Relativistic fluid dynamics university of waterloo. For ordinary velocities, the third and higher terms are negligible. We have derived the addition of velocity the moving frame u. Comparable to length contraction and time dilation a thing called mass increase happens when the object is in motion. We have discussed the effects of relativistic speeds on time now lets have a look on its effect on mass. When particles pe changes, its actually the energy of the field thats changing. In fact we do not have to appeal to such exotic machines to see relativistic e. There are a large numbers of experimental observations of this enhancement of mass of particles in high energy physics i. The equation for calculating the mass as seen by an outside observer is as follows. In contrast to the procedures commonly adopted in text.
This velocity dependent mass is known as relativistic mass. 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. Relativistic mass definition, the mass of a body in motion relative to the observer. In a certain sense this formula has become the symbol of science in the 20th century. This formula is a relativistic generalization of the formula 4. These confusing concepts and notations prevail in such classic texts as the ones by born8 and feynman. Let m 0 be the restmass of a particle and v its velocity. Relativistic mass definition of relativistic mass at. Mass is a property of a body that we have an intuitive feel for.
Deciding that masses of objects must depend on speed like this seems a heavy price to pay to rescue conservation of momentum. For a velocity of 100 kmhour, for example, the relativistic correction is 3. Guth of mit describes why the mass of a photon is not zero. Variation of mass with velocity and its derivation winner. 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. In his 1905 relativity paper, einstein expressed the variation of mass with velocity using the longitudinal and transverse masses. Relativistic definition of relativistic by merriamwebster. In special relativity and general relativity, the observed mass of an object moving with respect to the observer. 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. The equation is also valid for photons, which have m 0. The key to the exact formulas for relativstic mechanics is the formula for relativistic mass.
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. 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. The relative change in mass is also perceived when the body is in motion. Is the concept of the relativistic mass properly founded and used. Derivation of the relativistic momentum and relativistic. Relativistic mass and velocity physics stack exchange. 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. Relativistic definition is of, relating to, or characterized by relativity or relativism. 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. Electrons relativistic mass in terms of its relativistic.
What is the need for yet another paper on this famous relation, on which. Derivation of the relativistic momentum and equation of motion consider an accelerating body moving along a completely arbitrary trajectory. This collision has been used by many authors to derive expressions for the relativistic mass and relativistic. The simplest, and the full derivation of magnetism as a. Well, truth be told, the relativistic mass formula was derived first i. The derivation of this invariance essentially completes our task. The massvelocity relation in special relativity sociedade. 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. Deriving relativistic momentum and energy sebastiano sonego. 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. Abstract the expression for relativistic variation of mass with speed has been derived in the literature in the following ways. The word mass has two meanings in special relativity.
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. Pdf a new approach in the derivation of relativistic variation of. Pdf the expression for relativistic variation of mass with speed has been derived in the literature in the following ways. Furthermore, special relativity has shown that an increment of inertial mass, m. Oct 10, 2011 let there are two inertial frames of references s and s1. Electrons at lep are accelerated to even larger multiples of their energy 30gev compared to 5. Its quite wrong to assert that relativistic mass is obsolete. E mc2 m 01 v 2c212c2, 1 where m0 is the electron rest mass. Also, one must remember that the relativistic kinetic energy is mm 0c 2, and not equal to. Variation of mass with velocity physics assignment. 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. It would be silly, to put it mildly, to use relativity to solve a problem involving the length of a baseball trajectory.
S is the stationary frame of reference and s is the moving frame of reference. Relativistic mass, in the special theory of relativity, the mass that is assigned to a body in motion. American journal of physics offers its derivation via thought experiments, whereas others derive it considering an intercation between a photon and a tardion, and. 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. 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.
In his electron theory, lorentz obtained expressions for the transverse and longitudinal masses of the electron. To simplify the following proof of the key group properties we like to adopt the conventional matrix notation for l l l 0. If we use m for rest mass, as particle physicists usually do, we must write. Derivation of the special theory of relativity from. To get straight to the point the mass of an object will increase when traveling at relativistic speeds.
Is the concept of the relativistic mass properly founded. 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. 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. As will be shown in this paper, this belief is not well founded. Latexed february 2, 2008 abstract we present a new derivation of the expressions for momentum and energy of a relativistic particle. 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. Pdf a new approach in the derivation of relativistic.
Elementary derivation of the expressions of momentum. Derivation of the equation for relativistic mass physics forums. In physics, relativistic mechanics refers to mechanics compatible with special relativity sr and general relativity gr. Derivation of the equation for relativistic mass physics. The relativistic mass has been considered a virus by lev okun in his famous paper. T a second mass creation time, defined at a single mass. Let in an instantaneous inertial rest frame r of the body i. Relativistic energy derivation flamenco chuck keyser 12212014.
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. 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. 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. Relativistic mass fits naturally into this mechanical framework but it is not essential. Let there are two inertial frames of references s and s1. Relativistic mass definition of relativistic mass by the. 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. It is shown that the energymomentum relation can be simply determined by the requirements of spacetime translation invariance and relativistic invariance. This set is identical with the set of all lorentz transformations l. The relativistic timedilation is taken as a starting point for deriving the mass increase formula of special relativity. Gary oas of standford university did a study of a sample of the sr and gr textbooks. 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. Another consequence is the term rest mass and the corresponding symbol m 0. From the lorentzeinstein equation we have y,y yt 1.
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. T a second mass creation time, defined at a single mass point i. Pdf derivation of the energymomentum relation shan. 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. Variation of mass with velocity and its derivation. 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. 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. Let us derive and discuss the variation of mass with the velocity relation. The relativistic mass is the sum total quantity of energy in a body or system divided by c2. Of the ones published between 1995 and 2005 there were 60% of them which use relativistic mass.
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