The formula E = mc^2 has never been proven? [Answered: FALSE]

[huytoan]

The formula [math]E=mc^{2}[/math] is 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’s demonstration no more, but use dependent of inertial mass from velocity of a body:

[math]m = \frac{m_{0}}{\sqrt{1-v^{2}/c^{2}}}=m_{0}\gamma[/math] (1)

together with the Newton’s 2 law:

[math]F = \frac{d(mV)}{dt}[/math] (2)

for calculation that formula. But, the new mistake appear and, perhaps, in this situation, not could be recovered!!!

First, the itself formula (1) is estimated for only moving uniform straight-line body with the constant velocity V in an inertial reference frame (IRF) and having the inertial mass [math]m_{0}[/math] in reference frame in which the body is at rest. That mind:

+ If a body moving with the velocity [math]V_{1}[/math], then we have: [math]m_{1}= m_{0}\gamma_{1}[/math];

+ If a body moving with the velocity [math]V_{2}[/math], then we have: [math]m_{2} = m_{0}\gamma_{2}[/math];

.....

+ If a body moving with the velocity [math]V_{n}[/math], then we have: [math]m_{n}=m_{0}\gamma_{n}[/math];

....

where [math]V_{1}[/math], [math]V_{2}[/math], ... [math]V_{n}[/math] 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 [math]m_{1}[/math], [math]m_{2}[/math]...[math]m_{n}[/math] 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: [math]m = m(V)[/math], 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 [math]E=mc^{2}[/math] has never been proven ???

[swansont]

Your post hints at several problems with and reasons not to use relativistic mass. The full equation is [math]E^2 = m^2c^4 + p^2c^2[/math] The m in that equation is the rest mass, aka invariant mass, since it is invariant under a Lorentz transformation.

 

From this, one only arrives at [math]E = mc^2[/math] when p=0, i.e. the item is at rest. This equation, though, has been confirmed. An isomer of Fe-56 was measured to have a greater mass than the ground state in a Penning trap.

 

http://blogs.scienceforums.net/swansont/archives/278

[kleinwolf]

Some wide public books write like : position were [math] \vec{r} [/math]. Since the time has now to be local (the time is kept on the particle) get [math] \vec{p}=m_0\frac{d\vec{r}}{d\tau}=\gamma m_0\vec{v}[/math]

 

[math]\gamma=\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}[/math]

 

Kin. power is [math] P=\vec{F}\vec{v}=\frac{d\vec{p}}{d\tau}\vec{v}=\gamma\vec{v}\frac{d\vec{p}}{d t}[/math]

 

In order to get the energy we need to integrate P over time....

 

It can be shown that [math]\frac{d m c^2}{d t}=\frac{d(\gamma m_0 c^2)}{d t}=...(*)...=P[/math]

 

(*) calculation left to the reader.

 

Then, the kinetic energy is non-zero even if speed is zero...!!?

 

This means that a new energy concept that is not classical has to be introduced : rest energy [math] m_0 c^2 [/math]