Simple derivation for relativistic mass free download as pdf file. Relativistic mass definition of relativistic mass by the. Because of this, a bodys rest mass tends to be called simply its mass. In special relativity and general relativity, the observed mass of an object moving with respect to the observer. We have derived the addition of velocity the moving frame u. T a second mass creation time, defined at a single mass. 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. Derivation of the equation for relativistic mass physics.
Mass is a property of a body that we have an intuitive feel for. Pdf a new approach in the derivation of relativistic variation of. Relativistic solutions lecture 11 physics 411 classical mechanics ii september 21st, 2007 with our relativistic equations of motion, we can study the solutions for xt under a variety of di erent forces. Relativistic dynamics is derived based on the relativistic kinematics and one additional assumption, which allows the concept of mass. When particles pe changes, its actually the energy of the field thats changing.
In general, relativistic particles are classi ed by the mass mand spin s, where the value of. 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. Later on, to generalize the derivation, some authors such as beiser 4. Relativistic mass definition, the mass of a body in motion relative to the observer. 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. There is no such thing, what you call relativistic mass is just the sum of an objects rest mass and its relativistic kinetic energy. Therefore relativistic mass is not often used, simply the rest mass is calculated. However, the equation to the right does show that as a body approaches the speed of light, the mass of the object approaches infinity, the consequences of which are discussed below. Relativistic mass equation definition of relativistic mass. 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. The state of a system is described by a state vector. 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 particular, we can compute the rest mass of a particle formed when two particles annihilate into. A more straight way to understand relativistic mass.
The mass concept dialogue is a very standard one in physics. Relativistic energy derivation flamenco chuck keyser 12212014. Relativistic dynamics 2 this is correct, but it is not expressed in covariant form because 1 it is a relationship between space vectors only and 2 the dtis the timelike component of a displacement 4. The well known special theory of relativity voices a lot more about relativistic mass when there are comparative measurements of length and time in dissimilar frames. Derivation method of numerous dynamics in the special theory of. Derivation of the relativistic momentum and relativistic equation of motion from newtons second law and minkowskian spacetime geometry krzysztof rebilas zak.
Variation of mass with velocity special theory of relativity. Well, truth be told, the relativistic mass formula was derived first i. Relativistic wave equations and their derivation 5. Relativistic force once nature tells us the proper formula to use for calculating momentum, mathematics tells us how to measure force and energy. The relativistic timedilation is taken as a starting point for deriving the massincrease formula of special relativity. Let us consider a particle of rest mass m 0 in stationary frame of reference s. 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. It would take so much energy to get a massive object to a relativistic speed that its unrealistic. In relativistic mechanics, the timevarying mass moment. Relativistic mass definition of relativistic mass at.
In physics, relativistic mechanics refers to mechanics compatible with special relativity sr and general relativity gr. Abstract the expression for relativistic variation of mass with speed has been derived in the literature in the following ways. Anyways, since mass also increases at relativistic speeds with the total energy, we have a relativistic mass m and a rest mass, or proper mass, m o. Its quite wrong to assert that relativistic mass is obsolete. Derivation of the special theory of relativity from. Electrons relativistic mass in terms of its relativistic. Latexed february 2, 2008 abstract we present a new derivation of the expressions for momentum and energy of a relativistic particle. Derivation of the relativistic momentum and relativistic.
We can use the nonrelativistic equation because the velocity is much. Derivation of the special theory of relativity from invariance of action v. At these energy scales qualitatively new phenomena emerge. This will also be an opportunity to highlight an elementary but profound point that is widely overlooked. Lecture notes relativity physics mit opencourseware. But the action is so physical and geometrical that it is worth pursuing in its own right. Relativistic dynamics 2 this is correct, but it is not expressed in covariant form because 1 it is a relationship between space vectors only and 2. For many years it was conventional to enter the discussion of dynamics through derivation of the relativistic mass, that is the massvelocity relation, and this is probably still the dominant mode in textbooks. Derivation of relativistic variation of m ass considering the motion of a single particle. Gary oas of standford university did a study of a sample of the sr and gr textbooks. American journal of physics offers its derivation via thought experiments, whereas others derive it considering an intercation between a photon and a tardion, and. As proposed in the introduction and appendix a, the solution to the wave function for a free particle possessing mass is. The massvelocity relation in special relativity sociedade. The simplest, and the full derivation of magnetism as a.
Relativistic mass came into common usage in the relativity texts of the early 1920s written by pauli, eddington, and born. Derivation of relativistic momentum and mass part 1 duration. Documents and settingsphilip harrismy documentsteaching. Relativistic mass formula the mass concept dialogue is a very standard one in physics. Relativity 4 relativistic momentum department of physics. In these terms, the relativistic mass of the particle diverges m. Deriving relativistic momentum and energy sebastiano sonego.
Before i attempt to answer, let me make a strong suggestion. But whereas rest mass is routinely used in many areas of physics, relativistic mass is mostly restricted to the dynamics of special relativity. Starting from the classical newtons second law which, ac. Since even a free relativistic particle must move with constant velocity, how do we know that the action s nr is not correct in. This velocity dependent mass is known as relativistic mass. 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. Mathematically, we derive this obvious result as follows. More recently, however, it has been increasingly recognized that relativistic mass is a troublesome and dubious concept. Derivation of relativistic momentum and relativistic mass walter smith. Of the ones published between 1995 and 2005 there were 60% of them which use relativistic mass.
Chapter 5 the relativistic point particle to formulate the dynamics of a system we can write either the equations of motion, or alternatively, an action. The observables are represented by hermitian operators a. Start with relativistic conservation of momentum and energy relating the initial and final states of the rocket and exhaust for a. This collision has been used by many authors to derive expressions for the relativistic mass and relativistic momentum. Acquaintance with fourvectors not required for exam. Derivation of the relativistic momentum and relativistic equation of motion from newtons second law and minkowskian spacetime geometry krzysztof r. We have derived the addition of velocity the moving frame. Where m 0 and p 0, this equation again expresses the mass energy equivalence e m. Derivation of the equation for relativistic mass physics forums. Another consequence is the term rest mass and the corresponding symbol m 0. The relativistic point particle the equation of motion following by hamiltons principle is dv dt 0. Relativistic mass, in the special theory of relativity, the mass that is assigned to a body in motion. Guth of mit describes why the mass of a photon is not zero. Relativistic mass equation synonyms, relativistic mass equation pronunciation, relativistic mass equation translation, english dictionary definition of relativistic mass equation.
These confusing concepts and notations prevail in such classic texts as the ones by born8 and feynman. Where m 0 and p 0, this equation again expresses the massenergy equivalence e m. Therefore, experimentally, relativistic momentum is defined by equation \refeq2. The relative change in mass is also perceived when the body is in motion. We present a new derivation of the expressions for momentum and energy of a relativistic. In contrast to the procedures commonly adopted in text. This does not employ the use of the ridiculous relativistic mass concept. Right along with time, distance and mass, the kinetic energy of an object needs. Let us contrast the newtonian and relativistic equations for momentum, in terms of mass mand velocity v p n mv newtonian inertia 1 p r mv 1 q 1 v2 c2 relativistic inertia 2.
From the lorentzeinstein equation we have y,y yt 1. Alternative looks at time dilation and length contraction. Elementary derivation of the equivalence of mass and en. The existence of elastic collisions between asymptotically free particles. One of the oddest features of special relativity is the inability to go faster than the speed of light and this is absolutely true. The hallmark of a relativistic solution, as compared with a classical one, is the bound on velocity for massive particles. 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. Pdf 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. Which equation most rationally follows from special relativity and. Okun institute for theoretical and experimental physics itep, 117218 moscow, russia received 18 september 2008. The hallmark of a relativistic solution, as compared with a classical. The mass distribution in the gyroscope undergoes a relativistic distortion, and the center of mass is displaced away from the position of the accelerating force. Introduction to relativistic mechanics and the concept of mass. Relativistic mass and velocity physics stack exchange. Okun itep, moscow, 117218, russia the \famous formula e mc2 and the concept of \relativistic mass increasing with velocity, which follows from it, are historical artifacts, contradicting the basic symmetry of einsteins special relativity, the symmetry of 4dimensional spacetime. The relativistic timedilation is taken as a starting point for deriving the mass increase formula of special relativity. In the case of the relativistic point particle, it is rather easy to write the equations of motion. Derivation of relativistic momentum and relativistic mass. 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. 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.
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