Quote - So relativity is just an approximation based on limited information, much like Newtonian physics?  Hmm.

Yes, but the confirmation that the approximation it is accurate has been confirmed to a fractionally minute level. There's not a whole lot of room left for something new to be discovered

Let's put it another way: suppose relativistic time dilation had not been theorized. When people started placing hyperaccurate clocks on satellites (and fast aircraft), they would have seen that something was wrong because those moving clocks would have slowed down when they were moving (relative to the ground), but functioned perfectly when "stationary". The faster the clock moved, the more pronounced the effect.

So normal ideas, such as that time was an unchanging constant (which is an assumption of Newtonian physics), would have shown problems when we had the capability to move fast enough, at, say kilometers per second and highter. So there was a lot of room (from kilometers per second to about 300,000 kilometers per second) where we could see there was a problem with the idea of a constant, unchanging, flow of time wherever you looked.

With relativity, we've vastly increased the range of sizes and speeds in which things can be tested, either directly or through observation of what nature does in comparison to current theories. We've directly measured time dilation effects on particles that have been accelerated to within fractions of a percentage of light speed, and they line up perfectly with the theory, so there's not much room left for something unanticipated to happen (taking into account quantum effects which take over in certain situations, as mentioned above).