E = mc2 is certainly the most popular formula in physics but what does it mean?

The Mass-Energy Equivalence

This formula is simpler than other complicated formulas in physics. The ‘E’ gives the value of the energy of mass ‘m’ and ‘c’, the speed of light in a vacuum which is a constant quantity in the universe according to the special theory of relativity.

Image source – Pixabay

The Misconceptions

There is a trend of introducing mass-energy equivalence (E = mc2) in high school without the concept of special relativity. So, people might get derailed from understanding the true meaning of this formula.

This formula is often mistaken for Einstein’s relativity. However, it is actually one of many conclusions that we can draw from the relativistic approach of Einstein.

Also, my tutor in high school said that if a matter attains the speed of light, it completely converts into energy as given by that equation. But, Einstein didn’t infer such conclusions and neither do I. A mass cannot attain such velocity since the relativistic mass reaches an infinite value as it attains the speed of light.

Relativity leading to equivalence

The theory of relativity opposed the long-accepted conservation law of mass, concluding that mass increases as speed increases. Then resulted in the mass-energy equivalence which attempted to solve this by the unification of two conservation laws of physics, conservation of mass and energy to one single law, conservation of energy stating that mass is also one form of energy. So, this formula merged the principle of conservation of mass to the principle of conservation of energy and created a correspondence.

The insight to E=mc2 (Mass-Energy Equivalence)

E = mc2 is actually called the mass-energy equivalence. This means that a mass ‘m’ can be equivalent to energy, ‘m’ times square of the speed of light. Also, energy radiation carrying energy ‘E’ is equivalent to a mass given by, mass = Energy/( square of the speed of light in a vacuum). So according to it, mass and energy are equivalent terms.

In the words of Einstein, when a mass gives off energy ‘E’, its mass is decreased by E/(square of the speed of light). Also, the reverse process, pair production i.e production of mass from energy, has a possibility and is seen during high energy proton-proton collision.

For instance, let us consider a nuclear reaction in which a large amount of energy is released. In these reactions, there is a decrease in the mass of products compared to that of reactants. So the overall energy (mass-energy) associated with the reaction remains conserved, there is no change in energy.

Matter and Energy are only two things that exist in the universe if a thing is not one then its the other. And these things are equivalent to each other. Hence, energy prevails as the only entity in the Universe.

Experimental proof of E=mc2

Radioactive decay was the first experimental proof of this formula. The energy of the particles radiated from radioactive substance comes from the mass decrements of the substance. This leads to the conservation of energy throughout the reaction, as mass is a form of energy. The value of energy is given by E=mc2.

E=mc2 has also greater importance in nuclear physics. The energy that is required to form a nucleus is equivalent to the mass decrease after the formation of a nucleus from constituent nucleons and the value is given by equivalence relation.

Also, the reverse phenomena of production of pair of particles have been evident in Patrick Blackett’s cloud chamber (awarded the Nobel prize in physics 1948) and also in a proton-proton collision.

Its supports the hypotheses

Mass is a form of energy and energy generation from a mass is followed by a decrease in mass. The mathematical form allows the reverse phenomena of production of mass from energy and has helped to formulate a different hypothesis in physics.

Yet to be proven, the theory of Hawking radiation has its base on this formula. A pair of virtual particles are believed to be created in a black hole and enabling it to radiate particles. Also in hypothesized pair-instability supernova, there is an abrupt decrease in pressure due to the conversion of energy to a pair of neutrinos. This decrease in pressure induces the explosion.

Atom Bombs made possible (the nuclear energy)

Energy is numerically equal to 90 trillion times the mass expressed in a kilogram. So, the mass-energy equivalence suggests that the energy due to even a small mass is enormous due to the factor – square of the velocity of light in the formula. The study of the conversion of mass to energy led to nuclear reactions which resulted in the atom bomb.

During a nuclear reaction, a high amount of energy is liberated as given by this equation i.e from the mass. The nuclear power plant is as well as the nuclear weapons (like an atom bomb and hydrogen bomb) release energy on the basis of this relation.

E=mc2 has helped to redefine our understanding of mass as a form of energy. The above experimental proofs show the conversion of energy to mass and vice-versa. Further, this equivalence has opened new dimensions of understanding by forming the basis of different hypotheses. Its application has not only aided the understanding but also has enabled us to extract energy in large amounts so that the energy demand of the modern world is met with ease.

Ashwin Khadka is a PhD Scholar in Nano Energy and Thermofluid Lab in Korea University, Republic of Korea under Korean Government Scholarship Program. He has a Masters Degree in Physics from Tribhuvan University, Kathmandu, Nepal. He is a science enthusiast, researcher and writer.