Problem 2:(a) Since the four-velocity u = Yu (c, u) is a four-vector, you should immediately know what its transfor-mation properties are. Write down the standard Lorentz boost for all four components of u. Use these toderive the relativistic velocity transformation formulas.(b) In non-relativistic mechanics, the energy E contains an arbitrary additive constant. That is, no1physics is changed by the replacement E → E + Eo for any constant Eo. Using the fact that the four-momentum p = (E/c,p2,Py, Pz) must transform like a four-vector, show that this is NOT true in relativisticmechanics.

Answered: Image /qna-images/answer/2f3a1bc8-4ea7-4300-877d-3e02c19bb9d6.jpg

Answered: (a) Since the four-velocity u = Yu (c,…

Similar questions

A light source G is moving, with respect to an observer O, at an angle θ=�=154∘∘ between the direction of relative motion and the line of sight from O to G. The redshift of the light emitted by G and measured by O is z=0�=0. Find the speed of G with respect to O in units of c�, the speed of light. Enter your answer to 3 decimal places.
Consider a point charge q at rest, situated at the origin of some frame S. Its electric field, according to S is 9 E(,1) = 1 2/21 47€ 12 Of course, its magnetic field is zero. Now, you want to know what will happen to the fields if q moved to the right (positive x direction). Since it is at rest in the S frame, what you can do is go to another frame, S', then boost it to the negative x direction. This way, q moves to the right according to S'. Let the velocity of S'be v = -vi Solve for the magnetic field components as seen in the S' frame. Combine these to write down B'(x, t)
Consider a spacetime diagram in which for simplicity, we will omit the space coordinate z. That is, only take into account three axes, two axes that define the xy plane characterized by the spatial coordinates x and y, and a third axis perpendicular to the xy plane that corresponds to the temporal coordinate t (ct so that the three axes have the same dimensions ). This coordinate system S is in which an observer O describes the events that occur in the Universe from his point of view a) Draw the world line of a particle moving in the xy plane describing a circle with constant speed. b) Draw the world line of a particle that is accelerating from rest until it reaches a certain speed, which already remains constant. c) Now drop the spatial coordinate y. On the plane (x, ct) that describes the events seen by the observer O in his system S and considering the Lorentz transformations, draw the axes for a system S' in which an observer O' would describe the events that occur in the universe.…
Please explain in detail An observer P stands on a train station platform as a high-speed train passes by at u/c = 0.8. The observer P, who measures the platform to be 60 m long, notices that the front and back ends of the train line up exactly with the ends of the platform at the same time. (a) How long does it take the train to pass P as he stands on the platform, as measured by his watch? (b) According to a rider T on the train, how long is the train? (c) According to a rider T on the train, what is the length of the train station platform?
Problem 3: A mass m is thrown from the origin att = 0 with initial three-momentum po in the y direction. If it is subject to a constant force F, in the x direction, find its velocity v as a function of t, and by integrating v find its trajectory. Check that in the non-relativistic limit the trajectory is the expected parabola. Hint: The relationship F = P is still true in relativistic mechanics, but now p = ymv instead of p = mv. To find the non-relativistic limit, treat c as a very large quantity and use the Taylor approximation (1+ x)" = 1 + nx when a is small.
Consider a spacetime diagram in which for simplicity, we will omit the space coordinate z. That is, only take into account three axes, two axes that define the xy plane characterized by the spatial coordinates x and y, and a third axis perpendicular to the xy plane that corresponds to the temporal coordinate t (ct so that the three axes have the same dimensions ). This coordinate system S is in which an observer O describes the events that occur in the Universe from his point of viewc) Now drop the spatial coordinate y. On the plane (x, ct) that describes the events seen by the observer O in his system S and considering the Lorentz transformations, draw the axes for a system S' in which an observer O' would describe the events that occur in the universe. We must create a space-time diagram for the scenario presented in the problem. Only the x, y, and ct-axis must be taken into consideration. Thus, we have our three dimensions (ct, x, y). We'll remain with relativistic units for the…
A stationary observer O is standing on a platform of length 65 meters on earth. A rocket passes at a velocity of – 0.80c, parallel to the edge of the platform. The observer O notes that at a particular instant the front and back of the rocket simultaneously line up with the ends of the platform. (a) According to O, what is the time necessary for the whole rocket to pass a particular point on the platform? c = 3 × 10% m/s. (b) What is the rest length of the rocket according to an observer O' on the rocket? (c) According to O', what is the length of the platform? 65 m 0.8c O' Figure 2: Problem 4.
(a) A nuclear power plant converts energy from nuclear fission into electricity with an efficiency of 35.0%. How much mass is destroyed in one year to produce a continuous 1000 MW of electric power? (b) Do you think it would be possible to observe this mass loss if the total mass of the fuel is 104 kg ?