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Old Jan 22nd 2009, 09:44 AM   #1
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The formula E = mc^2 never have been proved?

The formula E = mc^2 estimated as one of the top ten of most beautiful formulae at any epoch, but the its demonstration at firth contained mistake by just Great Einstein! The lack of logical fundamental of the Einstein had advised by Aivs in “Journal of the Optical Society Of America”, 42, 540 – 543. 1952. After that, nobody take author demonstration no more, but use dependent of inertial mass from velocity of a body:
m = mo(1-B^2)^-1/2 = mo.γ (1)
together with the Newton’s 2 law:
F = d(mV)/dt (2)
for calculation that formula. But, the new mistake appear and, perhaps, in this situation, not could be recovered!!!
First, the itself formula (1) had estimated for only moving uniform straight-line body with the constant velocity V in an inertial reference frame (IRF) and having the inertial mass mo in reference frame in which it is at rest. That mind:
+ If a body moving with the velocity V1, then we have: m1 = mo1;
+ If a body moving with the velocity V2, then we have: m2 = mo2;
.....
+ If a body moving with the velocity Vn, then we have: mn = mon;
....
where V1, V2, ... Vn are value of unchanging velocity in a time interval, corresponding to uniform straight-line move of a body, but not value of an instantaneous velocity; similar to that, the m1, m2...mn are value of corresponding inertial mass calculated in IFOR1, IRF2, ... IRFn correspondingly, but not value of mass m as function of velocity with usual understanding above a function: m = m(V), in which V is a variable, because any upheaval of a velocity V lead condition of a IRF is broke – Lorenz’s transformation no longer effective – and then “how can we have the formula (1)?” That right, replace Eq. (1) in to Eq. (2) is unpossible for derivation, because V don’t change, so m must be don’t change too. And this derivation must be equal to zero!!! That the formula E = mc^2 never have been proved ???
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Old Jan 24th 2009, 10:03 PM   #2
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A paper available on the web by Herrmann agrees that Einstein never proved the formula:
http://arxiv.org/pdf/0805.1400v2

I don't know enough about the subject to form an opinion about whether it was subsequently proved.
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Old Feb 7th 2009, 03:29 AM   #3
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Originally Posted by Toan View Post
The formula E = mc^2 estimated as one of the top ten of most beautiful formulae at any epoch, but the its demonstration at firth contained mistake by just Great Einstein! The lack of logical fundamental of the Einstein had advised by Aivs in “Journal of the Optical Society Of America”, 42, 540 – 543. 1952. After that, nobody take author demonstration no more, but use dependent of inertial mass from velocity of a body:
m = mo(1-B^2)^-1/2 = mo.γ (1)
together with the Newton’s 2 law:
F = d(mV)/dt (2)
for calculation that formula. But, the new mistake appear and, perhaps, in this situation, not could be recovered!!!
First, the itself formula (1) had estimated for only moving uniform straight-line body with the constant velocity V in an inertial reference frame (IRF) and having the inertial mass mo in reference frame in which it is at rest. That mind:
+ If a body moving with the velocity V1, then we have: m1 = mo1;
+ If a body moving with the velocity V2, then we have: m2 = mo2;
.....
+ If a body moving with the velocity Vn, then we have: mn = mon;
....
where V1, V2, ... Vn are value of unchanging velocity in a time interval, corresponding to uniform straight-line move of a body, but not value of an instantaneous velocity; similar to that, the m1, m2...mn are value of corresponding inertial mass calculated in IFOR1, IRF2, ... IRFn correspondingly, but not value of mass m as function of velocity with usual understanding above a function: m = m(V), in which V is a variable, because any upheaval of a velocity V lead condition of a IRF is broke – Lorenz’s transformation no longer effective – and then “how can we have the formula (1)?” That right, replace Eq. (1) in to Eq. (2) is unpossible for derivation, because V don’t change, so m must be don’t change too. And this derivation must be equal to zero!!! That the formula E = mc^2 never have been proved ???
Simple minded as I am I would consider that
m = mo(1-B^2)^-1/2 = mo.γ (1)
is the best function which fits experimental results concerning the velocity dependence of the mass (Bucherer)
Multiplying both sides of (1) with the invariant c^2 which does not change the equality character, introducing the notation E=mc^2 and E(0)=m(0)c^2 and calling the first energy and the second rest energy we obtain
E=E(0)/sqr(1-b^2/c^2)
Is there more to say?
Notice that <mc^2)= <kgxm^2/s^2>=<joule>
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Old May 15th 2009, 05:10 AM   #4
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Originally Posted by Toan View Post
The formula E = mc^2 estimated as one of the top ten of most beautiful formulae at any epoch, but the its demonstration at firth contained mistake by just Great Einstein!
That paper did not contain any errors. The paper was reanalyzed by John Stachel and its logic explained. The analysis is found in

Einstein's first derivation of mass-energy equivalence, John Stachel and Roberto Torretti, Am. J. Phys. 50(8), Aug. 1982

The lack of logical fundamental of the Einstein had advised by Aivs in “Journal of the Optical Society Of America”, 42, 540 – 543. 1952.
The author's name is Ives, not "Aives" and he made an error as Stachel and Torretti explain.

In any case many other derivations came after that, even by Einstein.
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Old Jun 1st 2009, 11:22 PM   #5
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FYI: The equation $\displaystyle E^2 = m^2c^4 + p^2c^2$ reduces to the famous $\displaystyle E = mc^2$ when the momentum is zero; ie. when the particle is at rest. This is the equation that needs to be proven. The derivation of this more general equation can be found in any elementary text on relativity. Einstein was essentially a theoretical physicist, so I doubt he ever tried to prove it. On the other hand I know that the equation had been tested while Einstein was still alive.

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Last edited by topsquark; Jun 1st 2009 at 11:24 PM.
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Old Jun 2nd 2009, 06:38 AM   #6
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Originally Posted by topsquark View Post
FYI: The equation $\displaystyle E^2 = m^2c^4 + p^2c^2$ reduces to the famous $\displaystyle E = mc^2$ when the momentum is zero; ie. when the particle is at rest.
To be precise, since m in that expression is the particle's proper mass (aka rest mass) it follows that the energy is proper energy. Therefore

E_o = mc^2

Einstein also derived this expression in

Elementary Derivation of the Equivalence of Mass and Energy, Albert Einstein, Bulletin of the American Mathematical Society, Vol. 47, Number 1, pages 39-44 (1935)

The actual expression derived in that paper is

E_o = m

where Einstein uses units in which c = 1.

Last edited by Pmb; Jun 2nd 2009 at 06:40 AM.
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Old Feb 20th 2018, 10:54 AM   #7
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Is there any way to derive the mass-energy equivalence from fundamental concepts in Newtonian mechanics?
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Old Feb 20th 2018, 11:04 AM   #8
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Originally Posted by Ziang View Post
Is there any way to derive the mass-energy equivalence from fundamental concepts in Newtonian mechanics?
No, they are separate in Newtonian mechanics.

You can, however, measure the effect as 'mass defect' in Nuclear Physics.

https://www.google.co.uk/search?sour....0.hxMWK5zeCuk
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Old Feb 21st 2018, 06:43 AM   #9
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Is there any way to modify Newtonian mechanics so that the equivalence can be derived from classical concepts in absolute space and time?
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Old Feb 21st 2018, 06:52 AM   #10
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Give it up.
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