Physicist have said that if you were going the speed of light time would elapse faster off the moving object you are on than on it.So the reverse would be true if you went slower.Meaning less time would elapse when the object you are
You've got that almost correct but not quite.
You start with the Principle of Relativity. This principle of physics states that the laws of physics are the same in all allowable frames of reference.
In Special Relativity the allowable frames are
inertial frames of reference even though the bodies under observation may not be traveling at the same velocity with respect to each other. By an inertial frame we mean unaccelerated. Unaccelerated means moving at a uniform speed with no unbalanced forces acting on the bodies - they don't speed up, slow down, change direction or spin. No unbalanced forces includes no gravitational field.
The equations of Special Relativity state that duplicate clocks brought together and synchronized will desynchronize if they end up traveling at different speeds relative to each other. While the clocks are traveling in their inertial frames, observers traveling with the clocks will each note that their clock is accurately keeping time while the other clock is not. The other clock appears to be running slow. They say that because in a true inertial frame each observer can correctly state that it is the other guy who is moving, not himself. That is because there are no accelerating forces that they can feel (because there
are no accelerating forces acting on them).
Thus each observer can rightfully state they they are at rest and that it is the other guy who is moving. They base that opinion on the accuracy of their clock. Why do they believe that their clock is accurate? Because everything, not just the clocks, moving along with them is affected. The atoms oin their bodies are affected. The rate of nuclear decay is affected. The speed of neurotransmission is affected. Everything that would otherwise give them an environmental clue about the situation is affected in the precise proportion as given in the equations of Special Relativity such that there is no possible experiment, not even in theory, that they can run in their frame that will tip them off as to who is moving and who is at rest.
By now you can see the issue. Traveling at
any velocity relative to another observer will cause the time dilation effect. As they approach a relative velocity near the speed of light the effect starts increasing exponentially and becomes very obvious, at least in our
gedankenexperiment. In the real world you wouldn't be able to communicate with each other because, well, you'd be moving away from each other at near the speed of light.
But Special Relativity is called "special" for a very good reason. It is a limiting case that can't actually be accomplished in its purest form. In the above scenario where we initially synchronized the clocks we skipped a piece of history to get to our inertial frame where the observers were traveling at near the speed of light. One or both of the observers had to be accelerated in order for them to have the relative velocity. The observer who felt the accelerating force (or the one who felt the greatest accelerating force) is the one who, when they come back together, stop (again feeling an accelerating force) and compare clocks is the one who will have the clock that ran the slowest. Thus the paradox in the Twins Paradox is resolved. There
is no paradox.
But going slow will not make up the "lost" time for either of them. Traveling at any relative velocity, slow or fast, will have the same effect. The totality of the effect will be determined by the magnitude of the speed and the duration of time they endured the speed differential.
