Einstein's Formula for Energy of a Particle: Exploring the Meaning

[paweld]

I wonder what's the precise meaning of Einstein's formula for energy of a particle $$\frac{m c^2}{\sqrt{1-\frac{v^2}{c^2}}}$$. Is it total energy of particle (considering potential energy)? If it is then if we move (infinitesimally slowly) the particle from area of low potential to high its mass will increase. So the inertial mass is changing.

 

[ZapperZ]

I wonder what's the precise meaning of Einstein's formula for energy of a particle $$\frac{m c^2}{\sqrt{1-\frac{v^2}{c^2}}}$$. Is it total energy of particle (considering potential energy)? If it is then if we move (infinitesimally slowly) the particle from area of low potential to high its mass will increase. So the inertial mass is changing.

You should start by first reading one of the entries in our FAQ thread. After that, if you can get access to it, read this paper: E. Hecht, Am. J. Phys. v.77, p.799 (2009).

Edit: I found an online copy of the paper here:

http://physics.princeton.edu/~mcdonald/examples/EM/hecht_ajp_77_804_09.pdf

Zz.

 

[Entropia]

Einstein's famous formula, E=mc^2, is a fundamental equation in physics that relates the energy of a particle to its mass and the speed of light. The formula can also be written as E=γmc^2, where γ is the Lorentz factor, which takes into account the effects of special relativity on the mass of a moving particle.

The precise meaning of this formula is that it represents the total energy of a particle, including both its rest energy (mc^2) and its kinetic energy. It does not take into account potential energy, which is a separate concept in physics. So, if we were to move a particle from an area of low potential to high potential, its energy would not change according to this formula.

However, it is important to note that the mass of a particle does increase as its speed approaches the speed of light. This is due to the effects of special relativity, which states that the mass of an object increases as it moves faster and faster. So, in a sense, the inertial mass of a particle is changing as it moves, but this is not directly related to potential energy.

In conclusion, Einstein's formula for energy of a particle is a powerful and fundamental equation that describes the relationship between energy, mass, and the speed of light. While it does not take into account potential energy, it does account for the effects of special relativity on the mass of a moving particle.