REAL MEANING OF E=MC2 (PART- 2)

From the previous discussion, we had a clear cut ideology on mass and its measurement. We had a good agreement on the aspect that even if two objects are made of identical constituents, they does not weigh the same in general. Mass of something made out of smaller parts is not simply the sum of the mass of the parts. Instead, it depends on several factors. Also, we’ve learned that the extra energies (E_extra = M_extra C²) which are present within the object contribute to the mass of the object as

M_extra = E_extra/C²

            Since, C² is soo huge, this extra mass is billionth of billionth percent of total mass. This might be small but measurable.

Therefore, m ~= Amount of matter

You can see the full discussion here.

Okay.

 Now, here comes the fun part.

In all the examples we’ve discussed earlier the total mass of the object is always greater than the combined mass of its parts. But, at the starting of the article I quoted that the mass of the Hydrogen atom is less than that of combined mass of the electron and proton.

Why?

How does that work?

          It’s because potential energy of a system can be negative.

                   Suppose we call the energies of protons and electrons, infinitely far away from each other as zero. Since they attract each other, and tend to get together, their electro potential energies drops, just like your gravitational potential energy (Mgh) drops as you come down to the earth surface, which is also attracting you.

So, in a hydrogen atom, the potential energy of proton and electron in a hydrogen atom is negative.

          Now, the kinetic energy of the electron in the hydrogen atom is always positive, due to its movement around the nucleus.

But, as it turns out the negative potential energy of the atom is negative enough such that the sum of kinetic and potential energies of the electron and proton still comes out negative.

E_Kinetic + E_potential < 0

Therefore, M_extra = E/C² < 0.

          Therefore, hydrogen atom weighs less than its constituent parts.

Yeah! Blown?

          In fact, borrowing to the circumstances, all the atoms on the periodic table weigh less than its constituent elements.

Same is true for molecules.

The mass of an oxygen molecule is less than the combined mass of two oxygen atoms because, the potential energy of the oxygen atoms is negative after the formation of a chemical bond.

What about neutrons and protons themselves?

          The neutrons and protons are made of smaller materials called quarks, whose combined mass is 3000 to 4000 times smaller than the mass of the neutron and proton.

          Basically, this is from potential energy of quarks.

Then, what about the electrons in quarks?

          Atleast, in a standard model of particle physics, they’re not made of much smaller parts. Does that mean this is some sort of baseline mass that concerns pre Einstein work sense?

          This is a sort of question. But,

                   Crudely speaking, you can take this mass as the combination of various potential energies.

For instance, there is some potential energy due to the interaction of quarks and electron known as higgs field. And there is some potential energy due to the electric field they themselves produce and in the case of quarks, also with the gluon field.

Okay, what about Matter-Antimatter Annihilation?

          Doesn’t that has to be thought of mass being converted to energy?

Interestingly, NO!

      There’s a simple way to conceptualize even this process as converting one form of energy to other like potential energy, kinetic energy, light energy etc…

          You never need mass to energy out coming.

But, take my word.

YOU DON’T HAVE TO TALK ABOUT CONVERTING MASS TO ENERGY EVER!

          Instead, the punchline of this article is that mass isn’t a thing at all. It’s a property. A property that all energies exhibit. And in that sense even it is not correct to think of mass as indicator of amount of stuff in the material sense, you can think of it as the amount of energy possessed by the material.

So, without realizing that, you’ve been measuring the cumulative energy content of an object every time you use a scale.

The Einstein’s paper on this aspect is only 3 pages long and not that hard to read. I strongly encourage you to read it here.

I hope these articles have given you a really good meaning of E=MC² and the definition of mass.

Thanks for reading.