(Previous posts in this series: Part 1, Part 2, Part 3, Part 4, Part 5, Part 6, Part 7, Part 8, Part 9, Part 10)
For convenience, let me summarize the results that were arrived at in the previous post of the calculations of the Poynting vector by Rohrlich for a charge Q and detector D for the following five scenarios. S represents an inertial frame (such as freely falling in a uniform gravitational field) while E is the frame of the Earth.
Scenario 1: Both Q and D are floating freely in empty space in the absence of all forces
Conclusion: D will not detect any radiation and and thus Q is said to not radiate.
Scenario 2: Both Q and D are both falling freely in a uniform gravitational field
Conclusion: D will not detect any radiation and and thus Q is said to not radiate.
Scenario 3: Q is freely falling while D is on the floor in E
Conclusion: D will detect radiation and thus Q is said to radiate.
Scenario 4: Q is on the floor in E while D is freely falling
Conclusion: D will detect radiation and thus Q is said to radiate.
Scenario 5: Both Q and D are at rest on the floor in E
Conclusion: D will not detect radiation and thus Q is said to not radiate.
Let us see how Rohrlich’s results affect the two postulates that began this series of posts:
Postulate #1: If we can eliminate all other forces such as friction, all objects that are dropped from the same height in a gravitational field will fall at the same rate and hit the ground at the same time.
Postulate #2: An accelerating charge falling freely in a gravitational field will radiate energy.
The results of Scenario 3 support Postulate #2, that the falling electric charge will radiate and that radiation will be detected by a detector at rest in the frame.
But there are still three (at least) unresolved issues.
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