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## Main Question or Discussion Point

On this page, and in many, many other resources both in textbooks and online, derivations of time dilation and length contraction are given which lead to;

[tex]

\gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}[/tex]

[tex]t^{'}=\gamma t[/tex]

[tex]x^{'}=\frac{1}{\gamma}x

[/tex]

Now a great many derivations of the Lorentz Transformations, such as the one on this page, use the above formulae in some way to arrive at

[tex]t^{'}=\gamma \left(t - \frac{v}{c^2}x\right)[/tex]

[tex]x^{'}=\gamma \left(x- vt\right)[/tex]

It seems to me that the second formulae do not agree with the first. Am I missing something here. Do they in fact agree with substitution of some correct values?

I noticed that in his original 1905 paper, Einstein assumed the transformation between two referance frames was linear, and derived the Lorentz transformations directly. Is this way, i.e. all in one gulp, the correct way to go about their derivation?

Are the original formulae strictly speaking incorrect? Under what circumstances are they valid, if at all? As an additional question, does dropping the linear transformation assumption lead, in part, to general relativity?

[tex]

\gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}[/tex]

[tex]t^{'}=\gamma t[/tex]

[tex]x^{'}=\frac{1}{\gamma}x

[/tex]

Now a great many derivations of the Lorentz Transformations, such as the one on this page, use the above formulae in some way to arrive at

[tex]t^{'}=\gamma \left(t - \frac{v}{c^2}x\right)[/tex]

[tex]x^{'}=\gamma \left(x- vt\right)[/tex]

It seems to me that the second formulae do not agree with the first. Am I missing something here. Do they in fact agree with substitution of some correct values?

I noticed that in his original 1905 paper, Einstein assumed the transformation between two referance frames was linear, and derived the Lorentz transformations directly. Is this way, i.e. all in one gulp, the correct way to go about their derivation?

Are the original formulae strictly speaking incorrect? Under what circumstances are they valid, if at all? As an additional question, does dropping the linear transformation assumption lead, in part, to general relativity?