Undergrad Space is discrete or continuous?

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SUMMARY

In the discussion regarding the nature of space and time, it is established that Quantum Field Theory (QFT) treats spacetime as a continuous manifold, similar to classical General Relativity (GR). The distinction between QFT and Quantum Gravitation Theory is emphasized, as there is currently no accepted framework for Quantum Gravitation Theory, leaving questions about its implications unanswered. The conversation highlights the necessity of a classical spacetime manifold for the formulation of QFT.

PREREQUISITES
  • Understanding of Quantum Field Theory (QFT)
  • Familiarity with General Relativity (GR)
  • Knowledge of spacetime concepts
  • Basic principles of Quantum Gravitation Theory
NEXT STEPS
  • Research the implications of spacetime continuity in Quantum Field Theory
  • Explore the differences between Quantum Field Theory and Quantum Gravitation Theory
  • Study the formulation of classical spacetime manifolds in physics
  • Investigate current theories and models in Quantum Gravitation
USEFUL FOR

Physicists, students of theoretical physics, and anyone interested in the foundational concepts of spacetime in quantum theories.

Philipsmett
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According to QFT or Quantum Gravitation Theory space and time are discrete or continuous?
 
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Philipsmett said:
According to QFT or Quantum Gravitation Theory space and time are discrete or continuous?
This has been discussed here ad nauseum. I suggest a forum search.
 
Philipsmett said:
According to QFT or Quantum Gravitation Theory

Which one? They're not the same.

According to QFT spacetime is a continuous manifold, just like in classical GR, since QFT requires a classical spacetime manifold in order to be formulated.

We don't currently have an accepted "Quantum Gravitation Theory" so there is no way to answer your question for that case.
 
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Thread 'Two equivalent statements of time reversal symmetric Hamiltonian'

Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?
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