Use Minkowski metric to define space-time interval (proper time interval ) as the time interval ( aging interval), the moving atomic clock time interval with its displacement interval, will be the same aging interval as the Lorentz transform shows time dilation of the different atomic clocks. Local frame atomic clock time interval dilation between frames , but no aging dilation between frames. NO TWIN PARDOX Please tell me why I am wrong?

Donald, I'm still learning so I might be wrong, but I think the light clock is exempt from aging whereas a mechanical clock would not work because it would be affected. This is why the light clock was used rather then a mechanical clock. Light has no elements of time or space. That's why it works.

Did you want to say that the increase in the " space interval " of that object which is moving is being converted into the decrease in the " time elapsed "(dilated time)for that object ?

Wow. Just wow. Can't imagine a more brilliant, lucid way of explanation!

Yes, in fact it is considered that all of us are moving at the speed of light in the space-time.We mainly use that speed to travel through time but when we divert some of the speed in the space dimension we loose speed in the time dimension. Only light and massless particles are the one allowed to divert all of its speed in the space dimension.