Energy redshift paradox in the Schwarzschild solution

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Within the framework of General Relativity in one of its most simple forms, the Schwarzschild solution, a very interesting paradox can be proposed involving the conservation of work / energy. It’s a puzzle for the Relativity buff. In this short discussion I outline this energy redshift paradox, and the implications for an attempted solution.

http://physicspost.com/articles.php?articleId=179
 
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correct me if I am wrong but in the article erich states that acceleration is dx/dt^2 i think he forgot to raise the d to square because the notation for second deravative is d^2x/dt^2.
 


The energy redshift paradox in General Relativity is a fascinating and thought-provoking puzzle that challenges our understanding of the conservation of energy. The paradox arises from the fact that according to the Schwarzschild solution, the energy of a photon decreases as it travels away from a massive object. This seems to contradict the principle of conservation of energy, which states that energy cannot be created or destroyed, only transformed from one form to another.

The implications of this paradox are significant for our understanding of General Relativity and its predictions. It raises questions about the validity of the Schwarzschild solution and how it fits into the larger framework of General Relativity. It also challenges our understanding of how energy behaves in the presence of massive objects and whether the principle of conservation of energy holds true in all situations.

One potential solution to this paradox is the concept of gravitational time dilation, which suggests that time runs slower in a strong gravitational field. This would mean that the energy of a photon decreases not because it loses energy, but because time is passing slower for the observer measuring its energy. However, this solution is not without its own challenges and has been a subject of much debate and research.

Another proposed solution is the idea of gravitational potential energy, which suggests that the energy of a photon decreases as it climbs out of a gravitational potential well. This would mean that the energy redshift is not a violation of the conservation of energy, but rather a result of the photon's change in potential energy. However, this solution also has its own limitations and is still a subject of ongoing research and discussion.

Overall, the energy redshift paradox in General Relativity is a complex and intriguing problem that continues to challenge our understanding of the universe. It highlights the need for further research and exploration in this field and serves as a reminder that our understanding of the laws of physics is constantly evolving and subject to change.