If the same temporal effect occurs everywhere, e.g. all clocks run faster/slower, then it makes no difference, and, arguably, is meaningless. Time is only meaningfully faster or slower relative to some other comparable frame of reference.
Yet that’s why you ignore the facts. As I showed earlier. If you start with 100 units and it decays 2 units per year and then 10 years later accelerate, you used 20 units in 10 years of time. If then because of your increase in velocity it now decays at 1 unit per year and after 10 years you take a measurement, that is 10 units.
So you measure 30 units of decay, but it happened in 20 units of time. Not 30 units of time based upon the flawed belief it was always the same.
The twin can pretend like you he’s not aging slower, but relativity tells the lie to that belief. He’s aging slower weather he chooses to recognize it or not. Reality never changes, just your perception of what is reality. The twin ages slower regardless if he thinks he does or not, or even if he is totally unaware of it.
Again, we are not concerned with the rate decay happens now, but how it once did. Without factoring in the increased decay rate in the past, all your answers are flawed, as the math clearly shows, regardless that cognitive dissonance blinds you to it.
And they don't all run the same everywhere. As Einstein told you only when a system of coordinates K is chosen so that, in relation to it, physical laws hold good in their simplest form, the same laws hold good in relation to any other system of coordinates K' moving in uniform translation relatively to K.
Only when systems moving with the same approximate velocity is time close to being the same.
He also told you that The laws of motion in non-inertial frames do not take the simple form they do in inertial frames, and the laws vary from frame to frame depending on the acceleration. In a curved spacetime all frames are non-inertial. Gravity produces the same effect as acceleration.
In cosmological terms, we can see the Doppler time dilation of galaxies moving away from us and compare the rate of time we observe here with the rate we observe there (and they can look at us and see exactly the same effect).
Please, light travels at c regardless of the frame of reference. The twin in motion sees light travel at c just like the stationary frame. And he still aged slower. Your reasoning is flawed. Both twins see the same thing but neither of their time runs the same. Even Einstein admitted the futility of trying to sync clocks at distance.
You simply have no logical reason why light travels at c because they don't have one. Perhaps one day I will explain to you why light always travels at c regardless of velocity. Hint, its the same reason constants stay constant despite using longer or shorter ticks of time and rulers to measure them....
In terms of the ageing of bodies within the reference frame of, for example, the solar system (or the galaxy), local ('proper') time is well-defined as a reference against which frames in relative motion are compared. Proper time is the time in the frame in which the objects of interest are at rest. So to say that the proper time can vary with respect to the contents of that frame is meaningless.
You aren’t at rest despite every device saying you are. The objects of interest aren’t at rest either. In fact, no object can detect its own motion from inside its coordinate frame.
So let’s see, the GPS which is part of the galaxies local frame just as we are, has clocks which run at a different rate than ours. Your beliefs don’t seem to match reality.
Also, since the accelerating expansion of the universe is due to a scalar change in the metric (i.e. space itself is expanding), galaxies are not accelerating through space, so they maintain their inertial frames and there is no observable relativistic time dilation, only Doppler time dilation.
Yah, I was wondering when you would get to Fairie Dust to try to ignore observations. If redshift is due to the expansion of space and not recessional velocity, then Hubble’s law is useless and can’t be used to judge distance. But distance is based on Hubble’s law and the correlation between recessional velocity and distance.
If we were to divide a river up so it flowed in two directions or all, even though two ships would have no motion with respect to the water itself, they would still be accelerating away from one another and the energy of the river would be imparted to them.
But it’s the flawed belief in what redshift actually is that leads them to propose the magical expansion of nothing......
And if the scale of space is changing, then you doubly can not measure distance. You have nothing to verify any distance redshift relation to any magical expansion. Only recessional velocity as is proven in the laboratory unlike claims of Fairie Dust.
That’s why you must constantly switch back and forth between recessional velocity and expansion, else the absurdity would be apparent to everyone.