Now find t', the t coordinate of the event in frame S! Express your answer in seconds to three significant figures. ΜΕ ΑΣΦ ? t' = 10 S Learning Goal: To be able to perform Lorentz transformations between inertial reference frames. Suppose that an inertial reference frame S'moves in the positive x direction at speed with respect to another inertial reference frame S. In classical physics, the Galilean transformations relate the coordinates measured for an event in frame S to the coordinates measured for the same event in frame S'. Assuming that both frames have the same origin (i.e., at t = t' = 0, x = x' = 0), the Galilean transformations take the following simple form: t'=t, x'x vt, y' = y, z' = z. The Galilean transformations are not valid at very large speeds. To transform between inertial frames when v is close to the speed of light c, we need to use the Lorentz transformations of special relativity. Again, assuming that both frames have the same origin, the Lorentz transformations take the following form: ť' = x' = x-vt y' = y, z' = z. These equations become more manageable with the introduction of the quantity 2= (1 - v²/c²)-1/2 so that the Lorentz transformations become - t' = √(t − x), x' = √(x — vt), - y' = y, z' = z. Often, the space-time coordinates for an event will be given in the form (t, x, y, z), or just (t, x) when the y and z coordinates are not important.
Now find t', the t coordinate of the event in frame S! Express your answer in seconds to three significant figures. ΜΕ ΑΣΦ ? t' = 10 S Learning Goal: To be able to perform Lorentz transformations between inertial reference frames. Suppose that an inertial reference frame S'moves in the positive x direction at speed with respect to another inertial reference frame S. In classical physics, the Galilean transformations relate the coordinates measured for an event in frame S to the coordinates measured for the same event in frame S'. Assuming that both frames have the same origin (i.e., at t = t' = 0, x = x' = 0), the Galilean transformations take the following simple form: t'=t, x'x vt, y' = y, z' = z. The Galilean transformations are not valid at very large speeds. To transform between inertial frames when v is close to the speed of light c, we need to use the Lorentz transformations of special relativity. Again, assuming that both frames have the same origin, the Lorentz transformations take the following form: ť' = x' = x-vt y' = y, z' = z. These equations become more manageable with the introduction of the quantity 2= (1 - v²/c²)-1/2 so that the Lorentz transformations become - t' = √(t − x), x' = √(x — vt), - y' = y, z' = z. Often, the space-time coordinates for an event will be given in the form (t, x, y, z), or just (t, x) when the y and z coordinates are not important.
Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Katz, Debora M.
Chapter39: Relativity
Section: Chapter Questions
Problem 11PQ
Related questions
Question
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps
Recommended textbooks for you
Physics for Scientists and Engineers: Foundations…
Physics
ISBN:
9781133939146
Author:
Katz, Debora M.
Publisher:
Cengage Learning
Modern Physics
Physics
ISBN:
9781111794378
Author:
Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:
Cengage Learning
Principles of Physics: A Calculus-Based Text
Physics
ISBN:
9781133104261
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Physics for Scientists and Engineers: Foundations…
Physics
ISBN:
9781133939146
Author:
Katz, Debora M.
Publisher:
Cengage Learning
Modern Physics
Physics
ISBN:
9781111794378
Author:
Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:
Cengage Learning
Principles of Physics: A Calculus-Based Text
Physics
ISBN:
9781133104261
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Physics for Scientists and Engineers, Technology …
Physics
ISBN:
9781305116399
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
College Physics
Physics
ISBN:
9781285737027
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning