# Mass-energy equivalence

The mass-energy equivalence principle states that the mass of a system and its energy are the same property in any physical system.

Intuitively, it means that the total amount of mass in a body would be **conserved** as energy if the body was destroyed. Conversely, any amount of energy (e.g. in electromagnetic waves) could be transformed into a massive body.

In his theory of **special relativity** (1905), Albert Einstein expressed the mass-energy equivalence in terms of the formula: $$$E=mc^{2}$$$

$$m$$=mass; $$c=$$speed of light.

The mass-energy equivalence equation can be thought of as similar to liquid water and ice water. They both refer to the same thing but in a different state.

When particles **collide**, new particles of matter can be created from the energy released in the collision. The total energy is conserved.

An object with higher kinetic energy will have more mass-energy than an object with lower kinetic energy: $$$E_{\text{total}}=E_{\text{kinetic}}+E_{\text{rest}}$$$

The rest mass-energy $$E_{\text{rest}}$$ has an associated rest mass $$m_{\text{rest}}$$ according to mass-energy equivalence (i.e. $$E_{\text{rest}}=m_{\text{rest}}c^{2}$$).

The difference in mass due to kinetic energy will only be noticeable at **very high speeds/energies** because $$m=E/c^{2}$$ is very small in classical cases.

$$m$$=mass; $$c=$$speed of light.

The rest mass $$m_{0}$$ is the mass of a body which is at rest relative to the observer. It is an intrinsic property of a body and distinct from its mass $$m$$ as measured by an observer.

Intuitively, the rest mass is the mass (and hence the energy) stored in the **movement and interaction** of particles within the object.

The rest mass of an iron atom moving in a gravitational field is primarily determined by the mass of the neutrons, protons and electrons inside it and the interactions among these particles.

Rest mass **does not include** the mass present in the form of kinetic or potential energy from the movement or position of the object as a whole.

From the **mass-energy equivalence principle**, we can either talk about rest mass or **rest mass-energy $$(E_{0})$$**:$$$E_{0}= m_{0}c^{2}$$$.

**Photons** do not have a rest mass-energy since they are never "at rest". The energy carried is purely kinetic and given by the de Broglie relation $$E=pc =hf$$.

The total energy and mass of a system is **conserved**. A particle emitting a photon would lose mass corresponding to the mass-energy of the photon. A particle which absorbs a photon gains mass corresponding to the mass-energy of the photon.

$$c=$$speed of light; $$E=$$energy; $$p=$$momentum; $$h=$$Planck constant.