Hi Ralfcis,
You have already accepted the Centrifuge Experiment. It clearly demonstrates the Twin Paradox. It has no changing delay between Center and Arm Clocks because the distance between them is a constant and it has no Doppler Effects for the same reason. All it does have is two clocks running with different Dilation Factors in the same room. Thus the Dilation is due to the difference in space path lengths each clock travels in the Frame of the Room subjected to the same Real Time. Of course I'm misusing the term "Frame" as Relativity only considers a Shared Frame to mean Same Velocity relative to Light Speed.
Ralfcis wrote:Ouch, loose language sinks meaning. Everyone in a constant velocity frame, no matter what that constant velocity, is aging at the same rate (which is called the speed of light through time in relativity).
I think you meant:
"
Ouch, loose language sinks meaning. Everyone in a constant velocity frame, no matter what that constant velocity, is aging at the same Constant rate (which is called the speed of light through time in relativity)."
I added the word "Constant" because your expression implies the word "Identical". Different Velocities = Different Dilations = Different Clock Rates. That's all the Lorentz Dilation Equation tells us.
Or you could have said:
"
Ouch, loose language sinks meaning. Everyone in a constant Shared velocity frame, no matter what that constant velocity, is aging at the same rate (which is called the speed of light through time in relativity)."
I added the word "Shared" to make your statement accurate.
In a Universe where everything is moving at potentially different Velocities then the only Anchor that Einstein and Company could use for a constant reference is Light Speed. Thus: all speeds from 0 to c must be Relative to Light Speed. Just knowing the Differential Speed between two objects is insufficient information to compute their Clock Differential simply because the Lorentz Equation is Non-Linear.
For example: If Alice and Charlie had a speed differential of 24% of c and Alice was stationary then the Dilation differential is just based on Charlie going 24% of c. (a very small Dilation differential). Now kick Alice up to 75% of Light Speed and Charlie is still faster by the same 24%, then Alice is moving at 75% Light Speed and Charlie is at 99% Light Speed. Now the differentials in their respective Dilation's is Huge between them even though the differential is the same as when Alice was stationary and Charlie was 24% c. Why? Because the Lorentz Equation is Non-Linear and only cares about absolute velocity relative to Light Speed for a single object. Thus simple Math Problems in Relativity are bogus if the only information used is Differential Velocities between two objects. And that's the aspect that gets glossed over.
Prove it to yourself. Use the Lorentz Equation and find that the dilation's are:
(mps = miles per second)
Alice = 1 (speed=0 mps)
Charlie = 1.0300116938564743 (speed=44640 mps)
Now keeping the same differential speeds for Alice at 75% Light Speed and Charlie at 99% c:
Alice = 1.5089219472021371 (speed=139500 mps)
Charlie = 6.612614772453471 (speed=184149 mps)
The speed difference is a constant 44640 mps.. but with two very different dilation results based on their absolute velocities. That's the effect of using a non-linear equation.
That's what gets glossed over in Relativity Problems. They give you two different Velocities to compute the clock differentials while not stating these are actually absolute velocities while pretending all that matters is the differential in the two Velocities. Either that or the Lorentz Equation is wrong.. take your pick.
Anyway, all this shows that Clocks only Measure Local Time passage and are 1:1 with Local Aging. That's why I say clocks don't measure Real Time, just local passage of Time totally dependent on their Absolute Velocity through Space.
So to answer the Question of the OP:
Clocks measure the local passage of Time but act more like local speedometers.
Real Time is the Birds Eye view perspective connected to the Universes natural progression toward the future. The Arrow of Time is connected to this natural forward progression.
To explain where this natural progression forward in Real Time comes from.. would take us into Personal Theories and I won't go there on this Forum. Hopefully.. I've logically answered the OP at the cost of making a bunch of Relativists a bit angry at me.. lol.
Some Relativists may debate that the Centrifuge Experiment violates Relativity as it is composed of an infinite series of Frames due to Acceleration aspects caused by Rotation. Duh.. That can be worked out mathematically and is what I meant earlier when I said roughly: "after the Math dust settles".
Finally, that Gravity affects clocks means there is a connection between Gravity and Velocity. I could explain what that connection is but once again.. that would take us into Personal Theories and is a No-No on this Forum.
Otherwise, what I've said on this Thread is logically (and mathematically) sound and supported within. I see no reason to drag in external authorities given the internal format and logic I have used.
Ok, have to get to work.. Later.
Best wishes all,
Dave :^)