Einstein once said, "Time is what clocks measure." He was only partly right, time is also partly measured by distance separation. This is already self-evident in Don Lincoln's statement, "every object is always travelling through spacetime (not space) at the speed of light. The more velocity it has in space, the less velocity it has in time."
I will show time does not vanish from the face of a time dilated clock, it gets converted into distance separation. Furthermore, if space is indeed a form of time, there is no need for a separate concept of length contraction so it won't be included in these calculations.
Here is a classic STD (spacetime diagram) depicting the twin paradox of Alice at .6c relative to Bob on earth, going out 3 light years and then returning. Bob is depicted as stationary and Alice as moving but in fact both are moving from each others perspective. A single STD cannot properly depict relative velocity and workarounds must be employed to overcome this limitation.
Bob is the blue t-axis and Alice is the red time dilated t'-axis according to the formula t=Yt'. Y is 1.25 at .6c. The blue horizontal line is a line of simultaneity from Bob's perspective and the red is from Alice's perspective. These lines all have the same clock reading to create an artificial present. There's no way for Bob to see what happened across the universe when his clock hits 5 until all the clocks on his line report back to him by the speed of light delay. It's not a true instantaneous present but more of a staggered delayed present showing all events across space that were simultaneous to a particular perspective's particular clock reading (Bob time t=5 in this case).
There is an instantaneous present represented by the purple line. Each frame in the universe is stationary from its own perspective and its own atomic clock ticks out the same proper time at the same time rate. The clocks need to be sync'd at some point but after that, the universal accuracy of atomic clocks takes over and they do not require constant correction and re-syncing. Separation and relative velocity cause the clocks to have different readings from different perspectives. The clock readings do not tell the whole time, some of the time is hidden as distance measurement.
Bob's blue line, where every clock says 5, meets Alice at the 3 ly mark and her clock says 4 even though both clocks started out as 0. The part that's not accounted for is the distance separation has a time value of 1 from Bob's perspective according to the formula
t2=t'2+x2 , t'=t/Y
t=5, t'=4 and x=3 in this example.
the time component of distance at t'=4 is tx=t-t' =1
We can do the same analysis without having to redraw Alice's perspective as stationary.
t2/Y2=(t'2+x2 )/Y2 , t'=t/Y so
t'2=(t'2+x2)Y2 , t"=t'/Y so
Y2t'2=Y2t"2+x2 so from Alice's perspective
t'2=t"2+x2/Y2 and t'x=(t-t')/Y
Alice's t'=4, t"=3.2, x=3 and t'x=.8 which is the distance's contribution to the total time.
I could have just stated t'x=tx/Y but I wanted to show the calculations from both perspectives start out with the same basic formula and that the x2/Y2 component may look like length contraction but it's just a ratio from the derivation. It means nothing special.
Alice at t'=4 has lines that associate it with 3 different Bob times. This does not mean Alice at t'=4 is simultaneously equal to Bob t=5, 4 and 3.2. Alice t'=4 means 3 different things based on whether its from Bob's or her perspective or from the universal instantaneous perspective (which relativity does not formally recognize but I do for ralfativity).
The concept to take away from here is that a clock reading does not tell the whole story about what time it is. Each perspective has it's own clock reading of the delayed present that needs to be corrected by distance's contribution to time. Also there is an instantaneous present that is independent of perspective and connects all proper time readings within all frames.
In future discussions there will also be a perspective based present that is the same as the instantaneous present. The perspective is from an intermediate equal relative velocity to both participants. For example, this perspective would be a line at .33c in the STD above. Not important now.
The next topic will be how Alice's perspective is drawn differently in ralfativity and relativity.
Ralfativity Topic 2: Space is a Form of Time
Re: Ralfativity topic 2: Space is a form of time.
