Hahahaha I was able to resist peeking at what the mathless M's had to say so I will continue unfazed.
Physics is the correlation of patterns in physical phenomena to mathematical pattern recognition resulting in mathematical formulae. Here is a depiction of time dilation from Alice's perspective using her lines of perspective simultaneity at .6c.
You'll notice the turnaround point causes a sweep of lines while the slope of the lines of perspective simultaneity changes. (Perspective simultaneity is the same as relativity of simultaneity.) You'll also notice the top is the mirror image of the bottom.
Here is a depiction of age difference using lines of causal simultaneity.
Causal time has no perspective; there's no ambiguity of what event happened first. It may join all the same sync'd proper times but it is not a universal or absolute or Newtonian time but it is instantaneous with the speed of light delays stripped away and time laid bare. When one initiates a change in relative velocity, causal time is disturbed between the two parties. The result of the disturbance is that the purple lines of causal simultaneity is their spacing changes during the time of relative velocity imbalance and changes again after a new constant relative velocity is established between the parties.. (The green half speed lines of perspective simultaneity are drawn in to show they are the same as the purple lines.) The changes in spacing between the lines corresponds to shifts in the rate of causal time due to Alice's change in relative velocity and then Bob and Alice later agreeing on that change. A change in rate of time is a change in causal velocity through time but people have a real problem in understanding that time has a rate or velocity through time (ct'/ct). They just can't get that looking at a movie in fast forward or slow motion is looking at it through 2 different velocities through time and that the normal rate of time (pressing the play button) is c through time. You can watch a 2hr movie in an hour at fast forward and you can see Alice's televised motion at twice the speed of light time rate through time when she's going at .6c through space in the exact same way.
The numbering of Bob's time line is not affected by the disturbance in causal time so reciprocal time dilation is unaffected. But causal time uses a distorted numbering (purple numbers) of Bob's time line. It starts out the same but the change in relative velocity by Alice causes Bob's time numbers to change according to what was seen in the large STD using half speed lines of reciprocal simultaneity to determine age difference. Notice the swing of the purple line slope does not cause any age change in Bob throughout the swing. This means acceleration has no affect on ageing at the causal time level.
Here is an STD with Bob's blue lines of perspective simultaneity, Alice's red lines of perspective simultaneity, the green lines of half speed perspective simultaneity (difficult to see because they overlap all but 2 of the purple lines), and the purple lines of causal simultaneity which is independent of perspective.
Edited by ralfcis, 12 March 2019 - 07:30 AM.