special relativity - Mass-Energy relation

Einstein mass- energy relation states $E=mc^2$. It means if energy of a paricle increases then mass also increases or vice-versa. My question is that what is the actual meaning of the statement "mass increases"? Is really the mass of the particle increasing or what?

Answer

The rest mass of an object is, by definition, independent of the energy. But all other forms of mass are indeed increasing with the energy, as $E=mc^2$. With the relativistic interpretation of the kinetic energy, the total mass is $$ m = \frac{m_0}{\sqrt{1-v^2/c^2}}$$ Here, $m_0$ is the mass measured at rest, i.e. the rest mass. The corrected, total mass goes to infinity if $v\to c$ and it holds for the following interpretations of the mass:

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  the inertial mass, i.e. the resistance towards the acceleration, increases. For example, the protons at the LHC have mass about 4,000 times larger than the rest mass (the energy is 4 TeV), and that's the reason why it's so hard to accelerate them above their speed of 99.9999% of the speed of light and e.g. surpass the speed of light. It's impossible to surpass it because the object is increasingly heavy, as measured by the inertial mass

  
  
  


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  the conserved mass. If you believe that the total mass of all things is conserved, it's true but only if you interpret the "total mass" as the "total energy over $c^2$". In this conserved quantity, the fast objects near the speed of light indeed contribute much more than their rest mass. If you considered the total rest mass of objects, it wouldn't be conserved

  
  


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  the gravitational mass that enters Newton's force $Gm_1m_2/r^2$. If an object is moving back and forth, by a speed close to the speed of light, it produces a stronger gravitational field than the same object at rest. For example, if you fill a box with mirrors by lots of photons that carry some huge energy and therefore "total mass" $m=E/c^2$, they will increase the gravitational field of the box even though their rest mass is zero. Be careful, in general relativity, the pressure from the photons (or something else) creates a gravitational field (its independent component curved in a different way), too.

  
  

Despite this Yes Yes Yes answer to the question whether the total mass indeed increases, Crazy Buddy is totally right that especially particle physicists tend to reserve the term "mass" for the "rest mass" and they always prefer the word "energy" for the "total mass" times $c^2$.