Derivation of Lorentz Transformation

Just as an update:
I have now put this topic on a webpage Mathematical Inconsistencies in Einstein's Derivation of the Lorentz Transformation which should further clarify Einstein's mistakes.

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www.physicsmyths.org.uk
www.plasmaphysics.org.uk

For a photon along the positive x-axis:

x - c * t = 0
links x to t in frame k

x' - c * t' = 0
links x' to t' in frame k'

( x' - c * t' ) = lambda * ( x - c * t )
links the entire 2-dimensional domain ( x , t ) to the entire 2-dimensional domain ( x' , t' )

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For a photon along the negative x-axis:

x + c * t = 0
links x to t in frame k

x' + c * t' = 0
links x' to t' in frame k'

( x' + c * t' ) = mu * ( x + c * t )
links the entire 2-dimensional domain ( x , t ) to the entire 2-dimensional domain ( x' , t' )

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So we have two different ways to go from k to k'
Both must be true in SR.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by Michiel</i>
<br />For a photon along the positive x-axis:

x - c * t = 0
links x to t in frame k

x' - c * t' = 0
links x' to t' in frame k'

( x' - c * t' ) = lambda * ( x - c * t )
<b>links the entire 2-dimensional domain ( x , t ) to the entire 2-dimensional domain ( x' , t' )</b><hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">

Your conclusion (in bold) is incorrect. The last equation holds only for those values of x,t and x',t' for which x=ct and x'=ct' i.e. if both sides of the equation are identically zero (which obviously means by the way that lambda can be arbitrary). Otherwise you could not write this equation.

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www.physicsmyths.org.uk
www.plasmaphysics.org.uk

{ x - c * t = 0
{ x' - c * t' = 0

0 = lambda * 0 is true for all lambda, so there must be a lambda for which

x' - c * t' = lambda * ( x - c * t )

to describe the transition from k to k' in SR.

The need is to make 1+1=1 in SR is it not? The transformation is from 1+1=2 to 1+1=1 how else can you do this?

Suppose we start with:

{ x - c * t = applepie
{ x' - c * t' = applepie

Now look at:

applepie = lambda * applepie

This is true for all applepie if lambda = 1 and it is true for all lambda if applepie = 0
Under these assumptoins we can safely state:

x' - c * t' = lambda * ( x - c * t )

After this little excursion just choose applepie = 0 and Bob's your uncle.

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The photon travelling along the positive x-axis is only one SR-event. It must be a subset of all possible SR-events, and clearly it is. For all other SR-events we can say: x - c * t &lt;&gt; 0 and x' - c * t' &lt;&gt; 0