(a) Explanation Given Info: The S wave equation is ∂ 2 E ( x , t ) ∂ x 2 − 1 c 2 ∂ 2 E ( x , t ) ∂ t 2 = 0 The Galilean transformation for x-axis is x − v t , for time t ∂ x ′ ∂ t = − v , ∂ x ′ ∂ x = 1 , ∂ t ′ ∂ t = 1 , ∂ t ′ ∂ x = 0 (I) The formula to calculate the derivative with respect to x and t of the function E ( x ′ , t ′ ) is given by ∂ E ( x ′ , t ′ ) ∂ x = ∂ E ( x ′ , t ′ ) ∂ x ′ ∂ x ′ ∂ x + ∂ E ( x ′ , t ′ ) ∂ t ′ ∂ t ′ ∂ x ∂ E ( x ′ , t ′ ) ∂ t = ∂ E ( x ′ , t ′ ) ∂ x ′ ∂ x ′ ∂ t + ∂ E ( x ′ , t ′ ) ∂ t ′ ∂ t ′ ∂ t (II) Then ∂ E ∂ x = ∂ E ∂ x ′ , ∂ 2 E ∂ x 2 = ∂ 2 E ∂ x ′ 2 and ∂ E ∂ t = − v ∂ E ∂ x ′ + ∂ E ∂ t ′ (III) Use the equation (I) and (II) ∂ ∂ t ( ∂ E ∂ x ′ ) = ∂ ∂ x ′ ( ∂ E ∂ x ′ ) ∂ x ′ ∂ t + ∂ ∂ t ′ ( ∂ E ∂ x ′ ) ∂ t ′ ∂ t = − v ∂ 2 E ∂ x ′ 2 + ( ∂ 2 E ∂ t ′ ∂ x ′ ) ∂ ∂ t ( ∂ E ∂ t ′ ) = ∂ ∂ x ′ ( ∂ E ∂ t ′ ) ∂ x ′ ∂ t + ∂ ∂ t ′ ( ∂ E ∂ t ′ ) ∂ t ′ ∂ t (b) To determine To show that first relativity potulate that “All physical have the same form in all inertial frames” in the Lorentz transformation co-ordinates obeys.

University Physics with Modern Physics, Volume 2 (Chs. 21-37); Mastering Physics with Pearson eText -- ValuePack Access Card (14th Edition)

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ISBN: 9780134265414

Author: Hugh D. Young, Roger A. Freedman

Publisher: PEARSON

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Relativistic Energy and Momentum

According to classical physics, time flow is the same for every observer. But according to einstein's theory, time flow is different for different observers. The idea that time flow is not the same for all may sound strange because we may not experience …

Question

Chapter 37, Problem 37.70CP

(a)

To determine

To show that first relativity potulate that “All physical have the same form in all inertial frames” in the Galilean transformation co-ordinates violates.

(b)

To determine

To show that first relativity potulate that “All physical have the same form in all inertial frames” in the Lorentz transformation co-ordinates obeys.

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Chapter 37, Problem 37.69CP

Chapter 37, Problem 37.71PP

Chapter 37 Solutions

University Physics with Modern Physics, Volume 2 (Chs. 21-37); Mastering Physics with Pearson eText -- ValuePack Access Card (14th Edition)

Ch. 37.1 - As a high-speed spaceship flies past you, it fires...Ch. 37.2 - Stanley, who works for the rail system shown in...Ch. 37.3 - Samir (who is standing on the ground) starts his...Ch. 37.4 - A miniature spaceship is flying past you, moving...Ch. 37.5 - (a) In frame S events P1 and P2 occur at the same...Ch. 37.7 - According to relativistic mechanics, when you...Ch. 37.8 - A proton is accelerated from rest by a constant...Ch. 37 - You are standing on a train platform watching a...Ch. 37 - If simultaneity is not an absolute concept, does...Ch. 37 - A rocket is moving to the right at 12 the speed of...

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To show that first relativity potulate that “All physical have the same form in all inertial frames” in the Galilean transformation co-ordinates violates.

Solution Summary: The author explains how the wave equation in the Sprime frame has different form, hence the Galilean transformation violates the first relativity postulate.

Concept explainers

To show that first relativity potulate that “All physical have the same form in all inertial frames” in the Galilean transformation co-ordinates violates.

To show that first relativity potulate that “All physical have the same form in all inertial frames” in the Lorentz transformation co-ordinates obeys.

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Chapter 37 Solutions