What is Mass exactly?

 

            In physics, mass is generally defined as the quantity of matter. Matter is nothing but something which occupies space and has mass. Mass is an intrinsic property of a physical matter, but the question is how does the matter get this intrinsic property? We shall search the answer to this question in some definitions of mass.

INERTIAL MASS:

 According to Newton’s 2nd law of motion, 

F=ma

∴m=F/a 

 If same force F be applied in two different masses m1 & m2 and produces the accelerations a1 & a2 therefore we have, 

F=m1a1=m2a2

∴m1/m2=a2/a1 

Thus, the masses of two bodies are inversely proportional to the accelerations produced in them by a given force, irrespective of the magnitude of the force. So, higher force should be applied for higher mass to accelerate and for a lower mass, lower force should be applied. This is because of the inertia of the body and this corresponding mass is known as inertial mass. Here, mass can be defined as the measurement of inertia. Inertial mass tells us how much force is to be applied for a body to change its state of rest or motion. It is independent of any force (i.e) the inertial mass of a body is same throughout the universe.

GRAVITATIONAL MASS:

 Imagine you are holding a plastic ball and an iron ball in your hands. It is obvious that the iron ball weighs more than the plastic ball because of its larger mass, but as we have seen before that mass is a measurement of inertia and we have no change in state of being at rest, then how do you feel the mass of the ball? It's because of the gravitational pull of earth and the corresponding mass is known as gravitational mass. It is also the same as the inertial mass, but the difference is that the gravitational mass is directly proportional to the gravitational pull of an object(earth). From Newton’s law of gravitation we have,

F=-Gm1m2/R²

If m1&m2 be the masses of plastic ball and iron ball respectively, M be the mass of earth and F1&F2 be the force exerted by earth on m1&m2 respectively,

F1=-Gm1M/R²

F2=-Gm2M/R²

∴F1/F2=m1/m2 

From the above equation we shall say that larger force is needed to hold larger mass and lesser force is needed to hold lesser mass against the gravitational field. Weight and gravitational mass are completely two different things. Weight is the gravitational force acting on a body whereas, gravitational mass is the inertial mass which is attracted by the gravitational force.

CONCEPT OF ENERGY-MASS EQUIVALENCE:

        We still don't have a clue to our question, how does a matter get mass? atleast in Newtonian mechanics. Here, Einstein comes up with his legendary theory of special relativity. In his theory he proves that energy and mass are different manifestations of same thing.

E=mc² 

           If both energy and mass are the same thing, does mass change with the change in energy? Practically, the answer is yes. Mass changes with the energy in negligible amount. If a body of rest mass m0 moves at 'v' velocity, then the change in mass corresponding to kinetic energy is given by,

Here, mrel and m0 are the relativistic mass and rest mass of the body respectively. Rest mass is defined as the mass of the body at rest whereas, relativistic mass is the mass of the body traveling at 'v' velocity relative to the observer. 'v' is very less than the speed of light(c). Thus, mrel is approximately equal to m0. So, we can't observe a significant change in mass for an object which travels very slower than light.The above equation also states that anything which travels at the speed of light has zero rest mass. That's why photons and gluons are considered to be massless particles. The energy corresponding to rest mass and relativistic mass are called rest energy and relativistic energy respectively.

             Subatomic particles like proton and neutron are made up of fundamental building blocks of particles called quarks. Quarks give mass to neutrons and protons. Quarks are getting mass by interacting with a mysterious field that fills the whole universe called Higgs field. The more they interacting with the field they acquire more mass. Particles like photons do not interact with this field and it leads them to have zero rest mass and to travel at the speed of light.

               For proton, the interaction of the quarks in the Higgs field gives only one percent of the rest mass. The remaining ninety nine percent of the rest mass is obtained by the binding force or strong force which holds the quarks together. It is called gluon field. Other energies like chemical, thermal and kinetic energies are added to get the relativistic mass of a proton. Same goes for neutron also. Thus, the relativistic mass of a particle is just the relativistic energy of it.