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The relativistic mass is the sum total quantity of energy in a body or system (divided by c 2).Thus, the mass in the formula = is the relativistic mass. For a particle of non-zero rest mass m moving at a speed relative to the observer, one finds =.
The mass of an object as measured in its own frame of reference is called its rest mass or invariant mass and is sometimes written .If an object moves with velocity in some other reference frame, the quantity = is often called the object's "relativistic mass" in that frame. [1]
The relativistic mass of an object is given by the relativistic energy divided by c 2. [10] Because the relativistic mass is exactly proportional to the relativistic energy, relativistic mass and relativistic energy are nearly synonymous; the only difference between them is the units.
The concept of mass in general relativity (GR) is more subtle to define than the concept of mass in special relativity.In fact, general relativity does not offer a single definition of the term mass, but offers several different definitions that are applicable under different circumstances.
These include the relativity of simultaneity, length contraction, time dilation, the relativistic velocity addition formula, the relativistic Doppler effect, relativistic mass, a universal speed limit, mass–energy equivalence, the speed of causality and the Thomas precession.
Total energy is the sum of rest energy = and relativistic kinetic energy: = = + Invariant mass is mass measured in a center-of-momentum frame. For bodies or systems with zero momentum, it simplifies to the mass–energy equation E 0 = m 0 c 2 {\displaystyle E_{0}=m_{0}c^{2}} , where total energy in this case is equal to rest energy.
So relativistic energy and momentum significantly increase with speed, thus the speed of light cannot be reached by massive particles. In some relativity textbooks, the so-called "relativistic mass" = is used as well. However, this concept is considered disadvantageous by many authors, instead the expressions of relativistic energy and momentum ...
The relativistic kinetic energy for an uncharged particle of rest mass m 0 is T = ( γ ( r ˙ ) − 1 ) m 0 c 2 {\displaystyle T=(\gamma ({\dot {\mathbf {r} }})-1)m_{0}c^{2}} and we may naïvely guess the relativistic Lagrangian for a particle to be this relativistic kinetic energy minus the potential energy.