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

[walkeraj]

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?

 

[martinbn]

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.

 

[PeterDonis]

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.

 

[PeterDonis]

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.