# Why does the (relativistic) mass change & why?

I studied that when an object moves with a velocity comparable to the velocity of light the (relativistic) mass changes...but I am really eager to know how does this alteration take place....If anyone could really answer my question I would be graceful towards him/her.

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 I'm not comfortable enough on the topic of Special Relativity to give a full answer, but what you're referring to is not (necessarily) what is actually going on. When introducing the concept of an upper limit on velocity, many like to use the interpretation that the 'mass' of the object in motion is changing. Once you've studied the topic in a bit more depth, you see rather that it is better to talk about the relationship between energy and momentum, which does not require any mysterious changing masses. – Daniel Blay Aug 12 '12 at 11:50

In relativistic mechanics, there is a conserved quantity, relativistic momentum:

$\vec p = \gamma m \vec v$

$\gamma = \dfrac{1}{\sqrt{1-\frac{v^2}{c^2}}}$

where m is the invariant mass or less precisely, the rest mass.

Now, one interpretation is to identify $\gamma m$ as the relativistic mass, a speed dependent mass. But this is actually unnatural as it leads to the notion of directionally dependent inertia; objects having more inertia along the direction of motion.

In fact, it is more natural to identify $\gamma \vec v$ as the spatial components of a four-vector, the four-velocity $\mathbf{U}$.

Then, the four-momentum is just $m\mathbf{U}$ with spatial components $\vec p$:

$m\mathbf U = (\gamma m c, \gamma m \vec v)$

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+1 Good answer. Note that other quantities, such as temperature, can be anisotropic (directionally dependent); or at least working physicists in such disciplines as near-Earth space physics find it useful to talk of such things when dealing e.g. with the motions of ions in plasma bounded by the Earth's magnetic field. Nevertheless, the fact that it is simpler to speak of the four-velocity than an anisotropic mass is motivation enough to abandon the notion of relativistic mass. – Niel de Beaudrap Aug 12 '12 at 13:31
@NieldeBeaudrap, good comment and I'm considering editing my answer to address it. – Alfred Centauri Aug 12 '12 at 21:45
Not a good answer--- the relativistic mass is independent of direction, it's only when you take it out of the derivative, and interpret m as the ratio of F to a, rather than as the ratio of p to m, that the direction dependent business starts. So you shouldn't say that $\gamma m$ is a directional mass, or a transverse mass, because the generalization is of $p=mv$ not $F=ma$. Otherwise fine. – Ron Maimon Aug 13 '12 at 4:31
@RonMaimon, I didn't write "$\gamma m$ is a directional mass", I wrote "it leads to the notion of directionally dependent inertia". – Alfred Centauri Aug 13 '12 at 11:01

In Neutonian physics the mass of a particle of matter does not change . It is defined by

*F=m*a* , where F is the force necessary to apply to this specific mass m in order to accelerate it by an acceleration a.

When velocities approach the velocity of light, experiments have told us that the higher the velocity of the particle the more force must be applied for the same acceleration a.

The theory of special relativity addresses this behavior , and it has been validated again and again by experiments. From the link:

To an observer who is not accelerating, it appears as though the object's inertia is increasing, so as to produce a smaller acceleration in response to the same force. This behavior is in fact observed in particle accelerators, where each charged particle is accelerated by the electromagnetic force.

One can find the formula of the mass change in the above link.

Now there is no other answer to "why", then "because that is the way nature behaves".

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 I updated the question slightly. – Qmechanic♦ Aug 12 '12 at 11:59