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Go and read carefully the last part of the 1905 paper, where EinsteinThe MacLaurin is just the zero case for Taylor series, sure,
derived L/c² = m.
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He used ONLY the first term of a McLaurin series, which is valid for v/c
ratio lower than 0.1. Above this, the error using that interpretation of
Kinetic Energy (1/2 m v²) is unacceptable by any means.
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The expression over which he worked is at the final part of the paper:
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L.(Y-1) = L . 1/2 x² . (1 + 3/4 x² + 15/24 x⁴ + 105/192 x⁶ + ..)
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where x = v/c
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Einstein tried 7 times to correct this limitation, from 1906 to 1942,
when he finally gave up to find an expression of L/c² = m valid for the
whole range of v up to c.
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If you try to affirm that, in the above expression, using more McLaurin
terms make L/c² = m valid for values of v > 0.1c, without incurring in
major physical and conceptual errors, you have to rethink it all over.
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For instance, you could say that using x = v/c = 1/2 gives a
MULTIPLICAND of the basic KE, like
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1/2 (L/c²) v² . (1 + 3/4 . 1/4 + 15/24 . 1/16 + 105/192 . 1/64 + ..)
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then you are delusional and also violate every single concept of
newtonian mechanics since 1800, at least.
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You CAN'T ABUSE of gullibility of people like Einstein did with such
disgusting paper, WHICH IS WRONG from any approach that you make on it.
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In the best case, it would be directing you to think (erroneously) that
the RELATIVISTIC EXPRESSION OF MASS in Kinetic Energy is:
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M = Mo (1 + 3/4 . 1/4 + 15/24 . 1/16 + 105/192 . 1/64 + ..)
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M = Mo (1 + 3/16 + 15/384 + 105/12288 + ..)
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It would not look pretty to derive a new equation
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E = 1.235107422 Mo c²
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I would prefer Hassenhorl's derivation of E = 4/3 Mo c², developed in
March of 1905 and in the same Annalen der Physik, paper that Einstein
plagiarized BY THE OLD TRICK OF REVERSE ENGINEERING. Only that
Hassenhorl derived it FOR A CLOSED SYSTEM (A BLACK BOX), while Einstein
failed miserably by working with an OPEN SYSTEM (equations don't work).
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But, it's just me.
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A legion of imbeciles bought the crap written in only 2 pages, by
November 1905.
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