According to the concept of massenergy equivalence, the rest mass and relativistic mass are equivalent to the rest energy and total energy of the body, respectively. Is the concept of the relativistic mass properly founded. Pdf a new approach in the derivation of relativistic variation of. Pdf a new approach in the derivation of relativistic. What is the need for yet another paper on this famous relation, on which. Do you know that there is variation of mass with velocity in relativity that is mass varies with the velocity when the velocity is comparable with the velocity of the light. T a second mass creation time, defined at a single mass. Pdf derivation of the energymomentum relation shan. American journal of physics offers its derivation via thought experiments, whereas others derive it considering an intercation between a photon and a tardion, and. The key to the exact formulas for relativstic mechanics is the formula for relativistic mass.
Let in an instantaneous inertial rest frame r of the body i. The relativistic mass is the sum total quantity of energy in a body or system divided by c2. For a velocity of 100 kmhour, for example, the relativistic correction is 3. It would be silly, to put it mildly, to use relativity to solve a problem involving the length of a baseball trajectory. Let there are two inertial frames of references s and s1. The term relativistic mass tends not to be used in particle and nuclear physics and is often avoided by writers on special relativity, in favor of using the bodys total energy. At time tt0 that is in the start, they are at the same position that is observers o and o coincides.
Relativity 4 relativistic momentum department of physics. In his electron theory, lorentz obtained expressions for the transverse and longitudinal masses of the electron. Relativistic mass definition of relativistic mass at. February 2, 2008 the concept of velocity dependent mass, relativistic mass, is examined and is found to be inconsistent with the geometrical formulation of special relativity. Phy2061 enriched physics 2 lecture notes relativity 4 invariant mass we can now apply the relativistic definitions of energy and momentum to calculations of particle collisions. For ordinary velocities, the third and higher terms are negligible. Relativistic mass fits naturally into this mechanical framework but it is not essential. If relativistic mass is used it is easier to form a correspondence with newtonian mechanics since some newtonian equations remain valid, f dpdt p m r v also, in this picture mass is conserved along with energy. If we use m for rest mass, as particle physicists usually do, we must write. Latexed february 2, 2008 abstract we present a new derivation of the expressions for momentum and energy of a relativistic particle. Well, truth be told, the relativistic mass formula was derived first i. We have derived the addition of velocity the moving frame u.
With the assumption that the momentum m v v is conserved in such a collision, they concluded that the relativistic mass varies with speed according to eq. S is the stationary frame of reference and s is the moving frame of reference. Relativistic definition is of, relating to, or characterized by relativity or relativism. To simplify the following proof of the key group properties we like to adopt the conventional matrix notation for l l l 0. A simple derivation of the mass energy equivalence is given, starting from the relativistic momentum by applying the work of a force as the variation of the energy referred to an inertial frame of. Relativistic mass, in the special theory of relativity, the mass that is assigned to a body in motion. As will be shown in this paper, this belief is not well founded. Another consequence is the term rest mass and the corresponding symbol m 0. Pdf the expression for relativistic variation of mass with speed has been derived in the literature in the following ways. The relativistic mass has been considered a virus by lev okun in his famous paper.
Its quite wrong to assert that relativistic mass is obsolete. Elementary derivation of the expressions of momentum. Deriving relativistic momentum and energy sebastiano sonego. We have discussed the effects of relativistic speeds on time now lets have a look on its effect on mass.
The massvelocity relation in special relativity sociedade. Note that this relativistic mass increase is an undetectably small effect at ordinary speeds, but as an object approaches the speed of light, the mass increases without limit. The equation for calculating the mass as seen by an outside observer is as follows. E mc2 m 01 v 2c212c2, 1 where m0 is the electron rest mass.
American journal of physics offers its derivation via thought experiments, whereas others derive it considering an intercation between a photon and a tardion, and taking into account conservation of momentum and energy. Imho you can consider the equation which relates proper mass and relativistic mass horribile dictu as an experimental fact obtained by kaufmann, bucherer and probably many others. In contrast to the procedures commonly adopted in text. Derivation of the relativistic momentum and equation of motion consider an accelerating body moving along a completely arbitrary trajectory. To get straight to the point the mass of an object will increase when traveling at relativistic speeds. To get rid of relativistic mass and rest mass it is appropriate to replace the equation emc2 by the true einsteins equation e0mc2, where e0 is the rest energy. Relativistic mass definition of relativistic mass by the. In physics, relativistic mechanics refers to mechanics compatible with special relativity sr and general relativity gr. This collision has been used by many authors to derive expressions for the relativistic mass and relativistic.
In particular, we can compute the rest mass of a particle formed when two particles annihilate into pure energy and then form a new particle. Abstract the expression for relativistic variation of mass with speed has been derived in the literature in the following ways. The equation is also valid for photons, which have m 0. The above argument that e mc 2 demotes mass in favour of energyor rather, that it selectively demotes relativistic mass, but not rest massalso neglects the very definitions of mass and energy. It provides a nonquantum mechanical description of a system of particles, or of a fluid, in cases where the velocities of moving objects are comparable to the speed of light c. When particles pe changes, its actually the energy of the field thats changing. Derivation of the special theory of relativity from. A simple derivation of the mass energy equivalence is given, starting from the relativistic momentum by applying the work of a force as the variation of. The relative change in mass is also perceived when the body is in motion. It is shown that the energymomentum relation can be simply determined by the requirements of spacetime translation invariance and relativistic invariance. The word mass has two meanings in special relativity.
Relativistic definition of relativistic by merriamwebster. From the lorentzeinstein equation we have y,y yt 1. Electrons relativistic mass in terms of its relativistic. From the mass operations bar on the document list, choose whether to save all searchable items, checked items, or these items in the current returned set. The rest of relativistic kinematics, including the socalled lorentz transformation,9 follows from the fact that speed of light of photons and of all massless particles is the same in every inertial frame.
Let m 0 be the restmass of a particle and v its velocity. This velocity dependent mass is known as relativistic mass. In his 1905 relativity paper, einstein expressed the variation of mass with velocity using the longitudinal and transverse masses. While the reader is assumed to have a basic knowledge of di erential geometry, a brief outline of the some of the mathematics is presented here. Relativistic energy derivation flamenco chuck keyser 12212014. Variation of mass with velocity and its derivation winner. Derivation of the equation for relativistic mass physics. Of the ones published between 1995 and 2005 there were 60% of them which use relativistic mass. Velocity relative to the speed of light c is denoted as then relativistic mass m is given by m m 0 1 where, as noted previously. Derivation of the relativistic momentum and relativistic. Mass is a property of a body that we have an intuitive feel for. The relativistic timedilation is taken as a starting point for deriving the mass increase formula of special relativity. Oct 10, 2011 let there are two inertial frames of references s and s1.
In fact we do not have to appeal to such exotic machines to see relativistic e. Deciding that masses of objects must depend on speed like this seems a heavy price to pay to rescue conservation of momentum. Relativistic momentum and energy we have derived the addition of velocity equation for motion parallel to the motion of the moving frame uv x ux vux c2 now we need the equation for motion perpendicular to the direction of motion of the moving frame. These confusing concepts and notations prevail in such classic texts as the ones by born8 and feynman. This formula is a relativistic generalization of the formula 4. Relativistic mass and velocity physics stack exchange. However, in general theory of relativity, the gravitational mass which is the same as inertial mass according to the principle of equivalence is not equal to relativistic mass. Let us derive and discuss the variation of mass with the velocity relation. Relativistic mass definition, the mass of a body in motion relative to the observer. In special relativity and general relativity, the observed mass of an object moving with respect to the observer.
Relativistic mass is in fact a rather problematic concept, 8,9 and there is a growing consensus to avoid its introduction in the teaching of relativity. This is the relativistic formula for variation of mass with velocity, where m 0 is the rest mass and m is the relativistic mass of the body. The derivation of this invariance essentially completes our task. Also, one must remember that the relativistic kinetic energy is mm 0c 2, and not equal to.
Variation of mass with velocity and its derivation. There are a large numbers of experimental observations of this enhancement of mass of particles in high energy physics i. Derivation of the equation for relativistic mass physics forums. Is the concept of the relativistic mass properly founded and used.
Gary oas of standford university did a study of a sample of the sr and gr textbooks. Comparable to length contraction and time dilation a thing called mass increase happens when the object is in motion. Electrons at lep are accelerated to even larger multiples of their energy 30gev compared to 5. Variation of mass with velocity physics assignment. In a certain sense this formula has become the symbol of science in the 20th century. Mar 03, 2016 the derivation is quiet complex and i must believe that you know lorentz transformations for that as without it you cannot understand the derivation, but however given that you know lorentz transformations it is a very simple concept. T a second mass creation time, defined at a single mass point i. Guth of mit describes why the mass of a photon is not zero.
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