Azzam
Be careful about SR. This is just a theoretical circumstance, where there is no gravity, hence objects are fixed in size, there is only uniform rectilinear and non-rotary motion, light travels in straight lines, and Euclidean maths applies. Another way of putting this is that SR is not the same as all that which was written in 1905.
And, Einstein said this, not Paul Reed:
Einstein: SR & GR, 1916, section 18: "...provided that they are in a state of uniform rectilinear and non-rotary motion with respect to K; all these bodies of reference are to be regarded as Galileian reference-bodies. The validity of the principle of relativity was assumed only for these reference-bodies, but not for others (e.g. those possessing motion of a different kind). In this sense we speak of the special principle of relativity, or special theory of relativity. In contrast to this we wish to understand by the "general principle of relativity" the following statement: All bodies of reference are equivalent for the description of natural phenomena (formulation of the general laws of nature), whatever may be their state of motion. But before proceeding farther, it ought to be pointed out that this formulation must be replaced later by a more abstract one, for reasons which will become evident at a later stage"
Einstein: SR & GR, 1916, section 28: "In gravitational fields there are no such things as rigid bodies with Euclidean properties; thus the fictitious rigid body of reference is of no avail in the general theory of relativity".
Einstein: Foundation of GR 1916, section 3: "...the case of special relativity appearing as a limiting case when there is no gravitation".
So, put simply, there is no "objective existence" in SR, because it is a circumstance that does not exist, as such. It is just a theoretical 'sub-set' of GR in which the causal factor (ie gravity) is hypothetically removed. It can occur, effectively, when gravitational forces incurred by any given object are counterbalanced, in which case, the object retains a constant motion (which may be different wrt another object with constant speed) and a fixed shape, according to the theory. There is no length contraction in SR. There is no time dilation, this is a function of the misconceptualisation of time. Existence occurs at any given point in time, alteration happens, we can time the rate at which alteration occurs.
The observer cannot have any effect on phenomena, because sensing involves the receipt of physically existent phenomena. And anyway, what is received is a physically existent effect caused by interaction with the phenomena (reality) in question (aka light, noise, vibration, etc). The reality has ceased to exist before the observer senses the result of an interaction with it. Sensing having evolved to utilise these effects and enable organisms to have an awareness of reality.
Paul