Hi everyone, I am looking into relativity as preparation for university and I was wondering if anyone could help me out with this.

I am reading Six Not-So-Easy-Pieces and in it Feynman uses the Lorentz transformation and 'derives' it, by showing that Lorentz contraction is necessary to account for the null result of the Michelson-Morley experiment. He then shows that in a primed system that has contracted due to its motion, the distance to a fixed point will also contract and so an observer can calculate the 'real' distance as:

\begin{align}

x &= x'{\sqrt{1-\frac{u^2}{c^2}}}

\end{align}

As the primed system is moving towards the fixed point:

\begin{align}

x &= x'{\sqrt{1-\frac{u^2}{c^2}}} + ut

\end{align}

Thus:

\begin{align}

x' &= \frac{x - ut}{\sqrt{1-\frac{u^2}{c^2}}}

\end{align}

Now I don't like this way for two reasons:

1) It presupposes the Lorentz contraction rather than showing it as a result of the Lorentz transformation

2) It is seemingly invented to 'fix' the experiment

So, I asked Google and found http://galileo.phys.virginia.edu/classes/252/lorentztrans.html" [Broken]

Although I have yet to completely follow through with their reasoning, it too uses Lorentz contraction and time dilation.

So my question is firstly, is it OK to derive the Lorentz transformations using length contraction and time dilation. Surely that is a 'circular derivation'! If not, then how can it be derived by other means.

Thanks

I am reading Six Not-So-Easy-Pieces and in it Feynman uses the Lorentz transformation and 'derives' it, by showing that Lorentz contraction is necessary to account for the null result of the Michelson-Morley experiment. He then shows that in a primed system that has contracted due to its motion, the distance to a fixed point will also contract and so an observer can calculate the 'real' distance as:

\begin{align}

x &= x'{\sqrt{1-\frac{u^2}{c^2}}}

\end{align}

As the primed system is moving towards the fixed point:

\begin{align}

x &= x'{\sqrt{1-\frac{u^2}{c^2}}} + ut

\end{align}

Thus:

\begin{align}

x' &= \frac{x - ut}{\sqrt{1-\frac{u^2}{c^2}}}

\end{align}

Now I don't like this way for two reasons:

1) It presupposes the Lorentz contraction rather than showing it as a result of the Lorentz transformation

2) It is seemingly invented to 'fix' the experiment

So, I asked Google and found http://galileo.phys.virginia.edu/classes/252/lorentztrans.html" [Broken]

Although I have yet to completely follow through with their reasoning, it too uses Lorentz contraction and time dilation.

So my question is firstly, is it OK to derive the Lorentz transformations using length contraction and time dilation. Surely that is a 'circular derivation'! If not, then how can it be derived by other means.

Thanks

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