I always get a little uneasy that all the theories I can think of (at least sinc

Question

I always get a little uneasy that all the theories I can think of (at least since Newton) are constructed in a way such that they would be true in heaven and on earth ... but we can never go everywhere and test it out.

So here is the question:

Is there some good justification to implement something like the principle of relativity in scientific theories other than it turned out to work good so far?

Some more motivation:

We have an understanding of different places in space (and time) and what different velocities are. Like imagine me and my droogs cruising our skateboards down the neighborhood and there is a truck driving in the other direction. I see a cactus on the roadside and I wonder how the trucker in his ride sees it.

Now in the maths, space x? and spacetime t represent physical space and physical time. And if I know my coordinates, the form of the plant and its location and orientation in space, I can find out what I see and also what the trucker from his position sees. A coordinate transformation (replacing some letter on a piece of paper with some other letters in a systematic way) is conventually interpreted as taking the data from one "perspective" and transforming it into "another perspecitive".

It's supposed to be a fruitful approach to physics to consider only the observable quantities. Maybe I interpret the principle of relativity the wrong way, but I find it funny that a theory tells me there are spacetime events where I can never get to (outside the light cone). And simultaneously I'm guaranteed that if I'm there I would also be able to physics and come to the right conclusions. At the very least, I feel this is somewhat redundant - why not drop it?

Explanation / Answer

but I find it funny that a theory tells me there are spacetime events where I can never get to (outside the light cone).At the very least, I feel this is somewhat redundant - why not drop it?

Mathematical theories do not come a la cart, i.e. they are not patched together, cut as you go, constructs. Theories are axiomatic self consistent and sustained. They arise and are accepted because they explain usually a large number of observations to great accuracy. A theory is either invalidated by disagreeing with some data, or is consistent with all known data until further experimental research. Now mathematics being what it is, the theories are extended to non physically accessible regions, and one accepts the conclusions since the theory fits the known regions.

The specific example you use is not a particularly useful one, since calculations are done off the light cone in Feynman diagrams and now even more complicated calculations, which in the end are absolutely consistent with data to high accuracy, since the light cone excursions are virtual. Even if one could construct a theory where only the inside of the light cone were mathematical described , it would be a wrong theory for particle physics data.

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