Do lorentz transformations calculate what is really happening in the primed reference frame? Or do they calculate what the non-primed reference would think the primed reference's coordinates should be? I might be doing things wrong algebraically but it seems that: If I calculate from O things in O' knowing certain things about O. Then I calculate from O' using what I got in the previous calculation, and I don't get back what I know about O! Namely, O' says something different about myself! That's a contradiction! Also, In problems dealing with particle decay, or something of the kind, they usually tell me the mean lifetime of the particle. My interpretation is this: the particle's lifetime has been measured at rest with respect to my frame to be X. If that particle is travelling near C with respect to myself, I can assume that its meanlife time in ITS frame is the one I measured when it was at rest with respect to me. Is this right? Also: With respect to both frames measuring time dilation of the other, does the same happen with length contraction? Are all contradictions of this kind solved by the typical "you have to consider accelerations to solve this apparent paradox" ? I have other questions, but I don't really have them well thought out. I hope I wasn't unclear here. Thanks.