We came up with a theory?

Question

we were wondering if a decrease in length detected by an observer in objects that travel at any non-zero velocity is relative to that observer. This contraction (or as we thought is should be called the Lorentz contraction or Lorentz-Fitzgerald contraction) will only become noticeable at a substantial fraction of the speed of light; and the contraction is only in the direction parallel to the direction in which the observed body is travelling.

It is important to note that this effect is negligible at everyday speeds, and can be ignored for all regular purposes. It is only when an object approaches speeds on the order of 30,000,000 m/s, i.e. one-tenth of the speed of light, that it becomes important. As the magnitude of the velocity approaches the speed of light, the effect becomes dominant.

Please correct if wrong.

Answer 1

I can not comment about what you have called this effect (Lorentz-Fitzgerald contraction), as I do not really recall this effect name.  I only remember I took this in Physics III in the university (many years ago).

Otherwise everything else you mentioned is true.  Such relativity effects are noticeable only at speeds close to the speed of light.