relativistic

Examples of relativistic in the following topics:

• Relativistic Energy and Mass

  • Relativistic mass was defined by Richard C.
  • In the formula for momentum the mass that occurs is the relativistic mass.
  • In other words, the relativistic mass is the proportionality constant between the velocity and the momentum.
  • Today, the predictions of relativistic energy and mass are routinely confirmed from the experimental data of particle accelerators such as the Relativistic Heavy Ion Collider.
  • This figure illustrates how relativistic and Newtonian Kinetic Energy are related to the speed of an object.

• Relativistic Momentum

  • Relativistic momentum is given as $\gamma m_{0}v$ where $m_{0}$ is the object's invariant mass and $\gamma$ is Lorentz transformation.
  • As one approaches the speed of light, however, relativistic momentum becomes infinite while Newtonian momentum continues to increases linearly.
  • Thus, it is necessary to employ the expression for relativistic momentum when one is dealing with speeds near the speed of light .
  • This figure illustrates that relativistic momentum approaches infinity as the speed of light is approached.
  • Compare Newtonian and relativistic momenta for objects at speeds much less and approaching the speed of light

• Relativistic Kinetic Energy

  • Relativistic kinetic energy can be expressed as: $E_{k} = \frac{mc^{2}}{\sqrt{1 - (v/c)^{2})}} - mc^{2}$ where $m$ is rest mass, $v$ is velocity, $c$ is speed of light.
  • Indeed, the relativistic expression for kinetic energy is:
  • $KE = mc^2-m_0c^2$, where m is the relativistic mass of the object and m0 is the rest mass of the object.
  • At a low speed ($v << c$), the relativistic kinetic energy may be approximated well by the classical kinetic energy.
  • Compare classical and relativistic kinetic energies for objects at speeds much less and approaching the speed of light

• Problems

  • Find the incoming and outgoing velocity of a relativistic shock in terms of the energy density and pressure on either side of the shock.
  • Find the relativistic generalization of Bernoulli's equation for a streamline (you can neglect gravity).

• Relativistic Shocks

  • We will look at relativistic shocks as an example of relativistic hydrodynamics.
  • In particular we will look at the relativistic jump conditions across the shock.
  • In the non-relativistic limit for the second term we can take $V_w=V$, but we must look at the first terms more closely because the result depends on the difference of two quantities that are equal to lowest order in the non-relativistic limit.

• Spectrum of Synchrotron radiation

  • If the electron is non-relativistic its dipole moment varies as $e^{i\omega_B t}$ so we would expect radiation at a single frequency $\omega_B$.
  • The relativistic case is somewhat more complicated.
  • The electron still travels in the circular with a particular frequency but the electric field essentially vanishes except for a small region $\Delta \theta \sim 1/\gamma$. near the direction of the electron's motion (remember relativistic beaming).

• Relativistic Addition of Velocities

  • The speed of light in a collinear moving fluid is predicted accurately by the collinear case of the relativistic formula.

• Spin-Orbit Coupling

  • There are various fine structure splittings enter due to relativistic corrections.
  • This is due to a relativistic effect called Thomas precession.
  • More important to notice is that the spin-orbit term vanishes as $c\rightarrow \infty$, so it is indeed a relativistic correction.

• Non-relativistic particles

• Introduction

  • This requires sociologists to assume a relativistic perspective that basically takes a neutral stance toward issues of right or wrong or true or false.