Does the theory of relativity have any practical use outside of physics and astrophysics? I was talking to a smart friend of mine (a chemist) about special relativity .  He made the statement that "The theory of relativity is not used by anyone except physicist and astronomers.  No engineers use special or general relativity."  I said that atomic clocks for the GPS satellites need to account for relativity.  He said that the satellites could just use something like linear regression to estimate the time dilation without ever employing any relativistic equations.  I'm sad to say that I have not been able to think of any other applications, but, then again, I'm not a physicist, so maybe there are several applications.  Does anyone here know of any applications outside of physics and astronomy?  
 A: In high temperature (~100 million K) plasmas used for nuclear fusion research (which can be called plasma physics but also nuclear engineering), electromagnetic waves interact with charged particles moving at relativistic speed. Therefore relativistic effects on particles' mass affect things like how far into the plasma a wave can propagate. This is a very practical matter since electromagnetic waves are used for heating the plasma (RF heating) and for diagnosing its properties (so-called reflectometry [1]). High-temperature fusion plasmas have other examples (radiation, run-away electrons etc.) where accounting for relativistic physics is  important for designing the plasma confinement device and diagnostic tools.
[1] Wang et al. "Refractive and relativistic effects on ITER low field side reflectometer design" Review of Scientific Instruments 81, 10D908 (2010).
A: What are theories in physics?
They are mathematical models that map observations, and , very important, predict new phenomena. The mathematics is useful because it helps organize the data and gives precise predictions for new data.
Can one do without Newtons gravitational and mechanical theory? Where are they used?
They are used continuously and are within the formulae that mechanics have for calculating from strength in buildings to maximum velocities for cars ... They are inherent in the formulae given to engineers.
The newest theories illuminate for the few the underlying workings of nature, predict new possibilities, and from then on they are an underlying level , special relativity for sure, for all calculations used in different disciplines . We would not have the techinical civilization we have were it not for special relativity, which allowed understanding the microscopic level so that new devices could be made, from transistors to nanotechnology. 
So the theories are used for calculation  by few, and once the formulae are given to the many, the many use the theories without knowing that they do. 
It is not the same with General relativity, which only the GPS is using. That is mainly the province of cosmologists.
The answer to your friend's

He said that the satellites could just use something like linear regression to estimate the time dilation without every employing any relativistic equations

is that the reason for the dark ages until Newton's calculus time is that  nobody could usefully use linear regressions and such tools. If there were not the theories calculating  the GPS, there would be no GPS . Nobody would launch satellites to find  linear regressions!
