No, events in different inertial frames of references can be not isomorphic to each other..

Quoting myself from the article:

"Let’s consider a thought experiment. Two observers decided to observe some phenomena in some spatial area. Both observers meet, each takes a clean notebook where they will record the results of the observations. Then the first observer remains in same area, the second at some vehicle accelerates to near-light velocity. Each of them regularly records observable phenomena in the assigned region of space. Then the second observer returns, meets with the first observer, and they compare the results recorded in notebooks. Can there be different results in notebooks? To answer this question, it is necessary to remember that the space-time in this hypothesis is built around the selected observer, and is built with the requirement to satisfy to principle of causality. Therefore, for each of the observers, what he sees in the notebook should satisfy the principle of causality. This means that while observers may record different events, the causality principle must be followed for them. This means that for any observer the events during the transitions to another inertial frame of reference look isomorphic. However, if in any way the observer could see events at the same time in different reference frame, he would see that events in different reference frames are not isomorphic with respect to each other.

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