Consider a photon of frequency vo v' emitted by a source at rest in frame K'. The photon is detected by an observer in frame K, where K and K' are related in the usual manner. (Note that this means that frame K' is moving either directly towards or away from K along the line of sight.) Derive the expression for the line-of-sight Doppler effect (i.e., for recession or approach only, not some arbitrary direction of motion) by considering the energy-momentum 4-vector of a photon, and requiring that it must transform from one inertial frame to another in the same way as any other 4-vector.

Consider a photon of frequency vo v' emitted by a source at rest in frame K'. The photon is detected by an observer in frame K, where K and K' are related in the usual manner. (Note that this means that frame K' is moving either directly towards or away from K along the line of sight.) Derive the expression for the line-of-sight Doppler effect (i.e., for recession or approach only, not some arbitrary direction of motion) by considering the energy-momentum 4-vector of a photon, and requiring that it must transform from one inertial frame to another in the same way as any other 4-vector.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Related questions

Q: Show that if two events are separated in space and time so that a light signal leaving one event…

Q: In a certain inertial frame two light pulses are emitted, a distance 5 km apart and separated by 5…

Q: Problem 10: Suppose a 0.95-µg speck of dust has the same momentum as a proton moving at 0.999c.…

Q: Prove that for any relative velocity v between two observers, a beam of light sent from one to the…

Q: Consider two spacetime events with coordinate differences (At, Ax, Ay, Az) as given. In each case,…

Q: (a) Since the four-velocity u = Yu (c, u) is a four-vector, you should immediately know what its…

Q: Calculate the classical momentum of a proton traveling at 0.990c, neglecting relativistic effects.…

A: The formula used to calculate the classical momentum is,

Q: In a linear collider, two particles travel toward each other from opposite directions before…

A: velocity of electron (u) in lab's frame of reference = 23 cvelocity of positron (v) in lab's frame…

Q: Write down the relationship between the classical kinetic energy E and momentum p for a body of mass…

A: Have a look dear

Q: a) Calculate the classical momentum of a proton traveling at 0.974c, neglecting relativistic…

A: Mass of proton m = 1.67 * 10-27 kg speed of proton v = 0.974c where, c = 3 * 108 m/s .

Q: A spacecraft receding from the earth emits radio waves at a constant frequency of 109 Hz. If the…

A: Given data: Frequency f = 109 Hz

Q: An elementary particle of mass μ initially at rest in a frame S completely absorbs a photon that was…

A: Energy =μc2 Here, m is the mass and c is speed of light After absorbing the photon, the mass of…

Q: Suppose a particle orbit as a function of time (t) is given in an inertial frame K and the integral…

A: The space time interval between two events which are time dt and distance dr=(dx,dy,dz) apart is…

Q: Calculate the relativistic kinetic energy (in J) of a 930 kg car moving at 28 m/s if the speed of…

Q: A pion traveling at speed v decays into a muon and a neutrino, л - µ¯ + √₂. If the neutrino emerges…

A: At what angle does the μ come off. Given, π-→μ-+ν¯speed of pion=v

Q: A particle of some unknown rest mass m,, moving at +0.8c ây relative to a stationary laboratory,…

A: Given, for first body, mass = mx , velocity = 0.8c for second body, mass = m0 ,…

Q: One of the difficulties with the Michelson Morley experiment is that several extraneous effects…

A: The Michelson–Morley experiment is the most famous null experiment in the history of physics. They…

Q: meson traveling through a laboratory of length x at speed v decays after a lifetime T as determined…

A: Given:- A meson traveling through a laboratory of length x at speed v decays after a…

Q: Use the Lorentz transformations (4.26) expressed in the differential form to obtain the velocity Use…

A: For the x-axis, the equations in the moving frame in terms of variables in the rest frame are as…

Q: A shift of onefringe in the Michelson-Morley experiment corresponds to a change in the round-trip…

A: Michelson interferometer produces interference patterns by creating path difference. Morley used…

Q: Suppose that the speed of light in a vacuum ( c), instead of being a whopping 3×108m/s, was a rather…

Q: Consider that a particle of mass m decays into two particles of mass m1 and m2, and the first…

A: π+ → µ+ + νµMπ+=0.1396 GeV, m µ=0.1057 GeV and mv =0We need to find out: The Energy and Momentum of…

Q: Consider the inelastic collision. Two lumps of matter are moving directly towa and is moving at a…

A: GivenInelastic collisionMass of each lump, m=0.5 kgSpeed of each lump, v=0.88 c

Q: Consider a point charge q at rest, situated at the origin of some frame S. Its electric field,…

A: Given:velocity of S' wrt S is, v→ = −vi^in FOR S, we are given thatE→x→,t = 14πεo×qr2r^charge q is…

Q: Write down the relationship between the classical kinetic energy EE and momentum pp for a body of…

A: Classical kinetic energy E = (1/2)*m*v^2…

Q: Suppose that an observer with 4-velocity us measures the energy of a particle with 4-momentum p".…

A: Required: A coordinate-independent expression for the energy measured.

Q: Appearing in the lime·dilation and length-contraction formulas, Yv is a reasonable measure of the…

Q: Consider a non-relativistic particle moving in a potential U(r). Can either the phase or the group…

A: Consider a non-relativistic particle of mass m, moving in a potential U(x) associated with de…

Q: where mo is the mass of a resting particle in kilograms and c is the speed of light in meters per…

Q: How fast must a stick of length L=1.2m be moving if its length is measured by a stationary observer…

Q: Consider a spacetime diagram in which for simplicity, we will omit the space coordinate z. That is,…

A: Dear student as per the guidelines I will answer the first 3 subparts. Please repost the remaining…

Concept explainers

Central Force

Central force is the force that acts along the center of mass of one body to the center of mass of another body. Its direction from or away from a point on a body to another is called the center of the force. Such forces include gravitational force between two massive objects or electrostatic forces between two charged particles. So from atoms to planets, the central forces play an important role in shaping our daily lives. One of the remarkable features of central forces is that they are conservative, i.e. the total energy of a central force system can always be expressed as a gradient of a potential energy function.

Question

7.
Consider a photon of frequency vo v' emitted by a source at rest in frame K'. The photon is
detected by an observer in frame K, where K and K' are related in the usual manner. (Note that
this means that frame K' is moving either directly towards or away from K along the line of
sight.) Derive the expression for the line-of-sight Doppler effect (i.e., for recession or approach
only, not some arbitrary direction of motion) by considering the energy-momentum 4-vector of
a photon, and requiring that it must transform from one inertial frame to another in the same
way as any other 4-vector.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

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 rocket of initial mass, mi , starts at rest and propels itself by an engine ejecting photons backwards. After the rocket has reached a speed of v, it switches off its engine and its final mass is mf . By using four-momenta and three-momenta for the rocket and photon beam, calculate the ratio of the initial to final mass for the rocket as a function of β only. (β = v/c). Needs Complete typed solution with 100 % accuracy.
This problem deals quantitatively with the experiment of problem 1.1. Let 5denote the ground frame of reference and 5' the train's rest frame. Let the speedof the train, as measured by ground observers, be 30 m/sec in the x direction, andsuppose the stone is released at t' = a at the point x' = y' = 0, z' = 7.2 m.(a) Write the equations that describe the stone's motion in frame 5'. That is,give x', y', and z' as functions of t'. (Note: A body starting from rest and movingwith constant acceleration g travels a distance 1/2 gt2 in time t. Gravity produces aconstant acceleration whose lnagnitude is approximately 10 m/sec/sec.)(b) Use the Galilean transform,ation to write the equations that describe theposition of the stone in frame S. Plot the stone's position at intervals of 0.2 sec,and sketch the curve that describes its trajectory in frame 5. What curve is this?(c) The velocity acquired by a body starting from rest with acceleration g is gt.Write the equations that describe the three…
A particle of some unknown rest mass mx, moving at +0.8c Ây relative to a stationary laboratory, collides head-on with another particle of rest mass m,, moving at – 0.6c âx relative to the same stationary lab frame. After the collision, the two particles stick together and stay stationary. (a) What is m, in terms of m,? (b) What is the mass of the final stationary object in terms of m,? (c) What is the change in kinetic energy in this collision, in terms of m,c²? 0bc 0,8C
A nuclear process, producing two elcctrons moving in the opposite direction eachwith a velocity 0.7c and 0.8c when measured by an observer in the laboratory. Withthe use of Galileo transformation and Lorentz-Einstein transformation, calculate thevelocity of clectrons compared with the other electrons.