Start with relativistic conservation of momentum and energy relating the initial and final states of the rocket and exhaust for a. Its quite wrong to assert that relativistic mass is obsolete. Guth of mit describes why the mass of a photon is not zero. Relativistic mass equation definition of relativistic mass. Which equation most rationally follows from special relativity and. Derivation of the equation for relativistic mass physics forums. The observables are represented by hermitian operators a. We can use the nonrelativistic equation because the velocity is much. 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 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.
Derivation of relativistic momentum and mass part 1 duration. Relativistic dynamics is derived based on the relativistic kinematics and one additional assumption, which allows the concept of mass. E mc2 m 01 v 2c212c2, 1 where m0 is the electron rest mass. Relativistic mass and velocity physics stack exchange. The word mass has two meanings in special relativity. 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. Therefore, experimentally, relativistic momentum is defined by equation \refeq2. In physics, relativistic mechanics refers to mechanics compatible with special relativity sr and general relativity gr.
But whereas rest mass is routinely used in many areas of physics, relativistic mass is mostly restricted to the dynamics of special relativity. Since even a free relativistic particle must move with constant velocity, how do we know that the action s nr is not correct in. In these terms, the relativistic mass of the particle diverges m. Gary oas of standford university did a study of a sample of the sr and gr textbooks. It would take so much energy to get a massive object to a relativistic speed that its unrealistic.
Starting from the classical newtons second law which, ac. In special relativity and general relativity, the observed mass of an object moving with respect to the observer. Right along with time, distance and mass, the kinetic energy of an object needs. 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.
Relativistic mass came into common usage in the relativity texts of the early 1920s written by pauli, eddington, and born. Relativistic mass definition, the mass of a body in motion relative to the observer. Acquaintance with fourvectors not required for exam. 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 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. Where m 0 and p 0, this equation again expresses the massenergy equivalence e m. Derivation of the special theory of relativity from invariance of action v. Because of this, a bodys rest mass tends to be called simply its mass. The simplest, and the full derivation of magnetism as a. These confusing concepts and notations prevail in such classic texts as the ones by born8 and feynman. One of the oddest features of special relativity is the inability to go faster than the speed of light and this is absolutely true. 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.
Variation of mass with velocity special theory of relativity. This collision has been used by many authors to derive expressions for the relativistic mass and relativistic momentum. Derivation of the relativistic momentum and relativistic equation of motion from newtons second law and minkowskian spacetime geometry krzysztof r. Relativistic mass definition of relativistic mass at. We have derived the addition of velocity the moving frame u. The relativistic timedilation is taken as a starting point for deriving the mass increase formula of special relativity. Elementary derivation of the equivalence of mass and en. The mass concept dialogue is a very standard one in physics. At these energy scales qualitatively new phenomena emerge.
The relativistic point particle the equation of motion following by hamiltons principle is dv dt 0. 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. We present a new derivation of the expressions for momentum and energy of a relativistic. 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. Derivation of the relativistic momentum and relativistic. More recently, however, it has been increasingly recognized that relativistic mass is a troublesome and dubious concept. From the lorentzeinstein equation we have y,y yt 1. Abstract the expression for relativistic variation of mass with speed has been derived in the literature in the following ways. A more straight way to understand relativistic mass. 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.
Relativistic mass equation synonyms, relativistic mass equation pronunciation, relativistic mass equation translation, english dictionary definition of relativistic mass equation. The hallmark of a relativistic solution, as compared with a classical. Pdf the expression for relativistic variation of mass with speed has been derived in the literature in the following ways. Therefore relativistic mass is not often used, simply the rest mass is calculated. Mathematically, we derive this obvious result as follows. In relativistic mechanics, the timevarying mass moment. 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. Before i attempt to answer, let me make a strong suggestion. Later on, to generalize the derivation, some authors such as beiser 4. Relativistic mass definition of relativistic mass by the. In particular, we can compute the rest mass of a particle formed when two particles annihilate into. Introduction to relativistic mechanics and the concept of mass. T a second mass creation time, defined at a single mass. Pdf a new approach in the derivation of relativistic.
Relativistic energy derivation flamenco chuck keyser 12212014. Relativistic mass, in the special theory of relativity, the mass that is assigned to a body in motion. But the action is so physical and geometrical that it is worth pursuing in its own right. 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 method of numerous dynamics in the special theory of. 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.
Well, truth be told, the relativistic mass formula was derived first i. Relativistic force once nature tells us the proper formula to use for calculating momentum, mathematics tells us how to measure force and energy. 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. Latexed february 2, 2008 abstract we present a new derivation of the expressions for momentum and energy of a relativistic particle. The relativistic timedilation is taken as a starting point for deriving the massincrease formula of special relativity. Derivation of relativistic momentum and relativistic mass walter smith. Derivation of the equation for relativistic mass physics. In general, relativistic particles are classi ed by the mass mand spin s, where the value of. The state of a system is described by a state vector. Pdf a new approach in the derivation of relativistic variation of. When particles pe changes, its actually the energy of the field thats changing. The hallmark of a relativistic solution, as compared with a classical one, is the bound on velocity for massive particles.
Documents and settingsphilip harrismy documentsteaching. 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. This velocity dependent mass is known as relativistic mass. Deriving relativistic momentum and energy sebastiano sonego. The massvelocity relation in special relativity sociedade. The existence of elastic collisions between asymptotically free particles. In the case of the relativistic point particle, it is rather easy to write the equations of motion. 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. American journal of physics offers its derivation via thought experiments, whereas others derive it considering an intercation between a photon and a tardion, and. Relativistic wave equations and their derivation 5. Derivation of the special theory of relativity from. 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.
Mass is a property of a body that we have an intuitive feel for. This will also be an opportunity to highlight an elementary but profound point that is widely overlooked. Electrons relativistic mass in terms of its relativistic. 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. There is no such thing, what you call relativistic mass is just the sum of an objects rest mass and its relativistic kinetic energy.
Simple derivation for relativistic mass free download as pdf file. Relativistic mass formula the mass concept dialogue is a very standard one in physics. In contrast to the procedures commonly adopted in text. We have derived the addition of velocity the moving frame. Derivation of relativistic momentum and relativistic mass. Another consequence is the term rest mass and the corresponding symbol m 0. Lecture notes relativity physics mit opencourseware. Alternative looks at time dilation and length contraction. Okun institute for theoretical and experimental physics itep, 117218 moscow, russia received 18 september 2008. 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.
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