How to understand the conception of “mass /energy of rest”?

Answer 1

In classical physics, the total kinetic energy of a mass is 1/2 mv^2.

However, going to special relativity, the total kinetic energy is the total of 2 energies. I won't go to the math behind it, but basically the energies are from the motion of the particle and the existence of mass in the particle given by E= mc^2. This equation is the rest energy equation, relating the total rest energy to the total rest mass of the particle.

Rest mass is the mass of something when it is not moving. If something is moving, we just add the effects of the motion to this rest energy to fing the total kinetic energy of the particle.

Answer 2

When the transformations of special relativity are applied to problems involving conservation of energy and momentum, the solutions result in the equation for the energy of a moving object to be E = M*C^2 + .5*M*V^2, where V is the observed velocity and M is the "rest mass" of the object. This is different from the classical equation for the energy of a moving object which is E=.5*M*V^2. In the relativistic equation, if the object is stationary, V=0, but an amount of energy = MC^2 remains, and is considered the equivalent energy of the rest mass.

Answer 3

We make a fundamental assumption in our everyday life that everyone will agree on the mass of an object and its energy.

This assumption is wrong.

To see that this must be so think about a star receding from the Earth. It emits a nice blue photon. When the photon arrives at the Earth the Doppler effect shifts it towards the red, because the star was receding. But red photons have less energy than blue ones.

The solution to this riddle is, of course, that the photon was always a red photon as seen from the Earth, and remains a blue photon as seen from the star. So the relative motion of the Earth and the star causes observers on each to disagree about mass and energy (and a host of other things).

Now to correctly handle this it is necessary to break away from our usual way of handling space a time as though space is some kind of map on which things happen and t is the time at which they happen, because it is clearly not possible to create such a map that everyone will agree on. The solution is to describe spacetime as what mathematicians call a fibre bundle.

But this is far too tiresome for everyday use, so an alternative shortcut approach is adopted. This involves - for particles - making the frame of reference in which the particle is at rest "special" (it is not special in reality), and measuring its mass and energy in that frame. Everyone moving with respect to this rest frame can now calculate the mass and energy that they will observe in their frame just by knowing how they are moving relative to this rest frame.

Answer 4

Understand this: when two objects with discernible mass are moving at the speed of light relative to one another, they are pure energy. The problem is that we see relative rest as the normal state of being, rather than relative light speed. Less than light speed, relative to another object, is in fact a very unique state of being.