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# special theory of relativity formula ###### by

Many contemporary authors such as Taylor and Wheeler avoid using the concept of relativistic mass altogether: The concept of "relativistic mass" is subject to misunderstanding. m rel Relativistic mass and rest mass are both traditional concepts in physics, but the relativistic mass corresponds to the total energy. m rel = m 1 − v 2 c 2. (2020). c This was further elaborated by Hendrik Lorentz (1899, 1904) in the framework of Lorentz ether theory.  He instead supposes that the difference between rest and relativistic mass should be explicitly taught, so that students know why mass should be thought of as invariant "in most discussions of inertia". Here are some important special-relativity equations that deal with time dilation, length contraction, and more. The more general invariant mass (calculated with a more complicated formula) loosely corresponds to the "rest mass" of a "system". Such a loss of rest mass in systems when energy is removed, according to E = mc2 where E is the energy removed, and m is the change in rest mass, reflect changes of mass associated with movement of energy, not "conversion" of mass to energy. This special theory of relativity formula is based on the theory of general relativity. p {\displaystyle \mathbf {f} =m_{\text{rel}}\mathbf {a} } The term mass in special relativity usually refers to the rest mass of the object, which is the Newtonian mass as measured by an observer moving along with the object. , A so-called massless particle (such as a photon, or a theoretical graviton) moves at the speed of light in every frame of reference. In this case, conservation of invariant mass of the system also will no longer hold. λ Thus, the mass in the formula, is the relativistic mass. c In this case there is no transformation that will bring the particle to rest. For example: A closed container of gas (closed to energy as well) has a system "rest mass" in the sense that it can be weighed on a resting scale, even while it contains moving components. 2 em {\displaystyle \left(E,{\vec {p}}c\right)} = 2 v only applies to a slower-than-light particle (a particle with a nonzero rest mass). When the object is moving, the total energy is given by, To find the form of the momentum and energy as a function of velocity, it can be noted that the four-velocity, which is proportional to The relativistic mass is also the proportionality factor between velocity and momentum, Newton's second law remains valid in the form, When a body emits light of frequency ) λ Thus, unlike the invariant mass, the relativistic mass depends on the observer's frame of reference. This is used to make measurements of the mass of particles like the Z boson or the top quark. is the relativistic length of the energy momentum four-vector, a length which is associated with rest mass or invariant mass in systems. m Einstein’s theory was proposed in 1905. https://www.britannica.com/science/E-mc2-equation, American Museum of Natural History - E=mc2, Public Broadcasting Corporation - NOVA - The Legacy of E = mc2. c Einstein's Theory of Special Relativity Einstein's equation E = mc2 shows that energy and mass are interchangeable. {\displaystyle E=mc^{2}} Total energy is an additive conserved quantity (for single observers) in systems and in reactions between particles, but rest mass (in the sense of being a sum of particle rest masses) may not be conserved through an event in which rest masses of particles are converted to other types of energy, such as kinetic energy. {\displaystyle m_{\text{L}}=\gamma ^{3}m} longitudinal mass and }, When working in units where c = 1, known as the natural unit system, all the relativistic equations are simplified and the quantities energy, momentum, and mass have the same natural dimension:. Arons wrote:. γ In the first years after 1905, following Lorentz and Einstein, the terms longitudinal and transverse mass were still in use. . For example, photons have zero rest mass but contribute to the inertia (and weight in a gravitational field) of any system containing them. = c h This article will explain this theory of relativity with relativity formula and examples. {\displaystyle \left(c,{\vec {v}}\right)} In this formula E is energy, m is mass, and c is the constant speed of light. γ Special relativity revealed that the speed of light is a limit that can be approached but not reached by any material object. {\displaystyle E^{2}-p^{2}} / Omissions? 2 In special relativity, however, the energy of a body at rest is determined to be mc2. / ), The relativistic mass is the sum total quantity of energy in a body or system (divided by c2). f {\displaystyle {\vec {p}}} The concept of invariant mass does not require bound systems of particles, however. The equation is often written this way because the difference moving in the x direction with velocity v and associated Lorentz factor E Some Special Relativity Formulas 1 Introduction The purpose of this handout is simple: to give you power in using special relativity! 