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My experience on the forum showed me that some participants do not agree with the simple, “two line” derivations, of the equations that account for relativistic effects like time dilation, length contraction and Lorentz transformations, incriminating papers published by American Journal of Physics and probably by European Journal of Physics. The discussion with them is difficult taking into account the way in which they defend their point of view, rejecting start from the beginning the point of view of the opponents.

I propose an experiment, presenting a “two line” derivation of the Lorentz transformations, inviting those who agree with it and those who do not agree to present theirs punctual point of view.

Consider two inertial reference frames I and I’ in the standard arrangement and theirs relative position at a time t when detected from I and at a time t’ when detected from I’. The involved events are E(x=ct,y=0,t=x/c) in I and E’(x’=ct’,y’=0,t’=x’/c) in E’ the events being generated by the light signal that performs the synchronization of the clocks in the two frames. Because we can add only physical quantities measured in the same inertial reference frame we have in I

f(V)x’=x-Vt=x(1-V/c) (1)

f(V)x=x’+Vt’=x’(1+V/c. (2)

From (1) and (2) we obtain

f(V)=(1-V2/c2)1/2 (3)

and so

x=(x’+Vt’)/(1-V2/c2)1/2 (4)

x’=(x-Vt)/(1-V2/c2)1/2 (5)

Combining (4) and (5) we obtain

t=(t’+Vx’/c2)/(1-V2/c2)1/2 (6)

t’=(t-Vx/c2)/(1-V2/c2)1/2. (7)

Of course during the derivations the instructor could provide supplementary information.

Probably as an old fashioned teacher I fully agree with the derivation presented above. I invite teachers at all levels and learners to present theirs opinion.

sine ira et studio

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# Are two line derivations harmful in teaching special relativity

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