In general,the principle of relativity may be stated as "the shape of the mathematical expression of a law must be same for the observers".By an observer mean a system which his competent to verify the mathematical expression.
It is significant across many fields, but it appears not to be because simpler to understand classical laws are sufficient to describe most scientific processes to the level of accuracy that current measurement technology allows. We tend to follow Occam's razor and use the simplest tool that provides a sufficiently accurate answer.
Relativity becomes more important as the science tends towards extremes that the classical laws are unable to describe. In physics the headlines grabbed by the field have moved towards describing extremes (scale of universe, high energy collisions, speed of light etc), while in chemistry the extreme speeds of photons and electrons mean relativity is important. Relativity is important in chemistry and as a result biochemistry and therefore medicine...
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