Astronomy
1st Edition
ISBN: 9781938168284
Author: Andrew Fraknoi; David Morrison; Sidney C. Wolff
Publisher: OpenStax
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Textbook Question
Chapter 24, Problem 1E
How does the equivalence principle lead us to suspect that spacetime might be curved?
Expert Solution & Answer
To determine
The method by which the equivalence principle leads us to suspect that space time might be curved.
Answer to Problem 1E
The method by which the equivalence principle leads us to suspect that space time might be curved is explained with the help of example given below.
Explanation of Solution
Equivalence principle states that, the condition of free fall is equivalent to the condition of zero gravity. For example, an astronomer in a windowless spacecraft will not be able to differentiate between the situations when she is freely falling under the influence of gravity of some other planet or star or when she is far away from any gravitational influence of any star or planet in space.
According to general theory of relativity by Einstein; “Gravity is not a force but it is a result of the curvature of space-time caused by the uneven distribution of mass”. The fabric of space time is curved around a mass and as a result of this; a force is caused which is termed as gravitational force.
To understand how the equivalence principle lead to conclusion that space time might be curved one must take the example given below.
Consider a spacecraft in which no gravitational force is acting when it is moving in a space. When an astronaut shine a beam of light from one end of spacecraft towards the other end, due to the property of light that it travels in a straight line, beam of light hits another end at the point which is exactly in front of it.
Consider a spacecraft when it is in gravitational attraction of some other planet (Earth) and it falls freely, as the light travels in a straight line,it should hit the same point as before but the light follows the path of the spacecraft, if the spacecraft deflected, then light is alsodeflected. As the result is different from expected, the light travels with the spacecraft and it hits the different point as before.
This result gave the idea of general theory of relativity. According to itlight bends around the mass, but actually it travels in a straight line. To conclude both these facts Einstein proposed theory of relativity in which a mass bends the space time fabric
Conclusion:
Thus, the method by which the equivalence principle leads us to suspect that space time might be curved is explained with the help of example given below.
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Chapter 24 Solutions
Astronomy
Ch. 24 - How does the equivalence principle lead us to...Ch. 24 - If general relativity offers the best description...Ch. 24 - Einstein’s general theory of relativity made or...Ch. 24 - If a black hole itself emits no radiation, what...Ch. 24 - What characteristics must a binary star have to be...Ch. 24 - A student becomes so excited by the whole idea of...Ch. 24 - What is an event horizon? Does our Sun have an...Ch. 24 - What is a gravitational wave and why was it so...Ch. 24 - What are some strong sources of gravitational...Ch. 24 - Suppose the amount of mass in a black hole...
Ch. 24 - Imagine that you have built a large room around...Ch. 24 - A monkey hanging from a tree branch sees a hunter...Ch. 24 - Why would we not expect to detect X-rays from a...Ch. 24 - Look elsewhere in this book for necessary data,...Ch. 24 - Which is likely to be more common in our Galaxy:...Ch. 24 - If the Sun could suddenly collapse to a black...Ch. 24 - Suppose the people in Figure 24.4 are in an...Ch. 24 - You arrange to meet a friend at 5:00 p.m. on...Ch. 24 - You are standing on a scale in an elevator when...Ch. 24 - Look up G, c, and the mass of the Sun in Appendix...Ch. 24 - Suppose you wanted to know the size of black holes...Ch. 24 - Use the result from Exercise 24.21 to calculate...Ch. 24 - Since the force of gravity a significant distance...
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