According to Einstein’s theory of General Relativity, clocks run slower in gravity fields. The stronger the gravity, the slower the rate of time. But there are two components to gravity: the “gravitational potential” and the “gravitational field” – the latter is how fast objects accelerate when dropped, which on earth is around 9.8 m/s^2. Both are related to each other in the following way: gravitational field is the negative gradient of the gravitational potential. This means objects only accelerate when the gravitational potential varies over some distance. So the question arises, is gravitational time dilation due to the potential or the field? Most physicists would say “Why does it matter?” and I say “You have no idea how much it matters.” The answer, by the way, is evident in the following equation from General Relativity:
The term GM/R is basically the gravitational potential. This means time dilation depends on the potential. It also means each height above the surface of the earth (or distance from the center of the earth) happens to have its own time rate, and because these time rates vary with height, objects fall downward – toward the area of slower time rate. It may be said that acceleration is due to a time rate gradient.
But what if the gravitational potential does not change with distance? Say you produced a uniform potential field in an area – then there is no gradient, and thus there is nothing tugging on objects to accelerate them. And yet, according to the equation above, the time rate would be affected. This means the time rate of anything caught in such a field can be modulated without imparting any gravitational forces upon them. The gravitational potential at where you are sitting right now could be fluctuating and you won’t feel a thing. To make an analogy, the potential is like air pressure and field is like wind – it takes a difference of air pressure to produce wind. But if the pressure in a room is uniformly increased and decreased over time, even a feather resting on a table won’t stir.
What if gravity waves are not pulses in the gravity field but rather pulses in a uniform gravitational potential? Then these proposed billion dollar gravity wave detectors are defunct. Besides, Greg Hodowanec’s gravity wave detectors are far better suited for the job and can be built with ten bucks and a trip to RadioShack.
So this brings us to the issue of time travel. When modern science talks about time travel in context of General Relativity, it always involves black holes since these have intense gravitational fields and thus intense time warping characteristics. “Sure, it would be nice to time travel but oops, you’ll get torn apart in the process.” Not necessarily so. If you have just as intense a gravitational potential but remove the gradient, you can have just as much time warping minus the extreme forces. You could cut your time rate in half without spilling your coffee.
Of course, one might wonder how exactly does one produce a gradient-free gravitational potential? Seek and ye shall find.
