But when people refer to time travel, they generally mean arbitrary travel to nonsequential points in time. Going from 22:00 today to 17:00 yesterday to 10:00 today.
The difference here is between floating down a river with a strong current and being able to slow down or speed up your progress a bit (the restricted sense of "time travel" that you mentioned), and taking a ship out onto the ocean and going where you want (the more typical use of the term "time travel").
If you wish to call that time travel, you may. I guess people just reserve the term "time travel" for travel backwards in time, since that is so much cooler.
Technically, we're all traveling through time. In your case, you would simply be moving a little faster.
When I jump I push the entire universe down by about 30cm.
Makes the maths a reall bugger to work out though.
What is time on an atomic level? It's the speed at which interaction occur, transfer of energy mainly.
When you move at relativistic speeds those interactions occur "slower" (which is a self referential statement, but nothing I can do about that).
But you do not travel though time - you don't travel at all. The various forces that affect you work slower. It's like slowing down the motor of an assembly line robot. You are not moving through time just that things that you are made of do their thing less often.
Since you are moving slower, the rest of the word seems to move faster.
Which is why time travel is impossible - there is no place to travel to.
If two people program 60 lines of code per hour, one does so in a spaceship traveling nearly the speed of light and one does so on earth... after 1 year/365 days/8760 hrs they make a report on their progress and they don't have the same results? If a watch ticks every second, the faster you go the slower it ticks? Why? How?
Will people be buying a 2100 model Bugatti, hiring a driver, and working in the passenger seat to be more productive?
So, each person experiences 1 second ticking as normal, but if you were to look at both watches together, one would be much, much slower than the other.
This has actually been proven by syncing atomic clocks and putting one on the space shuttle. The one on the shuttle comes back showing a time a few milliseconds less than the one on the ground.
They'll be very slightly less productive in that situation because time has slowed down for them. For everyone sitting at home, time moves 1 second every 1 second. For passenger in Bugatti, a stopwatch says 0.99999* second for every 1 second felt by everyone else. So what feels 1 second to the passenger is 1/0.99999 = 1.000001 to everyone else. Hence he's actually slower.
When person A finishes (say a week later) and comes back, he'll find that person B finished "a long time ago." That is, person B finished, and then waited till person A came back (say for a year, depending on how fast person B was going).
What happened? Time went at different speeds for each person. They each took a week from their own point of view!
Which one is right? Both of them. Thats what relativity says. There is not one thing called "time" but that its "relative" (hence the name).
So, if your going to choose to hire one of them... you'd hire person B (assuming your business is on Earth).
You can also "time travel" by moving to an area of higher gravity (per general relativity). Time travels more slowly for you there, so you can let your original location get ahead of you, then go back there to effectively travel to "the future".
Of course, gravitational time dilation is a tiny effect, so you'd have to get near something unhealthy like a black hole to notice much difference.
Relativity states that time slows down as you approach the speed of light. Given that fact, lets say I hop in a spaceship and zip around the earth at near light speed for several years (Yes, I know there are problems with this in terms of increased mass, energy needed, etc.) Ok, so after several years I slow down and land. For me, it seems as if I've traveled into the future becasue the people on earth have experienced more time than I have.
How is that not time travel, at least in a functional sense? I get that by strict definition it may not be, but the result would be the same. It seems like in this sense time travel is not only possible but proven.