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Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett
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Light cones The idea of a light cone appears in the

Chapter 12, Problem 82E

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QUESTION:

The idea of a light cone appears in the Special Theory of Relativity. The xy-plane (see figure) represents all of three-dimensional space, and the z-axis is the time axis (t-axis). If an event E occurs at the origin, the interior of the future light cone (t > 0) represents all events in the future that are affected by E, assuming that no signal travels faster than the speed of light. The interior of the past light cone (t < 0) represents all events in the past that could have affected E, again assuming that no signal travels faster than the speed of light.

(a) If time is measured in seconds and distance (x and y) is measured in light-seconds (the distance light travels in 1 s), the light cone makes a \(45^{\circ}\) angle with the xy-plane. Write the equation of the light cone in this case.

(b) Suppose distance is measured in meters and time is measured in seconds. Write the equation of the light cone in this case given that the speed of light is \(3 \times 10^{8} \mathrm{\ m} / \mathrm{s}\).

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QUESTION:

The idea of a light cone appears in the Special Theory of Relativity. The xy-plane (see figure) represents all of three-dimensional space, and the z-axis is the time axis (t-axis). If an event E occurs at the origin, the interior of the future light cone (t > 0) represents all events in the future that are affected by E, assuming that no signal travels faster than the speed of light. The interior of the past light cone (t < 0) represents all events in the past that could have affected E, again assuming that no signal travels faster than the speed of light.

(a) If time is measured in seconds and distance (x and y) is measured in light-seconds (the distance light travels in 1 s), the light cone makes a \(45^{\circ}\) angle with the xy-plane. Write the equation of the light cone in this case.

(b) Suppose distance is measured in meters and time is measured in seconds. Write the equation of the light cone in this case given that the speed of light is \(3 \times 10^{8} \mathrm{\ m} / \mathrm{s}\).

ANSWER:

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Light cone is a space-time diagram seen in the Special Theory of Relativity. This space-time diagram is also known as Minkowski diagram. Here, xy-plane represents all of three-dimensional space, and z-axis is the time axis (t-axis). See diagram given in the problem

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