Why?
Ehhh evidence? We've yet to find any problems with special relativity, and it permeates ALL of theoretical physics. So if SR is wrong, then violations should show up somewhere. If SR and your theory are the same (i.e. give the same predictions), then the simpler one wins.
JG: Space and time are subject to non-linear equations. The best fit is the geometric mean. For orbital motion Einsteins formulas are the best fit. I use the Doppler Equations
Mass front = Mo (C/(C-v)
Mass rear = Mo (C/C+V)
The Doppler geometric mean mass is
Mx = [Mo / ( 1- (V/C)^2 ]^0.5
Thus Einstein is the geometric mean of Doppler . This is shown in my book
"Doppler Space Time" . (Available at used books or Amazon.com) I have no financial interest in the books. I only purchased 1000 and gave most away to libraries and those who wanted them on the internet. I self publish as a hobby and not a business. Right now I need to save $6000 to self-publish "Dot-wave unified field theory". I have sent 100 copies of the manuscript to 100 universities and await some responses. I am a retired EE, going to be 70 on Christmas eve. I get social security and a small pension. I like to work as a part time handyman helping older people for small pay. It is another hobby business but it earns a little money. I have been working on the dot-theory for 27 years.
In any event Einsteins equations are excellent for orbital motion but not good for linear motion. Experiments at MIT long ago verified that the mass in front of the moving object is larger than the mass in back of the moving object. Other universities verified MIT's findings.
The interesting thing is the Doppler length which helps explain the double slit experiment physically.
the Doppler length front = Lx (C/(C-V)
Doppler length rear = Lx (C/ (C+V)
The moving object has a forward length which approaches infinity as the velocity goes to light speed. The rearward length is cut in half. Thus as an object starts to move, it projects an image in front of it.
Doppler space time is only an approximation to the complexity of non-linear space time. It shows important characteristics which are useful. For example as we move a spaceship to higher and higher velocities, we run the risk of destruction by space particles. We can fortify the image in front of the spaceship by using the Doppler Length. Thus the particles will hit the forward defense image which will protect the spacecraft.
In this manner we can get up to 0.4 C before the spacecraft distortions destroy the occupants. As shown in Doppler Space Time, we can get to the moon in 3.5 hours by constant acceleration at 32 feet per second for half the trip and a constant deceleration of 32 feet per second for the remaining half of the trip. No weightlessness is involved since the occupants only feel normal gravity. The reversal of the proton thruster engine necessitates the reversal of seating during a short weightless period of less than one minute.
It would take 25.4 days to reach pluto. It would take 2 days and 5 hours to reach Mars or Venus. Of course such things are for the future since it will take time to produce the proton/photon engine.