earth at it's fastest orbital speed (rounded down to 58315kts), and appeared in future Earth at it's slowest orbital speed (rounded down to 56,935kts), your new airspeed will be 1380kts… right before the plane rips apart and you wish you made a parachute from an old sheet. Reversing that scenario, you would be flying backwards at that speed… err, I mean breaking up at that speed.
You mentioned teleportation, in theory it's possible with quantum entanglement, but that's only in the current space-time. The problem it brings up is even if you could make the second quantum state go through time, how do you know where to place your next quantum state without going there first? You would risk *teletimetravelporting* into a kite some jerk is flying, last time I checked, a kite wasn't healthy to embed in your spine. So, the point of that is you would definitely want to time travel in space where your chances of embedding matter into yourself are far less, which means you need a spacecraft… and even then, there's no guarantee that you will not embed yourself into a defunct Filipino satellite (yes, in 1000 years they may have a space program).
You've outlined the difficulties very well. Instantaneous time travel is just a Bad Idea, because so many factors increase your chances of error unacceptably. If time travel can happen, it will have to involve time dilation, as you mentioned. Which is the reason most people give for having never seen a time traveller. (Which is of course, a pointless answer, because someone who asks “If time travel was possible, why haven't we ever seen a time traveller?” is really just looking for a convenient way to end the conversation.)
Instantaneous time travel is probable, given a technological achievement beyond the capability of any species within our universe (using the big bang as the starting point, it's probable that no species has acquired enough knowledge to attain this technological achievement). Of course, this requires acceptance that we're at the most future possible point in time and that future events can not happen ahead of our present time (yet).
If you accept that we're on the edge of the future and no events have happened beyond our present moment, the answer to “why hasn't anyone seen a time traveler?” is simple: Humans, even other species, haven't invented it yet.
If you believe future events have already taken place and time travel has already been invented in the future, the answer is also simple (albeit frightening): The human species won't survive to experience time travel.