Topology of Spacetime: Can Singularities and Fermions Co-exist?

In summary, the lecturer in the video explains that a spacetime with spin structure, which is equivalent to the existence of fermions, must have a topology of ℝ×Σ, where Σ is the Cauchy surface. It is not clear if this is true, as there are spacetimes with singularities and this topology. However, if it is true, it would imply that singularities and fermions cannot co-exist in the same universe, which may lead to a paradox. There are currently no papers related to this topic, but it is a plausible idea to consider.
  • #1
Narasoma
42
10
I watched this video : https://www.youtube.com/watch?v=sOiifkFYck4
Here, the lecturer said that if someone wants a spacetime which contains spin structure (physically equal to the existence of fermions, CMIIW) should topologically ℝ×Σ, where Σ is the Cauchy surface.

Is that true? If so, then singularities and fermions can't co-exist in the same universe, which lead us to a paradox, right?
Anybody could give me some papers related to this topic please?
 
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  • #2
Narasoma said:
Is that true?

I'm not sure; I'm not familiar with any papers on the subject. However, it seems plausible.

Narasoma said:
If so, then singularities and fermions can't co-exist in the same universe

Why not? There are spacetimes with singularities that have topology ##R \times \Sigma##, where ##\Sigma## is a 3-manifold. The simplest example is FRW spacetime.

Narasoma said:
which lead us to a paradox, right?
o

If it's true (and I'm not sure it is, see above), it is only a paradox if you think our actual universe contains singularities; I take it we agree that it contains fermions. :wink: But we don't know that that's the case.
 

1. What is the topology of spacetime?

The topology of spacetime refers to the geometric structure of the universe including the dimensions, curvature, and boundaries. It is a fundamental concept in physics and helps us understand the behavior of matter and energy in the universe.

2. What is a singularity in spacetime?

A singularity in spacetime is a point where the curvature of spacetime becomes infinite. It is often associated with black holes, where the gravitational pull is so strong that even light cannot escape.

3. Can singularities and fermions co-exist in spacetime?

Yes, according to current theories, singularities and fermions can co-exist in spacetime. Fermions, which are particles such as protons and electrons, are governed by quantum mechanics and can exist within the curvature of spacetime created by a singularity.

4. How do singularities and fermions interact in spacetime?

The interaction between singularities and fermions is not fully understood and is an active area of research. Some theories suggest that fermions may be able to escape the gravitational pull of a singularity, while others propose that they may be destroyed by the extreme conditions.

5. What implications does the co-existence of singularities and fermions have on our understanding of the universe?

The co-existence of singularities and fermions challenges our current understanding of the laws of physics and the behavior of matter and energy in the universe. It also raises questions about the nature of black holes and the possibility of other exotic objects in spacetime.

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