# Mass Energy equivalence

P.J.Mazumdar

The relation between mass and energy has very important philosophical implications for Advaita philosophy, as it supports the theory of a single commonality beyond the Universe.

E=MC² actually does not mean that energy can be converted to mass or mass can be converted to energy.

What it means instead is that mass and energy are coexistent, when a given amount of mass exists in a system, the equivalent amount of energy exists with it, ie, this amount of mass can also be seen or expressed as its equivalent amount of energy; and when a given amount of energy exists in a system, this energy can also be seen or expressed in terms of its equivalent amount of mass.

It is conventional to say, in a nuclear bomb for example, that a certain amount of mass is converted into energy. But this is not a correct way of speaking. We can never say that mass exists alone before a reaction and after it, its equivalent amount of energy exists alone. Right before the explosion, some amount of mass had existed in the system and along with it, its equivalent amount of energy and after the explosion, some amount of energy is dispersed and along with it, its equivalent amount of mass.

Because of the factor c², the equivalent amount of energy for a given mass is very high.

In a nuclear bomb explosion which yields 9 x 1013joule (21.5 kiloton) of energy for example, the weight of this 21.5 kilotons of heat and electromagnetic and other radiation is just 1 gram.

(This example is taken from the Wikipedia entry, Mass Energy Equivalence)

If we consider this example carefully, here it does not mean that 1 gram of mass in the bomb has been converted into 21.5 kilotons of energy in the explosion.

Rather, we should see it like this. Before the bomb exploded, it had, along with the other mass–energy of the bomb, 1 gram of mass and this mass was coexistent with 21.5 kilotons of energy. These two terms, 1 gram of mass and 21.5 kilotons of energy, are two sides of the same coin, what is seen as 1 gram of mass from one side is seen as 21.5 kilotons of energy from the other side. After the explosion, the bomb releases this entity, which when expressed in mass is 1 gram and expressed in energy is 21.5 kilotons. So we can say either 1 gram of mass is released or 21.5 kilotons of energy is released.

If the bomb is exploded in a box which does not allow any escape of either mass or energy, we would find that the box weighs the same both before and after the explosion. But if we cut a window in the box which allows the escape of the energy through heat, light and radiation, we would find that the box has lost 1 gram in mass, which is equivalent to the 21.5 kilotons of energy released. If this box was within a larger box capable of absorbing all the energy, so that all 21.5 kilotons of energy is absorbed, we would now find that this larger box weighs 1 gram more.

Both the law of conservation of energy and the law of conservation of mass hence work side by side. Both are conserved together and remain intact before and after all chemical and physical reactions.

Thus we see that mass and energy are two words for the same phenomenon. They are two sides of the same coin.

The laws of conservation of mass and conservation of energy arise basically from the conservation of this ‘coin’; this ‘coin’ is never destroyed nor created anew and hence mass and energy, its two faces, are also neither destroyed nor created.This mass and energy are related by E=MC².

But right at this point, we must make a very important assertion: this equation E=MC² is legitimate only when used for rest energy and rest mass. When used for terms other than rest mass, to define relativistic mass for example, this can lead to logical inconsistencies.

This important consideration arises from the laws of relativistic physics, in which a particle travelling near the speed of light was said to become ‘heavier’ or acquire mass due to its speed. The amount of mass gained is defined by E=MC².

In the Standard Model of quantum physics, which is the accepted physical model of present science, mass as we remember comes from the interaction of a particle with the Higg’s field. This gives quantum particles their rest mass. Particles like photons which do not interact with the Higg’s field do not have this rest mass.

Now if we accept relativistic mass, this would appear to be an alternative way to acquire mass. Here it is not interaction with the Higg’s field but the speed of the particle itself which gives it mass, the extra relativistic mass, as it is termed. Where would this relativistic mass arise from? Is it different from the rest mass that a particle acquires through interaction with the Higg's field? These and other questions arise when we consider ‘relativistic mass’.

Hence we see that the term ‘Relativistic Mass’ is an unsound term which has no scientific justification abd raises problems at the very heart of the Standard Model. Because of this, several scientists including Einstein himself, who discovered the relation E=MC² advised that it should be used only for rest mass and the term relativistic mass should not be used at all. The extra energy that a particle acquires because of its speed near light should not be considered as mass and E=MC² should not be used to express this extra energy as (relativistic) mass.

Lev B. Okun in The Concept of Mass (Physics Today –– June 1989, Volume 42, Issue 6, pp 31) launched a strong attack against the very use of the term ‘relativistic mass’ and showed that it was an unnecessary term. He argued that ‘mass’ should be used only to mean ‘rest mass’ and what is termed as relativistic mass is in fact only the energy state of the particle. He argued that the equation E=MC² stands only for Rest energy=Rest mass × C² and this was Einstein’s meaning too.

"It is not good to introduce the concept of the mass M=m/(1–√v²/c²) of a moving body for which no clear definition can be given. It is better to introduce no other mass concept than the 'rest mass' m. Instead of introducing M it is better to mention the expression for the momentum and energy of a body in motion." Einstein 1948. (This image is taken from L.Okun's article in ‘Physics Today’)

For example, in the Wikipedia article stated above, it is said, “Even a single photon traveling in empty space has a relativistic mass, which is its energy divided by c²”.

This is a prime example of where using E=MC² gives illogical results, in this case a mass for a photon. A photon by definition is massless, it does not react with the Higg’s field and hence never acquires mass. From where would the mass of a photon arise? E=MC² must not be seen as a competitor to Higg’s in giving mass to particles. This is what using E=MC² carelessly can make it seem to be doing.

For example, while calculating the mass of a proton, we know that the sum of the rest masses of the quarks and bosons in it contributes only a small part of it and the major part is due to energy of the quarks and bosons as they interact with each other. Now, the rest mass of the proton is equivalent to the rest energy by E=MC². There is no controversy about this. Hence we can find the rest energy of the proton and calculate its mass with this equation. To find the rest energy, we use the sum of all the rest energies of each quark and boson plus the energies of their interactions, and from this total rest energy calculate the rest mass of the proton. This is a legitimate use of E=MC². But it would not be legitimate, or at least not as legitimate, to find the total energy of a quark (the sum of its rest energy + the energy of its interactions) and from this determine a value for the mass of the quark as it interacts (its relativistic mass). Thus it would not be legitimate to say that a quark ‘increases its mass’ or ‘becomes heavier’ within a proton due to its interactions.

Similarly, in this article on Wikipedia, it is again said: “If a box of ideal mirrors contains light, the mass of the box is increased by the energy of the light, since the total energy of the box is its mass.”

This is absolutely correct. But from here, we should not go on to make the fallacy of saying that a photon has mass. If we considered rest mass as the only mass, this problem of defining a photon as having mass would not have arisen. Again, overenthusiastic use of E=MC² has given rise to this logical inconsistency.

When we consider the rest mass of the box, then we have to consider the rest energy within it, and the energy of the photon enters into this equation. Hence the rest mass of the box certainly increases because of the energy added by the light.

But when we consider the photon, its increase is only an increase in energy. It is not legitimate at all to use E=MC² and convert mathematically the energy of the photon into mass, and then say this is the (relativistic) mass of the photon.

Thus it is important to remember both the power and the weaknesses of E=MC². Unbridled use of this equation can give rise to logical oddities.

The importance of mass and energy equivalence for Advaita is this:

E=MC² shows that mass and energy are equivalent, they are two sides of the same coin. But it is important to know that, they are not the same in our universe, though equivalent, they are two different entities in our Universe.

In the present Standard Model also, they are treated as two different entities. So also in the String Theory. But Advaita asserts that since they are equivalent and can be expressed as each other, there must be something in common to both of them. Since this commonality is not found in the universe, there must be something beyond the universe of which both mass and energy are two different expressions. There must be something which expressed in one way appears as mass in our universe and expressed in another way appears as the energy of the universe. Thus there must be an absolute commonality to the whole universe. This commonality is the ‘coin’ of which, not just mass and energy, but every thing in the universe, including consciousness, are but different faces.

This commonality is the Absolute of the universe, the Brahman.