Relative Gravity

previous experiments shown the small velocity up to the speed of light is created in a reference are created by imaginary shift. what will be happening if if the shift was real. it makes us feel that the motion in space axis is imaginary, for any real time. until this is not making any change in space axis in real, we cannot expect a velocity. but If the imaginary motion of an object is identified as real by an observer, here observer start to see the object is moving in space with a velocity.

From the earlier calculation it is clear that the measurement of velocity can vary for objects with the dependency on the frame, at larger distance in space, the matter tends to avoid dependency and hence resulting a larger velocity, if you are a believer of velocity it can lead you to pseudo repulsion. actually it is not happening. but you consider the shift in axis you will know that velocity is not an absolute scale of measurement but it is a property of shift.

Based on previous observations, when we tends to calculate the velocities of different matter at different state of dependency. we use the same two co-ordinate system.

CASE 1
consider three identities.
1) Absolute reference frame , A : it will control other two identities.
2) Observer, O: he is measuring the velocity of the next identity while depend on A with shift θ
3) Body (B): as O it is depend on A with a shift α
lets find out the measured velocity of B with respect to O.

From the first experiment of measuring motion and plotting in a two co-ordinate system, we identify that dependent object to the reference will adjust its time so that the plotted value of time of body(b) to time of reference will be same as the time of reference. so we can say any dependent matter is aligning on the time of reference, never escape from it. this explaining, why we have only the sense of three co-ordinate. Even if time is a co-ordinate no matter can move away or behind from the time of reference, it always stay with the time of the reference.

we can assume that, the size of a moving body(accelerating) will not be reduced when measured from the reference, while the body itself feel an increase of length.

you can see that in the case of a dependent motion, the observer is the reference and everything else is trying to be synchronized with observers time, which is achieved by reducing/increasing the speed of the clock. so the measurement by a body in dependency with reference observer with a shift not equal to zero, cannot observe what is actually happening, but it can by, calculating the reference's observation.

velocity = dx/du = tan(θ)

Note: here the velocity is unit less quantity, we just measure the ration of distance traveled in space to distance traveled in time.

d^2 = (dx)^2 + (dy)^2 + (dz)^2 + (du)^2
our new unit du is now measured like any length, and an imaginary quantity for any real time. we call it 'distance in time'.