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Article #84

Re: ABIAN DERIVATION OF E = Mc^2

#84
From: Jim Carr
Date: Tue, 12 May 1998 00:00
58 lines
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   ... relativity newsgroup added with followups there ...


abian@iastate.edu (Alexander Abian) writes:
> 
>I will once more derive below  E = Mc^2  from Lorentz equation via
>High School algebra while  mentioning and emphasizing my explanatory
>insight.

 The whole of your "derivation" is your question at the end:

>But then what could be more
>insightful, more intelligent, more reasonable  than to consider   
>Mc^2  as expressing the total energy of the system at velocity v and 
>to consider Mo c^2  as expressing the total energy of the system at 
>rest and hence to consider  M c^2  as the general expression of the total
>energy of the system  and denote it by  E. 

 The answer is, a derivation that shows that the rest mass increases 
 when a body absorbs electromagnetic energy.  That is the derivation 
 Einstein does to establish E = mc^2 (where my m is your Mo). 

>I will go step by step. 
> 
>  Assuming that we believe in the truthfulness of the Lorentz formula:
> 
> (1)                M = Mo (1 - (v^2/c^2))^(-1/2)

 What is your citation for this?  Lorentz used two different 
 relativistic masses, as I pointed out elsewhere.  This is the 
 transverse mass. 

>NOW THE WHOLE SUBTLETY OF NY REASONING IS IN THE OBSERVATION THAT  
>
>     Mc^2  - Mo c^2   =  1/2 Mo v^2  +  .......
>
>says that due to acquiring velocity  v  the total Energy of the
>system has acquired the "kinetic type"  energy which is  equal to
>the difference of  Mc^2  and  Mo c^2.  

 Nothing subtle, or innovative, there.  It is all in Einstein's 
 popular treatment of relativity, titled "Relativity". 

>I repeat  that assuming Lorentz equation   M = Mo (1 - (v^2/c^2))^(-1/2)
>the derivation of  E = Mc^2   (with my abovementioned insight)  amounts
>to multiplying both sides of   M = Mo (1 - (v^2/c^2))^(-1/2)  by  c^2
>and absolutely nothing else.

 Right.  In particular, there is no derivation at all to explain the 
 relation of this to the total energy of a particle. 

-- 
 James A. Carr   <jac@scri.fsu.edu>     | Commercial e-mail is _NOT_ 
    http://www.scri.fsu.edu/~jac/       | desired to this or any address 
 Supercomputer Computations Res. Inst.  | that resolves to my account 
 Florida State, Tallahassee FL 32306    | for any reason at any time. 
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From: jac@ibms48.scri.fsu.edu (Jim Carr)
Subject: Re: ABIAN DERIVATION OF  E = Mc^2
Date: 1998/05/12
Message-ID: <6jacds$2cr$1@news.fsu.edu>
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