If mass is just energy, how does thermal or kinetic energy transfer happen? [closed]

Question

If mass is just energy, as it's excitations on quantum fields that when they vibrate together a certain way, they end up a particle, then how does energy transfer work?

Specifically kinetic energy transfer, for example when a high energy particle hits another particle, the mass doesn't change, neither does what the particle is itself, but it moves slower and the particle it hits moves faster. How does this translate to what's happening on the quantum level, if mass and energy are just the same intrinsic property of a particle?

Is my question correct, or do I have a misunderstanding on how mass and energy are related?

Answer 1

In special relativity any particle or object composed of particles has an invariant mass, which does not change.

The length of the energy-momentum 4-vector is given by

The length of this 4-vector is the rest energy of the particle. The invariance is associated with the fact that the rest mass is the same in any inertial frame of reference.

For a particle/object in the inertial frame where its velocity is zero, $p$ is zero, this is the mass that can be converted to other particles which can have kinetic energy that can be used in fusion reactors..

One can always go to an inertial frame where the particle is moving and thus has kinetic energy, the invariant mass does not change. In your scattering example the invariant mass of the system of two particles does not change after scattering.

At the quantum level where interactions are calculated , special relativity holds (the theory validated by all experimental results up to now) so there is no extra invariant mass to the system due to different inertial frames.

Answer 2

When a high energy particle, say a neutron, hits another particle, say another neutron – the neutron's mass does change. For example, if instead the first neutron moving at some high speed $v$ is captured and placed in a box, where it simply bounces off the walls without losing any energy in the collisions, and you then weigh the box on a very precise scale, the mass measured will be:

$$\text{Box max + neutron rest mass + extra mass}$$

The "extra mass" term is equal to $E_{kinetic}/c^2$, which will be equal to:

$$\left(\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}-1\right) m_r $$ where $m_r$ is the rest mass (invariant mass) of the neutron.

That is why in physics we distinguish "rest mass" from "mass" in general. Rest mass as it implies is the mass of the particle or object in a frame of reference where it is stationary. This is the "minimum mass" of the particle, and corresponds to the energy confined within it (quarks and gluons in the case of a neutron).

For speeds $v$ not too close to the speed of light $c$, the above expression can be simplified to:

$$\frac{E_{kinetic}}{c^2}= \left[\frac{1}{2}\frac{v^2}{c^2}+\frac{3}{8}\frac{v^4}{c^4}+...\text{(even smaller terms)}\right] m_r $$

and if we keep only the first term, we get the familiar Newtonian expression:

$$E_{kinetic} = \frac{1}{2}v^2 m_r $$

This illustrates that, in general, the mass of a particle is dependent on the speed $v$ of the particle, and is a measure of the total energy (internal + kinetic) of the particle.

With that being said, in modern physics the quantity $$M=\frac{E_{total}}{c^2}=\frac{E_{rest}}{c^2}+\frac{E_{kinetic}}{c^2}$$

known as "relativistic mass" is rarely used, if ever. Instead we speak of total energy content $E_{total}$ and do not name it "mass," reserving that word for the rest mass $m_r$. But nonetheless, the total energy $E_{total}$ does manifest as mass $M$ in scenarios such as the weight of the particle in a box.