# Relativistic mass

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In special relativity, when a body reachs speeds near the light ones some strange effects could be appreciate by an external observator: Lorentz contraction, time dilatation and increase of mass. But, Is that last one correct?

In particle accelerators like LHC the mass of a proton "increases" when it reachs high speeds (99,9% of light speed!), due to the equation which describe its linear momentum ( this reason can be applied also to macroscopic bodies)

That could be write P=y*m*v, where y is the gamma Lorentz factor

But in reality, the mass of a particle can't change, it is always the same. In fact the relativistic mass is only the multiplication between the "mass at rest" of the particle and the gamma factor; The gamma factor is used for the speed of it, this error is due to an abbreviation of the linear momentum law for relativistic objects, error corrected by the experts.

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In the decades after Einstein's 'magic year' of 1905, physicists came to understand* that trying to set apart energy,

$E=\frac{mc^{2}}{\sqrt{1-v^{2}/c^{2}}}$

and 'dynamic mass',

$\textrm{inertia}=\frac{m}{\sqrt{1-v^{2}/c^{2}}}$

was quite futile, as they are proportional to each other with a universal constant as proportionality factor. Today, we no longer call mass this velocity-dependent quantity. We just call it kinetic energy. That's what it is. As to 'rest mass', it's just 'rest energy'. You can think of it as some kind of potential energy. If the body can't be broken apart by any process (decay, high-energy collisions), it still has this residual energy.

As an example, if a body of rest energy mc2  (or $$m$$, if you will; it's just a matter of units) decays into pieces of respective rest energies m1 and m2 , we know the liberated energy is (removing the unnecessary index 0 for 'rest', as mass is always rest energy),

$\triangle E=\triangle mc^{2}=mc^{2}-m_{1}c^{2}-m_{2}c^{2}$

This is energy that we can understand as previously contributing to the internal cohesion of the particle that has just decayed, and no longer is contributing to forming the masses m1 and m2 , but contributing to the kinetic energy of the decay products, now moving with speeds v1 and v2 .

Edited by joigus

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