[7] Modern Physics; Second edition; Randy Harris; Chapter 2; Special Relativity; 2008 In the derivation of LT in [7], three special cases are used to determine the constants A, B, C, D.
The result of this derivation gives the following: B = −Av, C = −Av/c2, D = A, A = γ. If you replace these values in LEx': x' = Ax + Bt LEt': t' = Cx +Dt you get LTx': x' = (x – vt)γ LTt': t' = (t – vx/c2)γ It is these two equations that are LT.
But during the derivation, the combination LEt', SC1 is not used. Therefore, we make a verification of a solution (as one should always do). We calculate LTt' in SC1: LTt': t' = (t – vx/c2)γ SC1: x' = 0, x = vt → t' = (t-v(vt)/c2)γ → t' = t(1-v2/c2)γ → t'= t/γ
My comment: In the derivation of LT in [7] is used LEx ', LEt', SC1, SC2, SC3 and as a result you get time dilation t' = tγ.
But the verification of the derivation, LTt' with SC1 gives us t'= t/γ.
This shows that the derivation of LT in [7] is not self-consistent! This is one of the reasons I said that SR is nonsense. I regret that everyone is upset by my conclusion but I have a lot more aspects of SR that I have analyzed in detail and everyone shows the same thing.