In this world the gravitational potential is the same in any point and thus the cosmological redshift is favoured as a kinetic phenomenon of
special relativity. In this case there is no need for an equation of the state specifying pressure in cosmology.
Nowak, "Non-commutative spacetime of Doubly
Special Relativity theories," International Journal of Modern Physics D, vol.
Spacetime Physics: Introduction to
Special Relativity, 2nd ed.
Time dilation is referenced in the theory of
special relativity. It is only really evident when objects travel close to the speed of light, so it's hard (though not impossible) to provide any practical examples from everyday life.
(Actually, a correction is also needed for
special relativity, since the satellites' rapid motion slows their clocks.
We are not interested in the well established formulation of
Special Relativity, which are well documented in texts and the internet, but rather in the role of the observers whose characteristics have been implicitly assumed and never been questioned.
As a result, his theory of
special relativity was essentially complete as first set out.
Einstein's theory of
special relativity completely transformed modern physics; not only did it do away with the old notions of absolute space and time, it also introduced some new and rather startling fundamental concepts.
The instantaneous "action at a distance" did not fit well into
special relativity, which is based on a finite speed of interaction.