Summary, etc.

It should be emphasized, that the only physical assumptions we exploited to derive Lorentz transformation were:

• The transformation from the reference frame of one observer to the reference frame of another observer only depends on the relative velocity of the observers. NB: This statement is essentially the principle of relativity;
• The velocities, two observers moving with respect to each other perceive, are the same in magnitude but of opposite direction;
• The space is isotropic;
• The transformation has to be simple (but nontrivial).

The existence of a fundamental constant c (the constant speed of light) comes as a result rather than an additional assumption (see formulas (2.10) and (2.11)).

Finally, it is easy to show, that if we add to the above assumptions one that says, that the velocity of one observer with respect to another cannot be arbitrarily large, we are left with Lorentz transformation as the only one that fulfills the imposed requirements.

At this point a question of historical nature arises: if the derivation is so elementary and requires so few natural assumptions, why noone did it 200-300 years ago? One possible reason, the author can think of, is that the idea of a universal time was so deeply rooted in physicists' minds, that they did not even conceive the idea of writing a transformation of t. Also, the authority of sir Isaac Newton, who believed in absolute space and time, influenced many generations of physicists. So, maybe it is sometimes a good idea not to trust authorities (?).