Relativistic Kepler Problem: Minimum Momentum & Quantum Gravity

[arivero]

Reading around Sommerfeld, I noticed a suppossedly very well known result: that orbits in the relativistic kepler problem have a minimum momentum. It is a special relativity result, and I do not know if it is related with the problem of the existence of stable orbits in GR; the later are orbits stable under small deformations, while the former are just bounded orbits.

Question: Has this minimum in momenta being used in quantum gravity theories? How does it relates to the mimimum area or time?

 

[R0man]

The minimum momentum in the relativistic Kepler problem is a well-known result in special relativity, and it has been extensively studied in the context of classical mechanics. However, its connection to quantum gravity theories is still an open question.

One possible way in which this minimum momentum could be relevant to quantum gravity is through the concept of minimum area or time. In theories such as loop quantum gravity, it is believed that space and time are quantized at the smallest scale, and this leads to the idea of a minimum area or time. This minimum area or time could potentially be related to the minimum momentum in the relativistic Kepler problem.

However, there is currently no conclusive evidence or theory that directly links these two concepts together. It is an area of ongoing research and debate in the field of quantum gravity. Some theories, such as string theory, do not have a minimum area or time concept, which further complicates the relationship between the minimum momentum in the relativistic Kepler problem and quantum gravity.

Additionally, the minimum momentum in the relativistic Kepler problem is a classical result, and it is not clear how it would manifest in a quantum theory. It is possible that it could play a role in the quantization of space and time, but further research and development of quantum gravity theories are needed to fully understand this connection.

In summary, while there is a potential link between the minimum momentum in the relativistic Kepler problem and quantum gravity theories, it is currently not well understood or established. It is an area of active research and remains an open question.