The theory of relativistic mass goes back to Hendrik Lorentz, who introduced the ideas of longitudinal and transverse electromagnetic masses of an electron in his paper called Electromagnetic Phenomena in a System Moving with Any Velocity Less Than That of Light in 1904. According to Lorentz, mass is the ratio of force to acceleration rather than the ratio of momentum to velocity. He wrote equations for mass parallel to the direction of motion and mass perpendicular to the direction of motion. He wrote equations of motion of electrons in an electromagnetic field in Newtonian terms F=ma where m increases with mass.
The precise relativistic expression (which is equivalent to Lorentz's) relating force and acceleration for a particle with non-zero rest mass m moving in the x direction with velocity v and associated Lorentz factor γ is:
ƒx = mγ3ax = mLax,It is thought that the chemist G.N. Lewis was the first to introduce the idea that mass is dependent on speed through the equation m= m0(1 – v2/c2)–1/2. Lewis and Richard C. Tolman worked together to come up with equations of speed-dependent mass. Together, they further developed the relativistic theory of force, momentum and energy. Their concept of relativistic mass is expressed through the formula F=d/dt(mv) instead of F=ma which can also be used with the equation E= mc2.
Furthermore, it was Tolman who said that the expression m= m0(1 – v2/c2)–1/2 corresponds to the mass of a moving system. Tolman's and Lewis' work gave strength to the theory of relativistic mass, especially because their equation for mass was similar to Lorentz' expression for "transverse mass." The term "relativistic mass" began to be used in textbooks around the 1920 thanks to the writings of Pauli, Eddington and Born. Overtime, when the invariant mass of particles became increasingly important to physicists, people began using the term "mass" to refer to invariant mass. This became the norm after the 1950s and the idea of relativistic mass increasing with velocity became less significant.
Einstein is another prominent figure in the development of the idea of relativistic mass. Einstein's E= mc2 contains m as mass, but m is now considered to be rest mass. Research suggests that Einstein actually rejected the idea of relativistic mass and advocated that the only way to talk about the concept of mass is through what is called "rest mass."
When looking at Einstein's equation E= mc2 and any equation where the symbol m for mass appears, the m almost always represents invariant mass as we now understand it. It is suggested that Einstein never used relativistic mass himself. The equation E= mc2 is only meant to be used in the rest frame of a particle. Therefore, it can be suggested that Einstein only introduced the idea that the mass of a body increases with energy content, not velocity.
When it comes to special relativity, objects with mass cannot travel at the speed of light. When the object begins to approach the speed of light, only then will the energy and momentum of the object increase. In 1934, Tolman further defined relativistic mass with the expression m= E/c2 which is true for all particles, even those moving at the speed of light. Particles that move slower than light, or have a nonzero rest mass can be expressed through the formula:
m = γm0Later, Minkowski introduced a mathematical approach to the concept of relativistic mass with the formulations:
F = dp/dtHere, invariant mass is the ratio of four-momentum to four-velocity. This expression is used in terms of space-time, energy-momentum four vectors, world lines, light cones, proper time and invariant mass. It is suggested that Minkowski's approach provides a more clear understanding of relativity.
In modern days of science, many have refrained from using the concept of relativistic mass because it is subject to misunderstanding. There is a far greater preference for using invariant mass. Regardless, there are still physicists who find that relativistic mass is fundamental to physics and is not a wrong concept.
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