11.How the rest mass changes in the gravitational field.
Let's try to get a formula for the connection of the rest mass of a particle with the gravitational potential in which it is located.
When a particle is accelerated in a gravitational field, its total energy changes by the product of its mass and the change in the
gravitational potential, and half of the energy goes to change the kinetic energy of the particle, and the other half goes
to change its rest energy. Let's write down the equation for the mass change taking into account E= - mPhi
Let's transform this equation
Neglecting the small term dm we come to the differential equation
We find the solution of this differential equation
Here Po is a coefficient having the dimension of the momentum. For each particle, it must have its own value. For example, for an electron
Po = 2.730924531 kg*m/s. Then, at the present value of the gravitational potential, the mass of the electron is equal to 9.1093837015*10^-31 kg.
You can easily see that to get the Po value for any particle, you just need to take the rest mass of this particle from the reference book
and multiply it by the speed of light.
Taking into account the above, the Energy-Momentum equation known from SRT
Can be converted to the following form
This means that the particles do not have an invariant mass, any mass is variant. The particle has only an invariant momentum,
which is related to the motion of a particle in time.