Time dilation is based on clock time.
Clock time is the time we measure with when doing experiments.
It is also the time according to our eyes.
In clock time, the speed of light is constant.
Most of Physics study is done using clock time.
Things age, and happen more slowly when the local rate of Clock Time is slower that the rate of Clock Time it is being compared with.
STR and GTR are theories based on on Clock Time
Clock Time theories tell us what we will see and what is happening according to our clocks.
There is an underlying time that natural activity is synchronised to - real time. One that is constant everywhere, and in which energy and momentum are independent and the speed of light is variable. It's rate is something like the rate of Earth's rotation, but without the fluctuations. A theory based on this interpretation of time can complement GR quite nicely.
Time Dilation is real insofar as it tells us the rate at which things happen in one reference frame relative to another. However, it is based on clock time, which is virtual.
Real time doesn't, and never will vary. Things can still happen at different rates in different reference frames measured against real time. The rate of time itself is constant.
Everything we see is some form of optical illusion.
UPDATE I will support this with an example
Jack and Jill live on the top and bottom floors of a skyscraper, respectively
When Earth rotates through one revolution, the rotation starts and stops at exactly the same time for Jack and Jill
If Jack, Jill, the skyscraper and Earth were immortal, a trillion revolutions of Earth would start and stop at exactly the same time for all four of them.
They would experience every revolution, every radian and every microarcsecond together. They would all rotate together in real time.
Jack would age round 20 minutes more than Jill and his clock would be advanced by just over twenty minutes compared with Jill's clock (based on experimental Gravitational Time Dilation data and assuming a 150m skyscraper)
This example highlights the following points:
- Clock Time is not the same as Real Time
- Things age more quickly at higher altitudes in Real Time
- Clock Time is variable
- Real Time is constant
- The Speed of Light is variable in Real Time
- The Speed of Light is constant in Clock Time
- Time Dilation applies to Clock Time not to Real Time