Relativistic mass

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Relativistic mass is a mass, e.g. of a particle (or an object) that any observer is seeing in their particular reference system of coordinates. It is the same as invariant mass (usually denoted in physics by ) of particle (or object), multiplied by factor, which tells how much mass (or rather enery) the moving particle has in relation to invariant mass e.g. . The invariant mass is sometimes called rest mass and then denoted by . E.g. .

It means that for different observers (moving with different velocities) the relativistic mass of the same particle or object is in general different which would mess the calculations in physics a little bit, and that's why physicists decided to introduce the notion of invariant mass that for every observer is the same and simplify calculations in physics. Presently when physicists says "mass" they always understand it as invariant mass though it is not that simple when non physicists get into a discussion since many of them assume that "mass is growing with its velocity" as it was understood still in Einstein's times. Of course the physics is the same but the terminology changed. Now the "mass that is growing with with its velocity" is called by physicists "energy" and relativistic mass or "inertial mass" by everybody else.

The "mass" on the right side of Einstein's equation is invariant (or rest mass) for a physicist and generally relativistic mass, or "inertial mass", for non physicists, which is rather non intuitive arrangement but luckily the Einstein's equation works for both kinds of mass (unless one wants specially accurate terminology, which then may involve also curvatures of spacetime).

Now we have a problem of which, invariant mass or relativistic mass is responsible for gravitation? It turns out that it is relativistic mass and therefore it is the energy content of mass. And that's why for light the gravitational effects are the same as for other "masses". Photons (particles of light) don't have invariant mass (their invariant mass is equal zero, that's why they are called "massless" particles). Yet they have relativistic mass (called energy in physics) and therefore they may take part in gravitational phenomena (as they do).

Energy of each photon , where is Planck constant, is frequency of light, is speed of light in vacuum, and is the wavelength of light, carried by this photon, to which our eyes react with seeing each photon frequency (or wavelengh) as a separate color. We see only light wavelengths between about 400 (violet end of spectrum) to 800 (red end of spectrum) nanometers (one nanometer being equal ), while other animals may have different eye sensitivities. Knowing the wave length (or color of the photon) we may calculate the relativistic mass of this photon. And if the light is very dimm and we were cats (humans don't have eyes sensitive enough and they need hundreds of photons to see anything) we could even see single photons as flashes of light on the retina of our eyes.

See also

Gravitation demystified.