Physics
Relativistic Dynamics
Relativistic dynamics is a branch of physics that describes the motion of objects at speeds approaching the speed of light. It incorporates the principles of special relativity, which include the concept of time dilation, length contraction, and the equivalence of mass and energy. Relativistic dynamics provides a more accurate description of motion at high speeds than classical mechanics.
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4 Key excerpts on "Relativistic Dynamics"
eBook - ePub- A.P. French(Author)
- 2017(Publication Date)
- CRC Press(Publisher)
The Lorentz transformations can then be regarded as a prescription for transforming the various components of a 4-vector from one set of axes to another—often described as the “mapping” of the vector onto various coordinate systems in the four-dimensional world. This way of representing the relativistic scheme of things is attractive in a formal sense, and can also be very useful if one has once learned to exploit it—which primarily means developing the appropriate fluency in matrix algebra. We shall not go any further with it here, however, since it is not essential and really adds nothing to the basic physics of relativity.Force in Relativistic Mechanics
In contrast to the Newtonian conception, it is easy to show that in relativity the quantity force, in general, is not codirectional with the acceleration it produces ... It is also easy to show that these force components have no simple transformation properties ... All these modifications, important as they are from the mathematical point of view, do not radically affect the conception of force. Yet an important point should be noted: on grounds of the rejection of an absolute simultaneity of two distant events, special relativity comes to the conclusion that action at a distance has to be excluded as a legitimate physical notion.Max Jammer, Concepts of Force (1957)In all of our discussion of Relativistic Dynamics so far, we have placed an almost exclusive emphasis on the use of the energy and momentum conservation laws for an isolated system of particles. We have tried to give some feeling for the variety of problems that can be discussed in these terms. But when all is said and done, this approach is not always the most convenient or useful. Many, many problems in dynamics can best be treated (and perhaps can only be efficiently treated) in terms of the motion of particles under the action of a given set of forces. Take the Rutherford scattering of α particles, for example. Granted that the force becomes vanishingly small at large separations between two particles (and it is this assumption that underlies all the calculations we have done in Chapter 6 and in this chapter), one can make perfectly correct statements about the relation between final directions and velocities of the colliding nuclei. But this does not tell us the probability that an α
eBook - ePub- Cornelius Lanczos(Author)
- 2012(Publication Date)
- Dover Publications(Publisher)
General relativity cannot be properly treated without the field concept, which belongs to the realm of the mechanics of continua. Our following exposition is thus restricted to the kinematics and dynamics of Special Relativity. However, the dynamical law of General Relativity falls within the scope of Lagrangian and Hamiltonian dynamics and will be included in our discussions.2. Relativistic kinematics. In his fundamental paper Einstein1 introduced the following two postulates:(a) All reference systems that move relative to each other with constant velocity are equally legitimate for the description of nature, without any preference for any particular one of them.(b) The velocity of light c is the same universal constant, measured in any of these systems.The second postulate leads to the following apparent absurdity. Consider an observer B moving relative to A with the velocity of light c. He emits a light signal in the direction of his own motion which moves relative to him with the velocity c. According to our common notions the velocity of this signal relative to A should be 2c, while the second postulate of relativity demands that it is c. Hence c = 2c, which is self-contradictory. This is no longer so, however, if we give up the intuitive notion of a time t which is the same for both observers A and B.According to Einstein we should not prejudice in advance the transformation equations which exist between the coordinates of the system A and those of the system B. Assuming that the motion of B relative to A occurs in the X-direction, we putwhere a, β, γ, δ are constants, since we do not want to lose the linearity of the transformation. But by abandoning the equation t = t′ (which corresponds to the choice γ = 0, δ = 1) we have gained the freedom of two additional constants.All formulae of special relativity gain greatly in simplicity, if we agree to measure the time in such units that the velocity of light becomes unity (this means that the usual time t is replaced by t/c). If we want to return to the formulae involving our ordinary time t, we have merely to change all t to ct and all v to v/c. We shall frequently make use of this simplification and thus agree that the invariant velocity of light has the numerical value c =- eBook - ePub
- Andrew Rex(Author)
- 2014(Publication Date)
- CRC Press(Publisher)
Chapter 9 Relativity Relativity is one of the most important and fascinating fields of study within physics. It’s generally split into two subfields—special relativity and general relativity—both of which were developed by Albert Einstein in the early twentieth century. Relativity accounts for how events are viewed from different frames of reference, when those frames of reference are moving with respect to one another or in strong gravitational fields. It also accounts for how light will appear to observers in different frames of reference. Many of the effects predicted by the theory of relativity are contrary to the predictions of classical physics and to perceptions based on everyday experience. These striking and sometimes shocking predictions have been verified repeatedly by experimental evidence. Probably the most famous prediction of special relativity is the equivalence of mass and energy, expressed in the formula E = mc 2. This equivalence manifests itself in many ways, particularly in atomic and nuclear physics (Chapter 7) and in the study of fundamental particles (Chapter 8). The implications are far reaching and include the production of nuclear energy and nuclear weapons. What’s the Difference between Special Relativity and General Relativity? Special relativity accounts for how material objects and light are viewed by observers traveling in different frames of reference, in constant, nonaccelerated motion with respect to one another. The fact that the speed of light is the same for observers in all reference frames is of fundamental importance. It leads to correct predictions about how the different observers measure the positions, lengths, and velocities of objects, and how they measure the passage of time 
eBook - ePub- Michael Esfeld, Dirk-Andre Deckert(Authors)
- 2017(Publication Date)
- Routledge(Publisher)
But this does not imply that when it comes to representing change, it is possible to obtain a representation that is both simple and informative about the change that actually occurs on the basis of initial conditions that consist in parameters attributed to the configuration of matter points at a given time. The correlated motions of quantum particles represented by means of an entangled wave function enable such a representation and are the reason why we have written down the fundamental dynamics of QFT in a non-relativistic manner in Chapter 4 (in the sense that this dynamics requires a notion of objective simultaneity). Relativity physics challenges this manner of representing change. In relativistic interactions, it is dynamical parameters situated in the past (and possibly also in the future) that capture the evolution of a given configuration, whereby the distance relations in the given configuration are not relevant for the dynamical structure. That is why relativity physics not only introduces a new dynamical structure but also challenges the ontology as given by the two mentioned axioms, because this ontology is built on matter points that are individuated by the distance relations in a given configuration and the change in these relations. In this chapter, we address this challenge. We first consider classical electrodynamics, which is the first relativistic theory, arguing that fields are part of the dynamical structure of this theory instead of new elements of the ontology and discussing an alternative theory of classical electrodynamics that works with direct particle interactions (i.e. the Wheeler-Feynman theory) (section 2). We then argue in general terms that the minimalist ontology pursued in this book remains a cogent stance also when it comes to relativistic physics (section 3) and show how Super-Humeanism combined with this minimalist ontology is a valid option also for general relativistic physics (section 4)
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