The Lorentz coordinate transformation assumes that t = t′ at x = x′ = 0. At what other values of x and x′ does t = t′?
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The Lorentz coordinate transformation assumes that t = t′ at x = x′ = 0. At what other values of x and x′ does t = t′?
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- Determine an expression for the total travel time of the light pulse, as measured by the following: A) an observer in the S frame (Use the following as necessary: c, d, and v.) B) an observer on the spacecraft (Use the following as necessary: c, d, and v.) What If? If the transmitted light beam has a wavelength λT, determine an expression for the shift in the wavelength of the light beam, as measured by the following C) an observer in the S frame (Use the following as necessary: c, v, and λT.) D) an observer on the spacecraft (Use the following as necessary: c, v, and λT.)Doppler Effect: This problem looks at wavelength shifts instead of frequency shifts. In this problem, AX is defined as the difference between the wavelength in the observer's frame and the source frame, and you can pick 2 to be equal to the wavelength in the source frame. a. Show that, for speeds u<The distance between two light pulses moving along the x-axis of the frame S is 2km. What is the distance between them from the point of view of an observer moving at a speed of 0.2c along the x-axis relative to S?A car is moving relative to a pedestrian with a Lorentz factor of 1.45. With the length of the car being 5.7m according to the pedestrian, what's the length according to the driver of the car (he's moving at the same speed of the car) ?Consider a general equation for the ratio the relativistic length to the proper length. Find an algebraic expression for v/c in terms of, ΔL/ΔLo Show the algebraic form of the equation that you apply and the final final expression.The distance to a particular star, as measured in the earth's frame of reference, is 7.11 light- years (1 light-year is the distance that light travels in 1 y). A spaceship leaves the earth and takes 3.35 y to arrive at the star, as measured by passengers on the ship. (a) How long does the trip take, according to observers on earth? (b) What distance for the trip do passengers on the spacecraft measure?Bonus Problem 2- We have measured the radius of Earth R= 6400 km. A cosmic particle which is moving with v = 0.95 c (where c is the speed of light) toward the center of Earth. a) What is the diameter of Earth from point of view of the particle! b) How long will it take for the particle to pass through the Earth?A star is 12.2 ly (light-years) from Earth. HINT (a) At what constant speed (in m/s) must a spacecraft travel on its journey to the star so that the Earth–star distance measured by an astronaut onboard the spacecraft is 4.36 ly? m/s (b) What is the journey's travel time in years as measured by a person on Earth? NO SCIENTIFIC NOTATION ANSWERS THANK YOUA.8. Show with the aid of the Lorentz transformation (A.28) that the quantity c²₁² — x² - y² – z² is an invariant, namely c²1² − (.x² + ¸‚µ‚² + =²) = (²² 1¹² — (x²² + 1,²² 1₁² +=²²)