Entanglement and Regions of Space in Vacuum

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SUMMARY

Sean Carroll asserts that adjacent regions of vacuum must exhibit high entanglement to maintain low energy levels, as discussed in his video between 53:30 and 54:30. He argues that low entanglement would result in significant energy presence, contradicting the nature of low energy vacuum regions. This concept aligns with his proposal outlined in the paper "Emergent Gravity and the Dark Universe" (arXiv:1606.08444) and further elaborated in his blog post on the emergence of space from quantum mechanics.

PREREQUISITES
  • Understanding of quantum entanglement
  • Familiarity with vacuum energy concepts
  • Knowledge of quantum field theory
  • Awareness of Sean Carroll's theoretical proposals
NEXT STEPS
  • Read Sean Carroll's paper "Emergent Gravity and the Dark Universe" (arXiv:1606.08444)
  • Explore the implications of vacuum energy in quantum field theory
  • Investigate the relationship between entanglement and energy in quantum systems
  • Review Sean Carroll's blog post on the emergence of space from quantum mechanics
USEFUL FOR

Physicists, quantum theorists, and anyone interested in the intersection of quantum mechanics and cosmology, particularly those exploring the implications of entanglement in vacuum regions.

expos4ever
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TL;DR
It is claimed that regions of empty space that are close to each other must be highly entangled whereas regions that are far from each other are less entangled. I want to understand why.
Sean Carroll (in a video) claims that regions of empty space (vacuum) that are near each other must be highly entangled. He appears to argue that if they were not, there would be "a lot of energy contained there" which - my conclusion - would not be consistent with these regions being low energy vacuum regions. OK, fine. What I don't get is this: Why would low entanglement between adjacent regions imply high energy?

The relevant bit is between about 53:30 and 54:30 in the following:

 
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