Incomplete geodesics in a singularity, do they warrant quantum concerns?

  • #1
walkeraj
17
4
Question: The idea of a continuum breaks down for a singularity when a geodesic become incomplete (the breaking of the idea that there was a continuous succession, where no part could be distinguished from neighboring parts, except by arbitrary division), and so with that does this indicate a scale change from classical to quantum? That is, is space-time necessarily geodesic incomplete at the quantum scale?
 
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  • #2
walkeraj said:
Question: The idea of a continuum breaks down for a singularity when a geodesic become incomplete (the breaking of the idea that there was a continuous succession, where no part could be distinguished from neighboring parts, except by arbitrary division), and so with that does this indicate a scale change from classical to quantum? That is, is space-time necessarily geodesic incomplete at the quantum scale?
You question is not clear to me, but if you are talking about the continuity of the geodesic, then all geodesics, complete and incomplete, are continuous. If fact they are smooth as in differentiable.
 
  • #3
walkeraj said:
The idea of a continuum breaks down for a singularity when a geodesic become incomplete
This is not correct. The "singularity" is not part of the manifold; the manifold itself is a perfectly valid continous open set.

The rest of your post is based on this invalid premise, and when that is corrected, your question is not well posed.
 
  • #4
walkeraj said:
with that does this indicate a scale change from classical to quantum? That is, is space-time necessarily geodesic incomplete at the quantum scale?
This looks like personal speculation, which is off limits here.

This thread is now closed.
 

FAQ: Incomplete geodesics in a singularity, do they warrant quantum concerns?

What is an incomplete geodesic in the context of a singularity?

An incomplete geodesic refers to a path in spacetime that cannot be extended indefinitely due to the presence of a singularity. In general relativity, singularities are points where the curvature of spacetime becomes infinite, leading to breakdowns in the laws of physics as we currently understand them.

Why do incomplete geodesics at singularities raise quantum concerns?

Incomplete geodesics at singularities raise quantum concerns because the classical description of spacetime fails at these points, suggesting that a quantum theory of gravity is needed to fully understand the phenomena. The breakdown of spacetime continuity implies that classical general relativity is insufficient, and quantum effects cannot be ignored.

How might quantum gravity theories address incomplete geodesics?

Quantum gravity theories, such as string theory or loop quantum gravity, aim to provide a framework where the singularities and incomplete geodesics of classical general relativity are resolved. These theories propose that spacetime is quantized at the smallest scales, potentially smoothing out singularities and extending geodesics in a consistent manner.

What role do incomplete geodesics play in black hole physics?

Incomplete geodesics are crucial in black hole physics because they are associated with the event horizon and the singularity at the center of black holes. Understanding these geodesics can provide insights into the ultimate fate of matter and information falling into a black hole and whether they can be reconciled with principles of quantum mechanics, such as unitarity and information preservation.

Are there experimental or observational methods to study incomplete geodesics and singularities?

Direct experimental or observational methods to study incomplete geodesics and singularities are currently beyond our reach due to the extreme conditions involved. However, indirect methods, such as observing the behavior of matter and radiation near black holes, gravitational wave detections, and studying the cosmic microwave background, can provide valuable clues. Future advancements in technology and theoretical models may offer more direct ways to probe these extreme regions of spacetime.

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