Reltavistic Mass || Special Theory of Reltavity

Mass Really Does Increase with Speed Deciding that masses of objects must depend on speed like this seems a heavy price to pay to rescue conservation of momentum! However, it is a prediction that is not difficult to check by experiment. The first confirmation came in 1908, measuring the mass of fast electrons in a vacuum tube. In fact, the electrons in an old-fashioned color TV tube are about half a percent heavier than electrons at rest, and this must be allowed for in calculating the magnetic fields used to guide them to the screen. Much more dramatically, in modern particle accelerators very powerful electric fields are used to accelerate electrons, protons and other particles. It is found in practice that these particles become heavier and heavier as the speed of light is approached, and hence need greater and greater forces for further acceleration. Consequently, the speed of light is a natural absolute speed limit. Particles are accelerated to speeds where their mass is thousands of times greater than their mass measured at rest, usually called the “rest mass”. …Or Does It? Actually, there is continuing debate among physicists concerning this concept of relativistic mass. The debate is largely semantic: no-one doubts that the correct expression for the momentum of a particle having a rest mass m moving with velocity v→ is p→=m1−v2/c2√v→. But particle physicists especially, many of whom spend their lives measuring particle rest masses to great precision, are not keen on writing this as p→=mrelv→. They don’t like the idea of a variable mass. For one thing, it might give the impression that as it speeds up a particle balloons in size, or at least its internal structure somehow alters. In fact, a relativistic particle just undergoes Lorentz contraction along the direction of motion, like anything else. It goes from a spherical shape towards a disc like shape having the same transverse radius. So how can this “mass increase” be understood? As usual, Einstein had it right: he remarked that every form of energy possesses inertia. The kinetic energy itself has inertia. Now “inertia” is a defining property of mass: more inertia means it's harder to accelerate, a given force accelerates it less.. The other fundamental property of mass is that it attracts gravitationally. Does this kinetic energy do that? To see the answer, consider a sphere filled with gas. (And let's assume there's negligible interaction between the molecules, true for a dilute gas.) The sphere of gas will generate a spherically symmetric gravitational field outside itself, of strength proportional to the total mass. If we now heat up the gas, the gas particles will have this increased (relativistic) mass, corresponding to their increased kinetic energy, and the external gravitational field will have increased proportionally. (No-one doubts this either.) So the “relativistic mass” indeed has the two basic properties of mass: inertia and gravitational attraction. (As will become clear in the following lectures, this relativistic mass is nothing but the total energy, with the rest mass itself now seen as "rest energy".) Footnote: For anyone who might go on sometime to a more mathematically sophisticated treatment, it should be added that the rest mass plays an important role as an invariant on going from one frame of reference to another, but the "relativistic mass" used here is really just the first component (the energy) of the four dimensional energy-momentum vector of a particle, and so is not a Lorentz invariant #Reltavistic #Mass #relativity