Derivation of Lorentz Transformation

More
19 years 1 month ago #12654 by Thomas
Replied by Thomas on topic Reply from Thomas Smid
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.


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

Please Log in or Create an account to join the conversation.

More
19 years 1 month ago #12655 by Michiel
Replied by Michiel on topic Reply from Michiel
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' )

___

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' )

___

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

Please Log in or Create an account to join the conversation.

More
19 years 4 weeks ago #12659 by Thomas
Replied by Thomas on topic Reply from Thomas Smid
<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.


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

Please Log in or Create an account to join the conversation.

More
19 years 4 weeks ago #12670 by Michiel
Replied by Michiel on topic Reply from Michiel
{ 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.

Please Log in or Create an account to join the conversation.

More
19 years 4 weeks ago #14349 by Jim
Replied by Jim on topic Reply from
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?

Please Log in or Create an account to join the conversation.

More
19 years 4 weeks ago #12675 by Michiel
Replied by Michiel on topic Reply from Michiel
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.

___

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

Please Log in or Create an account to join the conversation.

Time to create page: 0.317 seconds
Powered by Kunena Forum