How can energy creat mass?

Question

From $E=mc^2$, we know that energy can be mass. But how? Like how can particles (gluon, photon, W boson and others) create energy? What do they do? How do they move and create mass?

Answer 1

They don't create energy, they are energy. Energy and mass in special relativity are the same thing.

Your question's rather like asking "how can ice create water?" Ice and water are the same thing, just in different states. Energy & mass are similar.

Edit: as pointed out by Jan Lalinsky in a comment below, energy isn't exactly the same as mass; photons can have energy but not mass, for example. But the two concepts are still intimately related, and certainly massive particles such as the gluon are energy.

Answer 2

It was discovered by Einstain that the correct formula for the energy of a body of mass $m$ and velocity $v$ isn't just $\frac12 m v^2$, but rather

$$ E = \frac{mc^2}{\sqrt{1-v^2/c^2}} = mc^2 + \frac12mv^2 + \frac38 \frac{mv^4}{c^2} + ... $$

That means that even if a body does not move $v=0$., it still posesses the energy $E=mc^2$, called rest energy. If the body does not change, it is just there, constant. It can however be released in decay processes, when a particle of mass $m_1$ decays in two particles of masses $m_2$ and $m_3$, where $m_2+m_3<m_1$. If it happens then the rest enegry of the initial particle is greater than the sum of rest energies of the produced particles. the extra energy, $\Delta E = (m_1-m_2-m_3)c^2$ takes the form of the kinetic energy of the products, nd usually at least one of the prodcuts gets accelerated to very high speed, becoming a radiation. Similar thing happens in atomic reactors and bombs, though it is more complicated there, as itthey depend not on a simple decay, but on more complicated reaction; still in this reaction the sum of masses of substrates is greater than the sum of masses of products, which releases some part of the rest energy of substrates as the kinetic energy of products, which we then use for various purposes.

The oposite, transforming kinetic energy into rest energy, happens in particle colliders. When two particle with energy high enough collide, there is a chance that some of this energy will transform into new particles. The rest energy of a particle tells us the minimal amount of kinetic energy that is required to create this particle (though in practice we often need more energy than this, as because of laws like charcge conservation etc. new particles are often created in pairs or bigger groups). For example, if we collide electron with antielectron (both have mass 0.511 $MeV/c^2$) and we want to produce muon and antimuon (mass 105.658 $MeV/c^2$) in the reaction $$ e^- + e^+ \rightarrow \mu^- + \mu^+$$ each of the electrons needs to have kinetic energy of at least 105.547 MeV, or elese the will be not enough energy available to create the muons. That's why to discover new particles and investigate their properties we use accelerators, to give the colliding particle enough energy to produce these new particles.