Re: Mathematical Inconsistencies in Einstein's Derivation of the Lorentz Transformation

----- Original Message ----- 

From: "Thomas Smid" <thomas.smid@xxxxxxxxx>

Newsgroups: sci.physics.relativity

Sent: Sunday, September 04, 2005 4:31 AM

Subject: Re: Mathematical Inconsistencies in Einstein's Derivation of the Lorentz Transformation



Daryl McCullough wrote: 
Thomas Smid says...
>
>Daryl McCullough wrote:

>> Einstein's equations were these
>>
>> (3)   x' - ct' = lambda (x-ct)
>> (4)   x' + ct' = mu (x+ct)
>


[snip]

OK, but you should note that fully written your equations (3) and (4)
read

(1) x'(e1) - c t'(e1) = lambda (x(e1) - ct(e1))
(2) x'(e2) + c t'(e2) = mu (x(e2) + ct(e2))


so you can't use them to determine lambda and mu (and hence the Lorentz
transformation) like Einstein did.

Einstein assumes that equation (3) holds for _any_ event, not just for those events for which x-ct = 0. Please note where Einstein says that (3) ''is fulfilled in general'', which just means that it is assumed to hold for _arbitrary_ events. Likewise (4) is assumed to hold for _any_ event. Therefore, you may apply (3) and (4) to the _same_ event and add and subtract them as Einstein did. What may be confusing you is that Einstein does not make any effort to show why (3) and (4) hold for _arbitrary_ events. David McCullough has been kind enough to do that for you using the underlying assumption that the _general_ transformation equations are linear.

[snip]

Todd 

.

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