# Nuclear Fusion: Why is energy created from mass?

Ok, so nuclear fusion is given by the formula E=MC2, where E = Energy, M = Rest mass and C = 299792458. To my understanding, this means that if two protons collide under the incredibly high speeds/temperatures(like they do in the sun), they will fuse, having reduced mass and that mass is converted to energy.
But, I thought that energy could not be created or lost, it is always converted. In a nuclear reactor, nuclear energy is converted to thermal energy. In beta decay, if an electron is slowed by an atom, that lost kinetic energy is converted to bremsstrahlung X-rays(Electromagnetic radiation). So, why is energy created from mass? I can understand why antimatter can create energy from annihilation, basically 1 + -1 = 0 + γ + γ. Is it similar? Thanks.

Orodruin
Staff Emeritus
Homework Helper
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You will have an easier time with energy conservation if you consider that there is also an energy associated to a mass and that the total energy of an object can be written ##E = mc^2 + T##, where ##m## is the object mass and ##T## its kinetic energy. In special relativity, you will have the relation ##E^2 = m^2c^4 + p^2 c^2##, where ##p## is the momentum of the object. The thing to note is that even an object at rest has an energy, given by its mass. Thus, it is not really that mass is converted into energy as much as mass being converted into other forms of energy, as mass is a form of energy in itself.

Also see our FAQ on the subject: https://www.physicsforums.com/threads/what-is-the-massenergy-equivalence.763067/

TEFLing and Raiden60
ChrisVer
Gold Member
what do you mean energy created?
There is no energy created out of nothing. You have that your initial objects have some mass together: $m_1 + m_2$ and then the product has a mass $m < m_1 + m_2$.
The difference $m_1 + m_2 - m$ is released as photons or kinetic energy for the products (if you have more ).

You will have an easier time with energy conservation if you consider that there is also an energy associated to a mass and that the total energy of an object can be written ##E = mc^2 + T##, where ##m## is the object mass and ##T## its kinetic energy. In special relativity, you will have the relation ##E^2 = m^2c^4 + p^2 c^2##, where ##p## is the momentum of the object. The thing to note is that even an object at rest has an energy, given by its mass. Thus, it is not really that mass is converted into energy as much as mass being converted into other forms of energy, as mass is a form of energy in itself.

Also see our FAQ on the subject: https://www.physicsforums.com/threads/what-is-the-massenergy-equivalence.763067/
That seems to make sense. Thanks for explaining, it's given me a bit more understanding.

Basically the two particles lose potential energy between one another, therefore energy would be required to pull them apart. Hence a release of energy when two particles are smacked together to become one. (By dumbing stuff down I have always found it easier to understand.

Orodruin
Staff Emeritus
Homework Helper
Gold Member
Basically the two particles lose potential energy between one another, therefore energy would be required to pull them apart. Hence a release of energy when two particles are smacked together to become one. (By dumbing stuff down I have always found it easier to understand.

Except that it is wrong and not contributing to the understanding. When you want fusion to happen you are essentially trying to merge two positively charged nuclei. This means you have to overcome the repulsive Coulomb barrier to make them meet. This iss why you need to put energy into the system to create fusion, but if the Coulomb potential energy was all you got out of the fusion, there would be no point in trying to create it as you could at most get out the same amount of energy that you put into the system. This would also mean stars could not shine.

Net energy release in fusion is based on the resulting nucleus having less mass than the sum of the original ones.

Khashishi