# Why is special relativity still in use, if general relativity is more broad?

I always thought special relativity is only there because it is the building block for "The General theory of Relativity", until recently I encountered a text from my course book given below.

A more accurate formula for Doppler effect which is valid even when the speeds are close to light, requires the use of Einstein's special theory of relativity.

Is special relativity mentioned here only because this problem doesn't need to deal with the space-time curvature(I am quite new to relativity, please look it from a beginner point of view)? Or is there any other case in special relativity, which is not a part of the general relativity?

• Why is linear algebra still in use, if calculus is more broad? Nov 10, 2015 at 16:56
• When the stress-energy tensor is not too big (that is, usually, when gravitational fields are "weak" and your interactions and processes are not super high energy), and your frame of reference is inertial, special relativity is a really fine model of reality. For instance, quantum electrodynamics uses special relativity, and its predictions are incredibly accurate. You don't need general relativity to know that one apple and another apple add up to two apples; sometimes a simpler model gives the same results as a more complex one within the desired precision. So you choose the simple one. Nov 10, 2015 at 16:59
• same as Newton's laws, they are easier to use and still accurate for some applications
– user83548
Nov 10, 2015 at 17:00
• @WillO While I completely agree with the sentiment, calculus and linear algebra deal with two quite different things. Therefor unlike the example here where special relativity is obtained as a special limit of general relativity, linear algebra and calculus are actually different areas. One does not imply the other. Nov 10, 2015 at 17:01
• @prakharlondhe yes, it's a similar idea. Of course you can use Maxwell's equations to obtain more precise results, or even quantum optics, but usually ray optics are just fine for our purposes and, of course, it is much easier to develop an intuition about a simpler model Nov 11, 2015 at 12:36