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Derivation of Lorentz Transformation
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
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
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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.
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.
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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
<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
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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.
{ 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.
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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?
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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 <> 0 and x' - c * t' <> 0
{ 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 <> 0 and x' - c * t' <> 0
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