This is my first time posting on this site. I am a computer programmer that stumbled across a physics text book and have a question on special relativity. So firstly, I understand that there is no preferential inertial frame of reference. Secondly, as a A body travels faster relative to another body B at rest, body A experiences time dilation, effectively resulting in a forward jump in time. Thirdly, the speed at which a body in relative motion can travel is limited by the speed of light (c).
Due to the the first premise (that there is no preferential frame), could we not also argue that the body at rest is actually travelling at a negative velocity relative to the other body? Thus, if we consider the situation in from this reversed perspective, a time contraction is then experienced to the body moving at relative negative velocity. For instance, if we consider a person on Earth as being at rest (0 km/h), then could we think of a person standing on Pluto (which has an orbital velocity of 0.159 relative to Earch) as having a negative velocity relative to that of the person stationary on the surface of Earth, thus experiencing time contraction relative to the time experienced on Earth?
This can be confirmed by substituting a negative value in the standard time dilation equation for u^2. This results in a value greater than 1 occurring as the divisor, causing the numerator to 'shrink' in value, thus resulting in a 'time contraction' rather than time dilation.
With some searching, I have come across a number of examples of time dilation. However, all of them seem to assume that a body on rest is traveling at 0 km/h. Rather, I argue that such a body would be 'relatively' at rest, as from a greater perspective, this body is subject to the turning of the Earth about its axis, the movement of the Earth along its orbit around the Sun, the Sun around the Milky Way, and finally the Milky Way away from other galaxies due to the expansion of the universe.
If my above reasoning is correct, then it seems that if there was a body moving at 0 km/h relative to the expansion of the universe, then the Earth would be travelling faster than that body, which means that the Earth would experience time dilation relative to this body, and that body would experience time contraction relative to the Earth. If time dilation equates to a forward jump in time, then it stands to reason that time contraction would likewise equate to a backwards jump in time. Although, it occurs to me that perhaps it is more useful to not think of the body moving backwards in time, but rather to think of it as being stationary relative to the expansion of space-time, thus time is moving forward past the body experiencing time contraction.
I know I am not a physicist, but I was wondering if anyone could tell me if my above speculations are correct, or that I'm an idiot, or if all of this is already well documented somewhere (which I have yet to discover).
Any clarification would be greatly appreciated.